The antijam performance of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -ary noncoherent FSK with fast frequency hopping (one or more hops per symbol) is studied. A summary of terminology, definitions, and an overview of the literature is given. A general analysis method based upon circularly symmetric signal theory is presented. It provides a means for exact analysis of performance for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -ary operation with any combination of signal tone distribution (frequency bins contiguously or noncontiguously spaced), jamming distribution, jamming form (partial-band noise or multitone), and receiver system noise. Some previous results are derived as subcases of the general theory. A simple robust diversity combining technique of transmitting a symbol on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> hops followed by a majority vote decision is found to provide significant performance improvements. This improvement is comparable to that obtained by most error-correction coding methods. Illustrative calculations of performance were chosen to indicate trends rather than to be exhaustive. Performance is usually presented as probability of bit error versus fraction of the band jammed to emphasize worst-case operation.
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Bird et al. (1986) studied this question.
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