Estimation of polynomial-phase signals distorted by linear channels

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 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.