On The Fast Fading Multiple-Antenna Gaussian Broadcast Channel with Confidential Messages and Partial CSIT

TL;DR

This paper investigates secure communication over fast fading multiple-antenna Gaussian broadcast channels with confidential messages, assuming only statistical CSI at the transmitter, and develops solutions for optimal transmission strategies ensuring positive rates for both users.

Contribution

It derives the achievable rate region, provides an analytical solution for input covariance matrices, and proposes an iterative algorithm for optimizing transmission under partial CSI.

Findings

Both users can achieve positive rates under perfect secrecy.

The analytical solution and iterative algorithm effectively optimize transmission.

Numerical results confirm the necessary conditions for secure communication.

Abstract

In wiretap channels the eavesdropper's channel state information (CSI) is commonly assumed to be known at transmitter, fully or partially. However, under perfect secrecy constraint the eavesdropper may not be motivated to feedback any correct CSI. In this paper we consider a more feasible problem for the transmitter to have eavesdropper's CSI. That is, the fast fading multiple-antenna Gaussian broadcast channels (FMGBC-CM) with confidential messages, where both receivers are legitimate users such that they both are willing to feedback accurate CSI to maintain their secure transmission, and not to be eavesdropped by the other. We assume that only the statistics of the channel state information are known by the transmitter. We first show the necessary condition for the FMGBC-CM not to be degraded to the common wiretap channels. Then we derive the achievable rate region for the FMGBC-CM where the channel input covariance matrices and the inflation factor are left unknown and to be solved. After that we provide an analytical solution to the channel input covariance matrices. We also propose an iterative algorithm to solve the channel input covariance matrices and the inflation factor. Due to the complicated rate region formulae in normal SNR, we resort to low SNR analysis to investigate the characteristics of the channel. Finally, numerical examples show that under perfect secrecy constraint both users can achieve positive rates simultaneously, which verifies our derived necessary condition. Numerical results also elucidate the effectiveness of the analytic solution and proposed algorithm of solving the channel input covariance matrices and the inflation factor under different conditions.