Secrecy Sum-Rates for Multi-User MIMO Regularized Channel Inversion Precoding

Abstract

In this paper, we propose a linear precoder for the downlink of a multi-user MIMO system with multiple users that potentially act as eavesdroppers. The proposed precoder is based on regularized channel inversion (RCI) with a regularization parameter α and power allocation vector chosen in such a way that the achievable secrecy sum-rate is maximized. We consider the worst-case scenario for the multi-user MIMO system, where the transmitter assumes users cooperate to eavesdrop on other users. We derive the achievable secrecy sumrate and obtain the closed-form expression for the optimal regularization parameter α LS of the precoder using large-system analysis. We show that the RCI precoder with α LS outperforms several other linear precoding schemes, and it achieves a secrecy sum-rate that has same scaling factor as the sum-rate achieved by the optimum RCI precoder without secrecy requirements. We propose a power allocation algorithm to maximize the secrecy sum-rate for fixed α. We then extend our algorithm to maximize the secrecy sum-rate by jointly optimizing α and the power allocation vector. The jointly optimized precoder outperforms RCI with α LS and equal power allocation by up to 20 percent at practical values of the signal-to-noise ratio and for 4 users and 4 transmit antennas.

Physical Layer Security for Multiuser MIMO Communications

“…The MISO BCC with a generic number of malicious receivers was studied in [17,18], and it consists of a BS with M antennas that simultaneously transmit independent confidential messages to K spatially dispersed single-antenna users, which can cooperate and eavesdrop on each other. Although determining the secrecy capacity region for the generic MISO BCC is still an open problem, suboptimal transmission schemes have been proposed to achieve high secrecy sum-rates by controlling the amount of crosstalk between the users [19].…”

“…In the MISO BCC, linear precoding can be employed to control the amount of interference and information leakage to the unintended receivers introduced by the transmission of each confidential message [17][18][19].…”

“…The secrecy sum-rates achievable by linear precoding were obtained in [18] by considering the worst-case scenario, where for each intended receiver k the remaining K − 1 users can form an alliancek, and cooperate to jointly eavesdrop on the message u k . By noting that each user k, along with its own eavesdropperk and the transmitter, forms an equivalent multi-input, single-output, multi-eavesdropper (MISOME) wiretap channel [10], an achievable secrecy sum-rate R s is given by…”

“…Therefore, only one message is transmitted to one legitimate user, and the user does not experience any interference. By comparing (18) to R ⋆• s /K, we can conclude that for β ≤ 1, the RCI precoder achieves a per-user secrecy rate which has the same linear scaling factor as the secrecy capacity of a single-user system with no interference. When 1 < β < 2, the presence of interference results in a value of R ⋆• s that decreases with the SNR, as opposed to a constant value for C s,SU .…”

“…In [18], an iterative power allocation algorithm was proposed to obtain the maximum secrecy sum-rate for a fixed regularization parameter ξ. The algorithm was also extended to maximize the secrecy sum-rate by jointly optimizing the regularization parameter ξ and the power allocation vector.…”