Optimized Bernoulli Trial Technique for M Out of N Binary Integration of Radar Signals

Binary integration is used in radar systems where M successful events out of N trials represent the detection of a target where multiple pulse-repetition frequencies (PRFs) are used. If the probabilities of the single events are equal, the probability of M events occurring out of N can be represented by a binomial distribution. If, however, switching the PRF at each event causes differing clutter to interfere with the signal, the event probabilities are not binomially distributed but are represented by a more complicated polynomial. An optimization procedure is presented that minimizes the radar resources needed for the M out of N binary integration of detector outputs with unequal signal-to-interference noise ratios (SINRs). The amount of coherent integration for each PRF output is optimally adjusted to yield a minimum total integration time over the batch of PRFs. The optimized integration time is computed for a number of different sequences of detector output SINRs and compared to the results from a binomial distribution.