Complexity Measure of FH/SS Sequences Using Approximate Entropy

High complexity of frequency-hopping (FH)/spread-spectrum (SS) sequence is of great importance to high-security multiple-access communication systems, for it makes FH/SS sequence difficult to be analyzed. With the growing development in the design of FH/SS sequence in much wider fields, the well-known complexity measures - the linear complexity (LC), the linear complexity profile (LCP) and the k-error linear complexity (k-error LC) - are widely used but not sufficient to evaluate the complexities of the sequences available, such as the cryptographical sequence and the chaotic sequence families. In this paper, a new complexity metric to evaluate the unpredictability of FH/SS sequence based on the approximate entropy (ApEn) is proposed in the view of the maximal randomness of the sequences with arbitrary length. And the theoretical bounds of the ApEn are derived from a probabilistic point of view. Simulations and analysis results show that, the proposed ApEn works effectively to discern the changing complexities of the FH/SS sequences with small number of samples, which provide superior performance over its candidates.