Block Circulant Decomposition of Cross-Correlation Matrix for Transmit MIMO Beamforming

This paper deals with the design of transmit probing signal under the trade-off between good target discrimination (low cross-correlation beam pattern) and beam pattern design (desired auto-correlation beam pattern) in a Multiple-Input-Multiple-Output (MIMO) radar configuration. The quartic optimization problem, with a finite alphabet constraint on the probing signal and using Quadrature Phase Shift Keying (QPSK) in a multiplexed antenna system, is solved through a Fourier series approximation of the desired beam pattern by exploiting a block circulant property of the transmit signal matrix. The mean square error between an ideal and the proposed crosscorrelation beam pattern is -35 dB enhancing the attractiveness of the proposed approach.