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

TL;DR

This paper analyzes the performance of regularized channel inversion precoding in large MISO broadcast channels with confidential messages, deriving optimal parameters and proposing a new precoder that enhances secrecy rates under high SNR.

Contribution

It provides a deterministic approximation for secrecy sum-rate in large systems, derives optimal regularization and load parameters, and introduces a RCI-PR precoder that improves high-SNR secrecy performance.

Findings

Deterministic approximation for secrecy sum-rate as system size grows

Optimal regularization parameter and network load for maximizing secrecy rate

Proposed RCI-PR precoder significantly increases high-SNR secrecy sum-rate

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 achievable 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 $\beta=K/M$. We derive the optimal regularization parameter $\xi$ and the optimal network load $\beta$ 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 $1<\beta<2$. 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.