Source enumeration for large array using shrinkage-based detectors with small samples

It is interesting to determine the number of signals impinging upon a large array with small samples. We tackle this problem by using linear shrinkage coefficients of signal and noise subspaces, ending up with two shrinkage coefficient-based detectors (SCDs) for source enumeration. It is proved that the noise shrinkage coefficients are asymptotically Gaussian distributed as the number of antennas and number of samples tend to infinity at the same rate. Moreover, the noise shrinkage coefficients almost surely converge to one while the signal shrinkage coefficients are almost surely less than one as m,n→,∞ and m/n→c.With these properties, the threshold-like and heuristic SCD algorithms for source number detection are devised. Simulation results are included to illustrate their effectiveness.