Adaptive fuzzy frequency hopper

An adaptive fuzzy system generates the frequency hopping sequence for a spread spectrum communications system. The system learns rules from data and acts as a pseudorandom number generator. The IMSL uniform random number generator gives training samples. An adaptive scheme learns associations between previous samples and the current sample and encodes these as fuzzy rules. The output fuzzy set for each rule acts as a conditional probability density function. The if-part of the rule states the conditions. At each step thirty prior outputs, scanned according to a fixed sampling pattern, give a new sample distribution x _k. The vector x_k partially matches the if-part distribution of a fuzzy rule and partially fires that rule's output fuzzy set. With the estimated output fuzzy sets the fuzzy system computes the conditional density p_Y|X(y|x_k) for input field X and output field Y. Defuzzification yields the next number in the frequency hopping sequence. The rules, sampling pattern, and initial conditions fix the output sequence. An eavesdropper who did not know all three could not predict the sequence. This fuzzy system can generate a sequence uniform over any number of frequencies. We tested the fuzzy system with 100 and 1025 frequencies and compared it to a shift register with linear feedback. The fuzzy system had lower chi-squared values and thus gave a more uniform or more “random” spread than did the shift register. The fuzzy system was easier to change and harder to intercept