The Effects of Fading on Antijam Performance Requirements

The purpose of this paper is to analyze the impact of fading on the performance of both conventional and spread spectrum systems. The analyses presented herein take into account the effects of fading on the jamming signal as well as fading of the communications signal. It is assumed that the envelopes of both the desired signal and the jamming signal fade with a Rice distribution. The distribution of the signal-to-jammer ratio (
S/J
) is thus the result of squaring the ratio of two independent Rice random variables. An expression for the distribution of the ratio of two Rice random variables is obtained and this expression is used to evaluate the effects of fading on performance. Two cases are considered. In the first case, the fading is assumed to be slow compared to the duration of a message. In this case, the system performance is described by the probability that the message is successfully transmitted, averaged over all possible values of the
S/J
. This performance measure is often referred to as the availability of the system. In the second case, the fading is assumed to be slow compared to the symbol duration but fast compared to the message duration. In this case, the performance is best described by averaging the bit error rate over all possible values of the
S/J
. A number of numerical examples is presented. In general, these results show that, for the case of very slow fading (case 1), the communicators suffer a performance loss of up to 10 dB compared to the nonfading case, depending on the required availability and the fading parameters. In case 2, fading appears to have little impact on the jammer but a major impact on the communicators, so that losses of up to 20 dB compared to the nonfading case are observed. In case 2, the performance for the situation in which both the signal and the jammer fade is approximately the same as the performance in the situation where only the signal fades. It is shown that, as in the standard fading model in which only the signal fades, error correction coding with interleaving can be effective in reducing the losses caused by fading.