Performance evaluation of array processors for detecting Gaussian acoustic signals

Performance of detecting "noise-like" under-water acoustic signals are measured by probability of false alarm (P
FA
) and probability of detection (P
D
). Analytical expressions for P
FA
and P
D
are derived in terms of the eigenvalues of the covariance matrices of the received data under both hypotheses. Applications of this method to linear arrays with equal or unequal spacing and non-linear arrays are shown. As an example the optimal array performance for detecting Gaussian signals in both directional and independent Gaussian noises are evaluated and compared with that of a conventional beamformer envelope detector.