Nonparametric method for detecting the number of narrowband signals without eigendecomposition in array processing

A computational simple and efficient nonparametric method for estimating the number of signals without eigendecomposition (MENSE) is proposed for the narrowband signals impinging on a uniform linear array (ULA). When finite array data are available, a new detection criterion is formulated in terms of the row elements of the QR upper-triangular factor of the auto-product of a matrix formed from the cross-correlations between some sensor data. Then the number of signals is determined as a value for which this ratio criterion is maximized, where the QR decomposition with column pivoting is also used to improve detection performance. The proposed estimator is asymptotically consistent, and it is superior in detecting closely-spaced signals with a small number of snapshots and/or at low signal-to-noise ratio (SNR).