On the Number of Signals Resolvable by a Uniform Linear Array

An algebraic limitation on the maximum number of direction-of-arrival plane waves that can be resolved by a uniform linear sensor array is studied. Achievable lower and upper bounds are derived on that number as a function of the number of elements in the array, the number of snapshots, and the rank of the source sample-correlation matrix. The signals are assumed narrow-band and of identical and known center frequency. The results are also applicable in the coherent signal case and when directions of arrival are estimated from few snapshots. While in the multiple-snapshot case the lower bounds coincide with known asymptotic results, the upper bounds indicate the potential for resolving more signals than by present methods of array processing.