A ug 2 01 5 Optimal Power Allocation for A Massive MIMO Relay Aided Secure Communication

In this paper, we address the problem of optimal power allocation at the relay in two-hop secure communicati ons under practical conditions. To guarantee secure communica tion during the long-distance transmission, the massive MIMO (MMIMO) relaying techniques are explored to significantly enhance wireless security. The focus of this paper is on the analysis and design of optimal power assignment for a decode-and-forwar d (DF) M-MIMO relay, so as to maximize the secrecy outage capacity and minimize the interception probability, respectively. Our study reveals the condition for a nonnegative the secrec y outage capacity, obtains closed-form expressions for opti mal power, and presents the asymptotic characteristics of secr ecy performance. Finally, simulation results validate the eff ectiveness of the proposed schemes. I. I NTRODUCTION The open nature of the wireless channel facilitates a multiuser transmission, but also incurs the security problem. Recently, as a complement of traditional upper-layer encrypt ion techniques, physical layer security (PHY-security) has be en proposed to realize secure communications by making use of the characteristics of wireless channels, i.e., noise, fad ing and interference [1]. From an information-theoretic viewpoint, the performance of PHY-security is determined by the rate difference between the legitimate channel and the eavesdropper channel [2] [3]. Therefore, to enhance wireless security, it makes sense to simultaneously increase the legitimate channel ra te and decrease the eavesdropper channel rate. Inspired by thi s, various physical layer techniques have been introduced to improve the secrecy performance. Wherein, MIMO relaying technique gains considerable attention due to the followin g two reasons. First, the relay can provide a diversity gain and shorten the accessing distance, and thus improve the secrecy performance [4]. Second, MIMO techniques, such as spatial beamforming, can reduce the information leakage to the eavesdropper [5]. The beamforming schemes at the MIMO relay based on amplify-and-forward (AF) and decode-andforward (DF) relaying protocols were presented in [6] and [7], respectively. It is worth pointing out that the optimal beam design at the relay requires global channel state informati on (CSI) [8]. Yet, the CSI, especially eavesdropper CSI is diffi cult to obtain, since the eavesdropper is usually passive and kee ps silent. Therefore, it is impossible to realize absolutely s ecure communications over fading channels. In this context, stat istical secrecy performance metrics, e.g., secrecy outage capa city and interception probability, are adopted to evaluate wire less security [9]. Recently, an advanced MIMO relaying technology, namely massive MIMO (M-MIMO) relaying, is introduced into secure communications to further improve the secrecy performance [10]. Even without eavesdropper CSI, M-MIMO relaying can generate a very high-resolution spatial beam, and thus the information leakage to the eavesdropper is quite small. Mor e importantly, the secrecy performance can be enhanced by simply adding more antennas. Hence, the challenging issue of short-distance interception in secure communications c an be well solved. Note that in two-hop secure communications, the transmit power at the relay has a great impact on the secrecy performance, since it affects the signal quality at both the destination and the eavesdropper. An optimal power allocation scheme for a multi-carrier two-hop single-ante n a relaying network was given in [11] by maximizing the sum secrecy rate. However, the power allocation for a multi-ant en a relay, especially an M-MIMO relay, is still an open issue. In this paper, we focus on power allocation for DF M-MIMO secure relaying systems under very practical assumptions, i.e., no eavesdropper CSI and imperfect legitimate CSI. The contributions of this paper are three-fold: 1) We reveal the relation between the secrecy outage capacity and a defined relative distance-dependent path loss, and then derive the condition for a nonnegative secrecy outage capacity and the constraint on the minimum number of antennas. 2) We derive closed-form expressions for the optimal power at the relay in the sense of maximizing the secrecy outage capacity and minimizing the interception probability, respectively. 3) We present clear insights into the secrecy performance through asymptotic analysis. We show that the maximum secrecy outage capacity is an increasing function of the source power while the minimum interception probability keeps constant. The rest of this paper is organized as follows. We first give an overview of the DF M-MIMO secure relaying system in Section II, and then derive two optimal power allocation schemes for the relay in Section III. In Section IV, we presen t simulation results to validate the effectiveness of the pro posed schemes. Finally, we conclude the paper in Section V. II. SYSTEM MODEL We consider a time division duplex (TDD) two-hop massive MIMO (M-MIMO) relaying system, where a single antenna source transmits message to a single antenna destination wi th the aid of a relay withNR antennas, while a passive single antenna eavesdropper intends to intercept the information . Note that the number of antennas at the relay in such an MMIMO relaying system is quite large, i.e., NR = 100 or even bigger. It is assumed that there is no direct transmission be tween the source and the destination due to a long propagatio n distance. The relay system works in a half-duplex mode, whic h means any successful transmission requires two time slots. Specifically, the source sends the signal to the relay in the first time slot, and then the relay forwards the post-process ing signal to the destination in the second time slot. In this pap er, we assume the eavesdropper is far from the source and close to the relay, since it was concluded that the signal comes fro m the relay directly. Therefore, it is reasonable to assume th at the eavesdropper only monitors the transmission from the relay to the destination. We use √ αS,RhS,R, √ αR,DhR,D and √ αR,EhR,E to represent the channels from the source to the relay, the relay to the destination, and the relay to the eavesdropper, respect ively, whereαS,R, αR,D andαR,E are the distance-dependent path losses andhS,R, hR,D, and hR,E denote the channel fading coefficient vectors with independent and identically distr ibuted (i.i.d.) zero mean and unit variance complex Gaussian entri es. It is assumed that the channels remain constant during a time slot and fade independently over slots. Thus, the received signal at the relay in the first time slot can be expressed as yR = √ PSαS,RhS,Rs+ nR, (1) wheres is the normalized Gaussian distributed transmit symbol, PS is the transmit power at the source, and R stands for the additive white Gaussian noise with unit variance at t he relay. We assume that the relay has perfect CSI about hS,R by channel estimation. Then, maximum ratio combination (MRC) decoding is performed to recover the information. Specifically, the received signal is multiplied by a vector wR = h H S,R/‖hS,R‖. During the second time slot, the relay forwards the decoded signal ŝ through maximum ratio transmission (MRT). We assume that the relay has partial CSI about hR,D due to channel reciprocity impairment in TDD systems. The relatio n between the estimated CSÎ hR,D and the real CSIhR,D is given by hR,D = √ ρĥR,D + √ 1− ρe, (2) where e is the error vector with i.i. d. zero mean and unit variance complex Gaussian entries, and is independent of ĥR,D. ρ, scaling from0 to 1, is the correlation coefficient betweenĥR,D and hR,D. Thus, the received signals at the destination and the eavesdropper are given by yD = √ PRαR,DhR,Dr + nD, (3) and yE = √ PRαR,EhR,Er + nE , (4) respectively, wherePR is the transmit power of the relay, r = vRŝ is the forwarded signal withvR = ĥR,D/‖ĥR,D‖ being a MRT beamforming vector. nD and nE are additive white Gaussian noise (AWGN) samples with unit variance at the destination and the eavesdropper, respectively. III. O PTIMAL POWER ALLOCATION In this section, we aim to optimize the secrecy performance through allocating the relay power PR, since it affects the signal quality at both the destination and the eavesdropper . In what follows, we analyze and design the power allocation schemes in the sense of maximizing the secrecy outage capacity and minimizing the interception probability, respecti vely. A. Secrecy Outage Capacity Maximization Power Allocation Based on the received signal in (1), when performing MRC decoding at the relay, the channel capacity from the source t o the relay can be expressed as CS,R = W log2(1 + γR), (5) whereW is the spectral bandwidth and γR = PSαS,R‖hS,R‖ is the signal-to-noise ratio (SNR). Similarly, according t o (3) and (4), channel capacities from the relay to the destinatio and from the relay to the eavesdropper are given by CR,D = W log2 (1 + γD) , (6) and CR,E = W log2 (1 + γE) , (7) respectively, whereγD = PRαR,D ∣ ∣ ∣hR,D ĥR,D ‖ĥR,D‖ ∣