Analysis of quantized MRC-MRT precoder for FDD massive MIMO two-way AF relaying

Abstract

The maturing massive multiple-input multiple-output (MIMO) literature has provided asymptotic limits for the rate and energy efficiency (EE) of maximal ratio combining/maximal ratio transmission (MRC-MRT) relaying on two-way relays (TWR) using the amplify-and-forward (AF) principle. Most of these studies consider time division duplexing, and a fixed number of users. To fill the gap in the literature, we analyze the MRC-MRT precoder performance of a N -antenna AF massive MIMO TWR, which operates in frequency division duplex mode to enable two-way communication between 2M = ⌊N α ⌋ single-antenna users, with α ∈ [0, 1), divided equally in two groups of M users. We assume that the relay has realistic imperfect uplink channel state information (CSI), and that quantized downlink CSI is fed back by the users relying on B ≥ 1 bits per-user per relay antenna. We prove that for such a system with α ∈ [0, 1), the MRC-MRT precoder asymptotically cancels the multi-user interference (MUI) when the supremum and infimum of large scale fading parameters is strictly non-zero and finite, respectively. Furthermore, its per-user pairwise error probability (PEP) converges to that of an equivalent AWGN channel as both N and the number of users 2M = ⌊N α ⌋ tend to infinity, with a relay power scaling of Pr = 2M Er and Er being a constant. N We also derive upper bounds for both the per-user rate and EE. We analytically show that the quantized MRC-MRT precoder requires as few as B = 2 bits to yield a BER, EE, and per-user rate close to the respective unquantized counterparts. Finally, we show that the analysis developed herein to derive a bound on α for MUI cancellation is applicable both to Gaussian as well as to any arbitrary non-Gaussian complex channels.

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ORCID for L. Hanzo: orcid.org/0000-0002-2636-5214

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