Generalized ambiguity function for the MIMO radar with correlated waveforms

An ambiguity function (AF) for the multiple-input multiple-output (MIMO) radar with correlated waveforms is derived. It serves as a generalized AF for which the phased-array and the traditional MIMO radar AFs are important special cases. A simplified expression for the AF for the case of far-field targets and narrow-band waveforms is also derived. We establish relationships between the generalized MIMO radar AF metric and the previous works on AF including the Woodward's AF and the AF defined for the traditional colocated MIMO radar. Moreover, we compare the AF of the MIMO radar with correlated waveforms with the squared-summation-form AF definition. Simulation results show that the generalized MIMO radar AF achieves lower relative sidelobe level with proper design of the waveform correlation matrix or, equivalently, the transmit beamspace matrix.