For example, if a 1 kHz signal is spread to 100 kHz, the process gain expressed as a numerical ratio would be 100000/1000 = 100. Or in decibels, 10 log10(100) = 20 dB.
Note that process gain does not reduce the effects of wideband thermal noise. It can be shown that a direct-sequence spread-spectrum (DSSS) system has exactly the same bit error behavior as a non-spread-spectrum system with the same modulation format. Thus, on an additive white Gaussian noise (AWGN) channel without interference, a spread system requires the same transmitter power as an unspread system, all other things being equal.
Unlike a conventional communication system, however, a DSSS system does have a certain resistance against narrowband interference, as the interference is not subject to the process gain of the DSSS signal, and hence the signal-to-interference ratio is improved.
In frequency modulation (FM), the processing gain can be expressed as
- Gp is the processing gain,
- Bn is the noise bandwidth,
- Δf is the peak frequency deviation,
- W is the sinusoidal modulating frequency.