Dynamic range of the detectable parameters for polynomial phase signals using multiple-lag diversities in high-order ambiguity functions

Two lag diversities in the high-order ambiguity functions for single compon ent polynomial phase signals (PPS) was recently explored by Zhou and Wang. The lag diversity enlarges the dynamic range of the detectable parameters f or PPS, In this paper, we first find a connection between the above multipl e-lag diversity problem and the multiple undersampling problem in the frequ ency detection using discrete Fourier transform (DFT), Using the connection and some results on the multiple undersampling problem we recently obtaine d, we prove that the dynamic range obtained by Zhou and Wang is already the maximal one for the detectable parameters for single-component PPS, Furthe rmore, the dynamic range for the detectable parameters for multicomponent P PS is given when multiple-lag diversities are used. We show that the maxima l dynamic range is reached when the number of the lags in the high-order am biguity function (HAF) is at least twice of the number of the single compon ents in a multicomponent PPS, More lags than twice the number of single com ponents do not increase the dynamic range.