Precoder Design Algorithm Research Articles

Cross-Layer Optimization for Industrial Internet of Things in NOMA-Based C-RANs

This article investigates nonorthogonal multiple access (NOMA)-based cloud radio access networks (C-RANs), where edge caching is adopted to cut down the crowdedness of the fronthaul links. We aim to maximize the energy efficiency (EE) by jointly optimizing the power allocation, analog, and digital precoding, which turns out to be an intractable nonconvex optimization problem. To tackle this problem, we first select cluster heads using the selecting cluster-head (SCH) algorithm, where the analog precoding matrix can be resolved by means of maximizing the array gains. Then, the device grouping algorithm is proposed to group devices according to the equivalent channel correlations, and thus, the NOMA devices in the same beam are capable of sharing the same digital precoding vector. Finally, the joint digital precoding design and power allocation algorithm is proposed to decompose the resultant optimization problem into two subproblems and solve them iteratively by applying the Taylor expansion operation and the minimum mean square error (MMSE) detection. Simulation results validate that the proposed NOMA-based C-RANs with a hybrid precoding (HP) scheme can achieve higher spectral efficiency and EE than the traditional orthogonal multiple access (OMA)-based approach and two-stage HP scheme.

Sum-Rate-Optimal Statistical Precoding for FDD Massive MIMO Downlink With Deterministic Equivalents

Statisticalprecoding is considered as a promising technique to release the channel state information (CSI) acquisition overhead. This article investigates a linear precoder design for frequency-division duplexing (FDD) massive MIMO downlink with only statistical CSI. We use a beam-based statistical channel model to capture the spatial correlation characteristics of the channels. The objective of the precoder design is to maximize the ergodic sum-rate under total power constraint. Based on the minorize-maximize (MM) algorithm, a stationary solution of the ergodic sum-rate maximization problem can be obtained. The stationary solution is shown to be the same as the optimal solution to a stochastic weighted minimum mean square error (SWMMSE) problem. Further, we establish the approximations for rate expressions with deterministic equivalent. The deterministic equivalents of ergodic rates are only related to the precoding matrices and statistical CSI. According to these closed-form rate expressions, we propose a linear precoder design algorithm and obtain tractable expressions for precoding matrices. Numerical comparisons with the existing precoding approach demonstrate the significant advantages of the developed algorithm.

Robust Precoding for 3D Massive MIMO Configuration With Matrix Manifold Optimization

This paper investigates robust downlink precoding for three-dimensional (3D) massive multi-input multi-output (MIMO) configuration with matrix manifold optimization. Starting with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> channel model, we formulate the robust precoder design to maximize an upper bound of ergodic weighted sum-rate under a total power budget. We derive the generalized eigenvector structure for optimal precoder with matrix manifold optimization. However, since the precoding of multiple users is coupled in the structure, we maximize the objective function for each user in alternation and prove the solution of each individual problem is the generalized eigenvector corresponding to the maximum generalized eigenvalue. In accordance with this, we design an iterative algorithm and present its convergence analysis. Furthermore, we propose a Riemannian conjugate gradient (RCG) method to solve the generalized eigenvalue problem (GEP) for higher efficiency in the precoder design algorithm.

Location-Based Hybrid Precoding Schemes and QoS-Aware Power Allocation for Radar-Aided UAV–UGV Cooperative Systems

Unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) complement each other, promising a variety of benefits for unmanned cooperative systems. When infrastructures for communication are unavailable, such as disaster relief and patrol mission in sparsely populated areas, UGVs can be controlled to go to the esignated areas with the aid of a UAV. Specifically, the UAV hovers over the UGVs, sending commands to the UGVs and obtaining location information from the UGVs. In this paper, we consider integrating millimeter wave communication and UAV–UGV cooperative system. For high mobile unmanned cooperation systems, we develop two joint radar-aided hybrid precoding schemes, which are suitable for a fully connected (FC) hybrid precoding structure and partially connected (PC) hybrid precoding, respectively. Specifically, an effective hybrid precoding scheme is first proposed by using location information to jointly design hybrid precoding and power allocation. Moreover, we also derive the radar parameter estimation problem Cramér-Rao lower bound (CRLB). In order to ensure the minimum quality-of-service (QoS) of UGVs, we propose a QoS-aware power allocation scheme based on the difference-of-two-convex-function (D.C.) programming. Finally, a heuristic hybrid precoding design algorithm, where the analog precoding matrix is usually implemented by low-resolution phase shifters (PSs), is proposed based on antenna dynamic grouping and radar parameter acquisition, with the aim of maximizing the sum-rate of the UAV–UGV cooperative systems. Extensive computer simulation results indicated the validity of the proposed radar-aided location-based hybrid precoding schemes in the UAV–UGV heterogeneous cooperative system.

Machine Learning-Enabled Joint Antenna Selection and Precoding Design: From Offline Complexity to Online Performance

We investigate the performance of multi-user multiple-antenna downlink systems in which a base station (BS) serves multiple users via a shared wireless medium. In order to fully exploit the spatial diversity while minimizing the passive energy consumed by radio frequency (RF) components, the BS is equipped with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> RF chains and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> antennas, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M &lt; N$ </tex-math></inline-formula> . Upon receiving pilot sequences to obtain the channel state information (CSI), the BS determines the best subset of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> antennas for serving the users. We propose a joint antenna selection and precoding design (JASPD) algorithm to maximize the system sum rate subject to a transmit power constraint and quality of service (QoS) requirements. The JASPD algorithm overcomes the non-convexity of the formulated problem via a doubly iterative algorithm, in which an inner loop successively optimizes the precoding vectors, followed by an outer loop that tests all valid antenna subsets. Although approaching (near) global optimality, the JASPD suffers from a combinatorial complexity, which may limit its application in real-time network operations. To overcome this limitation, we propose a learning-based antenna selection and precoding design algorithm (L-ASPA), which employs a deep neural network (DNN) to establish underlaying relations between key system parameters and the selected antennas. The proposed L-ASPD algorithm is robust against the number of users and their locations, the transmit power of the BS, as well as the small-scale channel fading. With a well-trained learning model, it is shown that the L-ASPD algorithm significantly outperforms baseline schemes based on the block diagonalization and a learning-assisted solution for broadcasting systems and achieves a better effective sum rate than that of the JASPA under limited processing time. In addition, we observed that the proposed L-ASPD algorithm can reduce the computation complexity by 95% while retaining more than 95% of the optimal performance.

Hybrid Precoding Design for Energy Efficient Millimeter-Wave Massive MIMO Systems

In this letter, we propose a hybrid precoding design algorithm by utilizing RF chain selection to optimize the number of RF chains to achieve high energy efficiency (EE) with slightly spectral efficiency (SE) performance degradation. In this algorithm, we firstly reformulate the energy efficiency optimization problem, and resolve the hybrid precoding optimization problem with alternating minimization method to seek the approximate optimal analog precoder and digital precoder under the proposed structure. Then, we perform the transmitter RF chain selection to find the optimal RF chain set corresponding to better EE and SE performance. Simulation results show the proposed algorithm achieves the good trade-off between EE and SE performance when the transmit power constraint is no larger than 30 dBm.

Precoding Design for Energy Efficiency of Multibeam Satellite Communications

Instead of merely improving the spectral efficiency, improving the energy efficiency (EE) is another important concern for multibeam satellite systems, due to the power constraint of satellites. However, so far there has been no detailed work on the precoding design concerning the EE for multibeam satellite. In this letter, the EE maximization problem is investigated for multibeam satellite systems under the total power constraint as well as the quality of service constraints. Precoding design algorithms based on zero-forcing (ZF) and sequential convex approximation (SCA) are presented, respectively. In particular, these algorithms are verified by the real measured channel data of multibeam satellite systems. Numerical results show that the precoding algorithm based on SCA outperforms that based on ZF. It is also implied that the EE cannot be always improved by solely increasing the power of the satellite, while reducing the satellite operation power is an effective way for the EE improvement.

Joint Design of Beam Selection and Precoding Matrices for mmWave MU-MIMO Systems Relying on Lens Antenna Arrays

Wireless transmission relying on lens antenna arrays is becoming more and more attractive for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems using a limited number of radio frequency chains due to the lens' energy-focusing capability. In this paper, we consider the joint design of the beam selection and precoding matrices in order to maximize the sum-rate of a downlink single-sided lens MU-MIMO mmWave system under transmit power constraints. We first formulate the optimization problem into a tractable form using the popular weighted minimum mean squared error (WMMSE) approach. To solve this problem, we then propose an efficient joint beam selection and precoding design algorithm based on the innovative penalty dual decomposition method. To reduce the design complexity, we also propose a simplified algorithm by combining the interference-aware beam selection scheme with the WMMSE approach. Simulation results demonstrate that our proposed algorithms can converge in a few iterations and achieve near-optimal performance when compared to the fully digital precoding scheme, thus enabling them to outperform the competing methods.

Precoding and Cooperative Jamming in Multi- Antenna Two-Way Relaying Wiretap Systems Without Eavesdropper’s Channel State Information

This paper studies secrecy communications in a multi-antenna two-way relaying wiretap system. Each source node transmits user and jamming signals with distinct precoding vectors. Based on the assumption that the channel state information relating to the eavesdropper is unknown by the legitimate nodes, new precoding design algorithms are proposed. The jamming signals are designed to ensure that minimum interference is perceived by the other source node. The precoding vectors of the user signals are designed to form two parallel vectors in the equivalent wiretap channel at the eavesdropper. Two algorithms are proposed based upon the zero-forcing and matched-filter schemes, which are dubbed the selective zero-forcing-based precoding (SZFP) and matched-filter-based precoding schemes. Analytical and simulation results are presented to demonstrate that the SZFP algorithm is more applicable when the eavesdropper is equipped with a large number of antennas or the eavesdropper’s channels are in good condition.

Joint Source and Relay Precoding in Multiantenna Millimeter-Wave Systems

This paper considers the joint source and relay precoding design for millimeter-wave (mm-wave) systems under the assumption that the source, relay, and destination nodes are equipped with multiple antennas. We focus on the rate maximization problem with the per antenna power constraints at the source and relay while taking into account the computational complexity and sparse characteristics of mm-wave channels. We solve this problem as follows. First, the precoding problem is formulated by exploiting the sparse and low-rank structures of mm-wave channels which is nonconvex. Second, we reformulate this nonconvex problem into two semidefinite programming (SDP) subproblems, each having a rank one constraint. Third, we propose two algorithms to solve these two SDP subproblems: interior-point-based and low complexity algorithms. Finally, the original rate maximization problem is examined by iteratively utilizing the solutions of these SDP problems. The proposed interior-point-based method to solve the SDP problem uses the standard convex optimization tools followed by the random vector generation scheme to get the rank one solution. However, the proposed low complexity algorithm examines the SDP problem in one-dimensional spatial signal space (i.e., without rank relaxation) via a new augmented Lagrangian function method. Simulation results show that both algorithms achieve good performances, and the latter one is much faster than the former one with a slight decrease in performance. In addition, both algorithms achieve superior performances compared to the existing precoding design algorithms.

Linear Relaying Design for Spectrum Sharing Non-regenerative MIMO Cognitive Multiple-Relay Systems

In this paper, we study optimal precoding matrix for spectrum sharing multiple-input multiple-output (MIMO) cognitive multiple-relay systems. Our aim is to maximize the system capacity subject to the total relay transmit power constraint and the interference power constraint at the primary user. For general case, all the nodes have multiple antennas. The precoder design problem is a non-convex problem. Currently there is no global optimal solution for it. We propose a suboptimal algorithm in which we first transform the original precoder design problem to a unitary matrix constrained problem. And then, we develop a modified Riemannian steepest descent algorithm (MRSDA) to solve it. For the special case that the secondary user has a single antenna and other nodes have multi-antennas, we propose an optimal solution based on rank-one decomposition theorem to transform the original problem into a semidefinite programming. Simulation results demonstrate the effectiveness of the proposed precoding matrix design algorithms.

Practical linear precoder design for finite alphabet multiple‐input multiple‐output orthogonal frequency division multiplexing with experiment validation

A low complexity precoding method is proposed for practical multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. Based on the two-step optimal precoder design algorithm that maximises the lower bound of the mutual information with finite-alphabet inputs, the proposed method simplifies the precoder design by fixing the right singular vectors of the precoder matrix, eliminating the iterative optimisation between the two steps, and discretising the search space of the power allocation vector. For a 4 × 4 channel, the computational complexity of the proposed precoder design is reduced to 3 and 6% of that required by the original two-step algorithm with quadrature phase shift keying (QPSK) and 8 phase-shift keying (8PSK), respectively. The proposed method achieves nearly the same mutual information as the two-step iterative algorithm for a large range of signal-to-noise ratio (SNR) region, especially for large MIMO size and/or high constellation systems. The proposed precoding design method is applied to a 2 × 2 MIMO-OFDM system with 2048 subcarriers by designing 1024 precoders for extended channel matrices of size 4 × 4. A transceiver test bed implements these precoding matrices in comparison with other existing precoding schemes. Indoor experiments are conducted for fixed-platform non-line-of-sight channels, and the data processing results show that the proposed precoding method achieves the lowest bit error rate compared with maximum diversity, classic water-filling and channel diagonalisation methods.

基于VSINR的分布式多小区MU-MIMO预编码矩阵设计

In this paper, we propose a distributed precoder design algorithm based on virtual signal-to-interference- plus-noise ratio (VSINR) for multi-cell multi-user multiple-input multiple-output (MU-MIMO) system. As the problem of finding the optimal precoder to maximize the system throughput is non-convex and non-trivial, it is important to find low-complexity solutions. Motivated by the recent results in the distributed signal-to-leakageplus- noise ratio (SLNR) model, we aim to establish equivalence between the distributed VSINR maximization problem and the original centralized throughput maximization problem by designing the proper correction factor, and the correction factor is constructed to satisfy the equivalence condition that the sub-gradients w.r.t the precoder of the VSINR model and the system throughput model become zero at the same time. Then we can build a VSINR model which is proved to be Pareto optimal, thus the entire system throughput can be optimized by using precoders based on an appropriate distributed VSINR model. Finally we can distributedly solve the corresponding Pareto optimal precoding matrix problem based on local CSI (CSI, channel state information) and a closed-form solution of optimal transmitter precoder can be derived. Simulation results show that the proposed precoder can enhance the system throughput with varying transmitting SNRs, active users and interference factors, and outperform other existing distributed precoder design algorithms such as ZF, MRT and SLNR algorithms. Besides, the iteration in our proposed algorithm converges fast within 3 iterations, the approximate optimum can be achieved, and within 20 iterations, and the global optimum can be obtained. Therefore, our proposed algorithm can bring a significant increase to the average cell throughput while effectively saving the system overhead.

Joint Source and Relay Precoding Designs for MIMO Two-Way Relaying Based on MSE Criterion

Properly designed precoders can significantly improve the spectral efficiency of multiple-input multiple-output (MIMO) relay systems. In this paper, we investigate joint source and relay precoding design based on the mean-square-error (MSE) criterion in MIMO two-way relay systems, where two multi-antenna source nodes exchange information via a multi-antenna amplify-and-forward relay node. This problem is non-convex and its optimal solution remains unsolved. Aiming to find an efficient way to solve the problem, we first decouple the primal problem into three tractable sub-problems, and then propose an iterative precoding design algorithm based on alternating optimization. The solution to each sub-problem is optimal and unique, thus the convergence of the iterative algorithm is guaranteed. Secondly, we propose a structured precoding design to lower the computational complexity. The proposed precoding structure is able to parallelize the channels in the multiple access (MAC) phase and broadcast (BC) phase. It thus reduces the precoding design to a simple power allocation problem. Lastly, for the special case where only a single data stream is transmitted from each source node, we present a source-antenna-selection (SAS) based precoding design algorithm. This algorithm selects only one antenna for transmission from each source and thus requires lower signalling overhead. Comprehensive simulation is conducted to evaluate the effectiveness of all the proposed precoding designs.

Adaptive DSL Crosstalk Precancellation Design Using Low-Rate Feedback From End Users

The performance of extensions of digital subscriber line to higher data rates (VDSL) is limited by the effects of crosstalk among the wires in a bundle. For the downstream, a precoder can compensate for this. Without knowledge of the crosstalk channel matrix, the problem is to compute a suitable precoder based on limited feedback from the receivers. In this letter, an adaptive precoder design algorithm is derived. The algorithm works on a per-tone basis and assumes that each receiver sends back the sign of the symbol error to the transmitter. The algorithm computes the precoder iteratively using this information, without the need to estimate the crosstalk channel as an intermediate step. The asymptotic and acquisition performance is verified by simulations