Time delay and spatial signature estimation using known asynchronous signals

This paper considers the problem of estimating the parameters of known signals received asynchronously by an array of antennas. The parameters of primary interest are the time delays of the signals and their spatial signatures at the array. Estimates of the signal directions of arrival are also considered but are of secondary importance in this work. Maximum likelihood algorithms and more computationally efficient approximations are developed for both the case where all received signals are identical (the channel estimation/overlapping echo problem) and where they are all distinct. Conditions are also derived under which the standard matched filter approach yields consistent and statistically efficient parameter estimates. The issue of solution uniqueness is addressed, and in particular, an upper bound on the number of signals whose parameters may be uniquely identified is derived for a number of different cases. Typically, the bound is far greater than the number of sensors and is limited only by the number of data samples collected. Some representative simulation examples are also included to illustrate the algorithms' performance relative to the Cramer-Rao bound.