Blind deconvolution of polynomial-phase signals using the high-order ambiguity function

We consider the problem of estimating the parameters of a complex constant-modulus polynomial-phase signal that has undergone convolution with a linear time-invariant FIR channel. Such a signal is a sum of polynomial-phase signals, with special relationships among the parameters of the various components. Those relationships are used to develop a simple non-iterative algorithm for estimating the signal parameters. The algorithm is based on the recently developed high-order ambiguity function. The estimated parameters can be optionally supplied as initial conditions to a maximum likelihood estimation algorithm, thereby reducing the biases of the estimates and improving their statistical accuracy. As a by-product, estimates of the channel parameters are also obtained. The Cramer-Rao bound for this problem is also derived, and performance is illustrated by some numerical examples. Possible applications of the algorithms developed in the paper include the estimation of sonar, radar and communications signals in the presence of multipath.