Abstract-Wireless communication provides a wide coverage at the cost of exposing information to unintended users. As an information-theoretic paradigm, secrecy rate derives bounds for secure transmission when the channel to the eavesdropper is known. However, such bounds are shown to be restrictive in practice and may require exploitation of specialized coding schemes. In this paper, we employ the concept of directional modulation and follow a signal processing approach to enhance the security of multi-user MIMO communication systems when a multi-antenna eavesdropper is present. Enhancing the security is accomplished by increasing the symbol error rate at the eavesdropper. Unlike the information-theoretic secrecy rate paradigm, we assume that the legitimate transmitter is not aware of its channel to the eavesdropper, which is a more realistic assumption. We examine the applicability of MIMO receiving algorithms at the eavesdropper. Using the channel knowledge and the intended symbols for the users, we design security enhancing symbol-level precoders for different transmitter and eavesdropper antenna configurations. We transform each design problem to a linearly constrained quadratic program and propose two solutions, namely the iterative algorithm and one based on non-negative least squares, at each scenario for a computationally-efficient modulation. Simulation results verify the analysis and show that the designed precoders outperform the benchmark scheme in terms of both power efficiency and security enhancement.

The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem (which we call unimodular quadratic programming (UQP)), several computational approaches are devised and studied. A specialized local optimization scheme for UQP is introduced and shown to yield superior results compared to general local optimization methods. Furthermore, a monotonically error-bound improving technique (MERIT) is proposed to obtain the global optimum or a local optimum of UQP with good sub-optimality guarantees. The provided sub-optimality guarantees are case-dependent and generally outperform the π/4 approximation guarantee of semi-definite relaxation. Several numerical examples are presented to illustrate the performance of the proposed method. The examples show that for cases including several matrix structures used in radar code design, MERIT can solve UQP efficiently in the sense of sub-optimality guarantee and computational time.

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