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.
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