This paper studies the optimal bit allocation for shape-gain vector quantization of wireless channels in multiuser (MU) multiple-input multiple-output (MIMO) downlink systems based on linear precoding. Our design minimizes the mean squared-error between the original and quantized channels through optimal bit allocation across shape (direction) and gain (magnitude) for a fixed feedback overhead per user. This is shown to significantly reduce the quantization error, which in turn, decreases the MU interference. This paper makes three main contributions: first, we focus on channel gain quantization and derive the quantization distortion, based on a Euclidean distance measure, corresponding to singular values of a MIMO channel. Second, we show that the Euclidean distance-based distortion of a unit norm complex channel, due to shape quantization, is proportional to \frac{2^{-2Bs}}{2M-1}, where, Bs is the number of shape quantization bits and M is the number of transmit antennas. Finally, we show that for channels in complex space and allowing for a large feedback overhead, the number of direction quantization bits should be approximately (2M - 1) times the number of channel magnitude quantization bits.
In this paper, we solve the sum mean-squared error (MSE)-optimal 1-bit quantized precoding problem exactly for small-to-moderate sized multiuser multiple-input multiple-output (MU-MIMO) systems via branch and bound. To this end, we reformulate the original NP-hard precoding problem as a tree search and deploy a number of strategies that improve the pruning efficiency without sacrificing optimality. We evaluate the error-rate performance and the complexity of the resulting 1-bit branch-and-bound (BB-1) precoder, and compare its efficacy to that of existing, suboptimal algorithms for 1-bit preco…
Joint user selection and precoding in multiuser MIMO settings can be interpreted as group sparse recovery in linear models. In this problem, a signal with group sparsity is to be reconstructed from an underdetermined system of equations. This paper utilizes this equivalent interpretation and develops a computationally tractable algorithm based on the method of group LASSO. Compared to the state of the art, the proposed scheme shows performance enhancements in two different respects: higher achievable sum-rate and lower interference at the non-selected user terminals.
Relay-aided transmission is envisioned as a key strategy to combat severe path loss and link blockages emerging as unique challenges in millimeter-wave (mmWave) communications. This work considers a relay-aided multiuser mmWave communications scenario aiming at maximizing the sum rate through optimal transmit and relay precoder design. We propose a novel joint precoder design strategy, which exploits weighted minimum mean-square error (WMMSE) using its equivalency to sum-rate maximization. We obtain closed form expressions of transmit and relay precoders, and propose to compute them through al…
Low-resolution precoding techniques have gained considerable attention in the wireless communications area recently. Vital but hardly discussed in literature, discrete precoding in conjunction with channel coding is the subject of this study. Unlike prior studies, we propose three different soft detection methods and an iterative detection and decoding scheme that allow the utilization of channel coding in conjunction with low-resolution precoding. Besides an exact approach for computing the extrinsic information, we propose two approximations with reduced computational complexity. Numerical r…
We analytically approximate the expected sum capacity loss between the optimal downlink precoding technique of dirty paper coding (DPC), and the sub-optimal technique of zero-forcing precoding, for multiuser channels. We also consider the most general case of multi-stream transmission to multiple users, where we evaluate the expected sum capacity loss between DPC and block diagonalization precoding. Unlike previously, assuming heterogeneous Ricean fading, we utilize the well known affine approximation to predict the expected sum capacity difference between both precoder types (optimal and sub-…
In this paper, we study the hybrid precoding structures over limited feedback channels for massive multiuser multiple-input multiple-output (MIMO) systems. We focus on the system performance of hybrid precoding under a more realistic hardware network model, particularly, with inevitable dissipation. The effect of quantized analog and digital precoding is characterized. We investigate the spectral efficiencies of two typical hybrid precoding structures, i.e., the sub-connected structure and the fully-connected structure. It is revealed that increasing signal power can compensate the performance…
MIMO systems are considered as most promising for wireless communications. However, with an increasing number of radio front ends the corresponding energy consumption and costs become an issue, which can be relieved by the utilization of low-resolution quantizers. In this study we propose an optimal precoding algorithm constrained to constant envelope signals and phase quantization that maximizes the minimum distance to the decision threshold at the receivers using a branch-and-bound strategy. The proposed algorithm is superior to the existing methods in terms of bit error rate. Numerical resu…
In this letter, we study the performance of a downlink multiuser massive multiple-input multiple-output (MIMO) system with sub-connected structure over limited feedback channels. Tight rate approximations are theoretically analyzed for the system with pure analog precoding and hybrid precoding. The effect of quantized analog and digital precoding is characterized in the derived expressions. Furthermore, it is revealed that the pure analog precoding outperforms the hybrid precoding using maximal-ratio transmission (MRT) or zero forcing (ZF) under certain conditions, and we theoretically charact…
This paper considers the problem of constant envelope (CE) precoder designs for multiuser massive MISO downlink channels. The use of CE signals allows one to employ low-cost radio frequency chains and thereby facilitates the implementation of massive MIMO. However, the subsequent CE precoder designs are usually challenging owing to the non-convex CE constraints. The existing CE precoder designs consider minimization of some measures on the distortion levels of the received symbols, and they usually aim at improving the symbol-error rate (SER) performances. In this paper we formulate a minimum …
Aiming at maximizing the achievable sum-rate of wideband multiuser mmWave massive MIMO systems, the hybrid precoding is studied. Since each computation of the achievable sum-rate can be performed only after the analog precoder and digital precoder are both determined, the maximization of the achievable sum-rate has intractable computational complexity. By introducing the interference free (IF) achievable sum-rate, the design of the analog and digital precoders can be decoupled. To avoid the beam conflict and maximize the IF achievable sum-rate, a Hungarian-based codeword selection algorithm is…
Precoding design exploiting deep learning methods has been widely studied for multiuser multiple-input multiple-output (MU-MIMO) systems. However, conventional neural precoding design applies black-box-based neural networks which are less interpretable. In this paper, we propose a deep learning-based precoding method based on an interpretable design of a neural precoding network, namely iPNet. In particular, the iPNet mimics the classic minimum mean-squared error (MMSE) precoding and approximates the matrix inversion in the design of the neural network architecture. Specifically, the proposed …
This study proposes a symbol-level precoding algorithm based on the minimum mean squared error design objective under a strict per antenna power constraint for PSK modulation. The proposed design is then formulated in the standard form of a second-order cone program, allowing for an optimal solution via the interior point method. Numerical results indicate that the proposed design is superior to the existing approaches in terms of bit-error-rate for the low and intermediate SNR regime.
Consider the following problem: A multi-antenna base station (BS) sends multiple symbol streams to multiple single-antenna users via precoding. However, unlike conventional multiuser precoding, the transmitted signals are subjected to binary, unit-modulus, or even discrete unit-modulus constraints. Such constraints arise in the one-bit and constant-envelope (CE) massive MIMO scenarios, wherein high-resolution digital-to-analog converters (DACs) are replaced by one-bit DACs and phase shifters, respectively, for cutting down hardware cost and energy consumption. Multiuser precoding under one-bit…
We propose a unitary precoding scheme, namely polar-precoding, to improve the performance of polar-coded MIMO systems. In contrast to the traditional design of MIMO precoding criteria, the proposed polar-precoding scheme relies on the \emph{polarization criterion}. In particular, the precoding matrix design comprises two steps. After selecting a basic matrix for maximizing the capacity in the first step, we design a unitary matrix for maximizing the polarization effect among the data streams without degrading the capacity. Our simulation results show that the proposed polar-precoding scheme ou…
The high energy consumption of massive multi-input multi-out (MIMO) system has become a prominent problem in the millimeter wave(mm-Wave) communication scenario. The hybrid precoding technology greatly reduces the number of radio frequency(RF) chains by handing over part of the coding work to the phase shifting network, which can effectively improve energy efficiency. However, conventional hybrid precoding algorithms based on mathematical means often suffer from performance loss and high computational complexity. In this paper, a novel BP-neural-network-enabled hybrid precoding algorithm is pr…
Aiming at maximizing the energy efficiency (EE) of multicast multibeam satellite communications, we consider the precoding design under the total power and quality of service (QoS) constraints. Since the original EE maximization problem is nonconvex, it is sequentially converted into a concave-convex fractional programming problem by introducing some variables and using the first-order Taylor low bound approximation. Based on the Charnes-Cooper transformation, it is further converted into a convex problem. Then an iterative algorithm is presented to design the energy efficient precoding. To fi…
To enable user diversity and multiplexing gains, a fully digital precoding multiple input multiple output (MIMO) architecture is typically applied. However, a large number of radio frequency (RF) chains make the system unrealistic to low-cost communications. Therefore, a practical three-stage hybrid analogue-digital precoding architecture, occupying fewer RF chains, is proposed aiming for a non-orthogonal IoT signal in low-cost multiuser MIMO systems. The non-orthogonal waveform can flexibly save spectral resources for massive devices connections or improve data rate without consuming extra sp…
In this paper, downlink (DL) precoding and power allocation strategies are identified for a time-division-duplex (TDD) multi-cell multi-user massive Full-Dimension MIMO (FD-MIMO) network. Utilizing channel reciprocity, DL channel state information (CSI) feedback is eliminated and the DL multi-user MIMO precoding is linked to the uplink (UL) direction of arrival (DoA) estimation through estimation of signal parameters via rotational invariance technique (ESPRIT). Assuming non-orthogonal/non-ideal spreading sequences of the UL pilots, the performance of the UL DoA estimation is analytically char…
We propose a deep learning-based channel estimation, quantization, feedback, and precoding method for downlink multiuser multiple-input and multiple-output systems. In the proposed system, channel estimation and quantization for limited feedback are handled by a receiver deep neural network (DNN). Precoder selection is handled by a transmitter DNN. To emulate the traditional channel quantization, a binarization layer is adopted at each receiver DNN, and the binarization layer is also used to enable end-to-end learning. However, this can lead to inaccurate gradients, which can trap the receiver…
In this paper, we address the symbol level precoding (SLP) design problem under max-min SINR criterion in the downlink of multiuser multiple-input single-output (MISO) channels. First, we show that the distance preserving constructive interference regions (DPCIR) are always polyhedral angles (shifted pointed cones) for any given constellation point with unbounded decision region. Then we prove that any signal in a given unbounded DPCIR has a norm larger than the norm of the corresponding vertex if and only if the convex hull of the constellation contains the origin. Using these properties, we …
