Downlink Secrecy Rate of One-Bit Massive MIMO System with Active Eavesdropping

Abstract

In this study, we consider the physical layer security in the downlink of a Massive MIMO system employing one-bit quantization at the base station (BS). We assume an active eavesdropper that attempts to spoiling the channel estimation acquisition at the BS for a legitimate user, whereas overhearing on downlink transmission. We consider the two most widespread methods for degrading the eavesdropper's channel, the nullspace artificial noise (NS-AN) and random artificial noise (R-AN). Then, we present a lower bound on the secrecy rate and asymptotic performance, considering zero-forcing beamforming (ZF-BF) and maximum-ratio transmission beamforming (MRT-BF). Our results reveal that even when the eavesdropper is close enough to the intercepted user, a positive secrecy rate --which tends to saturation with increasing the number of BS antennas $N$---is possible, as long as the transmit power of eavesdropper is less than that of the legitimate user during channel training. We show that ZF-BF with NS-AN provides the best performance. It is found that MRT-BF and ZF-BF are equivalent in the asymptotic limit of $N$ and hence the artificial noise technique is the performance indicator. Moreover, we study the impact of \emph{power-scaling law} on the secrecy rate. When the transmit power of BS is reduced proportional to $1/N$, the performance is independent of artificial noise asymptotically and hence the beamforming technique is the performance indicator. In addition, when the BS's power is reduced proportional to $1/\sqrt{N}$, all combinations of beamforming and artificial noise schemes are equally likely asymptotically, independent of quantization noise. We present various numerical results to corroborate our analysis.

49 pages (onecolumn), 12 figures (Available in IEEE ACCESS(early access): https://ieeexplore.ieee.org/document/9006840)

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