The problem of detecting the presence of a known signal in multiple channels of additive white Gaussian noise, such as occurs in active radar with a single transmitter and multiple geographically distributed receivers, is addressed via coherent multiple-channel techniques. A replica of the transmitted signal replica is treated as a one channel in a M-channel detector with the remaining M-1 channels comprised of data from the receivers. It is shown that the distribution of the eigenvalues of a Gram matrix are invariant to the presence of the signal replica on one channel provided the other M-1 channels are independent and contain only white Gaussian noise. Thus, the thresholds representing false alarm probabilities for detectors based on functions of these eigenvalues remain valid when one channel is known to not contain only noise. The derivation is supported by results from Monte Carlo simulations. The performance of the largest eigenvalue as a detection statistic in the active case is examined, and compared to the normalized matched filter detector in a two and three channel case.