For these old POCSAG systems, my simplistic assumption in my previous post that simulcast delay spread could basically be ignored is certainly true. Another advantage of simple binary FSK in these older systems was that the receiver could be designed as a simple limiter-detector. At some point, say an intermediate frequency (IF) stage, an adaptive gain control (AGC) block could be applied to bring the received signal amplitude to some maximum value. It wouldn’t even matter much if this stage was overdriven to some extent. The detector could be a very simple frequency discriminator, which would deliver a binary output sequence suitable for slicing into a ±1 data stream. Outside of some specific circuits for recognizing synchronization patterns, this is about the degree of complexity of the front end of a POCSAG pager.

I have mentioned simulcast delay spread’ , a couple of times. The concept is similar to that of multipath delay spread in other land mobile systems. In order to do the calculation, it is first necessary to calculate the mean delay spread. This can be calculated mathematically as follows:

Once the mean delay is known, it can be used to compute the root mean square simulcast delay spread (SDS):

In these calculations, is the power at the receiver from the ith base station. Time delay itself will have to be computed with respect to some reference of time, some t=0. A natural model would be to assume that the transmission of a bit was synchronized from all base station transmit antennas in the serving area to some mark, say top dead center of the hour by GPS time. We can then compute the mean arrival time, with the first equation above, which is just a power-weighted average. By assumption, some of the path delays will be shorter and some longer than this average. We then compute the RMS SDS value by summing the power-weighted squares of the differences between the mean delay and the actual path delay for each base station, divide by the total power in all paths, and take the square root.

In some circumstances, the actual situation on the ground may involve some combination of simulcast and multipath delay spread. A typical environment for this would be the Los Angeles basin or Salt Lake City. Any high site in the downtown area of either city would have some opportunity to reflect back from the surrounding mountains and yield another contribution to the summation of power. For this reason, intelligent design models suggest both a combination of electrical down tilt on transmit antennas as well as directionality away from the back stop of the mountains. Anytime a propagation model, or the facts on the ground, suggest strong multipath, there is no intellectual problem at all in doing the calculation.

Another extension, which may be valuable in some circumstances, is to extend the summation into an integral. In most paging simulcast models, a single dominant path from BS to MS is all that has to be computed. However, this is not uniformly the case, and there is no computational issue in extending the formulae above into integrals or summations over integrals. The fundamental concepts remain intact.

Some literature on the topic of simulcast systems makes a great deal out of SDS as a metric for the quality of signal detection. I might agree that aiming for a design that keeps SDS below some fraction of symbol time is a solid goal. However, going for some fraction along the lines of $latex Subscript[\[Tau], s]/Subscript[T, s]

Before I proceed, I would like to direct your attention to an excellent paper on this entire topic written by my one-time co-worker, Selwyn Hill. The paper was delivered at a conference back in 1997 (time flies when you’re having this much fun, I guess.) Still, it remains an exceptional overview of the work that went into the design of the PageMart/WebLink 6400-FLEX network. This work was extended for the two-way ReFLEX network subsequently.

As Selwyn points out in the discussion of his Figure 13, a worst case scenario can arise during the symbol transition time when the receiver happens to be located near a position with two nearly equal signals from two distinct BSs. I have reproduced the figure here for reference:

Selwyn Hill's analysis of FM clicks in FLEX

Allow me to paint this picture using a phasor model for the two signals, while Selwyn’s Figure 13 shows a time-domain picture.

In this phasor model, let one phasor have a slightly larger amplitude, and be rotating just faster than the second with amplitude , implying a somewhat higher frequency in terms of both carrier and modulation deviation. Without any loss of generality, we can assume that the bit being transmitted as we begin this thought experiment as a -1 with a negative frequency deviation of from the carrier frequency, .

If we assume that the two phasors begin in phase and at some 0 of phase reference at the start of this mental exercise, then we have maximum constructive interference between the two received signals; and the envelope will be . If we peg our reference frequency at the carrier frequency less the deviation frequency of the slower phasor, then what we will see is the faster phasor rotating around this reference at the difference frequency between the two signals. At some point in time, the faster phasor will rotate into 180° with respect to the reference phasor, and the two signals will show maximum destructive interference. The envelope will be .

In this way we’ll see that classic beat frequency oscillation between the two signals at the difference frequency between them. However, there is another important feature here. That is that there will be a sharp reversal in phase as the envelope reaches its minimum. Many frequency detectors, including the simple FM discriminator, will produce a “click” at such a transition. This FM click noise phenomenon has been well-known since the early days of land mobile receivers. The traditional approach to solving the click noise problem in FM has been actually to build the receiver with an integrator filter, making it a phase demodulator. To compensate, the transmitter has included an opposite modulator pre-filter to differentiate the signal. So, broadcast FM audio is, in fact, PM. Some data FSK systems have been designed around this sort of approach. Gaussian Minimum Shift Keying (GMSK) and Generalized Tamed FM (GTFM) are examples.

As an aside, I find it rather bizarre that a search I just did for “FM click noise” shows three IEEE papers and one by myself on Brad Dye’s paging web site as the top hits. The technical world appears to be forgetting so many lessons learned, or at least google searches are. In standard audio FM, the clicks arise because of interference between multipath signals that yield Rayleigh fading of the received signals. The fades are, in effect, spatial beat frequencies that the receive antenna moves through as, say, your car, moves along. These fades due to multipath are typically a half-wavelength of the carrier apart. Each null corresponds to a 360° change in phase. Since an FM detector is essentially a phase differentiator, these sharp changes in phase lead to clicks in the detected audio. The faster the receive antenna moved through the Rayleigh fade nulls, the faster was the arrival rate of FM click noise. The solution, adopted back in the 1930s, was to turn FM into PM by means of pre- and post-filters on the modulating signal. Of course, the post-filter had to be an integrator. That turned the click into a step, and the step could be further eliminated by a DC decoupling that always existed between gain stages. Anybody remember this?

Back to this beat frequency in our pager. Let’s consider some typical parameters. Suppose that we’re using old VCO modulated transmitter equipment. At around 900MHz for a carrier center frequency, and with a peak frequency deviation of 4800Hz, you might get carrier accuracy of something less than 1kHz. Those VCO modulators had a lot of phase noise as well. A beat frequency at nearly 1kHz would be around the data rate of a 1200 bit/s POCSAG system. On the other hand, the more stable TCXO controlled, digitally modulated transmitters typical of a FLEX system were much more stable and gifted with much less phase noise; these might be stable to within ±10Hz or so. Going the other way, 6400 bit/s FLEX has a symbol time of
.

Clearly, the null times in 6400-FLEX are capable of being much longer than a symbol time unless some action is taken. In practice, this is a very typical design step. Network designers will utilize something like a cellular reuse plan with an insertion of frequency offsets in order to avoid such long nulls due to beat frequencies in the mobile receivers between adjacent transmitter signals.

So far, so good. We have designed in frequency offsets so that beat frequency nulls do not impact large numbers of bits. Now, let’s consider the impact of a symbol transition. Let’s assume that our larger signal has the lower path delay. Hence, as the impressed modulation makes a transition from towards , this larger phasor will begin to speed up relative to our original reference phasor. During the interval of time between the start of the first signal beginning to move up in frequency and the second signal beginning to transition, the first signal will achieve some significant frequency above that of the second. The greater the difference in path delays, the greater this transitional frequency difference will be. Therefore, the effective beat frequency between the two signals will also increase significantly, with the maximum possible being . Achieving this maximum is quite unlikely in practice, but getting to some reasonable fraction of this is quite possible. The main point is that during this transition, there will be a significant rate of arrival of phase reversals in the signal path. If these are differentiated by the detector, the consequence will be a shower of FM clicks in the signal path. As the second signal begins to make its transition to the higher symbol frequency, the two phasors will remain locked at some large frequency offset. During this interval, the arrival of phase reversals will be more or less constant. Then as the first signal achieves the new peak frequency deviation, and the second is catching up, the arrival rate of phase reversals will gradually reduce until, again, it becomes stable at the frequency offset between the two transmitters.

To recap this behavior, while the symbol is stable, the arrival rate of phase reversals is defined by the stability of the two transmitters and any frequency offset plan that the network designers have introduced. During the symbol transition, the arrival rate of phase reversals increases to some maximum defined by the difference in propagation delays between the two transmitted simulcast signals. As the symbol transition stabilizes, the arrival rate of phase reversals becomes stable again at the frequency offset between the two transmitter carrier frequencies, including the peak frequency deviation.

In a binary FSK receiver with a limiter-discriminator detector, this shower of phase reversals, which are differentiated to create a shower of FM clicks, may not be too damaging. The reason is that however extreme the excursion of the FM click might be, it will be driven to the “rail” by the limiter. If the direction of the click is in the same direction as the symbol, then it will have no impact at all. If it is in the opposite direction, then it may “take a slice” out of the bit for some short interval; but if the detector integrates the symbol energy, then even this will not be too significant except in high noise conditions. This is generally not the condition under which this kind of situation arises; typically these pernicious effects occur at high received signal levels.

The situation is much worse in a 4-level scenario as occurs in one form of 3200 bit/s FLEX and in 6400 bit/s FLEX. In such a scheme, a limiter cannot be used before the FM detector, since 4 distinct symbol levels have to be maintained. The receiver must have some form of level control and adaptive gain control. This will almost certainly be achieved with some kind of feedback loop monitoring the signal path and feeding back level and gain control information. The shower of FM clicks that will occur during the sort of symbol transitions that we described earlier will play serious havoc with such a detector. First, the clicks will drive the automatic level control in the opposite direction. Second, they will tend to reduce the AGC’s gain. Finally, they will tend to disturb symbol time recovery circuits. Each of these impacts can last far longer than the short inter-symbol transition time and yield incorrect symbol detection.

Of course, there is a simple solution; and it has been known for a long time. This would be to construct the receiver as a phase detector instead of a frequency detector. This is perfectly feasible for 4-level FLEX and ReFLEX. Unfortunately, many very inexpensive pager receivers are designed around ICs that were OK for POCSAG and very poor for 4-level FLEX. Paging carriers that have made the transition to 4-level FLEX years ago have found a relatively short list of pagers that have sufficient quality to function in a 4-level 6400 bit/s FLEX system; and they’ll stick with these until hell freezes over, for good reason.

So, first, let’s do a definition of what simulcast means in the context of digital radio paging. Simulcast means the simultaneous transmission of the same information content from multiple transmitters at distinct locations with significant overlap coverage by design. Here is a simple schematic diagram of what we mean:

Simulcast

The notion is that the recipient (or receiver) will obtain a higher signal to noise ratio by virtue of the summation of the bit energies from each of the separate transmitters. Likewise, assuming that each individual path between any given transmitter and the mobile receiver is independently faded and shadowed, simulcast provides significant redundancy to both fading and shadowing. Of course, like the picture, this idea is pretty simplistic. In order for the bit energies to sum at the receive antenna, they must be synchronized not just in terms of bit arrival time, but also in terms of carrier frequency and phase. Assuming for the time being that the modulation is a simple FSK, then the transmit frequency is for the duration of a bit. Likewise, if we begin by assuming that the bit times are long with respect to the propagation delays from transmitter to receiver, then the signal on the receive antenna will be the phasor sum of a set of sinusoids at nearly with independent arrival strengths and phase, where I’ve assumed the positive modulation swing without any loss in generality. An equation for the summation of the signals from N transmitters may be written as follows, a sum of sinusoids:

In this case, the are random numbers with some measure of central tendency to . Likewise, the amplitudes, , are also independent random numbers that must satisfy some physical constraints related to transmitter powers, transmit and receive antenna gains, expected path loss, shadowing and fading models, and so on. Furthermore, if we include the time-variability of amplitude, modulated frequency, and arrival phase, as shown in the equation, the details of received signal strength can become very complicated indeed.

However, some simplification is possible. First, if the time of any single bit is short with respect to time variations in amplitude, transmitter modulation frequency, and arrival phase, then the summation for any given bit becomes a summation of static phasors. We can then consider a few special cases. In one case, a single received signal dominates the rest by, say, 10dB or more. While I haven’t introduced the impact of receiver technology as yet, let’s assume that the simple binary FSK case will use a receiver with some FM capture effect. In this case, the capture effect simply suppresses the impact of the lower power signals and reception tunes to only the dominant signal. Furthermore, if the attack time of the adaptive gain block that is delivering capture is fast with respect to the rate of change of fading and shadowing, then any relative change among the received signals as to which is dominant will be tracked smoothly, with no significant loss in bit energy as a dominant signal fades and is replaced by another. If we think back to the notion of simulcast as a method to sum the signal energies of multiple transmitters, what we find instead is a mechanism that selects the dominant signal and rejects the others as interference.

In another special case, two dominant signals are received within 1 or 2dB of each other, that is, less than the capture threshold. In this case, the received signal becomes a sinusoid at the average carrier frequency with another sinusoidal amplitude envelope varying at the difference between the two carrier frequencies, a classic beat frequency system. To the extent that the design of the transmitter modulators is highly precise and accurate, this situation can lead to very long and deep fades that may last for far longer than a bit time. Early digital paging systems used voltage controlled oscillators (VCOs) for FSK modulation with a good deal of inherent phase noise. As a result, these early systems did not experience such long fades even when situations arose where the signals from two transmitters were practically equal at the receiver. Later systems used highly stable temperature controlled crystal oscillators (TCXOs) that were disciplined by GPS time references with digital modulation so that these beat frequencies could be highly pernicious. In such cases, without any other remedial design steps being applied, the two most power signals could simply cancel one another out, leaving a third signal to step forward and capture the receiver in cases where capture effect was part of the design.

Cases in which two dominant signals become nearly identical in received signal strength (RSS) are not as rare as one might naturally assume. Situations like this can arise quite easily in urban environments in high rise towers where any number of transmitters have good line of sight paths to parts of the building’s face. A large city such as New York, Chicago, Los Angeles, Dallas, and so on, may have as many as a dozen or more transmitters that are within five to ten miles of high rise towers in the dense urban core. Not all of these are visible from any given part of the building, but if a paging receiver is simply walked around the perimeter of the tower (inside of course), there may be any number of locales at which two or more transmitters “beat” against one another with destructive combining as a consequence. Assuming that in these situations there is always a next most powerful signal and that the receiver’s automatic gain control (AGC) in the IF stage that delivers capture effect is rapid enough, there is no loss in reception as far as the user is concerned.

In fact, in the broader context of mobile radio, this performance can be considered a highly sophisticated form of soft handoff along the lines of a similar theory in the CDMA cellular world. Now, in direct sequence spread spectrum (DSS) CDMA cellular, the transmissions intended for a given mobile station (MS) are modulated by a unique spreading code used only by that MS. Assuming that the multiple paths that might exist between the serving base station (BS) and the MS can be resolved as distinct by the chip times of the spreading code, then the use of an appropriate RAKE receiver in the MS can allow the radio power in each distinct path to be aligned and summed constructively at the receiver. By extension, if multiple BSs transmit the same information in a simulcast fashion, on the same carrier frequency and with the same spreading code, then in principle the MS can also sum together the bit energy received not just from multiple paths from a single BS, but also the bit energy from multiple paths from multiple BSs. Of course, this requires appropriate synchronization of bit times at the MS, which requires some dynamic knowledge of path distance between the various BSs and the MS. In principle, this CDMA soft handoff is feasible; in practice, it requires a fair investment in processing power and communications bandwidth among BSs and BS controllers (BSCs).

Consider as against that computationally intensive cellular approach the inherent simplicity of the similar effect in paging. Just as in the case of soft handoff in CDMA cellular, the same information is transmitted simultaneously from more than one BS. In fact, most paging systems are designed so that there is an overlap in coverage between anywhere from three to six or so BSs throughout the serving region. However, handoff from one BS to another requires absolutely no computation or direction on the network side. Instead, handoff is completed gracefully and dynamically at the MS as rapidly as on a bit-by-bit basis without any expenditure of processing power at all.

Of course, the implementation of such a scheme is not without its costs. The POCSAG digital paging system began with only 512 bit/s on the forward channel; and in the modern world of 4G LTE et al, this is a trivial amount of bandwidth. It is even less when you consider that any given POCSAG pager used less than 100 bits to receive a numeric page and that the likelihood of receiving such a page in the busy hour might be 25% or so. The FLEX paging system operates at 6400 bit/s with a form of four-level Gaussian Minimum Shift Keying (4-GMSK) and a highly complex interleaving scheme; but still, the amount of forward channel bandwidth that any given receiver will utilize is trivial compared to the data bandwidths on a cellular system.

However, signal reception in land mobile communications is a function of a relatively simple and short list of factors. One of these is signal to noise or signal to interference ratio on a bit-by-bit basis. This is also designated or contrast ratio. Since received energy per bit, where is received power and is bit time, it is clear that other things being equal, the longer the bit time the greater the energy per bit. Likewise, the longer the bit time, the lower the noise per bit , since the receive filter bandwidth can be reduced in inverse proportion to . Therefore, contrast ratio is delivered a kind of double whammy (that’s a highly technical term) by the current trend to increased bandwidth in cellular and WiFi communications.

Another factor that impacts is signal fading and shadowing. In the case of a simulcast paging system, while any given forward path from transmitter to receiver is subject to similar fading and shadowing statistics as in other land mobile systems such as cellular, the multiplicity of forward paths, together with capture effect at the receiver, completely changes the statistics from a single-path Rayleigh or Ricean fading model to something much closer to a gaussian channel. At a minimum, a well-designed simulcast channel will show exceptional diversity characteristics relative to cellular operation. As well, since the duration of any fade is short with respect to the longer symbol times in paging, channel coding is very simple in systems like FLEX in contrast to what is required in systems like LTE or WiFi, where fade durations can be very long relative to bit times.

Paging systems therefore operate at fairly high contrast ratios without co-channel interference; that is, they are noise-limited and noise per bit is low. Modern cellular systems operate at fairly low contrast ratios with high co-channel interference; that is, they are interference-limited and interference per bit is high. Channel diversity in simulcast paging networks is significant, meaning that fading mitigation techniques are minimal. Channel diversity in cellular tends to be pointless, the compensation for a poor channel being to perform a computationally intensive handoff procedure, with corresponding decision costs. In general, cellular systems are designed for maximum system capacity at a specified high bit error rate (typically 3% raw, before error correction) while simulcast digital paging systems are designed for minimum message error rate (MER) at a specified channel capacity (say 6400 bit/s). I invite you to consider the differences in these two design approaches.

To explain a little further, the specified 3% raw BER threshold in cellular is associated with a tolerable quality of voice communication using CELP codecs or their equivalent. These will deliver acceptable voice quality with an average 3% BER. The evolution of cellular to higher capacity systems over the years has revolved around newer modulation and channel coding methods that can deliver higher reuse plans and higher bandwidth while maintaining this BER or better in the worst case carrier to interference ratio (CIR) conditions. For a contrast, the evolution of digital paging networks has revolved around newer technologies that have increased channel capacity; for example, POCSAG at 512, 1200 and then 2400 bit/s and then FLEX at 1600 binary, 3200 binary, 3200 4-level, and finally 6400 bit/s 4-level. Each channel capacity increase required significant modifications in base station technology in order to maintain acceptable message error rates for subscribers. These technology changes have included reductions in BS Effective Radiated Power (ERP), antenna down-tilt, modulation technology, simulcast synchronization, frequency plans (yes, frequency plans, even though operating on the same nominal frequency), satellite modulation methods, receiver designs, and so on. In a digital paging system, the acceptable BER necessary to deliver a customer-acceptable MER is significantly higher than the cellular design threshold of 3% raw BER or so.

As a consequence of these very different design methodologies, modern digital paging systems are naturally more robust to disasters and outages than cellular systems. Given the degree of redundancy in a simulcast paging system, such a network is capable of surviving the loss of as many as 75% or more of its base stations and still providing service to its coverage area. Paging operators will frequently take this into account in their deployments, and provide extra hardening to BSs that are designated as critical; for example, redundant power, battery backup, redundant antennas, and so on. Since most paging systems in North America also use satellite methods, often Very Small Aperture Terminals (VSAT), for communications to and from BS sites, they are immune to ground-based causes for lost comms to sites; for example, back-hoe cable cuts, flooding, or fire. To avoid loss of satellite communications, network operators can and do distribute their satcomms over multiple satellites and design their critical BS sites with quickly or remotely repointable VSAT dishes.

This is not to say that cellular communications fails to work, or even that it works poorly; but there are trade-offs. Early cellular systems demonstrated extremely poor in-building penetration. This was generally because the outside walls of the average building introduced anywhere from 10 to 20dB of path loss, and that amount of increased power on either the forward or reverse channels would introduce too much co-channel interference to other cells reusing the same frequency. This problem meant that indoor shopping malls, underground parking garages, subway trains and platforms, and similar structures had very poor coverage. As cellular systems have evolved, these problems have been mitigated by the deployment of low-power indoor base stations and repeaters; for example, here and here. In some cases, the costs for this increase in RF density has been born by the developers of the real estate, in other cases by the cellular providers, in some instances the costs may be shared. Ignoring the costs, the mitigation technique must be to increase the forward channel SNR inside the building without increasing the signal strength from the base station, and thereby upsetting the balance of power in the cellular reuse plan. On the reverse channel, if the inherent maximum power of the MS is too limited to handle the path loss introduced by the building walls, then some form of power boost must be introduced to compensate. Of course, in this I’m considering a repeater and not an interior BS or “micro-cell.”

Unfortunately, the evolution of digital paging stalled in the early 2000s. I was personally chairman of groups chartered to define next generation technologies at that time. By 2003, it was obvious that the industry had gone into a period of retrenchment from which it hasn’t recovered ten years later. Although there are many technologies that could be used to advance the design concept of simulcast in digital paging, the lack of new capital investment in this sector has not just limited the recovery of paging in business terms; it has also created an entire generation of radio engineers who reject the possibility of that anything from paging has any merit whatsoever, prima facie. Having personally moved from the cellular to the paging sector in 1996, I count myself one of that number at least historically.

Just to consider what might constitute an updated simulcast scheme, consider the possibility of using an OFDMA model. The aim would be to keep symbol times low with respect to simulcast delay spread (SDS). Unfortunately, I haven’t introduced the concept of SDS yet; for now, assume that it is an objective measure of how long it takes for symbol transitions to settle down as they arrive from the various BS transmitters that a MS can see. For now, I prefer to leave the precise definition of SDS for a later blog post. By transmitting data over multiple subcarriers simultaneously, overall data rate can be increased while keeping the ratio of SDS to symbol time within some acceptable fraction, say, , where is SDS and is symbol time. Interestingly enough, this approach was used in one forward channel configuration of the original Skytel ReFLEX50 system. By employing the distinction between common control channels and traffic channels that was included in both the ReFLEX and InFLEXion systems, it would be possible to maintain a low complexity, long battery life receive model for common control channel operation, and only invoke more complex receiver technologies (such as FFT decoding) for the traffic channel.

Consider then the question of linear superposition of simulcasting sources in an OFDMA model. Each subcarrier will now arrive at the receiver as a superposition of simulcast transmissions. Two approaches may be considered. In the first, each transmitter sends exactly the same subcarrier to encode exactly the same information bit. In the second, each transmitter may encode the same bit by a distinct subcarrier. This second approach may be considered a kind of forward channel frequency redundancy to avoid frequency selective fading. The first approach is closer to the traditional FSK simulcast method, but now distributed over a larger schema of subcarriers.

If the maximum distance between transmitter and receiver in a macro-scale system was, say, 3km, then the propagation time is roughly 10µs. For a nice round number, consider that SDS is about 10% of this, and this allows for a symbol time of 10µs and a baseband width of around 100kHz. The IEEE 802.16 standard suggests as many as 2048 roughly 10kHz subcarriers in a 20MHz bandwidth. This suggests a trade-off of smaller subcarrier bandwidth, 10kHz, for more data in subcarriers, easily supported within a macro-scale deployment. Now, consider simulcasting over a forward channel scheme like this with the attendant benefits already outlined for paging systems. Models like this were before the paging industry roughly ten years ago.

The question that occurs to this author is that, given certain needs for highly robust communications systems for first responders in the instance of disasters, terrorist attacks, and similar situations, why would such a system, incorporating simulcast, never be considered, even intellectually? What drives the single-minded focus of radio engineers at present to the cellular reuse model to the exclusion of all else? To the extent that digital paging systems continue to deliver extremely robust performance by virtue of employing simulcast, why wouldn’t this technology at least be considered for next generation critical response radio networks?

As an aside, after my rhetorical questions, I should point out that I have skimmed over many of the practical technical issues in high-speed simulcast networks, such as 6400 bit/s 4-level FLEX and ReFLEX. I’ll return to some of these issues in later posts.

Before going further, it might be worth to show the phase trellis for binary MSK and GMSK. We’ll come back to these diagrams in what follows.

When looking at these diagrams, there are a couple of things worth noting. First, they show exact phase accumulations at the optimum sampling times. Second, if they were differentiated to show, instead, instantaneous frequency, the result would be a classic “eye diagram“. A quick consideration of the instantaneous changes in line-slopes on the MSK trellis suggests that, assuming filtering or bandwidth issues over the channel, that the eyes would be very open indeed. Unfortunately, those assumptions are not particularly good, which is why designers were lead to GMSK in the first place.

MSK phase trellis

GMSK phase trellis

M-GMSK and ReFLEX

In the reverse channel, ReFLEX specifically calls for a Gaussian filter with a 3 dB frequency in the range of 2,400 Hz. The frequency is independent of the inbound symbol rate, and so the modulation index depends upon symbol rate. In the forward channel, the specification is a little more ambiguous, stating that a 10^th order Bessel filter with a 3 dB frequency of about 3,900 Hz should be applied. It should be recognized that a 10^th order Bessel filter is a good approximation to a Gaussian filter. Therefore, both the forward and reverse channels in ReFLEX are at least Gaussian FSK (GFSK).

Apparently, the variations in the ReFLEX modulations have to do with the modulation indices and the time bandwidth products of the various binary and 4-level schemes that are used. Table II summarizes these for the various options on the forward and reverse channels.

The parameters shown in the Table essentially define 6 pulses for transmission in ReFLEX, two on the forward channel and four on the reverse channel, as given by their time-bandwidth product, . The following figures show these pulse shapes in sequence.

Forward channel BT=2.4 pulse

Forward channel BT=1.2 pulse

Reverse channel BT=6 pulse

Reverse channel BT=3 pulse

Reverse channel BT=0.75 pulse

Reverse channel BT=0.5 pulse

It can be noted that the last pulse, for is precisely the pulse used in GMSK, which is inherently a partial response signaling system with intentional ISI. In ReFLEX, this pulse is employed only on the reverse channel for 4-level signaling at 4800 baud (9600 bit/s). This signaling scheme was used by Skytel; but to my knowledge, it was not deployed elsewhere. The Skytel system lacked the antenna diversity of later systems, such as those deployed by PageMart (aka WebLink), PageNet, and Arch. As a consequence, the Skytel system had relatively poor reverse channel coverage. In later designs, efforts were taken to ensure that reverse channel coverage exceeded forward channel coverage for various overall design principles. We’ll consider those principles in subsequent posts. For now, the reader might go back to the binary GMSK phase trellis diagram shown at the beginning of this post and consider the impact of running a 4-level GMSK system. The phase trellis automatically becomes more complex by virtue of having, in effect, a scale-2 instance of itself superimposed over the original.

In practice, quadrature phase detectors are almost never used in paging mobiles, although they have been employed in base station receivers on the reverse channel. Instead, the receiver of choice is a discriminator or FM detector. Of course, these receivers are sensitive to instantaneous frequency and not phase. Herein lies a significant rub.

Click noise

FM click noise has been recognized virtually since the first land mobile voice system was delivered. A model for click noise was developed by Rice. As is well-understood in the modeling of Rayleigh fading, deep nulls in received signal strength tend to occur at distances of about 1/2 the wavelength of the carrier. The following image demonstrates this:

Rayleigh fading

It is perhaps less-widely appreciated that received signal phase generally shifts by 180° as the receiver traverses such a null. As well, the same thing occurs when two nearly identical sinusoids “beat” against one another. The figure below shows phase discontinuity clearly.

Beating between sinusoids, showing phase discontinuity

For an FM receiver, differentiating these sharp changes in phase will produce equally sharp clicks, which can be quite pernicious in an audio system. The figure below gives an example for an example simulcast signal constructed in phasor representation as follows:

with

The point of this construction is to show what can happen when nearly equal carriers combine at the receive antenna in a simulcast system. In this example, the relative values are 0, -0.9, -6, -20 & -40 dB. The dominant beats are between the 0 and -0.9 dB carriers, with the lower value carriers filling in when the two dominant signals null one another out. Note that the figure shows some phase wrapping where phase values are constrained to lie within ; these discontinuities do not, in themselves, yield FM clicks since they are artifacts of the presentation. Likewise, the small shifts in frequency from a nominal “0″ reference value (the leading “1″ in the series which should be understood as ) are showing a few parts per hundred of frequency shift from the primary carrier’s frequency. For this phasor representation, this carrier frequency has been subtracted out. In practice, frequency errors would normally be only a few parts per million or less with modern TCXO and GPS disciplined frequency synthesizers, except where frequency offsets are purposely programmed in. In fact, this latter practice is quite common with newer transmitter equipment since otherwise simulcast nulls can last around seconds at a time. It is preferable to engineer simulcast nulls to be of shorter duration by introducing these purposeful frequency offsets.

In any case, the point of the figure is not to show the practical arrival rate of simulcast nulls but rather to demonstrate their impact on recovered carrier phase.

The figure shows unmodulated amplitude and phase; however, in the presence of an angle modulation, these significant steps in carrier phase can be very troublesome. In a paging mobile receiver, of course, the aim is to recover data, not audio. For binary receivers, spurious FM clicks can be dealt with by simply driving the output of the detector to the “rails”. This may yield short durations of signal time during which the detected signal is completely wrong; however, since these clicks are of extremely short duration relative to most paging bit times, the impact is limited.

Amplitude and phase for a simulcast signal

The following figure shows the instantaneous frequency values for the same signal; that is, the time derivative of the phase.

Instantaneous frequency for simulcast signal

On the other hand, for multi-level FSK, the impact is much more significant. In this case, the recovered signal cannot simply be quantized immediately with a limiter amplifier, since this would destroy the desired four discrete signal levels. In addition, automatic gain control and level control is typically included in order to adapt the recovered signal stream to the reference values of the 4-level slicer or analog-to-digital converter that will yield the recovered symbol at the appropriate sampling time. And speaking of appropriate sampling time, this is estimated usually be a symbol clock recovery circuit that involves first, some non-linear operation on the analog data stream (like squaring), and then passing the result to a phase-locked loop or other time-stabilizing circuit. The presence of these random FM clicks plays havoc with both the gain and level control circuitry as well as with symbol time recovery circuits.

In the world of paging, these pernicious effects were first noted by carriers who wanted to achieve 6400-bit/s signaling with FLEX, which, like ReFLEX, uses 4-level FSK on the forward channel. Hence, this was arguably the first time that the paging industry had to deal with the issues caused within a simple FM discriminator detector by simulcast. I have written about these issues elsewhere; and another extremely detailed and practical view on the matter was prepared by Selwyn Hill when we worked together at PageMart on this problem. I’ll let the self-motivated reader review this material for him or her self.

ReFLEX partial response signaling

So, the good news is that the intersymbol interference in high speed ReFLEX is reduced by the use of a simple FM detector; but the bad news is that FM detectors are prone to the negative impacts of FM click noise in the case of multi-level signaling. The table below gives some notion of the relative values of ISI for ReFLEX given either a phase detection or frequency detection full response signaling approach to data recovery.

Of course, one natural approach to dealing with this combination of problems would be to give up on full response signaling and adopt a partial response signaling method.

For the variety of cases in ReFLEX, Eqn. 7 (see the previous post in this series) generalizes to

Table III shows the feasible sets of phase differences that may be associated with various cases in ReFLEX taken as partial response signaling channels.

TABLE III

Possible Phase Differences for ReFLEX PRS

Channel
F 1600 bit/s 2-level	±3π, 0
F 3200 bit/s 2-level	±3π/2, 0
F 3200 bit/s 4-level	±3π, ±2π, ±π, 0
F 6400 bit/s 4-level	±3π/2, ±π, ±π/2, 0
R 800 bit/s 4-level	±12π, ±8π, ±4π, 0
R 1600 bit/s 4-level	±6π, ±4π, 2π, 0
R 6400 bit/s 4-level	±3π/2, ±π, ±π/2, 0
R 9600 bit/s 4-level	±π, ±2π/3, ±π/3, 0

For those cases in which there is less than a single rotation around the unit circle for the outer symbols, an over-sampled differential phase detector is probably a better choice than a discriminator detector. These cases are 3200 bit/s binary and 6400 bit/s 4-level on the forward channel, and 6400 bit/s and 9600 bit/s on the reverse channel.

In the spirit of brevity, Table I (see the previous post in this series) is not expanded here for the various cases of 4-level modulation. However, it should be clear that the same form of table, if somewhat more complex, could be constructed for the detection of 4-level ReFLEX “GFSK” as for binary GMSK.

Other Advantages

While the first approach in the detection of ReFLEX is to use similar methods as for FLEX, including the use of the Toshiba TA31149FN, the “half deviation” of ReFLEX makes the successful discrimination of forward channel frequency symbols at 6400 bit/s very difficult. At this rate in ReFLEX, h = 0.5 and the modulation is a form of MSK so that the symbol spacing is exactly at the theoretical Nyquist/Fourier limit. At the same rate in FLEX, h = 1, and resolution of the individual symbols is feasible with an FM discriminator [9].

Channel errors due to any number of factors such as modulation inaccuracy, fast Doppler shifts, Rayleigh fading, simulcast delay spread, beat frequency oscillations between simulcasting transmitters, receiver IF filter mismatches and differential group delay, comparator threshold errors, and so on, all combine to make operation at the theoretical limit of FM problematic indeed.

Moreover, experience with FLEX and ReFLEX has shown that the use of discriminator detectors yields other unexpected problems in the presence of simulcast delay spread. The most pernicious of these is the generation of pulses or “FM click noise” due to the differentiation of phase steps that occur at the amplitude nulls of beat frequency envelopes of transmitters whose symbol frequencies have some relative offset. I refer again to Selwyn Hill’s excellent paper on this topic.

These frequency offsets occur in two ways. The first is due to more or less static offsets between transmitter carrier frequencies during the stable part of the symbol. For high quality base station transmitters, these offset frequencies are of the order of a few Hertz typically, unless purposely configured otherwise. At the null, received phase changes by 180º. The second is due to the delay time between the arrival of symbol edges from transmitters that are at different electrical distances from the receiver. This effect is a dynamic form of the first in the sense that instantaneous frequency difference between the two received signals rapidly increases as the one from the closer transmitter, which is slewing toward the new symbol, beats against the one from the further transmitter, which is still at the original symbol frequency. There are many permutations of the orders of arrival, symbol frequencies, delay times, and relative amplitudes that complicate analysis. However, the main point is that a cascade of pulses can be generated by the differentiation function in the receiver during symbol transitions in the simulcast environment.

Besides distorting the received signal, these pulses often have the negative side effects of yielding inaccuracies in the threshold values in the comparators that map base-band “audio” onto digital levels and of creating jitter in symbol clock recovery circuits.

A phase detector of the sort used for GMSK in, say, the GSM or CDPD, would also be subjected to significant phase shifts from time to time in a simulcast environment. However, lowering the modulation index actually mitigates the effects that arise at symbol transition times. [In my humble opinion, the worst case is 4-level 3200 bit/s FLEX.] For the situations in which static beat frequencies arise and yield symbol detection errors due to the 180º phase changes arriving at the beat frequency, interleaving and error correction are suitable mitigations.

In other words, by constraining the received signal to lie within the space of constant envelope continuous phase modulations (CECPM), FM click noise cannot arise from any cause. In contrast, by treating the received signal as FSK, click noise is not just allowed for, it is guaranteed.

Summary

In this and the previous post, I’ve compared and contrasted the use of MSK and Gaussian pulse shaping in ReFLEX and the GSM. While GSM limits itself to binary GMSK with , ReFLEX operates with , and 0.5 ≤ BTb ≤2.4. As well, ReFLEX uses both binary and 4-level signaling. So, for whatever it might be worth any longer, I’d recommend the use of differential phase detection methods, rather than FM discriminators, for ReFLEX when and . The construction of transmitters for mobile devices is beyond the scope of this contribution, but there are guidelines in the references or from a review of the current literature on the GSM or GMSK.

Acknowledgements

I’d like to acknowledge the help of Vic Jensen and Doug Ayerst then of Motorola for their assistance in communicating the design goals for the ReFLEX modulation. I’d also like to acknowledge the comments of Alan Paris, then of Skytel, in distinguishing some of the specific ISI effects as between phase and frequency detection methods in his review of an earlier version of this material. That earlier version of this was done back in 2003, eight years ago now. How time flies when you’re having fun!

First, this post is going to get technical. Sorry. If you’re not into that sort of thing, you might just want to skip all the way down to the conclusions or skip this whole post altogether. OTOH, if you’re into things wireless, this might be refreshing in the sense that you may walk away with a better appreciation for the level of technical detail that went into the design of modern digital paging systems.

Introduction

I’m going to do a comparison and contrast of the modulations used in ReFLEX on the forward and reverse channels at various symbol rates relative to the GMSK used in the GSM. Outside of the obvious difference in bit rate, the other two parameters are the modulation index, and the filter time-bandwidth product. As well, ReFLEX uses 4-level signaling in a number of cases while the GSM is binary. It might be worth noting that the modulations used in one-way FLEX and on the InFLEXion control channels are essentially similar to those in ReFLEX. Here, I’m going to concentrate on ReFLEX.

FSK, MSK and GMSK

Frequency Shift Keying (FSK) is a well-known means to transport modulated binary data. In its simplest form, an assignment of discrete frequencies is made to discrete symbols; and where the symbols are binary, the modulation appears to be a kind of FM in which the base-band “audio” is a two-level Pulse Amplitude Modulated (PAM) signal. By mapping the peak frequency deviations from a nominal carrier frequency to the binary PAM levels, it is easy to achieve binary FSK (BFSK). The occupied bandwidth can be considerably larger than what is necessary however. In what is known as Minimum Shift Keying (MSK), the goal is to achieve the closest possible spacing of the discrete frequencies that constitute physical symbols on the channel. This minimum spacing is , where is the symbol time; so , or , where is the frequency deviation and is called the modulation index.

When used in the context of multi-level FSK (MFSK), “frequency deviation” must be defined carefully to refer, not to the peak frequency deviation of the outer symbols, but rather to the frequency deviation of the inner symbols closest to the nominal carrier. One way to encode this notion is to associate the information symbols with M values as follows:

We can then define a data sequence for modulation as

which is then the frequency-modulation component of an equivalent quadrature low-pass signal as follows:

Eqn 3

In this context, if is a non-return-to-zero (NRZ) unit pulse with a duration of , then the frequency deviation is just when is unity. For the special case of 4-FSK, which is of interest in ReFLEX, the values of are ±1, ±3, and the discrete symbols would be relative to the carrier.

Characteristics of MSK

In the case of MSK, is the unit pulse, and with binary signaling, and the phase trellis is very simple. Since , phase accumulates at a rate of every symbol time. For runs of +1 or –1, phase accumulates by every 4 symbols.

MSK has a very compact spectrum with the bulk of the transmitted power contained in a major lobe of bandwidth . Unfortunately, MSK also has very significant side-lobes, and filtering out these side-lobes generates AM effects. If the filtered signal is transmitted with a Class C, non-linear power amplifier, the side-lobes are regenerated, yielding spurious out-of-band emissions that are undesirable.

Gaussian MSK

One approach to “fixing” MSK is to introduce a Gaussian shaping filter into the modulation chain. This chain would consist of the sequence of information symbol impulses, , driving an NRZ pulse generator feeding the Gaussian filter followed by a frequency modulator. If the impulse response of the Gaussian filter is

where is the 3 dB bandwidth, then the pulses, in Eqn 2, are the result of this filter operating on NRZ pulses, and

where

is the complement of the cumulative distribution function (CDF) of the Gaussian (Normal) distribution.

It is common to represent the bandwidth of the Gaussian filter parametrically in terms of the product . For the form of binary GMSK used in the GSM service, .

Fig. 1- Gaussian Pulse with BT=0.5; Click for larger version.

There are any number of interesting observations that may be made about this pulse, which is a Gaussian-filtered NRZ pulse.

1. It is non-causal, being of infinite duration in both directions of the time axis.
2. The area under the curve is exactly 1, and by symmetry, exactly 0.5 on either side of 0. About 0.3% of the area is below or above .
3. Changing the time-bandwidth product simply scales the pulse in time relative to what is shown. Hence, more or less area falls between as is increased or decreased from 0.5.
4. The use of this pulse yields deterministic inter-symbol interference (ISI) in the phase trellis of GMSK. There would be considerable over-lap of pulses centered at with the pulse shown at , because the width of this pulse is about .

Full and Partial Response Signaling

Per Eqn. 3, the accumulated phase at discrete symbol times is a result of the integral of the data sequence , and hence, of the sequence of pulses and the . One detection policy would be to sample after the contribution of each pulse to the accumulated received phase. This implies waiting at least one complete symbol interval after the center of the pulse, given the curve shown in Fig. 1. A more traditional approach, suitable for more compact pulses in which most of the area under the pulse is concentrated between , would be to sample at half-symbol times; e.g., , , ….

Depending on the nature of the receiver, this policy can to errors since 22% of the area under the pulse is outside of . It therefore depends on whether or not the receiver is sensitive to the frequency (time rate of change of phase) or the accumulated phase of the signal as to how much inter-symbol interference (ISI) is experienced by the receiver because of this pulse structure.

In the case of GMSK, the contribution to the accumulated phase at the center of the symbol time will only be 50% of the final value attributed to ultimately. In other words, the phase difference between adjacent whole symbol times is approximately

Eqn. 7 is approximate in this case because of the 0.67% of area that remains outside the main lobe of the pulse between .

Most communication engineers are familiar with the notion of full response signaling in which the signal received at any time is based on a one-to-one mapping to the symbol transmitted. In partial response signaling, of which the present case is an example due to ISI, the received signal is based on a functional combination of transmitted symbols. Eqn. 7 represents that combination for GMSK. In the case of binary GMSK, used in the GSM, the results are straightforward: if two adjacent symbols are +1, then ; if both are –1, then ; and if , then . GMSK is a member of a broad class of constant envelope continuous phase modulations (CECPM) that attracted a good deal of interest as the GSM standards were being developed [1] – [6].

In most cases of full response signaling, ISI is avoided by using Nyquist pulses of the first class, in which the amplitudes of adjacent pulses vanish at prescribed sampling instants. In FSK, this class of Nyquist pulse is not to the point since it is the area under the pulse curves and not their amplitudes that leads to ISI. Nyquist dealt with this problem as well, and defined his “third criterion” for the avoidance of ISI in situations where signaling is based on the integration of pulses [7].

Detection of GMSK

Nearly optimal detection of binary GMSK is thus based upon estimating the received symbol with one symbol time of delay at the center of the symbol time. Table I gives a better idea of the process.

TABLE I

Expected Phase Differences for Symbol Sequences

π/2	π/2	+1	+1	+1
π/2	0	+1	+1	–1
0	0	+1	–1	+1
0	–π/2	+1	–1	–1
0	π/2	–1	+1	+1
0	0	–1	+1	–1
–π/2	0	–1	–1	+1
–π/2	–π/2	–1	–1	–1

Note that there are 9 possible combinations of the 2 phase differences and 8 possible combinations of the 3 adjacent symbols. The pattern of adjacent phase differences and is infeasible, taken in either order. Similarly, the pattern of adjacent 0 phase differences can arise in 2 different ways. The ambiguity can be resolved only by knowing the initial symbol correctly. Thus, a single bit error before a pattern of alternating bits can lead to an error catastrophe.

Either differential phase detectors or quadrature receivers are suitable for detection of binary GMSK. Discussion of the expected bit error rates is beyond the scope of this post, but the literature is completely filled with this material because of the application of GMSK in the GSM, CDPD, GPRS, and so on. Likewise, there are DSP techniques that may be employed to optimize the construction of modems for CECPM [4], [8].

Historical Note

It is worth observing that one of the reasons that a non-linear CECPM was chosen for the GSM, as opposed to the linear modulations later adopted in North American Digital Cellular, was a view to optimizing the areal density of information transmission as measured in, say, bits/s/Hz/sq.km. For exactly the same reason that paging uses a CECPM, the proponents of GMSK in the formative days of GSM held that the capture effect would assist in rejecting co-channel interference, and therefore drive up the reuse number for this form of modulation. Of course, these cellular designers were not envisaging any kind of soft handover complete with simulcasting; but rather, simply improving co-channel interference rejection (CIR).

Nonetheless, the GSM achieved a reuse number of 3 when most analog cellular systems, employing traditional frequency modulation for voice, had a reuse number of 7 and required 3-way antenna sectorization. While there was huge debate at the time, I was of the opinion that the original TIA IS-54 TDMA standard could have been deployed with a reuse number of 4. I do not believe that this was ever attempted in practice since this reuse plan would have conflicted with the existing 7×3 reuse for AMPS. IS-54 employed π/4-DQPSK; and this modulation would never quite have achieved N=3. At the time, I expect that carriers in transition from analog to digital cellular did not care to set aside blocks of frequency for DAMPS and to re-engineer their antenna systems to lay out an N=4 plan for digital. In contrast, IS-95 CDMA fit neatly onto the existing 3-way sectorization model of AMPS base stations. Of course, it forced the allocation of entire blocks of 1.5MHz at a time to the digital transition. Obviously, the engineers working for the CDMA carriers had to run with this mandate in spite of the capacity reduction for analog cellular users.

My point is that all the world believes that GSM is brilliant and paging is old technology. Yet the two are built on extremely similar foundations for very similar reasons.

Go figure.

Next time…

Since this post is rather long already, I’m going to break it into segments. In the next segment, I’ll get into more detail on the various pulse shapes and parameters used in ReFLEX, together with their pros and cons.

Having worked on these systems myself for years, I thought it might be worth reviewing a few of the aspects of paging/NPCS that make it so resilient to disaster.

Simulcast on the forward channel

As we’ve mentioned before, paging systems simulcast on the forward channel. In many typical situations, a paging device is simultaneously receiving signals from a half dozen or more transmitters. The receiver employs a limiter detector to capture one of these and rejects the rest. However, even if the closest transmitters were all to collapse for any reason whatever, there are almost always enough in the vicinity to all for messaging to continue. In the major urban centers like NYC, LA, DFW, Miami, Chicago and so on, paging systems may have over 30 simulcasting transmitter towers. Even if the dozen or so transmitters in the dense urban core are taken out, there are two dozen more left in the suburban area that can still provide service, if with somewhat reduced in-building penetration. As I have mentioned elsewhere on this blog, simulcast methods are also used in the APCO P25 system. At the time I’m writing this, a good deal of Radio Resource Magazine’s “Mission Critical University” web page is devoted to APCO P25 material.

In contrast, the design of cellular systems are predicated on minimizing cell-to-cell co-channel interference. Taking out all of the sites in the urban core of a city will essentially kill all cellular coverage there. Excess capacity is not redistributable in such a system, unless there is a functional site to redistribute it to.

Reduced dependance on ground communications

Major nationwide paging systems use satellite communications for both forward and reverse channel traffic. At WebLink Wireless, we pioneered the use of digital satellite communications for paging, first for one-way, and later, using VSAT for two-way/NPCS. I am not certain what the situation is at USA Mobility presently, but in the days of WebLink, we distributed our site traffic across three independent geo-stationary satellites. Any urban center generally had sites that were scattered across two of these satellite links so a failure of either one would not take out all sites in the city. Some markets in dense rainfall regions (e.g., Miami) required larger than standard-issue VSAT antennas to compensate for the statistics of link outage to rainfall; but in practice, even the densest storm cells would impact only a site or two at a time. Built-in network message retransmission methods generally compensated for such temporary site-by-site outages in the cases where simulcast did not.

More than this, the complete absence of ground back-haul links to the base station sites removes all outages due to the failure of those links from any cause. Whether it is a link loss due to a cable being cut by a construction crew or flood-water covering a pedestal, cellular and other broadband systems depend as much on wired communications as do traditional home phones.

No local, non-redundant control systems

In addition not having ground-based back-haul, paging systems do not have the local infrastructure of cellular telecomms. Major urban cellular networks have local base-station controllers and central office switching centers. Even if these COs were locally redundant, a localized disaster will generally take them all out of service, along with the back-haul methods to and from them. Paging systems, in contrast, have remote switching centers for the control of all radio traffic. As well, these centers are redundant in the sense that all traffic normally routed to one via satellite links is equally accessible to another. Therefore, should a major up-link in say, Georgia, go down for any reason, its traffic can be taken over gracefully by a center in, say, California or Illinois.

Limited, “movable” local switches

Messaging systems rely largely on Internet access for receiving and returning traffic. Having said this, pagers can, of course, be called via the PSTN to local or 800 numbers. For Internet access, it is feasible to distribute traffic in and out of a nationwide network to completely redundant server farms located “in the cloud”. Likewise, it is feasible to reroute digitized phone traffic, including voice messages, using VoIP methods across Internet links from one physical access location to another. While it is true that PSTN-based voice messaging to pagers with only local phone numbers may be taken out by a local disaster in the same way as would impact a wired or wireless local phone operator, whether cellular or not, this will not completely isolate communications to a typical pager. Users will still be reachable by email, web-site messaging, TAP, TNPP, WCTP, and so on. Likewise, those with two-way devices will still be able to communicate with one another, and with the big, bad Internet. Those with 1-800 numbers will also have the flexibility of not losing even the PSTN voice messaging, since these numbers can quickly be redirected to other switch locations.

Even local switches can be replaced on a rapid basis if it is necessary. A nationwide operator can bring up a new switch from “spares” and have incoming phone lines brought into a new local site. The spare switch does not have to be local, exactly. Incoming local traffic need only be received and converted to Internet methods and then forwarded to the replacement switch for the duration of the local disaster. The spare can be populated with user account information from back-office accounting systems that are, themselves, redundant to failures in the operator’s internal IT systems.

Reverse channel redundancy

Just as the forward paging channel is redundant due to simulcast, the reverse channel in NPCS is redundant because of the reuse of the reverse channel over multiple base station receive sites. This is discussed in depth in other posts on this web site.

Critical sites

Carriers can designate certain sites “critical” and provide extra protection to these. For example, if it is assumed that some natural disaster could take out the electrical grid that would power base station operations, then these designated critical sites could be engineered with local battery backup sufficient to last for some period of time. Because of forward and reverse channel redundancy, these critical sites could provide communications with reduced in-building coverage in such situations. For example, a carrier might designate 3 or 4 sites as critical in a dense urban core with a nominal count of 12 sites. These could be provisioned with battery backup, remotely switchable VSAT antenna systems, and so on.

Critical traffic

To extend the battery-life of critical sites, base stations can be operated on a reduced usage cycle. Naturally, this approach would also reduce system traffic capacity; and this may have other consequences. However, should it become essential to give precedence to high priority traffic for some period of time, then systems can be put in place to shed lower priority traffic and allow only messages for first responders or to prioritize these.

Sites in the sky

Space Data Corporation of Chandler AZ is a pioneer in the application of NPCS to a unique approach in providing wireless coverage in hard to reach locations; namely, using base stations on weather balloons. In addition to providing systems now for telemetry and telematics in the field, such systems also have appeal to military and first-responder users. They can be used for tactical support in military theaters of operation; and they are equally applicable for disaster support situations whether in urban or remote settings. By using the inherent capability of NPCS networks to roam between systems, Space Data’s approach could be rapidly deployed in the event of a disaster in such a way as to augment an existing, if damaged, NPCS network on the ground.

Summary

Well, enough. Here are another set of reasons for continuing with paging/NPCS: they hold up in times of adversity amazingly well. While the nation is concerned about wireless systems suitable for disaster notification and first responders, it seems to my simple brain that pushing paging/NPCS networks down and off the list of those under consideration is somewhat counter-productive. Of course, every law enforcement officer wants some fancy Dick Tracy smartphone so that they can get images of the bad-guy two minutes after the bad-deed is logged by some fancy video system with facial recognition software behind it. Maybe such things are the wave of the future, and I’d be surprised if they aren’t the subject of much research in labs around the country and the world. However, for now, in this real world, would a terse text (or binary data) message not often be sufficient? Is this not especially true when you consider the inherent ability of a paging/NPCS network to support efficient broadcast messaging to dozens, or even millions of devices?

Well, it’s true. In the FLEX set of protocols, which includes FLEX itself, ReFLEX, & InFLEXion, the suite of protocols that are provided to deliver certain applications or application-enablers (called FLEXsuite) has a recursive stack model. Now, I don’t know how many pointless debates, roughly akin to the old medieval philosophical arguments about how many angels could dance on the head of a pin, I have read over the years about what OSI stack layer this, that or the other function should properly fall into. Too many.

The origin of the OSI stack derives from early work on the TCP/IP stack which itself originated in the DARPANet (“before they dropped the D”) and models for structured architecture and design of software systems. If this fails to ring any chimes with you, please consider the work on this topic of Mike Padlipsky; e.g., RFC 871, RFC 872, RFC 874,The Elements of Networking Style, and so on. IMHO, if you don’t know Padlipsky, you don’t know networking.

Back in the day, spear-heading the whole structured design and analysis movement was Edward Nash Yourdon from IBM, whose publications include more than a few gems in the world of software engineering. Through the early 1980s, I took many Yourdon courses and together with various co-workers, came up with methods to adapt this style of thinking about computer systems into the arena of real-time systems for process control and telecommunications. My point is that if you put a few of Padlipsky’s papers on the background of the DARPANet and Yourdon’s papers on structured design, it is not too difficult to see the threads come together that yielded the original layered protocol models in DARPANet -> ARPANet -> TCP/IP -> ISO OSI.

The essence of structured design can be summed up as follows:

• Design should be as modular as possible, but no more so.
• Design elements that are related to one another should be grouped together.
• Black boxes should be used when possible so that information and processing that is irrelevant to other parts of the system can be altered or improved with zero impact elsewhere.

“Structured design is the art of designing the components of a system and the interrelationship between those components in the best possible way. “
”Successful design is based on a principle known since the days of Julius Caesar: Divide and conquer.” – Edward Yourdon

For folks interested in more detail on Yourdon’s structured method, look at his Wiki.

I am harping about structured design in the context of layered protocol models to point out that in failing to recognize where they came from in the first place, the whole modern world has slavishly adopted a set of ad hoc heuristics as if they were commandments engraved in stone. Then, when it becomes of value to violate these rules, there is a great deal of heavy lifting involved. In the original though process, the concept was as simple as hiding information about, say, the details of network routing from devices that had to interpret ASCII for a screen display. Over the years, the notion of protocol layers has ossified to the extent that thinking outside the box is tantamount to a deadly sin in certain circles.

Take, for example, the notion of a secure Virtual Private Network (VPN). Frequently, it is of value to connect together two geographically distinct private TCP/IP networks whose IP address ranges are taken from the private allocations, and whose internal details are hidden from the public Internet behind firewalls, proxies, and gateway routers. These distinct networks are often operated by the same company at different office locations, and one of them may be a simple as one person with a home office or roaming with a laptop or smartphone. Still, the concept is to maintain the isolation of the two networks from the public Internet while simultaneously joining TCP/IP traffic between the two as if they were co-located by using publicly available Internet routes.

In order to pull this trick off, routers (or routing software) at either end inspect IP datagrams to see if the destination address is known to be at the other office location. If so, its IP datagrams are encrypted and “encapsulated” inside some form of special IP datagram that must be routed towards another compatible and special form of VPN router (h/w or s/w) that can invert the process and recover the original datagram for routing at the remote end.

Now, if you look at the Wikipedia article on VPNs that I linked to above, you will see some of the mental gymnastics that must be accomplished in OSI stack models to achieve this effect. The reason is that IP routing is supposed to happen at the network layer, end of story. Above the network layer is the transport layer and below the network layer is the link layer. The transport layer does not offer VPN services since these are other network layer services, nor can the IP layer look down to the link layer for VPN services.

There are no VPN services envisaged at any layer of the OSI protocol model. The network layer has to perform a slight of hand to create, in effect, another network layer in order to work sideways, as it were, stackwise. This can only be achieved is some remote router is in on the trick and can recognize when to invert the slight of hand to reveal the hidden IP datagrams that the originator buried, in violation of the stack commandments.

This kind of thing is achieved easily with the recursive stack model of FLEXsuite. Below are two diagrams that show two different approaches to routing that are supported in FLEXsuite.

FLEXsuite end-to-end routing

FLEXsuite content routing

The basic protocol for routing in FLEXsuite is the Uniform Addressing and Routing protocol (UAR). The interesting thing about UAR is that UAR can carry UAR, as well as other protocols in FLEXsuite. In this way, FLEXsuite is recursive, since in effect, one protocol layer can call itself. Furthermore, one of the FLEXsuite protocols designed to support any variety of encryption methods is the Data Security Identifier (DSI) protocol. In FLEXsuite, a UAR payload can be encrypted and carried within a DSI payload which is itself routed by yet another UAR envelope.

Let us consider for a moment this notion of end-to-end versus content routing. An end-to-end routing policy is implicit in a layered stack model such as TCP/IP or OSI. Network datagrams destined from a sender to a recipient may be inspected for their destination address (in principle, anyway) along the way, but the contents of the datagram is interpreted only at the recipient. UAR supports this model, but also supports content-only routing. The distinction is indicated by a flag that is set by the sender. In content routing, a gateway protocol strips off the UAR envelope and converts the payload, as appropriate, for transmission to the intended recipient. This form of routing is useful, for example, when a user with a two-way pager wants to send email to a recipient on the Internet. Under the general assumption that no existing Internet router has a clue about UAR, the user’s UAR packet is delivered to an interpreter within the paging network that sees an SMTP request with a destination address of the form “name@domain.com” and the end-to-end routing flag turned off. This interpreter takes the content and places it in an SMTP PDU with the destination address requested by the user and with a return address consistent with the user’s network account information.

Any variety of content-routing methods can be implemented in this way. For example, UAR can request that payloads be delivered to HTTP addresses, routed to facsimile devices with NANP or international phone numbers, or even delivered as a phone call through a text to speech interpreter. There is even a specific protocol, the Wireless Communications Transfer Protocol (WCTP), that has been designed to carry FLEXsuite payloads between carriers and other “FLEXsuite-aware” enterprises. WCTP is worthy of a big write up on its own, and at some point, I’ll get around to that. For now, note that WCTP is an XML-based protocol that can transport FLEXsuite content over the Internet. UAR allows for content routing or end-to-end routing via WCTP to an arbitrary uniform resource identifier (URI).

Since a UAR envelope can contain another UAR envelope, it is then feasible to create a sequence of envelopes within envelopes that can cover almost any arbitrary sequence of delivery models. For example, pager could create an outer UAR envelope that requested content routing using WCTP to some URI for a remote network. Let us say that this outer UAR envelope carried another UAR envelope that requests end-to-end routing to a pager on the remote network. The URI in the original case will be for some gateway box that receives WCTP XML structured payloads, and when it gets this end-to-end UAR payload, it forwards it to the destination pager. At the destination pager, let us say that the UAR is opened to reveal a DSI package that comprises an encrypted payload. Let’s further suppose that this DSI payload indicates encryption with the private key of the recipient pager. When the task of decryption is completed, the pager device finds yet another UAR payload, this one is addressed to a local URI that identifies, say, an application on the device designed to display personal security alerts. Let us hypothesize that the originating device was a security unit on the user’s automobile and the recipient device was a personal unit carried by the user. Of course, any number of different use cases could be imagined.

Note how there is absolutely no humphing about the implementation of what is basically a two-point VPN between the two devices owned by this one individual and operating, apparently, on two distinct carrier’s networks. In my hypothetical case, one device is a telematics unit in a vehicle that detects some form of alert condition while the other is a smart device that appears to support multiple third-party applications along the lines of existing smart phones.

Without going into further tedious explanations, UAR can route to a wide variety of addressing models including IP addresses and ports, URI/URL structures, phone/facsimile numbers in a variety of numbering plans, other pagers either on or off-network; and in doing so it can employ a wide variety of protocols, including SMTP, HTTP, WCTP, “phoneto”, “faxto”, and on and on. In certain cases, only content-routing is appropriate; for example, text-to-speech conversion for a phone call. In other cases, combinations of end-to-end and content routing can be employed in complex combinations.

About a year ago, I proposed a similar recursive stack model to ANSI TIA TR50, a body engaged in consider standards for machine-to-machine communications (M2M). I believed then, and continue to believe now, that many of the issues surrounding the delivery of small telemetry payloads between arbitrary M2M systems in ways that can incorporate unique and powerful security methods. What is better, these methods have been proven in service for over a decade now on and between a variety of networks for exactly this kind of application.

I cannot say that my proposal was well-received. Unfortunately, I couldn’t find any organization willing to support my participation in the forum, and so I withdrew without having had the opportunity to follow through with much of an explanation. I suppose that it died on the agenda after I failed to attend for a few meetings. Yet another pity. TR50 is presently working on RESTful protocol models for its work, and this notion has apparently made its way into ETSI work on M2M as well.

The REST model involves requests by clients to servers for services that can be represented, typically, in the form of some document that can be transferred from the server to the client. The model further involves a notion that communications are stateless, even though the server may be stateful; that is, each service request is self-contained and does not depend upon any previous or subsequent communication. Furthermore, the REST model assumes a layered protocol model such that the client cannot actually detect whether it is connected to the remote server or some proxy agent.

The REST model has four aspects to its interface. First, resources are identified by URIs. Second, resources are manipulated through their representations; that is, through their URIs and resource metadata. Third, messages are self-descriptive; for example, content may identify how it is to be parsed by including its MIME type. Fourth, if the access to one resource may yield requirements to access other resources, these should be included in terms of URIs for these other resources, likely in the form of hypertext links to them.

It should be noted that UAR and FLEXsuite are RESTful with the enhancement that since FLEXsuite supports a recursive, layered protocol stack, certain communications methods are supremely simple to achieve.

Anyone interested in more detail on FLEXsuite can obtain a copy of the protocol from the American Association of Paging Carriers.

This notion is generally given the head, “encapsulation” and a typical interpretation is shown graphically below for UDP packets encapsulated within IP datagrams over some form of frame relay. (Note that this diagram is from the Wikipedia article on the Internet Protocol.)

Encapsulation in UDP/IP

Now, imagine that you are in the role of a radio receiver sitting around waiting for some encapsulated PDU to be delivered to you. Because of the encapsulation rule, you are compelled to consider each PDU in its own right; that is to say, in its entirety. You cannot tell if you have a well-formed PDU until you receive all of its data elements, especially the ECC field which is generally placed at the end of the PDU. You must then validate the PDU for accuracy before you proceed, lest you make a mistake in interpretation of the address or data fields. In virtually every case of such analysis, assuming that you are operating on the typical shared channel, the PDU in question will not have been for you; and the result of your work will be to discard the data. At the same time, if you are running on a battery, every 10 nanoJoules of energy that you consumed from the battery for every instruction you processed to do this work will also be eligible for discard. In short, you’ll be lifted many bales of hay only to drop them before you carry them onto the boat.

Now, this is the world of the tubes of the Internet and the world of telecoms as currently practiced. It works well in that world since virtually every box that the designers of the Internet and all of the switches in the world were intended to be plugged into the electrical grid. I’ll grant you that the designers occasionally would get around to wondering how big a pile of batteries they might need to satisfy some externally imposed specification about operation if, heavens forfend, the grid every died on them. But I assure you that those considerations were invariably made after the fact.

You’ve been hired as a receiver

But you are now hired as a radio receiver of data streams, and your life depends upon your battery. You die when your battery dies. What do you think now about this encapsulation rule? If the only data element that tells you whether you need to bother with analyzing the rest of a PDU is the destination address, why would you be the least bit interested in wasting your precious battery energy to work out whether the ECC checks out on someone else’s PDU?

Paging was “Green” before its time?

Why indeed? The upper crust may be dining on batteries tonight, but this is the energy ghetto out here in radio-ville. Or maybe, we put the “green” spin on this, and tell the world that if you want to send and receive data over the radio waves, that you can do so and save the planet at the same time by taking your encapsulation rule and putting it where the compact fluorescent bulb don’t shine.

I have a cool idea…

So, oh TCP/IP-obsessed world, listen up. What if we restructured the forward channel as follows (I just had this cool idea, you should hear this):

1. Throw away encapsulation rules.
2. Establish a synchronized framing system.
3. In the first part of a frame, send nothing but an ordered list of destination addresses for any mobile that will receive data in this frame.
4. Follow this list with another ordered list of pointers to where the corresponding receiver (whose address appeared in the same order earlier) can recover their data.
5. Let the pointer include information as to the time, frequency (channel number), data type, and size of the data field.

What do you think of that? Then, receivers wouldn’t have to wake up until that part of the frame structure where they knew that the address lists would be sent. If they didn’t see their address in the list for that frame, they could just go to sleep until the next frame time. Hey, but wait, maybe we could do this too. I have another idea suddenly. This is so cool.

Extending sleep times for a greener system…

What if we made the frame structure so that we could broadcast something in an overhead frame some times that told all the mobile receivers that they’d only have to wake up for every second frame, or every fourth frame or every eighth frame or something. We’d just have to send out this power of two parameter, and that way the mobiles would figure out from their addresses which frame to wake up for. So, if we made this parameter equal to 3, for example, then they’d only be waking up in every eighth frame. Then, they’d almost always be asleep. Even in that frame, they’d only have to wake up for the short amount of time that the address list was being sent. Most times, there’d be no data for them, and they could go back to sleep right away. All they’d need would be a really good internal clock that would be synchronized to this frame structure to run an interrupt and get them awake in time again.

That’s so cool, isn’t it. An even greener network. Fewer batteries in the trash! Yeah!

Wait, what are you saying? It’s been done. What? You know, this happens to me every time I get a good idea. Someone had my idea before.

Who? Guys in paging, you say? What? They couldn’t have been that smart. You say they did all of this decades ago… Millions upon millions of mobile UIS work this way? What!

Yep. All joking aside, that’s the way a modern digital paging system works. Those Luddites in paging purposely, with malice and forethought, opportunity, motive, and capacity, threw away this central tenet of layered protocols; viz., encapsulation, in order to deliver a wireless system that optimized battery life. They knew what they were doing, and they went ahead and did it anyway on purpose. A typical pager, like the Motorola Advisor Elite might run for a month on a single AA cell on a network with a collapse of 3.

Collapse, you say?

Yes, collapse. That’s FLEX jargon for the power of 2 value that controls the framing cycle that tells a pager which frame to look for its address in. A collapse of 3, which is pretty typical, creates a structure that repeats every 8 frames. FLEX (and ReFLEX and InFLEXion) frame times are 1.875s long. So a system with a collapse of 3 has a repeat time of 15s. The time to send an address burst is generally a few hundred milliseconds, and so the amount of time that a pager is active on the paging channel is 10% or so. Even then, most of the functions in the pager (that might chew up those valuable 10 nanoJoules of energy per instruction cycle) are disabled except for those elements needed to receive and decode the address list. Only if there is a pattern match here does the rest of the device’s machinery get wound up. Mobiles automatically assign themselves to the right frame by consider their address, modulo 2^collapse.

It is perhaps worth recognizing that all of those basic PDU data elements are still present; destination address, data, ECC, source address, data type, etc. They have just been completely reorganized with the aim of minimizing energy usage to achieve reception.

So, what do you think oh-TCP/IP people? Would you pitch encapsulation for a greener network?

A greener network, a greener world

In any case, the FCC issued a Second Report and Order and Second Further Notice of Proposed Rule for Private Land Mobile Radio (PLMR) Spectrum in 2003; and then they followed this up with a Third Report and Order and Third Further Notice of Proposed Rule for Private Land Mobile Radio (PLMR) Spectrum in 2004. This latter document clarifies rules for narrowbanding paging only channels and also clarifies migration dates for industrial & business radio and public safety pools. In pursuing more efficient use of spectrum, the Commission has taken the approach that the same data rate should fit into half the spectrum in certain PLMR applications.

This 2004 rule-making impacts anyone operating in the PLMR industrial/business and public safety spectrum pool on non-paging-only channels in the 150-174MHz or 421-512MHz bands. This includes a good number of hospitals around the United States who are operating their own private paging systems.

For whatever reasons, the rule-making does not apply to operations on paging only channels in the industrial/business at 462.750-462.925 (8 channels), 152.480, 157.740, or 158.460 MHz or in the public safety pool at 152.0075 or 157.4500 MHz. It also doesn’t apply to commercial paging operators.

The rule-making requires the affected operators to move from 25kHz to 12.5kHz channels. For the base station to transmit, this is simple enough to achieve by reducing the modulation index, in most cases. For mobile stations to transmit, it demands a complete swap out of the device. Now, it’s possible to operate in a kind of mixed mode system until the rules kick in. For any operator beginning this process now, it would be simple enough to gradually swap in new compatible devices that could operate on the existing network; and then make the final transition at the last possible minute. For systems in which the annual attrition of devices is around 25% or so per year, this would be a completely comfortable way to proceed.

January 1, 2013 is the deadline for migration to 12.5kHz technology. From January 1, 2011 until this date, applications for new operations or modification of existing operations in the affected bands will only be accepted if the equipment already meets the 12.5kHz requirements. So, for someone with a stable system in a hospital somewhere, the clock is already counting down with less than 2 years to go.

As I mentioned already, to meet the new requirements the frequency deviation (modulation index) will have to be cut in half from 4.5kHz to 2.25kHz. When this is done, many existing pagers will likely fail or deliver sub-standard performance. Therefore, having a migration plan is of the essence.

Luckily for operators who are impacted by this situation, there is a step towards a solution. It is provided by Unication.

Unication's Narrowband Solution

This device will operate under both the old and new frequency plans in a flexible manner. Therefore, an operator could gradually swap out existing pagers for these devices and only make the transition to the new frequency plan in their infrastructure under a graceful migration scheme. A PDF on this pager is available here. (Please note that if you click on the link, it may take a few moments for the shadowbox that pops up to fill with data, depending on your Internet speed. Be patient, it will work. You should be able to download the PDF once the file has loaded, if you wish to. )

I can only speak highly of the folks at Unication, and if you are impacted by this rule-making, please contact them.

Here are some names & numbers:

• Vic Jensen 954-333-8222
• Kirk Alland 817-926-6771
• Tim Meenan 972-424-8908

I’m sure that they can steer you right in dealing with this problem, including how to handle your infrastructure equipment if this is a technical issue for you.

Who markets paging?

The fundamental issue, I think, is that the attention of the world has been captured the truly amazing capabilities of broadband cellular devices. Not that devices like iPhones aren’t amazing, I have one and no longer have a pager myself (sad to say). But they are also marketed as being amazing, and paging services and devices are not. Since existing narrowband systems have not got the remotest chance to compete on the same footing, and certainly no one within the narrowband business sector is even attempting to market their services to the public any more, paging systems have only a niche appeal. Part of this was due to Motorola exiting the paging business several years ago. Up to that time, Motorola devoted a certain amount of their huge marketing budget in the paging sector. Unlike the cellular industry in which even smaller carriers would at least advertise in their own local markets, the nationwide paging carriers in the US spent nothing on advertising, leaving that to Motorola and its competitors. As well, since the paging sector has been contracting for a decade now, and many of the founders of the industry are no longer employed within it, my personal belief is that the folks still working in paging from day to day are so demoralized about their offering that they themselves feel defeated.

S/370s & iPhones

What makes the wonderful broadband device so much more flexible than the old-tech existing pager, even the best two-way pager? Item the first: devices like iPhones are pretty high-grade Unix boxes with much more power than the mainframes or minicomputer of a few of decades ago. In the mid-1970s, I worked for Control Data in their IBM plug-compatible division. An IBM System/370 system back then might have 8 active disk drives, each the size of a dish washer, spinning a 10-disk, 20-surface removable platter system. The top and bottom surfaces were used only for servo-control of the flying head array, so they carried no useful data. The other 18 usable surfaces stored 1 Megabit of data each, for a grand total of about 2 MBytes of data per drive and 16 MBytes in the entire system. Core memory (almost literally core memory, if you ever saw that) might have comprised a few kBytes of DRAM. The first DRAM chips that I saw in these systems were 1kbit each. To store a kByte of data required 11 of these chips, 8 for data and 3 for error checking code (ECC); so 1MByte would have required 11,000 of these. Rather impractical that. Later, in my time, 4kbit chips came on the scene. An IBM S/370 filled a huge computer room, and required a large staff to maintain and operate. You’ve probably seen rooms like this in old movie shows. These mainframes didn’t network, at least not in the current sense of the word; this was well before the day of TCP/IP.

So, iPhones & iPads and all their competition truly are amazing. My iPhone 3Gs has 32GB of storage, a whopping 2,000 times as much as an S/370 mainframe of roughly 35 years ago. That’s about 1dB per year, if you look at it that way. Of course, this also points out another difference between paging systems and cellular devices, no one’s doing any R&D in paging any more; no one’s pushing that envelope. The last company that I worked for, Trace Technologies LLC, was doing R&D in assisted GPS devices on ReFLEX networks; and it basically went belly up in the water about 4 years ago. Its parent, Gabriel Technologies, lives on in the form of a legal action about some of this technology. To the best of my knowledge, there is some development going on in narrowbanding some one-way paging systems to satisfy certain FCC requirements, and in ReFLEX for private systems. The annual R&D budget spent world-wide in this sector now must be at least 3-4 orders of magnitude less than that spent in the broadband wireless sector.

Paging R&D

In the period from 2002-2005, the paging sector was working on the delivery of new two-way devices with some new manufacturers. By and large, this effort died when the carriers decided not to purchase and deploy any of these new devices, after having encouraged these new entrants to invest their R&D efforts in this area. Many of these devices incorporated features similar to current smartphones; e.g., Unix OS, more FLASH memory, better screens, support for 3rd party applications, TCP/IP stack models, and so on. In spite of years of development, none of these devices ever made it to manufacture and release. Retrenchment of the industry, and the corresponding mindset, won the day, if winning is the word. In this way, those who did invest in this sector were taught a useful lesson; viz., don’t bother.

Data rates in simulcast systems

Of course, there is a fundamental limitation to macro-scale narrowband systems that the cellular industry has been working to tear down for decades now; namely, data rates. The data rate in a simulcast system is limited by what is called simulcast delay spread (SDS). In a conventional land mobile system, the extra time it takes for a symbol transition to stabilize at a receiver, called the excess delay spread, is due to the distribution of path lengths over all of the multiple ways that electromagnetic waves can travel from the transmit antenna to the receive antenna. In the case of a simulcast system, excess delay spread still exists, but it is generally trumped by the path lengths between all of the simulcasting transmit antennas and the mobile receive antenna. Let’s say that the current symbol being received is a logical “1″ and the next symbol will the a logical “0″. Depending upon capture effect conditions, the receiver may not properly detect this “0″ until all of the signals from the strongest and more distant transmitters arrive carrying the new logical value.

For the sake of an example, let’s say that this excess simulcast path length is 10km in a typical urban scale system. That might be because the mobile is 2 km from the nearest transmit site and 12km away from the furthest relevant site, or some combination like this. This yields an SDS value of about 33µs. Now, the symbol time has to some factor longer than the SDS in order to avoid symbol detection errors. There are a few rules of thumb for this; we could say we’d like the SDS to be only 1/10th a symbol time or 1/4 a symbol time, or something like that. In FLEX and ReFLEX, the maximum symbol rate on the forward channel is 3200 baud, which gives a symbol time of 312.5µs, which is a factor of 10x longer than 10km worth of SDS. Both FLEX and ReFLEX support a 4-level signaling scheme on the forward channel, so this 3200 baud can deliver 6400 bit/s.

However, 6.4kbit/s is a far cry from the 600Mbit/s that is the current limit for 802.11n using 64-QAM and four 40MHz channels. Now, this 802.11n system isn’t going to achieve these rates on an urban scale; but even LTE cellular proposes 100Mbit/s data rates on the downlink and 50Mbit/s on the uplink. Sure, these data rates likely require certain optimal conditions for any given user to obtain; say, limited mobility, good line-of-sight (LOS) or near LOS conditions, etc.; but even a suboptimal LTE link looks like being orders of magnitude faster than the best that ReFLEX would have to offer.

Now, about that battery…

So, why worry about this narrowband stuff? Well, if I ever actually use my iPhone to browse the tubes of the Internet (TOIT), I can literally watch the battery drain at about a rate of about 1% or so ever couple of minutes. The good news is that my iPhone has a computational power greater than that IBM S/370. Did I mention that that IBM S/370 ran off a 3-phase supply and had power cables the thickness of your thumb? No, well, it did. I saw a tech totally fuse one of those cables once when the motor-generator set that powered the system had an internal failure. Big bright flash! Apparently an electrician doing some maintenance work had let the ground line float. Bad idea. Now, the power consumption of the iPhone in use is not as bad as that S/370, but it’s still up there as far as pulling current out of its state-of-the-art non-consumer-replaceable battery is concerned.

Sure, some of that power is going to the beautiful screen. Some of it might be going to the internal GPS. I have the Navigon app, which runs that GPS device pretty hard in full tracking mode, I think. If I use Navigon for directions in my car, I can barely hold the battery level constant even with the device plugged into the car charger. Having said that, Navigon is so cool: I’ve completely pitched all the stand-alone GPS devices (Garmins & Magellans) that I used to have. They were expensive and kept breaking and required map updates every year that were much more costly than the combination of iPhone and Navigon put together. However, a lot of that current consumption is going to the combination of TCP/IP stack and radio.

Here’s the deal with TCP in a radio world. TCP’s job is to make sure that data gets through properly every time. If a data packet arrives in error, it’s TCP’s job to ask for it again, and again, and again, until it’s right. Say you’re doing Skype on your smartphone, or streaming video, or whatever. Any packet for your voice that arrives in error at the other side will need to be resent, and quickly. Any missed packet for the video that you’re watching has to be requested again. This isn’t such a big deal when you’re browsing the TOIT on your desktop; it’s plugged into the wall. But you can compute the amount of battery life that corresponds to one standard TCP/IP packet transmission. Let’s try this, for a ballpark guess.

Say your smartphone’s transmitter runs at 100mW ERP. Say your typical TCP/IP packet is 1kB long. Say your data rate is 1Mbit/s. So, your radio burst is 8ms long and that’s costing 0.8 Joules of energy. Well, you’re Li-ion battery has say about 1000mA-hr, which is 3600 Joules. So that packet is about 0.02% of your battery. Put the other way around, 45 of those packets are 1% of your battery. Well, how many of these packets would you send for a 3-minute Skype call? How many just to ACK the downlink while streaming video from YouTube? The answer is going to be quite a few. This simple calculation just accounts for the transmitter. It doesn’t deal with the battery cost of the MIPS to run the audio or video codecs, the TCP/IP stack or any CPU cycles being run by the application or OS.

Here is a truly interesting paper from some researches at Intel. It is entitled “Energy per Instruction Trends in Intel® Microprocessors”. It shows that the amount of energy consumed per instruction (EPI) in some modern Intel processors, like the popular Pentium4 are increasing relative to earlier devices. In general, EPI values are in the range of 10 to 40 nJ. Let’s take 10 nJ as a working number.

Now, I’ll let the interested reader go to Google on their own and search for “CELP codec MIPS” or “video codec MIPS”. What you’ll find is that a voice codec will cost you about 10MIPS and a video codec over 10x that, say 200-300MIPS. So, with a processor running at 10 nJ per instruction and a voice codec chewing up 10MIPS, you get 100mW. That’s about the same power as the transmitter.

Here’s a trend for you: the iPhone 4 uses the A4 processor and has a 1420 mA-hr battery. The iPad2 uses the A5 processor and has a 25W-hr battery.

How about this for a contrast: a typical pager might last for a month on a non-rechargeable AA cell.

The value of battery life?

Can you think of any applications that might require a completely unattended low data-rate wireless link for which minimal power consumption and high data accuracy were the absolute spec factors?

At Trace Technologies, we were working on a GPS tracking device that worked on ReFLEX and would last, in its lowest power consumption mode, nearly a year running from an internal 1100mA-hr rechargeable battery. In normal operation, it would run nearly a month between charges. We only got to deliver about 300 of these units to the US DoE before we were shut down, but what the heck. Still a great device that I’d still defy the cellular guys to beat. Of course, you can’t buy it any more, though I think that there are around 700 in a trailer somewhere in the mid-West.

A speculation

Here’s a thought. Imagine you scaled a simulcast system down to where the SDS was, say, 300ns. This would correspond to a configuration in which the distance between dominant and secondary transmitters was only 100 meters or so; a small scale system. Now, you could manage a symbol rate of around 1Mbaud. Suppose you cranked up the modulation index to get a ton of processing gain and you used a multi-level form of Gaussian Minimum Shift Keying (just like ReFLEX did) or maybe a version of Tamed FM (like I did at NovAtel back in the mid-80s). Anyway, some kind of multi-level CECPM. Hmm…

Wonder what the data capacity of an in-building telemetry system like that might be…

BER vs Eb/No in cellular

The analysis of BER vs Eb/No for modern cellular systems is a fine and well-developed art. A fairly representative work on the matter is a 1999 paper by Lotter and van Rooyen and published in IEEE J. on Sel. Areas in Comm., vol 17, No. 12, Dec 1999, pp 2181-2196. At the time of this writing, the link is active and will yield a PDF of the paper. For the purposes of this post, I’m going to refer to material in this paper, not because I take it to be the alpha and omega of cellular system design, but rather because it is accessible and representative of the analysis of modern cellular systems. I’ll call this paper LvR for short in this post.

In working out what value of signal energy per bit (Eb) is received, the steps generally involve considerations of what energy per bit is transmitted and then what the channel does to that energy before it reaches the receive antenna. In most schemes, the Eb transmitted can be handled deterministically, while land mobile channels are treated in a highly statistical manner. The upshot is that estimates of Eb at a receiver can typically only be given as averages together with statements about the likelihood of variation about the average which depend significantly on the PDFs being employed in the analysis. A simple method to get at the signal energy per bit that is transmitted is to consider the power being transmitted in the modulated part of the signal, and multiplying that by the symbol time, and then, if necessary dividing that further to account for non-binary multi-level encoding should that be involved. It is important to consider what I mentioned about the “modulated part of the signal” since some modulation methods will transmit power uselessly in an unmodulated carrier. In any case, a typical calculation proceeds in terms of getting an Eb transmitted, then reducing that by some estimate of path loss, and then adding in considerations of the statistics of the channel.

The calculation of noise energy per bit (No) involves considerations of thermal noise power and some fundamental notion of channel bandwidth. Since we are concerned with a ratio of energies; that is, signal energy per bit and noise energy per bit, our units have to be Joules. For working out Eb, we’ll get Joules by taking power in Watts and multiplying by time in seconds. In the case of No, it is more typical to work out noise power in Watts and then divide by bandwidth in Hertz. Now, if the estimate of No is to be independent of the details of receiver design, and more specifically of the implementation of any front-end filter, the bandwidth used to come up with No has to be chosen only on the basis of signal structure. The standard way of doing this, whether in mathematical analysis or practical measurement is to cancel out terms having to do with data rate and noise bandwidth. In effect, what this means is that practical Eb/No measurement are done in terms of signal power versus noise power reference to bits (as possibly opposed to symbols). To a certain extent, this bit of arcana (another joke) is ironic in that writers will strive to ensure that their readers are focussed on the notion of signal or noise energy per bit, and then somewhere along the way the units of power come into play. Watch for this slight of hand yourself.

As far as thermal noise is concerned, noise power will be kT, where k is Boltzmann’s constant and T is absolute temperature. Calculated in this way, noise power depends only on some estimate of the operating temperature of the receiver; but of course, this says little about the actual interference-limited performance of a cellular system. A much more practical approach for cellular would be to use an estimate of interference energy per bit, Io, instead of No. Cellular systems are almost always designed so that the expected thermal noise floor at either the mobile or base station receiver is swamped by the total interference power due to co-channel operation within the system, at least within the high-traffic core of the system. There are, arguably, some fine points as to whether highly synchronous interferers are more or less problematic than thermal noise. For modern direct sequence spread spectrum (DSSS) CDMA systems, it is likely and acceptable to treat the impact of Io as if it were a thermal noise, at least as far as its impacts on BER are concerned.

No or Io?

However, the estimate of Io proceeds in a fundamentally different way than for No. While No is estimated on the basis of receiver temperature, Io depends largely on the geometry of the cellular plan, and more specifically on considerations of frequency reuse and cell sectorization. The newbie reader can take a look at this Wikipedia article for further background information on cellular concepts. While early cellular systems, such as AMPS, employed lower reuse and antenna sectorization schemes, modern DS-CDMA systems shoot for the most extreme reuse possible; viz., all bandwidth reused in all adjacent cells. This extreme target for reuse further emphasizes the interference-limited nature of modern cellular system designs.

In such extreme reuse designs, the practical concern becomes less Eb/No and more the ratio of intended carrier power to total interference power (C/I or CIR) for either the forward channel (base to mobile) or the reverse channel (mobile to base) when the mobile is at the cell edge or in some similar locale of high path loss to the intended carrier and low path loss to interferers (or to receiver self noise). For such system designs, it is quite possible to have CIRs that are extremely marginal and even negative (on a dB scale). The only way to proceed in such a scheme (or at least, the accepted way) is by introducing the processing gain of spread spectrum to provide some immunity to this high degree of system self-interference. Processing gain is a concept not strictly limited to spread spectrum, although that is where it sticks in many people’s minds (I think). More generally, processing gain is a consequence of using a wider passband than baseband and can be computed as the ratio of the two. In particular, standard broadcast FM has a positive processing gain in the same way as cellular CDMA does.

A DS-CDMA system that transmitted a signal with a bit rate of 10kbit/s in a passband of 1MHz would have a processing gain of 20dB. It is this processing gain that is of the essence in DS-CDMA schemes of all sorts, and without it they would collapse in a New York second.

In LvR, the authors choose a Nakagami distribution for their analysis of channel behavior for a variety of reasons, but in the main because it is adaptable through parameters to cover a wide range of channel conditions that they are interested in. LvR considers both line-of-sight (LOS) and non-line-of-sight (N-LOS) channels in small cells as well as typical conditions in macro-cells. They are especially interested in modeling cellular systems with adaptive antenna arrays at the base station to implement spatial filters in DS-CDMA systems.

Now, I shall let the interested reader peruse LvR on their own time. For the purposes of this post, I’m going to concentrate on some of their results as given in several graphs towards the end of the paper. First, it is worth noting that they demonstrate one of the troublesome aspects of UHF land mobile communications generally; namely, that as Eb/No is increased, BER does not improve past some floor value. This is shown; for example, in their Figures 11-13. For the reader considering those figures while reading this post, note that their parameter, M, represents the number of antenna elements in an assumed antenna array, and that M=1 would be the case of a traditional single element receive antenna (whether directional or omni). The fundamental and disappointing fact, as shown in these figures, is that it is impossible to achieve raw BERs of better than a few percent no matter how good the Eb/No is.

For the design and implementation of a DS-CDMA cellular network, this is rather disappointing since it implies that a 60dB processing gain system would prove no better in the field than one with 10dB. Much of the early work on DSSS was applied in communications systems for which this BER floor did not exist; for example, secure satellite communications. A good deal of the early debate on the relative capacity of DS-CDMA had to do with such real-world aspects of land mobile communications that seemed not to be appreciated by the proponents of CDMA, leading to highly inflated claims about potential capacity improvements. I personally attended a meeting near Chicago’s O’Hare Airport in May 1989 hosted by an interested cellular carrier at which CDMA proponents made a presentation claiming a 40-times capacity gain over existing AMPS cellular. At subsequent meetings, the presentation was gradually amended down through 20x, 10x,… as more and more practical aspects were accounted for.

The benefit of spatial filtering in DS-CDMA

LvR shows significant BER vs Eb/No improvements as higher resolution spatial filtering is implemented at the receiver. This is to be expected since spatial filtering simultaneously rejects multi-path signals that yield fading of the desired signal (self-interference) as well as co-channel interference from adjacent cells. In terms of reduction of the BER floor, the impact is profound. Frequently, a raw BER of 3% is a suitable target for digital cellular systems for which some form of CELP coding will be used for voice. LvR Fig. 16 shows that a DS-CDMA system with no spatial filtering could achieve a capacity of 30 users or so per cell. This estimate is far closer to the truth of practical systems than the early claims made by CDMA proponents about 10 years before this paper was published. These days there is likely to be little merit in going back over the TDMA/CDMA capacity debate, as CDMA has undoubtedly won the day.

LvR Fig. 16 also shows the capacity improvements to be achieved by implementing spatial filtering; at the same 3% BER, and a M=3 (3-element) antenna array, capacity is increased by around 10 times. This is the good news; the bad news is the complexity of adding antenna arrays. In the case of the forward channel, it is almost impossible to consider an M=3 antenna array since the required spacing between antenna elements of 1/2 wavelength is infeasible for hand-held mobile stations.

Hence, LvR’s results on spatial filtering are mainly applicable to performance improvements on the reverse channel (base station to receive); and leave capacity estimates at around 30 active users, give or take, when the forward channel is concerned.

Back to paging

What if the benefits of processing gain, interference rejection, and fading immunity could be achieved without any computational complexity in an elegant manner? If someone invented such a system and deployed it, would the world beat a path to that fellow’s door? Apparently not, because these systems have been in use for years and they are considered by most folks to be technical back-waters unworthy of consideration. They are your friendly neighborhood paging systems.

Early digital paging systems employed simple binary FSK modulations in which a 100 bit/s signal would be transmitted over a 25kHz channel. A quick estimate yields a processing gain of around 20dB. Over the years, this degree of gain has been reduced as bit rates have increased and channel occupancy has been constant. High capacity FLEX and ReFLEX systems transmit 3200 baud in a 25kHz channel yielding something more like a 10dB processing gain. Still, 10dB is not to be sneezed at.

Paging systems use simulcast on the forward channel. In a modern simulcast system, all data transmissions are synchronized to GPS time to sub-microsecond accuracy. (Certain timing offsets are sometimes purposely introduced, but that is a slightly different topic.) Symbol times are kept long relative to the sizes of the serving area, and therefore, received modulation parameters (amplitude, frequency and phase) have generally stabilized at the receiver within 25% of a symbol time after first reception of a symbol change from the nearest transmitter at the mobile station. It is important to think clearly about this since it is so alien to anything in a cellular system in which all transmissions from every base station are different: in a simulcast system, every transmitter in the serving area is sending essentially the same modulated data. (There are differences in certain sync patterns, but this can be ignored for now.)

Of course, at any mobile station at any arbitrary location in the serving area there will be an equally arbitrary pattern to the received signal strength (RSS) from the multiple transmitters in its vicinity. Most paging receivers are designed with some relatively fast-attack AGC or limiter in the front end, as a consequence of which, they will display an FM capture effect. The impact of this design feature is the suppression of simulcast signals that are more than 2 or 3 dB down from the strongest (electrically closest) transmitter. Capture effect and passband/baseband processing gain also work together to suppress not only simulcast interference but also receiver thermal noise, as is well known from FM theory. Thermal noise suppression is not a benefit of DSSS.

What about fading? Well, this of course still impacts the reception of any given transmitter’s signal at the mobile in a simulcast system for all the same reasons that Rayleigh (or Rician) fading occurs on any UHF land mobile channel. However, this fading only applies to the self-coherent signals from any given transmitter. The entire assemblage of simulcasting transmitters are not carrier coherent. In fact, for a variety of reasons some minor carrier offsets are often purposely induced to avoid synchronous fading effects between adjacent transmitters. (At WebLink, we received patents on the use of non-linear simulated annealing methods to achieve these design benefits. So much for being a technical back-water. But I digress.) Hence, during a fade of the dominant (and captured) transmitter’s signal, the next strongest signal will be captured once the dominant signal has fallen 2dB or so below the dominant signal. In this way, an elegant form of hand-off is achieved without any computational work at all! This works in the simplest paging receiver when, say, a user walks from one side of an office building to another or the instant he drives from behind some obstruction to an open space.

Consider this oh cellular-obsessed world: instantaneous and computation-free and completely accurate soft-hand over. What would you pay for this? In effect, what this implements is a forward channel multi-antenna system in which the channel spacing is certainly more than 1/2 wavelength, and in which a virtually instantaneous maximum gain selector switch is applied. However you want to think about it, it inherently achieves much the same effect as shown in LvR as far as eliminating the BER floor typical of single-carrier Rayleigh fading land mobile channels. As a result, the simulcast forward channel is far closer to a classic AWGN channel than anything else in land mobile.

What about the reverse channel? In answering this question, I’ll limit myself to the ReFLEX system as designed for WebLink Wireless and still (as far as I’m aware) running for USA Mobility. The mobile station transmits only one signal, of course. There is no simulcast here. However, the network is deployed such that each mobile’s transmission will likely be received at 3 or more base station receivers. Typical numbers of base station receivers that will report reception back to the network is often as high as 10, and I recall seeing as many as 19 in one case in Dallas. That was a bit of overkill, I admit; and later enhancements to capacity changed that. However, the main idea is still there; i.e., diversity on the reverse channel in terms of multiple base stations simultaneously detecting any given mobile’s transmission.

At each base site, there are typically two diversity antennas and two completely independent optimal-gain diversity receivers. In this way, 2-branch diversity combining is achieved at each receiver at a physical layer before logical combining occurs at a macro-level in the network. Each receiver independently reports its receive data for all inbound activity within a frame time by relaying all of it received data back over a satellite link to a centrally located controller (called an RF-Director in the WebLink system). This controller (basically a real-time Unix box) analyzes all of the data reports received from all receivers in the vicinity of the transmitting mobile and reconstructs an estimate of the mobile’s signal based on a programmatically chosen method. It is usually sufficient to base the choice on either the first reported data or the data with the strongest RSSI (received signal strength indicator). In this way, the typical ReFLEX reverse channel implements something like 10-branch diversity.

I have neglected to mention another very simple difference between cellular and simulcast systems; raw power. A typical paging system might run the forward channel transmitters at 100 to 300W. A typical cellular transmitter might run at 35W or so. FLEX and ReFLEX receivers typically achieve rated BER at around -128dBm on the antenna, which is around 10dB more sensitive than cellular mobiles. In summary, a paging system has a 20dB advantage before any other considerations. One of the simple reasons for the improved sensitivity is the narrow baseband of paging devices relative to cellular units. Likewise, many cellular device designs are less concerned about noise-limited performance since they will generally operate in an interference limited environment. Assuming that the average co-channel noise power is above the -118 dBm level by a reasonable margin, noise limited performance of a mobile is unimportant and a cost factor in construction that can be neglected.

The combination of FM processing gain and narrower baseband yield inherently better sensitivity for the simplest paging receiver.

Summary

So, here’s the result in a nutshell: paging is a cellular system! It is one in which the serving cell structure is distinct on the forward and reverse channels. On the forward channel, handover is completely, instantaneously, and accurately mobile-directed. On the reverse channel, there is, in effect, an urban-scale distributed M-element antenna system, where M is typically on the order of 10-20. As I continue this tale, you will learn that paging systems can have paging and traffic channels, that paging systems are internally TCP/IP-based but that more sophisticated and elegant stack models and protocols are used at the edges, that the address/data structure has been tuned to save battery life, that paging systems can support strong security through a public key infrastructure (PKI) with elliptic curve cryptography (I know ‘cos I wrote the standards), and on and on and on.

Well, I’m done at this for now. Why beat this poor dead horse any more? Still, it never ceases to amaze me how the design elegance of FLEX and ReFLEX digital paging systems seems completely escapes the notice of the technorati.

What say you all?