Performance of multiple-access frequency-hopped systems in the presence of spurious tones

Frequency hopping (FH) can be used to combat jamming. In multiple access applications such as for satellite communications, multiple FH signals are combined by frequency division multiple access (FDMA). The frequency synthesizers in such an application have requirements for fast switching times, a large number of hop frequencies, wide hopping bands, and very small resolution. The need to meet all these requirements simultaneously makes the synthesizer implementation challenging. Furthermore, the need for hopping makes it more difficult to control spurious tones compared to nonhopped systems. It is useful to be able to determine the effects of spurs on performance in order that the synthesizer specification not be unnecessarily stringent and expensive. In this paper, an approach for analyzing the effects of spurious signal levels is provided. Both the signal tone, such as used in various forms of FSK and PSK, and the spurious tone are added together with some random phase difference. This combined tone results in an equivalent signal power with a corresponding SNR, which is then used for computing the new error rate. The effective error rate is then computed by averaging the error over all the possible phase differences. The loss in effective SNR due to spurs is then computed. As a detailed example, this approach is applied to non-coherent FSK modulation for both fast (one or more hops/symbol) and slow (more than one symbol per hop) hopping. The application of this approach to other modulations is summarized.