Precoding by Pairing Subchannels to Increase MIMO Capacity with Discrete Input Alphabets

We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on the X-Codes in \cite{Xcodes_paper} to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using Singular Value Decomposition (SVD) and X-Codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and a $2\times 2$ real rotation matrix for each pair (parameterized with a single angle). This precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is solved by {\em i}) optimizing the rotation angle and the power allocation within each pair and {\em ii}) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz {\em et al.}, and is significantly better than Mercury/waterfilling strategy by Lozano {\em et al.}. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.Comment: submitted to IEEE Transactions on Information Theor

Linear Precoding for MIMO Channels with QAM Constellations and Reduced Complexity

In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, a novel and efficient methodology to evaluate the input-output mutual information for a general Multiple-Input Multiple-Output (MIMO) system as well as its corresponding gradients is presented, based on the Gauss-Hermite quadrature rule. Then, the method is exploited in a block coordinate gradient ascent optimization process to determine the globally optimal linear precoder with respect to the MIMO input-output mutual information for QAM systems with relatively moderate MIMO channel sizes. The proposed methodology is next applied in conjunction with the complexity-reducing per-group processing (PGP) technique, which is semi-optimal, to both perfect channel state information at the transmitter (CSIT) as well as statistical channel state information (SCSI) scenarios, with high transmitting and receiving antenna size, and for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder, and the maximum diversity precoder for QAM with constellation sizes $M=16,~32$, and $~64$ and for MIMO channel size $100\times100$

On Precoding for Constant K-User MIMO Gaussian Interference Channel with Finite Constellation Inputs

This paper considers linear precoding for constant channel-coefficient $K$-User MIMO Gaussian Interference Channel (MIMO GIC) where each transmitter-$i$ (Tx-$i$), requires to send $d_i$ independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution, to receiver-$i$ (Rx-$i$) for $i=1,2,\cdots,K$. We define the maximum rate achieved by Tx-$i$ using any linear precoder, when the interference channel-coefficients are zero, as the signal to noise ratio (SNR) tends to infinity to be the Constellation Constrained Saturation Capacity (CCSC) for Tx-$i$. We derive a high SNR approximation for the rate achieved by Tx-$i$ when interference is treated as noise and this rate is given by the mutual information between Tx-$i$ and Rx-$i$, denoted as $I[X_i;Y_i]$. A set of necessary and sufficient conditions on the precoders under which $I[X_i;Y_i]$ tends to CCSC for Tx-$i$ is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Further, we propose gradient-ascent based algorithms to optimize the sum-rate achieved by precoding with finite constellation inputs and treating interference as noise. Simulation study using the proposed algorithms for a 3-user MIMO GIC with two antennas at each node with $d_i=1$ for all $i$, and with BPSK and QPSK inputs, show more than 0.1 bits/sec/Hz gain in the ergodic sum-rate over that yielded by precoders obtained from some known IA algorithms, at moderate SNRs.Comment: 15 pages, 9 figure

Downlink Precoding for Massive MIMO Systems Exploiting Virtual Channel Model Sparsity

In this paper, the problem of designing a forward link linear precoder for Massive Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, we employ a novel and efficient methodology that allows for a sparse representation of multiple users and groups in a fashion similar to Joint Spatial Division and Multiplexing. Then, the method is generalized to include Orthogonal Frequency Division Multiplexing (OFDM) for frequency selective channels, resulting in Combined Frequency and Spatial Division and Multiplexing, a configuration that offers high flexibility in Massive MIMO systems. A challenge in such system design is to consider finite alphabet inputs, especially with larger constellation sizes such as $M\geq 16$. The proposed methodology is next applied jointly with the complexity-reducing Per-Group Processing (PGP) technique, on a per user group basis, in conjunction with QAM modulation and in simulations, for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder or the plain beamformer and with $M\geq 16$

Asymptotic Analysis of SU-MIMO Channels With Transmitter Noise and Mismatched Joint Decoding

Hardware impairments in radio-frequency components of a wireless system cause unavoidable distortions to transmission that are not captured by the conventional linear channel model. In this paper, a 'binoisy' single-user multiple-input multiple-output (SU-MIMO) relation is considered where the additional distortions are modeled via an additive noise term at the transmit side. Through this extended SU-MIMO channel model, the effects of transceiver hardware impairments on the achievable rate of multi-antenna point-to-point systems are studied. Channel input distributions encompassing practical discrete modulation schemes, such as, QAM and PSK, as well as Gaussian signaling are covered. In addition, the impact of mismatched detection and decoding when the receiver has insufficient information about the non-idealities is investigated. The numerical results show that for realistic system parameters, the effects of transmit-side noise and mismatched decoding become significant only at high modulation orders.Comment: 16 pages, 7 figure

Power allocation and linear precoding for wireless communications with finite-alphabet inputs

This dissertation proposes a new approach to maximizing data rate/throughput of practical communication system/networks through linear precoding and power allocation. First, the mutual information or capacity region is derived for finite-alphabet inputs such as phase-shift keying (PSK), pulse-amplitude modulation (PAM), and quadrature amplitude modulation (QAM) signals. This approach, without the commonly used Gaussian input assumptions, complicates the mutual information analysis and precoder design but improves performance when the designed precoders are applied to practical systems and networks. Second, several numerical optimization methods are developed for multiple-input multiple-output (MIMO) multiple access channels, dual-hop relay networks, and point-to-point MIMO systems. In MIMO multiple access channels, an iterative weighted sum rate maximization algorithm is proposed which utilizes an alternating optimization strategy and gradient descent update. In dual-hop relay networks, the structure of the optimal precoder is exploited to develop a two-step iterative algorithm based on convex optimization and optimization on the Stiefel manifold. The proposed algorithm is insensitive to initial point selection and able to achieve a near global optimal precoder solution. The gradient descent method is also used to obtain the optimal power allocation scheme which maximizes the mutual information between the source node and destination node in dual-hop relay networks. For point-to-point MIMO systems, a low complexity precoding design method is proposed, which maximizes the lower bound of the mutual information with discretized power allocation vector in a non-iterative fashion, thus reducing complexity. Finally, performances of the proposed power allocation and linear precoding schemes are evaluated in terms of both mutual information and bit error rate (BER). Numerical results show that at the same target mutual information or sum rate, the proposed approaches achieve 3-10dB gains compared to the existing methods in the medium signal-to-noise ratio region. Such significant gains are also indicated in the coded BER systems --Abstract, page iv-v