Combined Radar and Communications with Phase-Modulated Frequency Permutations

This paper focuses on the combined radar and communications problem conducts a thorough analytical investigation effect of phase frequency change communication sensing functionality. First, we consider classical stepped waveform modulate data using M-ary shift keying (MPSK). Two important tools in design, namely ambiguity function (AF) Fisher information matrix (FIM) are derived, based which, make conclusion that MPSK modulation has negligible local accuracy. Next, extend analysis to incorporate permutations propose new signalling scheme which mapping between incoming waveforms is performed an efficient combinatorial transform called Lehmer code. We also provide receiver modified Hungarian algorithm. From perspective, optimal maximum likelihood (ML) detector derive union bound nearest neighbour approximation block error probability. discuss broader structure AF derivation quantify accuracy FIM. Extensive numerical examples provided illustrate our results.