Studies Of Beamforming Technique In Wireless Physical Layer Security

Physical layer security exploits the characteristic of the wireless channel to achieve secure communications. Unlike the typical techniques for secure communications, the physical layer security does not depend on the limited ability of the eavesdropper. Along with the rapid development of multi-antenna systems, the beamforming-based physical layer security can efficiently exploit the spatial degree of freedom to enlarge the difference between the legitimate channel and the eavesdropper’s channel. Thus, the physical layer security can achieve the reliability and the security for the wireless communications, and has been the research hotspot in the wireless communications. The low-complexity beamforming design under different criteria, the robust beamforming design for different channel uncertainty models, the secrecy performance analysis on the limited feedback beamforming and so on, these studies have been the key and difficult problems in the physical layer security. This thesis studies these problems under different cases for the channel state information(CSI) of the legitimate and the eavesdropper’s channels.Firstly, for the perfect CSI case, this thesis studies the secrecy sum rate maximization problem and the signal-to-interference-plus-noise ratio(SINR) balancing problem in the multi-antenna Gaussian multi-receiver wiretap channel(MG-MRWC) model, where the secrecy capacity region is difficult to obtain and the inter-user interference(IUI) causes the cross-talk problem. The beamforming algorithms based on the thinkings of zero forcing(ZF) and signal-to-leakage-and-noise ratio(SLNR) are proposed. To demonstrate the validity of the SLNR metric, the secrecy performance is analyzed for different number of antennas in the multiple-input single-output multi-antenna eavesdropper(MISOME) system. For the secrecy sum rate maximization problem in the MG-MRWC model, three novel algorithms are presented: the first kind ZF(ZF-I), the second kind ZF(ZF-II) and the enhanced SLNR(E-SLNR). Different with these two ZF algorithms, the E-SLNR algorithm jointly considers the IUI and the leakage at the eavesdropper. And thus, the E-SLNR algorithm does not rely on the number of antenna, and outperforms the ZF algorithms with lower complexity. For the SINR balancing problem in the MG-MRWC model, the ZF-SINR algorithm and the modified SLNR(M-SLNR) algorithm are proposed for the purpose of the tradeoff between the complexity and the secrecy performance. The typical semidefinite relaxation(SDR) algorithm has high complexity because of random processing. The ZF-SINR algorithm requires zero leakage at the eavesdropper so that the secrecy performance is limited. The M-SLNR algorithm selects the model between the E-SLNR algorithm based on equal power allocation(EPA) and the algorithm based on the sufficient condition according to the SINR requirement at the eavesdropper. When the SINR requirement is low, the E-SLNR algorithm based on EPA is used. Otherwise, the algorithm based on the sufficient condition is adopted. The simulation results show that the M-SLNR algorithm can achieve good secrecy performance with low complexity.Considering the case of imperfect CSI on the legitimate and the eavesdropper’s channel in the multiple-input single-output single-antenna eavesdropper(MISOSE) model, the thesis proposes robust artificial noise aided beamforming algorithms, which improve the secrecy performance. In the existing literature, the artificial noise is exploited to withstand the effect of imperfect CSI on the eavesdropper’s channel. However, for the case of imperfect CSI on the legitimate and the eavesdropper’s channel, the artificial noise aided strategy has not been adopted. For the deterministic uncertainty model, a worst-case robust algorithm is proposed to solve the worst-case secrecy rate maximization(WC-SRM) problem by transferring the initial non-deterministic polynomial hard(NP-hard) problem into a single-variable optimization problem along with a series of semidefinite program(SDP) problems. For the stochastic uncertainty model, a robust algorithm is presented to solve the outage-probability secrecy rate maximization(OP-SRM) problem. This algorithm uses the mathematical relationship between the stochastic uncertainty model and the deterministic uncertainty model to convert the OP-SRM problem into the WC-SRM problem. Additionally, a robust algorithm based on average performance is proposed to solve the average secrecy rate maximization(A-SRM) problem. The rank of the input covariance matrix is proved to be one. The simulation results demonstrate the effectiveness of these robust algorithms and show that the transmit power allocated for the artificial noise depends on the CSI uncertainty levels on the legitimate and the eavesdropper’s channels. When the level of uncertainty on the legitimate channel is larger, it should be conservative on allocating transmit power to the artificial noise; whereas, when the level of uncertainty on the eavesdropper’s channel is larger, more transmit power should be allocated for the artificial noise.Then, considering the case of statistical information on the eavesdropper’s channel in the multi-antenna Gaussian wiretap channel(MGWC) model, the transmit power allocation algorithm for the information-bearing signal and the artificial noise is proposed to minimize the total transmit power. After that, the achievable secrecy rate of the limited feedback beamforming is analyzed. In the MISOSE and the multiple-input multiple-output multi-antenna eavesdropper(MIMOME) models, the robust designs are considered for the cases of imperfect CSI on the legitimate channel under the deterministic uncertainty model and the stochastic uncertainty model. For the deterministic uncertainty model, the proposed algorithm can withstand the effect of the CSI error on the legitimate channel. For the stochastic uncertainty model, two robust algorithms are proposed, where the suboptimal algorithm exploits the mathematical relationship between the stochastic uncertainty model and the deterministic uncertainty model to transfer the probabilistically constrained problem into the deterministically constrained problem, and the other algorithm uses the Markov inequality to convert the probabilistically constrained problem into average-constraint problem so that achieves the average performance with low complexity. In the MISOME model, the secrecy rate of the limited feedback beamforming is obtained. And then, a new feedback strategy is proposed. When the channel gain exceeds a fixed threshold, the legitimate receiver sends the index of the optimal beamforming vector and the secrecy rate back to the transmitter. Otherwise, the legitimate receiver just tells the transmitter to keep silent. By using this strategy, the throughput decreases. However, the secure communication is guaranteed with lower feedback spending. The impact of the number of antenna, the number of feedback bits and the signal-to-noise ratio(SNR) gain on the secrecy rate is analyzed on the basis of approximate secrecy performance analysis. Thus, the condition of the positive secrecy rate and the requirement for the number of feedback bits with fixed secrecy rate loss is obtained.Finally, for the case where no channel information is known by the transmitter, a robust algorithm is proposed under the deterministic uncertainty model in the MG-MRWC system. Compared with other robust designs, the worst-case robust design under the deterministic uncertainty model is more conservative. However, the worst-case robust design has effective solution and deterministic performance so that it has attracted much attention. Because the transmitter has no information about the eavesdropper’s channel, the power minimization(PM) problem is studied, where the object is to minimize the transmit power of the information-bearing signal under the constraints of the mean square error(MSE) at the legitimate receiver and the fixed total transmit power. Thus, the remained transmit power is used to transmit the artificial noise isotropically. A robust transceiver design is proposed to solve the PM problem. The proposed algorithm uses the alternative optimization method to transfer the PM problem into two SDP problems, which can be solved by interior-point methods effectively. The simulation results demonstrate the effectiveness and the convergence of the proposed algorithm.