Transmit beamspace design for direction finding in colocated MIMO radar with arbitrary receive array

The transmit beamspace design problem for colocated multiple-input multiple-output (MIMO) radar is considered. We show that the MIMO radar transmit beampattern can be designed so that it is as close as possible to the desired one, the power is uniformly distributed across the transmit antennas, and most significantly, the rotational invariance property at the receive array with arbitrary geometry is satisfied. The latter enables a straightforward application of search-free direction of arrival estimation techniques such as ESPRIT in the unconventional case with the receive array of arbitrary geometry. The transmit beamspace design problem is cast as an optimization problem which is non-convex in general, but can be solved efficiently using the semi-definite programming relaxation technique.