Superimposed Versus Regular Pilots for Hardware Impaired Rician-Faded Cell-Free Massive MIMO Systems

Abstract

We consider the uplink of a cell-free (CF) massive multi-input multi-output (MIMO) system with superimposed pilot (SP) transmission, wherein user equipments (UEs) superimpose low-powered pilots onto data signals. This is unlike regular pilot (RP) transmission, where data and pilots use orthogonal spectral resources. Our CF mMIMO system has hardware impairments which occur due to i) low-quality radio frequency (RF) chains at the access points (APs) and UEs; and ii) dynamic analog-to-digital converter (ADC) architecture at the APs, which enables each RF chain to be connected to different resolution ADC. We derive a closed-form spectral efficiency (SE) expression for this CF system, wherein UEs observe practical spatially-correlated Rician-faded channels. The derived lower-bound is generic, and reduces to the ones in the existing CF mMIMO SP works, which have only considered ideal hardware . Using this lower-bound, we optimally balance pilot and data transmit powers to maximize the SE. We analytically show that the optimal power balance is insensitive to AP impairments, but sensitive to that of UEs. We numerically show that SP can provide a higher SE than RP for low-to-severe hardware impairment levels, when supported by dynamic ADC architecture at the APs. With low resolution ADCs, RP always outperforms SP. The RP is also shown to be suitable for low UE speeds.