Ravinder David Koilpillai

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 in [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\in [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 non-zero 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 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.

The massive multiple-input multiple-output (MIMO) full-duplex two-way relaying (FD-TWR) literature has extensively investigated power scaling for rate guarantees by considering a fixed number of users. We investigate the pairwise error probability (PEP) and the per-user rate of a FD-TWR with Nr relay antennas that employs maximal ratio combining/transmission to enable two-way communication between K FD users. We propose novel relay and user powers scalings, with both Nr and K tending to infinity, and show that the PEP of each user converges almost surely to its AWGN counterpart. These power scalings are different from the existing ones, which are derived by fixing K and by assuming that only Nr tends to large values. We show that the analysis developed herein applies to both Gaussian and non-Gaussian complex channels with finite number of moments. We numerically show that when both K and Nr increase concurrently to large values, the proposed power scaling schemes not only have better per-user PEP and rate than the existing schemes, but they are also robust to the FD self loop-interference power.

We investigate a limited feedback precoder based on symbol pairwise error probability (PEP) for a block-faded K × nt downlink multiple-input multiple-output (MIMO) channel. In the considered system, K = ⌊ntα⌋ single-antenna users feedback quantized channel state information to the nt-antenna transmitter using B bits per-transmit-antenna per user. We analytically show that for α <(1/2), B ≥ 1 and nt → ∞, both symbol PEP and achievable rate of each of the K downlink users almost surely converge to the symbol PEP and achievable rate of K parallel additive white Gaussian noise (AWGN) channels, respectively. We show that the encoding complexity of the precoder is O(ntK). We also show that if channel coefficients estimated by the user are corrupted by AWGN noise, the symbol PEP and achievable rate of each user almost surely converge to the symbol PEP and achievable rate in a scaled AWGN channel with B>1 and nt → ∞. For correlated channels, we derive a condition, which enables the proposed precoder almost surely to cancel multi-user interference for large nt values. Finally, we numerically compare the bit error rate, encoding complexity, and per-user achievable rate of the proposed scheme with the existing designs.