A couple of years ago, I created a computer simulation of digital radios with some TIA-102 (a.k.a. Project 25) characteristics. I was motivated to create these computer simulations by information being passed around in some public safety radio circles that narrowband digital radios may have inadequate system coverage compared to analog FM. I wanted to understand if there was a theoretical basis that would contribute to this reduction.

I specifically modeled a four-level, frequency-shift-keyed transmitter (similar to the current TIA-102 Phase-I C4FM digital modulator) and a π/4QPSK transmitter (similar to the future TIA-102 Phase II CQPSK digital modulator) with matched receivers. When I ran these digital radio models through performance tests, I uncovered a potential for reduced system coverage in the 4-FSK modulation scheme.

The 4-FSK modulation suffers from a signal-quality problem that reduces system performance. Since learning of it, I have wrestled with how to share the information with the mobile radio community.

I have no personal interest in the TIA-102 standard, except to recognize its potential as a definitive step in the evolution of digital public safety radio. I have yet to verify with hard evidence that this problem has been observed in an actual operating digital narrowband system.

There are potential limitations to these new systems, however, that should be taken into account during system planning and design.

Receiver characteristics

System coverage depends primarily on how well a radio receiver can discern a signal from any local channel noise and provide recognizable communications. The ratio of signal power to channel noise in the receiver is called the carrier-to-noise ratio. The greater the C/N value, the better the communications potential of the radio. Various parameters can affect the C/N of any receiver:

  • transmit signal power.
  • transmit signal quality, especially the noise immunity of the modulation scheme, which is important in digital radio design.
  • receiver sensitivity, which is strongly dependent on the receiver's effective bandwidth and the channel noise. Wider bandwidths detect more noise.

Transmit signal power — A narrowband signal, by itself, does not reduce radio range.

Consider the example where two radios have identical modulated waveforms with identical output power, but different bandwidths — one being narrower than the other. A radio's transmit power is defined as the average power of the signal over the radio's operating bandwidth.

For the same average power, the narrowband transmitter will have greater energy per Hertz as a wideband transmitter. At the receiving end, the narrowband receiver will have less noise to overcome because of its narrower effective bandwidth.

Given these conditions, the narrowband receiver will have a greater C/N value than its wideband counterpart and, therefore, should have a greater radio range — not less. Of course, the waveforms and modulations of digital and analog radios are different, and any comparison based solely on transmit power is incomplete.

Transmit signal quality — The primary design difference between analog and digital transmitters is their modulation method.

Most legacy mobile-radio systems use analog frequency modulation to transmit audio information over the RF carrier.

Digital systems use a variety of modulation schemes, including frequency-shift keying, phase-shift keying, amplitude modulation, (sometimes also referred to as linear modulation) and time-based schemes, such as pulse-position-modulation. Digital systems can carry large quantities of data using high-density signaling with base-2 multiples of signal states, such as binary (21 ), quadrature (22 ), and higher dimensions (2n ).

Digital design techniques

Two basic design techniques used in digital modulation affect the quality of the digital signal before it modulates the RF carrier: symbol orthogonality and pulse shaping.

An ideal digital modulation will enable the signal to be detected in high-noise environments. This is best accomplished with a modulation scheme using orthogonal symbol states. With this technique, modulated symbols are separated as far as possible in phase space for maximum energy-per-bit spacing.

The significance of orthogonal symbols is especially apparent in the presence of increased channel noise, where the C/N will reduce and the symbol states will spread from having well-defined phase states to having ill-defined ones. In spite of this phase spreading, the receiver will still detect each symbol state with a low probability of error because there is essentially no symbol overlap between orthogonal states.

Orthogonal symbol modulation schemes are highly noise-immune with superior BER performance at low C/N values. Both π/4QPSK and CQPSK are orthogonal modulation schemes. Non-orthogonal modulation schemes perform differently. Non-orthogonal symbols cannot be separated far enough in phase or bit energy to prevent them from overlapping.

Consequently, when these symbols are demodulated in the presence of high noise, the receiver can't distinguish between adjacent, overlapping symbol states. This results in a high probability of detection error.

Non-orthogonal modulation schemes are less noise-immune, with poorer BER performances. Both the 4-FSK and C4FM schemes are non-orthogonal.

To better maintain the narrow-bandwidth spectral isolation and to reduce channel interference, the TIA-102 standard requires that digital signals be pulse-shaped prior to modulation to reduce what is termed spectral blooming. Pulse-shaping rounds off the edges of a digital signal's square wave to reduce abrupt changes in the modulation with each change of symbol state.

This pulse shaping is done with a tightly specified, raised-cosine rolloff filter having a rolloff factor of 0.2 — a tight specification. Such tight filter specifications can cause high sensitivities to timing jitter, and they contribute to increased inter-symbol interference.

This ISI noise component can reduce the overall receiver BER performance, and it is especially problematic for less-noise-immune, non-orthogonal modulation schemes, such as the 4-FSK transmitter I modeled.

Receiver sensitivity — Digital systems are measured by their bit-error-rate performance over varying C/N. A receiver's effective bandwidth is defined differently in analog and digital systems. The effective bandwidth is generally estimated as the width of the receiver's channel passband between the 3dB points above and below its center frequency of operation.

For FM radios, however, the Carson's Rule bandwidth is used (defined as between the -20dB points) and is about 12.6kHz for a typical wideband (25kHz-spaced) analog FM radio.

For digital radios, the effective receiver bandwidths can be defined by the baseband filters and the symbol rates. The symbol rate of the TIA-102 radio is 4,800 symbols per second (9,600bps at 2 bits/symbol).

The cosine filter's 20% rolloff factor, mentioned earlier, defines an effective channel bandwidth of [1.2 × 4800] = 5,760Hz for the TIA-102 receiver design. This receiver design is specified for both the C4FM and CQPSK systems.

Signal levels, rather than C/N ratios, are the norm for specifying receiver sensitivities. To convert them to C/N ratios requires knowledge of the theoretical noise power of receivers. The different noise thresholds for these receivers can be found from their effective bandwidths using the general equation for thermal noise power:

Pn = kTW

Pn = thermal noise power
k = Boltzman's constant (1.38 × 10-23 J/K)
T = antenna temperature (°K)
W = effective bandwidth of the receiver (Hz)

A more convenient number for the kT factor at 300° Kelvin is -174dBm/Hz. Add to this number the effective receiver bandwidth (converted to dB), and the thermal noise of each receiver can be derived.

For an FM radio, this equates to [10 log(12,600Hz)] = +41dB, which, when added to -174dBm, results in -133dBm of thermal noise power in the FM receiver's channel. The noise power for the 5,760Hz digital receiver used for both the 4-FSK and π/4QPSK models is similarly determined to be -136.4dBm.

When these noise figures are subtracted from the specified input signal levels, the equivalent C/N ratio (in decibels) can be determined.

Computer models

In my study, I modeled the FSK and PSK modulations using quadrature (22 ) signal states and fashioned these designs in accordance with the TIA-102 digital standards for symbol encoding, modulation and raised-cosine, pulse-shaping filter parameters. The 4-FSK transmitter model encoded two symbol states (00, 10) at ±600Hz frequency deviation from the center carrier and the additional symbol states (01, 11) at ±1,800Hz frequency deviation from the center carrier. This resulted in a waveform equivalent to the C4FM modulation.

The second model, a π/4QPSK transmitter, used the TIA-102 phase-encoding scheme, resulting in a waveform equivalent to the CQPSK modulation.

For the receiver, I modeled a phase-lock-loop FM detector. The FM detector is the receiver specified in the TIA-102 standard suite intended to receive the C4FM and CQPSK signals. Unfortunately, my simulation could not reliably detect the π/4QPSK signal with the FM detector as modeled, so I used a simple quadrature detector for the π/4QPSK instead.

Between the transmitter and the receiver, I inserted a simulated Gaussian white-noise channel to simulate a varying C/N. I used no dynamic Doppler or multipath simulations.

This was a simple way to generate ideal, static BER curves for analysis. I used the 5% BER threshold to compare the performance of these two digital models. Beyond this 5% threshold, vocoder audio rapidly degrades and becomes unintelligible.

My performance tests sampled many C/N values to plot BER performance curves for each of the digital system models. From these curves, I found that the 5% BER threshold was reached at a different C/N value with each model.

For the 4-FSK transmitter with the FM detector (the C4FM-like model), the 5% threshold was reached at C/N = 14 dB. For the π/4QPSK with a quadrature detector (the CQPSK-like model), the 5% threshold was reached at C/N = 7 dB.

This wasn't a surprising difference between the two systems because they do differ by a few decibels in theory, but the poor performance of the 4-FSK system was unexpected. When I investigated why the 4-FSK digital system had performed so differently, I found that the transmit-signal quality was reduced by the combination of non-orthogonal FM symbol states, complicated by the ISI from the tight rolloff filter.

Next, I had to determine if the model was giving me valid results, so I compared these threshold values with various specifications and published data of the measured performances of TIA-102-type radios. Using published signal strengths expected for these radios, and subtracting the receiver noise power calculated previously, I converted the signal levels in the specifications to their equivalent C/N ratios for their appropriate effective bandwidth.

The TIA-102 standard specifies the 5% threshold at -116dBm, which translates to a C/N = 20.4dB. A government Web site was used as a reference for various measured signal strengths for a typical C4FM narrowband radio receiver. There, the 5% BER threshold was reported to be at a signal level of -121.4dBm, which translates to C/N = 15dB — close to my 4-FSK model's performance curve.

Another reference was found in a manufacturer's data sheet that advertised its receiver's performance, at the 5% BER threshold, to be at a circuit merit figure of 2, with C/N = 14dB. It seems, therefore, that my 4-FSK model's 5% BER threshold of 14dB C/N was typical of 4-level FM systems, possibly better than expected for the C4FM TIA-102 specified design.

Performance vs. range

The most obvious place where a difference in range performance would be realized is in the fringe areas of radio system coverage where low C/N ratios result from low signal strengths at the radio's range limits.

The analog FM receiver has some advantages in these low-signal areas with its ability to capture and track a received signal through increased static noise as signals fade.

FM detectors use a technique called threshold extension that provides FM detection sensitivities as low as C/N = 6dB. The FM reception becomes unintelligible below this threshold level, which is where FM receivers are generally set to mute (squelch).

Although the narrowband digital radio has the advantage of constant audio quality over the majority of coverage area, its quality falls rapidly in fringe areas. Weak signals in these areas create audio artifacts in the digital receiver that sound like pops, echoes and missing syllables. For a digital 4-FSK type of system, these fringe-area artifacts can become especially problematic when the C/N falls below 14dB because the 5% BER signal threshold is exceeded and the vocoder ceases to reliably detect audio.

So, how do these different performances compare in range capability? The graph on page 56 shows C/N curves for the modeled digital modulation schemes compared to a legacy FM system's expected range in the fringe areas (defined as C/N < 30dB). Each threshold point is labeled on these curves to compare the C/N sensitivities of each radio technology. The typical wideband FM system becomes unintelligible at about C/N = 6dB, while the modeled narrowband 4-FSK digital system becomes unintelligible at the measured 5% BER of C/N = 14dB.

Effects on coverage

To understand how these C/N sensitivities can affect the radio coverage, we'll consider how the C/N thresholds are related to the range between the transmitter and receiver.

To illustrate, I've used a simple free-space propagation profile, where transmit power falls off, as the square of the propagated distance, resulting in a 6dB drop in power (one-fourth relative power reduction) for every 3dB of increased range (twice the relative distance).

At every point along the range axis, the propagated signal strength is identical for each receiver. However, because each receiver has a unique C/N value, the FM receiver would detect more noise — about 10 log(12.6 ÷ 5.76) = 3.4dB more noise — at every point in the coverage area, as illustrated by the shift to the left of the FM curve.

The threshold difference between the FM and 4-FSK curve is 4.6dB. Because of the poorer BER performance, the 4-FSK digital system would reach its 5% threshold much closer to the base station than its FM counterpart, in spite of a better receiver noise figure.

This was the just the kind of theoretical basis for reduced range I was seeking.

The poor transmit-signal quality of a non-orthogonal 4-FSK makes it difficult for the FM detector to reliably receive the digital signal in noisy environments. The 4-FSK receiver requires the greater C/N ratios closer to the transmit site to reliably detect its signals.

This 4.6dB difference in threshold translates to a 2.3dB theoretical reduction (~30%) of usable range between the 4-FSK and FM systems.

As a practical example of what this may mean, if an FM system, providing a usable range of 30 miles, was replaced with a 4-FSK type of digital narrowband system, the new system's range has the potential of being reduced to only 21 miles.

Therefore, in situations where a range reduction is noted after installing a new digital narrowband system, check for the usual technical problems first, and don't assume the delivered power from a narrowband transmitter is to blame. It may be the digital-signal quality that is at fault, and the only cure will be to invest in more infrastructure.

Of special interest in the graph is the difference in system coverage of the narrowband π/4QPSK digital modulation model. Comparing the π/4QPSK C/N curve to the wideband analog FM system, there is a 2.4dB improvement in thresholds points.

The superior BER performance of the π/4QPSK model, with a measured 5% BER and C/N = 7dB, shows the π/4QPSK radio may detect signals well into the channel noise, and continue to operate long after the FM radio's mute threshold has been reached.

This translates into a potential system range improvement of about 32%, extending the FM range of our hypothetical system from 30 to nearly 40 miles, primarily due to the high-quality orthogonal symbol modulation scheme in the π/4QPSK transmitter.

Predictions and performance

These digital-radio-modeling-study results indicate the potential for coverage differences between wideband analog and narrowband digital systems because of differences in design and radio performance. The most important coverage factor for the digital radio is its BER performance. When planning new digital systems, the receiver's C/N and the potential range at the 5% threshold may be the most important factors considered.

However, the C/N is seldom, if ever, considered by many LMR system designers when modeling the digital coverage. With the lack of C/N considerations, radio system designs that seem to perform well in computer modeling programs, or even in controlled low-noise laboratory environments, may perform poorly in the real world where radio channel noise is prevalent, unpredictable, and always changing.

This is the primary reason why many coverage predictions don't agree with real-world performance.

LMR system upgrades can be achieved, with minimal coverage loss, by responsible system planning and engineering, combined with realistic expectations of performance for these technologies.

Bartlett is a freelance technical writer who has worked in the wireless technology field for more than 20 years. He can be reached at bartlets@erols.com.