Analyzing Coverage Probability of Multitier Heterogeneous Networks Under Quantized Multiuser ZF Beamforming

In this paper, we analyze the coverage probability of a large-scale heterogenous cellular network (HetNet) where base stations (BSs) are equipped with multiantennas, serving a number of single-antenna user equipments (UEs) in the downlink-space division multiple access (SDMA). Adopting the tool of stochastic geometry, we analyze the coverage probability under the quantized zero-forcing beamforming (ZFBF). This analysis, however, intricate as a typical UE in a given cell experiences: i) a residual inter-user interference (IUI) rendered by the quantization error; ii) quantization-driven statistical correlation between its attending signal power and IUI; iii) Nakagami-type fading environment, induced by postprocessing ZFBF; and iv) intercell interference (ICI). Current related literature has not effectively accounted for issues (i), (ii), and (iv) and commonly resorted to simplifying scenarios of full SDMA (i.e., exponential fading), independency of IUI and attending signal power, approximating IUI via an exponential random variable, and the quantization cell approximation (QCA). Our analysis relaxes such limiting assumptions; it includes the more relevant random vector quantization (RVQ) method, and compared to the literature, does not resort to the evaluation of a higher order differentiation for the evaluation of the coverage probability by exploiting our previously developed method. We further introduce three novel approximations of the coverage probability: RVQ-M, RVG-G, and QCA, which the first two approximations are given in semi-closed-form formulas (requiring a simple integration step) and the last approximation is in a closed-form expression. All approximations are numerically affordable, and we confirm the RVG-G approximation is the most accurate one. Finally, we exploit our analysis to study several practically insightful issues to shed some lights on: 1) for given feedback capacity and number of UEs, when desification becomes beneficial; 2) how multitierness of HetNets can be exploited for substantially reducing feedback capacity; and 3) an adaptive share of feedback capacity for the purpose of CDI as well as channel quality information (CQI) feedbacks, when there is an uplink penalty subjected for the feedback procedure and the scheduled data rate at each BS is specified adaptively based on the quantized CQI.