In this paper, we present a method of detecting the range and Doppler phase of a point target using multiple antennas. As a key illustrative example, we consider a 4 x 4 system employing a unitary matrix waveform set, e.g., formed from Golay complementary sequences. When a non-negligible Doppler shift is induced by the target motion, the waveform matrix formed from the complementary sequences is no longer unitary, resulting in significantly degraded target range estimates. To solve this problem, we adopt a subspace based approach exploiting the observation that the receive matrix formed from matched filtering of the reflected waveforms has a (non-trivial) null-space. Through processing of the waveforms with the appropriate vector from the null-space, we can significantly improve the range detection performance. Also, another very important target aspect is the velocity with which the target is moving, and to determine that, the exact Doppler phase shift induced by the target motion needs to be estimated with reasonable accuracy. To accomplish this task, we develop a strategy that uses the MUSIC algorithm to estimate the Doppler phase, and we use simulations to show that the phase estimates obtained are reasonably accurate even at low SNRs. © 2012 IEEE.