Closed-form Design of the Covariance Matrix for Shaping the Transmit Beam-pattern in Planar Collocated MIMO Radars

Planar multiple-input multiple-output (MIMO) radar transmit beam-pattern design has gained increasing attention in recent years. Conventional planar MIMO radar methods use iterative approaches to design the covariance matrix of transmitting waveforms in order to achieve desired beam-pattern. These methods consume considerable amount of time to respond, specially for large number of antennas in planar arrays. On the contrary, the closed-form based methods, need less computation time than iterative ones. In this paper we propose a closed-form method based on two dimensional (2D) Fourier series coefficients (FSCs) to design the waveform covariance matrix of desired beam-pattern in elevation-azimuth coordinates, using a 2D array. Since the resulted matrix is not assured to be positive semi-definite, eigenvalue decomposition is employed to convert the resulted pseudo-covariance matrix (pseudo-CM) into a covariance matrix. The designed covariance matrix is positive semi-definite and also fulfills the uniform elemental power constraint. The computation time of the proposed method is lower than that of iterative methods which makes it appropriate for real-time applications. Furthermore, it beats the current closed-form methods in terms of mean square error (MSE). To demonstrate the performance of the proposed method, simulation results are presented.