### ASA 126th Meeting Denver 1993 October 4-8

## 4pUW2. Large sets of frequency hopped codes with nearly ideal
orthogonality properties.

**Scott T. Rickard
J. Robert Fricke
**

**
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*Dept. Ocean Eng., MIT, Rm. 5-218, 77 Massachusetts Ave., Cambridge, MA
02139
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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(N[sup 2]) codes. These codes are ``full'',
which means every available frequency is used in every code. The Reed--Solomon
method, in contrast, generates O(N[sup k]) 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.]