Unitary design of radar waveform diversity sets

In this work, multiple radar waveforms are simultaneously transmitted, emitted from different antennas. The goal is to process the returns in such a way that the overall ambiguity function is a sum of individual ambiguity functions, such that the sum better approximates the ideal thumbtack shape. A unitary design for the illustrative 4x4 example prescribes the scheduling of the waveforms over four transmit antennas over four PRIs. Further, it dictates how the matched filtering of the returns over four PRIs is combined in such a way so as to achieve both perfect separation (of the superimposed returns) AND perfect reconstruction. Perfect reconstruction implies that the sum of the time-autocorrelations associated with each of the four waveforms is a delta function. The net result of the processing of four PRIs over four virtual antennas yields 16 cross-correlations all of which ideally exhibit a sharp peak at the target delay. Conditions for both perfect separation and perfect reconstruction are developed, and a variety of waveform sets satisfying both are presented. Doppler compensation is achieved by a data-dependent weighting of the different PRI matched-filtered outputs prior to summing. Simulations are presented verifying the efficacy of the proposed unitary waveform matrix designs in conjunction with the proposed Doppler compensation technique.