On resolving 2M-1 narrow-band signals with an M sensor uniform linear array

The problem of determining the maximum number of narrowband signals whose parameters can be estimated with a linear array of M equally spaced sensors is examined. While this number previously has been taken to be M-1 when the signals are mutually uncorrelated, it is shown how to estimate directions and amplitudes for as many as 2M-1 signals. This over twofold increase is accomplished by retaining snapshot-to-snapshot phase information usually lost in algorithms based on spatial correlation matrices. The approach uses length 2M real signal vectors rather than the usual M complex vectors. It is shown that 2M of these real vectors are linearly independent with probability one, and, thus, in the presence of additive white noise, the parameters of 2M-1 signals can be estimated. An algorithm for determining directions and amplitudes is presented. Because of the algorithm's computational complexity, its application is limited to small M and low time-bandwidth products.<
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