On the Ambiguity Function of Random Binary-Phase-Coded Waveforms

The ambiguity function of truly random binary-phase-coded waveforms, as an approximation to those waveforms commonly employed in binary-modulated pseudonoise systems/encoded radar systems, is investigated. In a statistical sense, the ambiguity function is analytically derived in which the normally used deterministic cross-correlation process is replaced by its ensemble average. Various Doppler filter responses are presented and discussed. The results are compared with those obtained by transmitting an aperiodic maximum length pseudorandom sequence. It is shown that the ambiguity function of the latter case is closely represented by the ensemble-average response of the truly random binary signal.