Performance analysis of the optimum beamformer in the presence of correlated sources and its behavior under spatial smoothing

In this paper, we first study the signal cancellation and interference rejection effects of the optimum (constrained least squares or minimum variance) beamformer in the presence of partially and fully correlated interfering sources. In particular, we derive expressions for the output power and the gain in the interference direction of the beamformer in terms of the source powers, correlation, and the sensor noise power, and show quantitatively the penalties arising from increasing correlation in several scenarios of interest. Next, we show that spatial smoothing progressively decorrelates the sources at a rate that depends on the spacing and directions of the sources, and thus relate the degree of smoothing to the improvement in signal cancellation and interference rejection behavior provided by spatial smoothing. Results of computer simulations are included to support our analysis.