Optimal fast-time beamforming with linearly independent waveforms

An optimal radar transmitter and receiver architecture is proposed for increasing the available degrees of freedom for beamforming optimization by exploiting the capability to transmit linearly independent waveforms from each element of a phased array radar. This effectively encodes clutter returns with a spatial signature which enhances clutter-rejection performance in a combined space/fast-time processor. The theory which enables the exploitation of the additional degrees of freedom is developed for a general set of linearly independent waveforms and demonstrates that the overall transmit-receive performance in a clutter-limited scenario is independent of the transmit waveforms and, moreover, that the optimality achieved is better than that which would be achieved by adaptive transmit and receive weights in a conventional adaptive beamformer. Furthermore, it is proposed that transmit waveforms can be conveniently synthesized as linear superpositions of orthogonal functions with appropriate range ambiguity and spatial cross-correlation properties, and transmit and receive architectures are devised for both transmit beampattern/waveform synthesis and optimal space/fast-time processing.