Dynamic range determination 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 component polynomial phase signals (PPS) was previously explored by Zhou and Wang (see IEEE Signal Processing Letters, vo1.4, p.240-2, 1997). The lag diversity enlarges the dynamic range of the detectable parameters for PPS. We prove that the dynamic range obtained by Zhou and Wang is already the maximal one for the detectable parameters for single component PPS. The dynamic range for the detectable parameters for multi-component PPS is given when multiple lag diversities are used. We show that the maximal dynamic range is reached when the number of the lags in the high-order ambiguity function (HAF) is at least twice of the number of the single components in a multi-component PPS. More lags than twice of the number of the single components does not increase the dynamic range.