In this paper, we investigate transmit beampattern optimization techniques for a multiple-input multiple-output (MIMO) radar in the presence of a legitimate communications receiver and an eavesdropping target. The primary objectives of the radar are to satisfy a certain target detection criterion
and to simultaneously communicate safely with a legitimate receiver by maximizing the secrecy rate against the eavesdropping target. Therefore, we consider three optimization problems,
namely, target return signal to interference plus noise ratio (SINR) maximization, secrecy rate maximization and transmit power minimization. However, these problems are non-convex
due to the non-concavity of the secrecy rate function, which appears in all three optimizations either as the objective function or as a constraint. To solve this issue, we use Taylor series approximation of the non-convex elements through an iterative
algorithm, which recasts the problem as a convex problem. Two transmit covariance matrices are designed to detect the target and convey the information safely to the communication receiver. Simulation results are presented to validate the efficiency of the aforementioned optimizations
