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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.

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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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In secure spatial modulation (SM) networks, power allocation (PA) strategies are investigated in this paper under the total power constraint. Considering that there is no closed-form expression for secrecy rate (SR), an approximate closed-form expression of SR is presented, which is used as an efficient metric to optimize PA factor and can greatly reduce the computation complexity. Based on this expression, a convex optimization (CO) method of maximizing SR (Max-SR) is proposed accordingly. Furthermore, a method of maximizing the product of signal-toleakage and noise ratio (SLNR) and artificial noise-to-leakageand noise ratio (ANLNR) (Max-P-SAN) is proposed to provide an analytic solution to PA with extremely low-complexity. Simulation results demonstrate that the SR performance of the proposed CO method is close to that of the optimal PA strategy of Max-SR with exhaustive search and better than that of Max-P-SAN in the high signal-to-noise ratio (SNR) region. However, in the low and medium SNR regions, the SR performance of the proposed Max-P-SAN slightly exceeds that of the proposed CO.

Millimeter wave (mmWave) communication has been regarded as one of the most promising technologies for the future generation wireless networks because of its advantages of providing a ultra-wide new spectrum and ultra-high data transmission rate. To reduce the power consumption and circuit cost for mmWave systems, hybrid digital and analog (HDA) architecture is preferred in such a scenario. In this paper, an artificial-noise (AN) aided secure HDA beamforming scheme is proposed for mmWave MISO system with low resolution digitalto-analog converters (DACs) and finite-quantized phase shifters on RF. The additive quantization noise model for AN aided HDA system is established to make an analysis of the secrecy performance of such systems. With the partial channel knowledge of eavesdropper available, an approximate expression of secrecy rate (SR) is derived. Then using this approximation formula, we propose a two-layer alternately iterative structure (TLAIS) for optimizing digital precoder (DP) of confidential message (CM), digital AN projection matrix (DANPM) and analog precoder (AP). The inner-layer iteration loop is to design the DP of CMs and DANPM alternatively given a fixed matrix of AP. The outerlayer iteration loop is in between digital baseband part and analog part, where the former refers to DP and DANPM, and the latter is AP. Then for a given digital part, we propose a gradient ascent algorithm to find the vector of AP vector. Given a matrix of AP, we make use of general power iteration (GPI) method to compute DP and DANPM. This process is repeated until the terminal condition is reached. Simulation results show that the proposed TLAIS can achieve a better SR performance compared to existing methods, especially in the high signal-to-noise ratio region.Index Terms-Hybrid digital and analog, mmWave, security, artificial Noise, low-resolution digital-to-analog converter(DAC)