Optimum beamformer strategy for detecting signals in clutter noise

We apply the Neyman-Pearson (NP) test to obtain optimum detection of a region with fully developed speckle in clutter noise. The NP- test gives maximum detection probability, with a given clutter level. Assuming Gaussian signals with known covariance matrix for signal and noise, a sufficient statistics is found as a quadratic form of the element signals, with weight-matrix given by the signal and noise covariance matrices. Several beamforming methods, including standard beamsum (BS), and short lag spatial coherence (SLSC) can be expressed in the same way as a quadratic form, with different weight-matrices. By eigenvalue decomposition of the weight-matrix, the beamformer output can be written as a square sum of standard beamsum terms, with the eigenfunctions as apodization windows. The receive beamprofile can be calculated as the square sum of the Fourier transform of the eigenfunctions. In this way the weight-matrix can be optimized both for detection and spatial resolution/side lobe level. A simulation experiment was performed: a circular-shaped uniform speckle region was set in band-pass filtered white noise, with SNR= 9 dB. The NP-test showed the best detection performance, but slightly higher sidelobe level than BS. SLSC showed poorer detection performance than the two other methods, as well as higher sidelobes.