Optimal Design of Secrecy Massive MIMO Amplify-and-Forward Relaying Systems With Double-Resolution ADCs Antenna Array

Abstract

This paper focuses on a secrecy constrained massive multiple-input multiple-output (MIMO) relaying system in terms of the optimal design of system parameters such as the optimal total number of antennas at relay, where a more practical mixed analog-to-digital converters (ADCs) scheme, double-resolution ADCs scheme, is proposed. In the proposed double-resolution ADCs scheme, the total $M$ antennas at relay are divided into two parts, one of which includes $M_{0}$ antennas with medium-resolution ADCs only requiring 5~12 quantization bits and the remainder of which consists of $M_{1}$ antennas with low-resolution ADCs. The transmission from relay to destinations is exposed to a passive eavesdropper. For such massive MIMO relaying systems, we first derive the total achievable ergodic rates of legitimate users as well as the corresponding secrecy outage rates. Then, a reasonable energy consumption model is modeled so that the secrecy energy efficiency (SEE) is derived, where the effect of the source power, the resolutions of ADCs, and the ratio of the antenna numbers with medium- and low-resolution ADCs are exploited perfectly. The presented numerical results show that replacing high-resolution ADCs with medium-resolution ADCs is beneficial for improving the system SEE while the effect on the total achievable rate is very small. Specially, three main insights are achieved: 1) there exists an optimal value of the source power at which the SEE is optimal; 2) with given ratio $M_{0} :M_{1} $ , the optimal value of quantization bits of medium-resolution ADCs is upper-bounded, under which the system has higher SEE, that is to say, we obtain the upper bound of the resolution of the medium-resolution ADCs; and 3) the optimal number of the total antennas is impacted jointly by the number $b_{0}$ of the quantization bits of medium-resolution ADCs and the ratio $M_{0} :M_{1}$ . Specially, while the optimal number of the total antennas is 100 or so for the pure high-resolution ADCs systems, the one for the proposed double-resolution ADCs systems would up to 500~700. Moreover, the optimal antenna number is increasing with the decrease of $b_{0} $ and the ratio $M_{0} :M_{1} $ so that the system performance can be improved further.