On Quantization for Masked Beamforming Secrecy Systems

Abstract

This study investigates how to quantize the masked beamforming systems to maximize the secrecy rate for MISOSE (multiple-input, single-output, single-eavesdropper) channels and assume that this eavesdropper equipped with only single antenna, where only partial channel state information (CSI) at the legitimate receiver is available to the transmitter. In this case, the artificial noise (AN) leaks to the legitimate receiver due to CSI quantization. In the literature, all quantization bits are used to quantize the beamforming vector. Then the null space of this quantized beamforming vector is used to transmit the AN. We find that such quantization schemes can result in serious interference at the legitimate receiver. To overcome this issue, we propose that the beamforming vector and the AN vector should be quantized separately, where the beamforming vector should be selected from a codebook to maximize the beamforming gain and the AN vector should be selected from another codebook to minimize the leakage (or interference). Theoretical results show that separate quantization can significantly reduce the AN leakage at the legitimate receiver. Furthermore, based on the proposed quantization scheme, we show how to allocate bits to separately quantize the beamforming vector and the AN vector to maximize the secrecy rate. By using the proposed quantization and bit allocation schemes, the secrecy rates of masked beamforming systems can be improved compared to the conventional quantization schemes. Simulation results corroborate the theoretical results.