BLIND DECONVOLUTION OF POLYNOMIAL-PHASE SIGNALS USING THE HIGH-ORDER AMBIGUITY FUNCTION

We consider the problem of estimating the parameters of a complex cons tant-modulus polynomial-phase signal that has undergone convolution wi th a linear time-invariant FIR channel. Such a signal is a sum of poly nomial-phase signals, with special relationships among the parameters of the various components. Those relationships are used to develop a s imple non-iterative algorithm for estimating the signal parameters. Th e algorithm is based on the recently developed high-order ambiguity fu nction. The estimated parameters can be optionally supplied as initial conditions to a maximum likelihood estimation algorithm, thereby redu cing the biases of the estimates and improving their statistical accur acy. As a by-product, estimates of the channel parameters are also obt ained. The Cramer-Rao bound for this problem is also derived, and perf ormance is illustrated by some numerical examples. Possible applicatio ns of the algorithms developed in the paper include the estimation of sonar, radar and communications signals in the presence of multipath.