Proportional fairness analysis of massive MIMO Two-tier multiuser downlink with subchannel pairing

This paper presents a proportional fairness throughput analysis of a millimeter wave massive multiple-input multiple output (MIMO) small base station (SBS)-assisted downlink with subchannel (SC) pairing. We derive an analytical expression for evaluating the average logarithmic throughput with SC-pairing and proportional fairness in two-tier network with amplify-and-forward (AF) and decode-and-forward (DF) SBSs. Analytical expressions are derived for the probability density function (PDF) of logarithmic throughput, and the average logarithmic throughput with statistical channel state information (CSI) based gain at AF SBS. It has been shown that the percentage error between simulation and analytical results decreases with increase in number of SC N and number of antennas, and is upper bounded by 0.28% and 0.79% when N≥16 for AF and DF SBSs, respectively.