Gerschgorin radii based source number detection for closely spaced signals

We first analyze the resolution performance of the Gerschgorin radii based source number detector proposed by Wu, Yang and Chen (see IEEE Trans. SP, vol.43, no.6, p.1325-33, 1995) for independent closely-spaced plane waves. Based upon the analysis, we can easily verify the resolution threshold of the Gerschgorin radii based algorithm. For improvement of the detection performance, we then further propose a weighted Gerschgorin radii algorithm. With closed-form expressions and simulations, we find that the analyzed performance in terms of the number of sensors, the relative angular separation of emitters, and the signal-to-noise ratios can properly characterize their behaviour for source number detection.