Analysis of Quantized MRC-MRT Precoder For FDD Massive MIMO Two-Way AF Relaying

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 (TWRs) 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 an N-antenna AF massive MIMO TWR, which operates in a frequency-division duplex mode to enable two-way communication between 2M = [N
^α
] single-antenna users, with α ∈ [0, 1), divided equally into 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 are strictly nonzero and finite, respectively. Furthermore, its per-user pairwise error probability 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 P
_r
= (2ME
_r
/N) and E
_r
being a constant. 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.