Large sets of frequency hopped codes with nearly ideal orthogonality properties

Abstract

Significant performance improvements would be realized in many sonar systems if only it were possible to have multiple pings in the water at any given time. The use of orthogonal frequency hopped codes is one way to achieve multiple, simultaneous access. These codes can be designed to have nearly ideal autoambiguity and low cross-ambiguity properties. In some applications it is desirable to use codes drawn from a very large set, say O(10 000). This paper discusses how such a set can be generated. Specifically, the trade-off between auto/cross ambiguity properties, time-bandwidth product, and code set size when generating large sets are explored. For codes with N frequency hops, the focus is on techniques for generating more than O(N) codes, which characterizes most code generation techniques. Others are nonlinear in N. In particular, the Golomb–Costas method generates O(N2) codes. These codes are ‘‘full’’, which means every available frequency is used in every code. The Reed–Solomon method, in contrast, generates O(Nk) codes, where k is a trade-off parameter proportional to sidelobe level in the cross-ambiguity function. Reed–Solomon codes, however, are not ‘‘full.’’ The trade-off between fullness and number of codes is illustrated. [Work supported by C. S. Draper Laboratory.]