Abstract
High-resolution methods for estimating signal processing parameters such as bearing angles in array processing or frequencies in spectral analysis may be hampered by the model order if poorly selected. As classical model order selection methods fail when the number of snapshots available is small, this paper proposes a method for noncoherent sources, which continues to work under such conditions, while maintaining low computational complexity. For white Gaussian noise and short data we show that the profile of the ordered noise eigenvalues is seen to approximately fit an exponential law. This fact is used to provide a recursive algorithm which detects a mismatch between the observed eigenvalue profile and the theoretical noise-only eigenvalue profile, as such a mismatch indicates the presence of a source. Moreover this proposed method allows the probability of false alarm to be controlled and predefined, which is a crucial point for systems such as RADARs. Results of simulations are provided in order to show the capabilities of the algorithm.
Highlights
In sensor array processing, it is important to determine the number of signals received by an antenna array from a finite set of observations or snapshots
When the signal-to-noise ratio (SNR) is lower than 5 dB, the MDLB gives the best probability of detection and acceptable results for the probability of false alarm, but requires an important computational complexity
When the SNR is greater than 5 dB, the EXPONENTIAL FITTING TEST (EFT) outperforms all the other tests in terms of Pd with a P f a still lower than 10%
Summary
It is important to determine the number of signals received by an antenna array from a finite set of observations or snapshots. For a small sample size, where we define a sample as small when the number of snapshots is of the same order as the number of sensors, this condition is no longer valid and the noise eigenvalues can instead be seen to have an approximately exponential profile This problem of detecting multiple sources was readdressed by means of looking directly for a gap between the noise and the signal eigenvalues [19]. In this way, and as an alternative to the traditional approaches, we recently proposed a method [20] to obtain an estimation of the number of significant targets in time reversal imaging.
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