Optimal power allocation (PA) strategies can make a significant rate improvement in secure spatial modulation (SM). Due to the lack of secrecy rate (SR) closed-form expression in secure SM networks, it is hard to optimize the PA factor. In this paper, two PA strategies are proposed: gradient descent, and maximum product of signal-to-interference-plusnoise ratio (SINR) and artificial-noise-to-signal-plus-noise ratio (ANSNR)(Max-P-SINR-ANSNR). The former is an iterative method and the latter is a closed-form solution. Compared to the former, the latter is of low-complexity. Simulation results show that the proposed two PA methods can approximately achieve the same SR performance as exhaustive search method and perform far better than three fixed PA ones. With extremely low complexity, the SR performance of the proposed Max-P-SINR-ANSNR performs slightly better and worse than that of the proposed GD in the low to medium, and high signal-to-noise ratio regions, respectively.
In this paper, given the beamforming vector of confidential messages and artificial noise (AN) projection matrix and total power constraint, a power allocation (PA) strategy of maximizing secrecy rate (Max-SR) is proposed for secure directional modulation (DM) networks. By the method of Lagrange multiplier, the analytic expression of the proposed PA strategy is derived. To confirm the benefit from the Max-SRbased PA strategy, we take the null-space projection (NSP) beamforming scheme as an example and derive its closed-form expression of optimal PA strategy. From simulation results, we find the following facts: in the medium and high signal-to-noiseratio (SNR) regions, compared with three typical PA parameters such β = 0.1, 0.5, and 0.9, the optimal PA shows a substantial SR performance gain with maximum gain percent up to more than 60%. Additionally, as the PA factor increases from 0 to 1, the achievable SR increases accordingly in the low SNR region whereas it first increases and then decreases in the medium and high SNR regions, where the SR can be approximately viewed as a convex function of the PA factor. Finally, as the number of antennas increases, the optimal PA factor becomes large and tends to one in the medium and high SNR region. In other words, the contribution of AN to SR can be trivial in such a situation.
The security of spatial modulation (SM) aided networks can always be improved by reducing the desired link's power at the cost of degrading its bit error ratio performance and assuming the power consumed to artificial noise (AN) projection (ANP). We formulate the joint optimization problem of maximizing the secrecy rate (Max-SR) over the transmit antenna selection and ANP in the context of secure SM-aided networks, which is mathematically a non-linear mixed integer programming problem. In order to solve this problem, we provide a pair of solutions, namely joint and separate solutions. Specifically, an accurate approximation of the SR is used for reducing the computational complexity, and the optimal AN covariance matrix (ANCM) is found by convex optimization for any given active antenna group (AAG). Then, given a large set of AAGs, simulated annealing mechanism is invoked for optimizing the choice of AAG, where the corresponding ANCM is recomputed by this optimization method as well when the AAG changes. To further reduce the complexity of the above-mentioned joint optimization, a low-complexity two-stage separate optimization method is also proposed. Furthermore, when the number of transmit antennas tends to infinity, the Max-SR problem becomes equivalent to that of maximizing the ratio of the desired user's signal-tointerference-plus-noise ratio to the eavesdropper's. Thus our original problem reduces to a fractional programming problem, hence a significant computational complexity reduction can be achieved for the optimization problem. Our simulation results show that the proposed algorithms outperform the existing leakage-based null-space projection scheme in terms of the SR performance attained, and drastically reduces the complexity at a slight SR performance reduction.
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