Bounds on the volume and height distributions for the MIMO radar ambiguity function

The multiple-input multiple-output (MIMO) radar delay-Doppler ambiguity function is introduced as the sum of all auto- and cross-ambiguity functions of the set of K spatially diverse waveforms. The integral of this function over the range-Doppler frequency region occupied by spread clutter relates to the clutter's power at the output of the matched MIMO receiver, and it serves as a measure of orthogonality of the waveforms in this region. We derive the upper bound on the attainable "clear area" for the ambiguity function, and we show that, with respect to the conventional single-waveform ambiguity function, the maximum clear area is K times smaller for the MIMO system.