Cut your losses

Apr 1, 2010 12:00 PM, By Jay Jacobsmeyer, P.E.

FM theory can be used to predict how narrowbanding will affect system coverage

More From
Networks & Systems

» more

In June 1995, the FCC adopted rules to "refarm" or "narrowband" private land-mobile radio frequencies below 512 MHz. To ensure more efficient use of this spectrum, the FCC mandated narrower channel spacings and established new limits on effective radiated power (ERP) and antenna height above average terrain (HAAT).

Narrowbanding is a spectrum-efficiency requirement that requires the equivalent of at least one user per 12.5 kHz for voice channels, and at least 9.6 kb/s per 12.5 kHz for data channels. Users can meet this requirement by one of several means:

Analog FM with reduced deviation on a 12.5 kHz-wide channel,
Digital Project 25 on a 12.5 kHz-wide channel, or
2-slot TDMA on a 25 kHz-wide channel.

Phase I Project 25 radios are designed to operate on 12.5 kHz-wide channels and are a good choice for narrowbanding for many reasons, but the FCC does not require the use of Project 25, nor does it require digital radios of any kind for narrowbanding.

The least cost and thus preferred solution for some users is to replace 25 kHz FM radios with 12.5 kHz FM radios. Manufacturers limit FM transmissions to 12.5 kHz primarily by limiting the FM deviation, and a factor of two reduction in deviation is considered sufficient to comply with the FCC emission mask.

FM improvement factor

The bandwidth of an analog FM transmitter is largely determined by the modulation index, ß. Modulation index is the ratio of the peak frequency deviation to the maximum modulating frequency, ß = ?f /f_m. Most land-mobile radios use wideband frequency modulation, meaning that the modulation index is greater than 0.5. Wideband FM is a nonlinear modulation technique that exhibits a threshold effect. As the input carrier-to-noise ratio to an FM detector increases — generally, above 9 dB — a corollary rapid increase in output signal-to-noise ratio occurs, to the point where the output signal-to-noise ratio actually is higher than the input carrier-to-noise ratio. This behavior continues to about 12 dB, where the maximum improvement is reached. This effect, also known as FM capture, is shown in Figure 1. The improvement in signal-to-noise ratio over linear modulation such as AM is called the FM improvement factor and is a function of the type of detector used. The FM improvement factor for a frequency discriminator is given by Equation 1.

FM narrowbanding and static coverage

The tricky part about applying the FM improvement factor to radio coverage is the service threshold. If the service threshold is 12 dB SINAD, the carrier-to-noise ratio (C/N) at the input to the FM detector is only 4 dB (for a 25 kHz-wide channel), which is well below capture, meaning that the FM improvement factor does not strictly apply.

According to Annex A of TSB-88.1-C, reducing the deviation by half increases the required C/N in this case from 4 dB to 7 dB. However, 12 dB SINAD corresponds to a delivered audio quality (DAQ) of 2.0, which is unsatisfactory for most users. For this reason, we will assume that the service threshold is above FM capture and that the loss in signal-to-noise ratio due to narrowbanding is simply 6 dB.

A reduction of 6 dB is a factor of 4 and assuming r^-4 propagation, the effective radius of our repeater will be reduced by 4^¼, or 1.4. Area is proportional to radius squared, so the loss in coverage is a factor of 2.0. In other words, the licensee must double the number of repeater sites to strictly maintain the original geographical coverage. If the propagation is better approximated by r^-2, the coverage loss is a factor of 4.0 and the licensee must quadruple his repeater sites. These models are overly simplified and we will see shortly that, in practice, the situation is not quite this bad.

FM narrowbanding and fading channel coverage

To this point we have assumed a static channel with the user in a stationary position. In a mobile radio environment, random phase fluctuations cause an effect called random FM that destroys the FM improvement factor. In other words, wideband FM does not offer any signal-to-noise ratio improvement on a multipath fading channel. In fact, unless the FM deviation is very large, the output signal-to-noise ratio is actually less than the input C/N.

Despite the effects of random FM, the output signal-to-noise ratio in a mobile receiver still increases with increasing modulation index, following the 6 dB/octave behavior of Equation 1. Thus, more deviation is better, even on multipath fading channels, and the signal-to-noise reduction of 6 dB due to narrowbanding still applies.