Resource Allocation for a Massive MIMO Relay Aided Secure Communication

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 encryption techniques, physical layer security (PHY-security) has been proposed to realize secure communications by making use of the characteristics of wireless channels, i.e., noise, fading and interference. From an information-theoretic viewpoint, the performance of PHY-security is determined by the rate difference between the legitimate channel and the eavesdropper channel. Therefore, to enhance wireless security, it makes sense to simultaneously increase the legitimate channel rate and decrease the eavesdropper channel rate. Inspired by this, various physical layer techniques have been introduced to improve the secrecy performance.

MIMO:

MIMO(multiple-input and multiple-output) is a term used in Radio. It is used for multipath propagation where the capacity of a radio signal can be increased using multiple transmitter and receiver antennas. It is different from smart antenna techniques used to uplift the capacity of a single data signal like diversity and beamforming.

MIMO relaying technique gains considerable attention due to the following two reasons;

First, the relay can provide a diversity gain and shorten the accessing distance, and thus improve the secrecy performance.

Second, MIMO techniques, such as spatial beamforming, can reduce the information leakage to eavesdropper. It is worth pointing out that the optimal beam design at the relay requires global channel state information (CSI). Yet, the CSI, especially eavesdropper CSI is difficult to obtain, since the eavesdropper is usually passive and keeps silent. Therefore, it is impossible to realize absolutely secure communications over fading channels.

Masssive MIMO:

Recently, an advanced MIMO relaying technology, namely massive MIMO (M-MIMO) relaying, is introduced into secure communications to further improve the secrecy performance. 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. 

More importantly, the secrecy performance can be enhanced by simply adding more antennas. Hence, the challenging issue of short-distance interception in secure communications can be well solved.

 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 with the aid of a relay with NR antennas, while a passive single antenna eavesdropper intends to intercept the information.

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 between the source and the destination due to a long propagation distance

The relay system works in a half-duplex mode, which 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-processing signal to the destination in the second time slot.

Optimal Power Allocation:

We are aiming 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, respectively.

Simulation Results:

To examine the effectiveness of the proposed power allocation schemes for DF M-MIMO secure relaying systems, we present several simulation results for the following scenarios. We set NR = 100, W = 10 kHz, ρ = 0.9 and ε = 0.01 without extra statements. For convenience, we normalize the path loss from the source to the relay as αS,R = 1 and use αR,D and αS,E to denote the relative path loss. Specifically, αR,E > αR,D means that the eavesdropper is closer to the relay than the destination. In addition, we use SNRS = 10 log10 PS , SNRR = 10 log10 PR and SNRmax = 10 log10 Pmax to represent the SNR in dB at the source, the relay and the constraint at the relay, respectively

First, we verify the accuracy of the theoretical expression in Theorem 1 with SNRS = SNRR = 10 dB and αR,D = 1. As seen in Fig. 1, the theoretical results are well consistent with the simulations in the whole αR,E region with different outage probability requirements, which proves the high accuracy of the derived results. Given an outage probability bound by ε, as αR,E increases, the secrecy outage capacity decreases gradually. This is because the interception ability of the eavesdropper enhances due to the short interception distance. In addition, for a given αR,E , the secrecy outage capacity improves with the increase of ε, since the outage probability is an increasing function of the secrecy outage capacity.

Next, we show the performance gain of the proposed optimal power allocation schemes compared to a fixed power allocation with SNRS = 10 dB, SNRmax = 15 dB and αR,E = 5. It is worth pointing out that the fixed scheme uses a fixed power PR = 15 dB regardless of channel conditions and system parameters. 

The secrecy outage capacity maximization power allocation scheme performs better than the fixed power allocation scheme. Especially in the high αR,D regime, the performance of the proposed scheme improves sharply, while that of the fixed allocation scheme nearly remains unchanged. This is because the legitimate channel capacity is limited by the source-relay channel capacity under this condition, but the fixed scheme is regardless of αS,R and PS. In the low αR,D regime, the secrecy outage capacities of both schemes approach zero due to rl > 1, which verifies Theorem 2 again. In terms of interception probability. 

The proposed scheme also outperforms the fixed power allocation scheme. Consistent with the theoretical claims, the interception probability approaches zero when αR,D is large enough.

Finally, we check the asymptotic characteristics with αR,D = 1. As shown in Fig. 4, as PS tends to zero, the maximum secrecy capacities with different αR,E approach zero. In the large PS regime, the maximum secrecy outage capacity will be saturated, which is in agreement with Proposition 1 again. From Fig. 5, it is seen that the minimum interception probability is independent of PS. Additionally, the interception probability floor becomes higher with the increase of αR,E.

Conclusion:

First presented is a secrecy performance analysis for a DF M-MIMO secure relaying system with imperfect CSI. In order to guarantee a nonnegative secrecy outage capacity, there is a constraint on the minimum number of antennas at the relay. Then, by maximizing the secrecy outage capacity and minimizing the interception probability, we proposed two optimal relay power allocation schemes. At last, we revealed the asymptotic characteristics of maximum secrecy outage capacity and minimum interception probability with respect to the source power.