A triangular adaptive lattice filter for spatial signal processing

In this paper an adaptive lattice structured filter for processing of narrowband spatial data as received by an array of sensors is described, This spatial lattice filter is shown to take on a triangular structure in the spatial domain, composed of N(N-1)/2 individual two multiplier lattice cells for an array of N sensors. This is considerably more than an equivalent order lattice for the prediction of a statioary time series, and is neccesary to cope with the possibly non-Toeplitz covariance matrices that arise from multipath signals and irregularly spaced arrays. It is shown however that in a hardware implementation of the filter, advantage can be taken of parallel procesing, reducing the total computational cost to O(N) processing cycles. It is also shown how the same lattice structure can be used to evaluate the prediction coefficients for the sensor signals from the lattice reflection coefficients - this being efficiently carried out with the use of systolic processing.