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 N, 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 N, 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 N, 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 N, 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.

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 = [Nα] 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 = [Nα] tend to infinity, with a relay power scaling of Pr= (2MEr/N) and Erbeing 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.

We design a precoder for non-concurrent two-way relaying (ncTWR) where a base station (BS) serves a transmitonly user equipment (TUE) in the uplink and a receive-only user equipment (RUE) in the downlink. The RUE experiences backpropagating interference (B!). The proposed precoder is designed such that it not only cancels the B! experienced by the RUE but more importantly, enables receive data decoding with high diversity. The high diversity precoder is designed by deriving the closed-form pairwise error probability (PEP) expressions, and by optimizing the precoder elements to minimize the PEP. We analytically show that with Nr-antenna relay, Nb-antenna BS, and Nu-antenna TUE and RUE, both BS and RUE decode their respective data with a diversity order of min(Nu2, (Nr- Nu)Nb) at high receive signal-to-noise ratio. We also numerically show that the proposed design has lower bit error rate than the existing state-of-the-art ncTWR designs.

We investigate a limited feedback precoder based on symbol pairwise error probability (PEP) for a block-faded K×ntdownlink 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 αt→ ∞, 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 ntvalues. Finally, we numerically compare the bit error rate, encoding complexity, and per-user achievable rate of the proposed scheme with the existing designs.

For a block fading nt× nr,nt> nrMIMO channel, we propose a precoding scheme that achieves both ntnrth order diversity as well as rate of ntsymbols per channel use, feeding back B(nt-1) bits as partial channel state information to the transmitter (CSIT), where 2Bis the number of quantization states available. We establish the optimality of the uniform quantizer which achieves minimum loss in coding gain due to quantization of feedback values of our precoding scheme in comparison to the non-uniform quantization. We also lay down the guidelines for constellation sets with which our precoding scheme can achieve full diversity. We also derive the order of complexity involved in computing the precoder matrix and show that it is independent of the size of constellation sets. We compare our BER results with that of precoding schemes in the literature utilizing full CSIT as well as that with partial CSIT. We also investigate the loss in error rate performance due to imperfect channel knowledge at the receiver and present simulation results to verify our claims.

In this paper, we consider a slow-fading nt×nrmultiple-input multiple-output (MIMO) channel subjected to block fading. Reliability (in terms of achieved diversity order) and rate (in number of symbols transmitted per channel use) are of interest in such channels. We propose a new precoding scheme which achieves both full diversity (nt×nrth order diversity) as well as full rate (ntsymbols per channel use) using partial channel state information at the transmitter (CSIT). The proposed scheme achieves full diversity and improved coding gain through an optimization over the choice of constellation sets. The optimization maximizes dmin2for our precoding scheme subject to an energy constraint. The scheme requires feedback of nt- 1 angle parameter values, compared to 2ntnrreal coefficients in case of full CSIT. Further, for the case of nt× 1 system, we prove that the capacity achieved by the proposed scheme is same as that achieved with full CSIT. Error rate performance results for nt= 3,4,8 show that the proposed scheme performs better than other precoding schemes in the literature; the better performance is due to the choice of the signal sets and the feedback angles in the proposed scheme.

In this paper, we propose new non-coherent spacetime block code (STBC) designs, which achieve full transmit diversity as well as high rates. We first present a search procedure to generate full-diversity non-coherent unitary space-time codebooks for any number of transmit antennas (nt) and time slots (T ¿ 2nt), using radial coordinates of points lying on the surface of a sphere in RT-nt. The search method generates codebooks having a specified minimum chordal distance, which allows flexibility in achieving coding gain. Further, we propose another unitary design using circulant matrices for any nt, by restricting the search only to suitable constellation sets in R2for the case of T = 2nt. For the latter design, we present two different optimizations; i) to maximize the minimum chordal distance, and ii) to maximize the expected chordal distance. The proposed designs use an analytical design criterion which guarantees full diversity. The proposed designs are shown to outperform Jing and Hassibi codes reported previously in the literature.