Transmit beamforming for colocated MIMO radar

MIMO radar has seen growing interest in recent years owing to the many advantages that it offers over conventional radar, including spatial diversity and enhanced target direction resolution. Unlike standard phased array (SIMO) radar that transmits scaled versions of a single waveform from its many transmit antennas, a MIMO radar can transmit distinct waveforms from each antenna. Such an increase in the number of degrees of freedom for waveform design can potentially be used to obtain beamforming performance similar to SIMO radars with a far fewer total number of transmit and receive antennas. In recent literature, the problem of finding a signal correlation matrix that achieves a desired transmit beam pattern has been addressed, but a closed form solution for this problem has been lacking. In this paper, we first formulate a new spatial ambiguity function that simultaneously specifies the transmit beam pattern as well as the cross-correlation beam pattern. We then provide a closed form solution for the signal correlation matrix whose spatial ambiguity function is closest to a desired function (in the mean square sense), when using colocated uniform linear arrays. Further, we show how a suitable tapering window could be applied on the signal correlation matrix to tradeoff sidelobe levels for mainlobe width in the spatial ambiguity function.