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We investigate the problem of enumerating source signals impinging on an array of sensors given noisy, limited observations. The assumption of a large sample size is indispensable for most of the existing approaches so that they suffer significant performance degradation when only a small number of samples is available. Random matrix theory can capture the asymptotic distributions of the eigenvalues accurately and provide good approximations even for a finite sample size. In this paper, we take into account the relationship and distributions of the noise and signal eigenvalues based on random matrix theory and derive a simple two-step test. Numerical simulations demonstrate that it is capable of correctly determining the number of sources in the case of small sample sizes. [ABSTRACT FROM PUBLISHER]

This paper presents the results of a comprehensive study of the shingled writing process and various signal processing and data detection approaches applied to the readback waveforms. The recording simulations include realistic head fields, a random granular media, magnetostatic and exchange interactions, and a READ head sensitivity function. Readback waveforms are examined in both one and two dimensions in terms of signal characteristics (linear and nonlinear), noise behavior (stationary and signal-dependent), and intertrack interference. Different equalization and detection approaches are compared and about a 10% density gain is reported for such 2-D magnetic recording compared with traditional single-track recording. These gains depend strongly on the number of readers, the reader positioning, and the reader width. [ABSTRACT FROM AUTHOR]