Multiple-channel detection in active sensing

The problem of detecting the presence of a known signal in multiple channels of additive noise, such as occurs in active radar with a single transmitter and multiple geographically distributed receivers, is addressed via coherent multiple-channel techniques. The transmitted signal replica is treated as one channel in a suitable M-channel detector with the remaining M - 1 channels comprised of data from the receivers. To accommodate this approach, an invariance result for the distribution of the eigenvalues of a Gram matrix is derived. The result implies that false alarm probabilities for any detector based on a function of the eigenvalues are not changed if one data channel contains a signal replica, provided that the other M - 1 channels only Gaussian noise and all channels are independent.