The problem of obtaining long sequences with finite alphabet and peaky aperiodic auto-correlation is important in the context of radar, sonar and system identification and is called the coded waveform design problem, or simply the signal design problem in this limited context. It is good to remember that there are other signal design problems in coding theory and digital communication. It is viewed as a problem of optimization. An algorithm based on two operational ideas is developed. From the earlier experience of using the eugenic algorithm for the problem of waveform design, it was realised that rather than random but multiple mutations, all the first-order mutations should be examined to pick up the best one. This is called Hamming scan, which has the advantage of being locally complete, rather than random. The conventional genetic algorithm for non-local optimization leaves out the anabolic role of chemistry of allowing quick growth of complexity. Here, the Hamming scan is made to operate on the Kronecker or Chinese product of two sequences with best-known discrimination values, so that one can go to large lengths and yet get good results in affordable time. The details of the ternary pulse compression sequences obtained are given. They suggest the superiority of the ternary sequences.
Coded waveform design global optimization bi-parental products Hamming scan
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