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Large System Analysis of Linear Precoding in MISO Broadcast Channels with Confidential Messages

Giovanni Geraci, Romain Couillet, Jinhong Yuan, Iain B. Collings

Published Aug 18, 2016• 80 citations
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Abstract

In this paper, we study the performance of regularized channel inversion (RCI) precoding in large MISO broadcast channels with confidential messages (BCC). We obtain a deterministic approximation for the achiev-able secrecy sum-rate which is almost surely exact as the number of transmit antennas M and the number of users K grow to infinity in a fixed ratio β = K/M. We derive the optimal regularization parameter ξ and the optimal network load β that maximize the per-antenna secrecy sum-rate. We then propose a linear precoder based on RCI and power reduction (RCI-PR) that significantly increases the high-SNR secrecy sum-rate for 1 < β < 2. Our proposed precoder achieves a per-user secrecy rate which has the same high-SNR scaling factor as both the following upper bounds: (i) the rate of the optimum RCI precoder without secrecy requirements, and (ii) the secrecy capacity of a single-user system without interference. Furthermore, we obtain a deterministic approximation for the secrecy sum-rate achievable by RCI precoding in the presence of channel state information (CSI) error. We also analyze the performance of our proposed RCI-PR precoder with CSI error, and we determine how the error must scale with the SNR in order to maintain a given rate gap to the case with perfect CSI. Index Terms Physical layer security, broadcast channel, random matrix theory, linear precoding, multi-user systems. ar X iv

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In this paper, we study the performance of regularized channel inversion precoding in MISO broadcast channels with confidential messages under imperfect channel state information at the transmitter (CSIT). We obtain an approximation for the achievable secrecy sum-rate which is almost surely exact as the number of transmit antennas and the number of users grow to infinity in a fixed ratio. Simulations prove this anaylsis accurate even for finite-size systems. For FDD systems, we determine how the CSIT error must scale with the SNR, and we derive the number of feedback bits required to ensure a constant high-SNR rate gap to the case with perfect CSIT. For TDD systems, we study the optimum amount of channel training that maximizes the high-SNR secrecy sum-rate.
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In this paper, we consider the broadcast channel with confidential messages and external eavesdroppers (BCCE), where a multi-antenna base station simultaneously communicates to multiple potentially malicious users, in the presence of randomly located external eavesdroppers. Using the proposed model, we study the secrecy rates achievable with regularized channel inversion (RCI) precoding by performing a large-system analysis that combines results from stochastic geometry and random matrix theory, where the number of users K and the number of transmit antennas N both grow to infinity in a fixed ratio. We obtain explicit expressions for the probability of secrecy outage and an upper bound on the rate loss due to the presence of external eavesdroppers. We show that both these quantities scale as \fraclambda_esqrt{N} as the density of external eavesdroppers λ_e grows, irrespective of their collusion strategy. Furthermore, we derive a practical rule for the choice of the regularization parameter, which is agnostic of channel state information and location of eavesdroppers, and yet provides close to optimal performance.
In this paper, we study the performance of the Regularized Channel Inversion (RCI) precoder in a multi-user MIMO system with malicious users. We consider the general case when the number of users per transmit antenna β can take any value. We derive the optimal regularization parameter that maximizes the achievable secrecy sum-rate via large-system analysis, which we show to be accurate via simulations. We find that the secrecy requirements limit the number of users per transmit antenna that can be served with non-zero sum-rate. We show that for large signal-to-noise ratio, RCI can achieve secrecy without reducing the sum-rate if β; 1, then the secrecy requirements result in a poor sum-rate.
We design a linear precoder based on the principles of the generalized regularized channel inversion (RCI) precoder that achieves confidential broadcasting in a two-cell network. In each cell of the network, an N-antenna base station (BS) communicates with K single-antenna users. We consider coordinated beamforming where the BSs in the two cells do not share messages but the users in the two cells feed back their channel state information to both BSs. In the precoder design, we determine the optimal regularization parameter that maximizes the secrecy sum rate. To this end, we derive new channel-independent expressions for the secrecy sum rate in the large-system regime, where K and N approach infinity with a fixed ratio μ = K/N. Moreover, we propose a power-reduction strategy that significantly improves the secrecy sum rate at high transmit signal-to-noise ratios when μ is higher than 0.5.
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