Signal covariance matrix optimization for transmit beamforming in MIMO radars

MIMO radars use multiple waveforms simultaneously to improve performance. A beamforming method that exploits this waveform diversity has been proposed previously. This method works by optimizing the covariance matrix of the waveforms to obtain an approximation of a desired beampattern. The previous method uses gradient descent to optimize the beampattern with the constraint on the power of each antenna element. We show how this method can be extended to obtain rank-deficient covariance matrices and also to handle the total power constraint. The conjugate gradient method is used in addition to the gradient descent. In this paper, we also propose converting the constrained beampattern optimization problem into an unconstrained one. This can be done by using the method of Lagrange multipliers, but also removing all constraints and then scaling the result so that the total power constraint is satisfied. Using this approach, the beampattern optimization can be written as a least squares problem.