Hybrid precoding for mmWave massive MIMO systems with generalized triangular decomposition

Hybrid precoding has been recognized as a promising technology for millimeter wave-based massive MIMO systems. As an improved scheme for conventional hybrid precoding structures, the adaptively-connected structure requires low hardware cost and has attractive system performance. In this paper, we propose an adaptive hybrid precoding (AHP) scheme for multi-user massive MIMO systems. The hybrid precoder design is formulated as minimizing the difference between the hybrid precoder and the full digital precoder, and a rough design and revision based AHP (RDR-AHP) algorithm is developed to seek for a near-optimal solution. The proposed RDR-AHP algorithm is achieved by a three-step process including rough design of baseband precoder based on singular value unification, stepwise design of radio frequency precoder and baseband precoder revision. Simulation results demonstrate that the proposed scheme achieves higher spectral efficiency than existing schemes with same hardware cost in millimeter wave channel.

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.

International audience

Hybrid precoding design can be challenging for broadband millimeter-wave (mmWave) massive MIMO due to the frequency-flat analog precoder in radio frequency (RF). Prior broadband hybrid precoding work usually focuses on fully-connected array (FCA), while seldom considers the energy-efficient partially-connected subarray (PCS) including the fixed subarray (FS) and dynamic subarray (DS). Against this background, this paper proposes a machine learning based broadband hybrid precoding for mmWave massive MIMO with DS. Specifically, we first propose an optimal hybrid precoder based on principal component analysis (PCA) for the FS, whereby the frequency-flat RF precoder for each subarray is extracted from the principle component of the optimal frequency-selective precoders for fully-digital MIMO. Moreover, we extend the PCA-based hybrid precoding to DS, where a shared agglomerative hierarchical clustering (AHC) algorithm developed from machine learning is proposed to group the DS for improved spectral efficiency (SE). Finally, we investigate the energy efficiency (EE) of the proposed scheme for both passive and active antennas. Simulations have confirmed that the proposed scheme outperforms conventional schemes in both SE and EE.

The study of hybrid precoder has been focused on the application of the low-resolution phase shifters (PSs) since they can reduce the power consumption of RF chains. In this paper a heuristic iteration algorithm is proposed to design hybrid precoder and combiner in mmWave massive MIMO systems to improve the PSs quantization performance using MMSE criterion. This heuristic algorithm first builds a cost function, which can continuously converge to the optimal solution of the quantized shifter phases with constant modulus constraints. Simulation results show that the proposed design of hybrid precoder can achieve significant performance with low-complexity in mmWave massive MIMO systems.

Large-scale antenna arrays which provide high beamforming gain are commonly used to combat the serious path-loss in millimeter wave (mmwave) systems. Traditionally, the beamforming is completely implemented at the baseband or the digital domain, which, however, causes high hardware cost and power consumption. The hybrid precoding method which can effectively avoids these problems is, therefore, more attractive. However, the design of hybrid precoder is challenging due to the constant modules of phase shifters. To solve this problem, we propose a novel hybrid precoding approach from the perspective of geometric construction in this paper. The new method can significantly reduce the number of RF chains meanwhile still achieve an almost optimal performance in terms of sum rate. The proposed algorithm is compared with the popular orthogonal matching pursuit algorithm (OMP) via numerical simulations, and shows that our proposal can increase the system spectral efficiency with reduced computational complexity.

Due to its inherent ability in reducing hardware cost and power consumption while maintaining high system capacity, hybrid precoding is deemed as one of the key technologies in the upcoming 5G/6G millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, it is challenging to design high performance hybrid precoders/combiners with low computational complexity. In this paper, based on the singular value decomposition (SVD) technique and the concept of equivalent channel, joint hybrid precoding strategies with high spectral-efficiency and low complexity are proposed for both single-user and multi-user massive MIMO systems. Specifically, for single-user massive MIMO scenarios, after transforming the design of hybrid beamforming into the problem of maximizing the square of sum eigenvalues for an equivalent channel, a two-stage successive method is conceived to design the analog precoder and combiner jointly, and the corresponding equivalent channel is constructed. Then, the digital precoding and combining operations are realized directly by applying the SVD technique to the matrix of equivalent channel. Meanwhile, the hybrid precoding strategy is extended to the multi-user scenario for achieving high performance resultant from multi-user diversity. Extensive simulations are conducted to verify the effectiveness of the precoding/combing schemes. The results show that our proposed schemes can achieve superior performance with lower complexity compared to the existing ones.

Characterizing rate regions provides a critical theoretical foundation for evaluating multi-user communication system performance, yet this aspect remains underexplored in hybrid precoding (HP) research. To bridge this gap, we develop a nonlinear HP scheme incorporating dirty-paper coding (DPC) for weighted sum-rate maximization (max-WSR) in massive multiple-input multiple-output broadcast channels (MIMO-BC), enabling characterization of achievable rate regions in hybrid architectures. Exploiting uplink-downlink duality, we reformulate the intractable downlink nonlinear HP as an equivalent more tractable uplink hybrid combining problem. Subsequently, the downlink nonlinear HP is derived from the dual uplink hybrid combiner through joint transceiver optimization. Formulating the max-WSR problem in this manner facilitates the characterization of achievable rate regions. The ergodic rate region quantifies the average rate vectors over channel fading states, thereby establishing a theoretical foundation for multi-user system analysis. Numerical results demonstrate that the achievable rate region of the proposed DPC-based nonlinear HP closely approaches the optimal capacity boundary.

When wireless transmission is performed over the bandwidth in the order of a gigahertz, high-resolution analog-to-digital converters (ADCs), and the large number of radio frequency chains significantly increase the power consumption. To address this issue, one promising technique is to use low-resolution, even one-bit ADCs. Another promising technique is to apply a hybrid precoding architecture to reduce the number of RF chains. In this paper, we propose to combine those techniques to reduce the hardware costs in multi-input multi-output system. Our objective is to optimize the hybrid precoder with the aim of increasing the achievable rate. To this end, we first derive an expression for the achievable rate in flat fading channels based on the Bussgang theorem, which is able to reformulate the nonlinear quantitative process as a linear function with identical first- and second-order statistics. To solve the non-convex hybrid precoding design problem, we treat the hybrid precoding design as a matrix factorization problem, which can be solved with an efficient alternating minimization algorithm. That is, we solve the digital precoder and the analog precoder in an alternative way in two separate subproblems. To find the optimal precoder in the first subproblem, we first prove the optimal structure of the digital precoding matrix. With it, we transfer the digital precoding design to a power allocation problem, the closed-form solution of which is then optimally found by using Karush–Kuhn–Tucker conditions. In the second subproblem, due to the non-convex modulus-norm constraint, it is challenging to directly solve the analog precoder. To resolve this problem, we propose to optimize the phases in the analog precoding matrix and adopt the subgradient algorithm to find the local optimal solution. Our simulation results show that the proposed hybrid precoding design effectively improves the achievable rates.

In this paper, we investigate a new approach for simultaneous wireless information and power transfer (SWIPT) in point-to-point multiple-input multiple-output (MIMO) system with spatial switching (SS) reception. The new approach is based on the generalized triangular decomposition (GTD). The approach takes advantage of the GTD structure to allow the transmitter to use the strongest subchannel jointly for energy harvesting and information exchange while these transmissions can be separated at the receiver to comply with the SS system requirements. An optimal solution is developed in the paper for SWIPT based on GTD that jointly obtains the optimal subchannels assignment and maximizes the total data rate while meeting the minimum requirement of the harvested energy with limited total transmitted power. The theoretical and numerical results presented in this paper show that the proposed approach significantly outperforms the state of the art spatial domain SWIPT systems based on the singular value decomposition (SVD).

In this letter, we propose a hybrid analog–digital precoder design to enhance the physical layer security of millimeter-wave (mmWave) multiple-input single-output (MISO) systems with partial channel knowledge. We derive a closed-form expression for the average signal-to-interference-and-noise ratio (SINR) of the eavesdropper (Eve) as a function of the hybrid precoder. Using the average SINRs of Eves, we derive a secrecy rate lower bound. Then, we propose a low-complexity artificial-noise-aided (AN-aided) hybrid precoder design to maximize the secrecy rate lower bound. Numerical results show that the proposed AN-aided hybrid precoder achieves comparable performance to that of the fully digital precoder, with much lower hardware complexity. Moreover, the proposed AN-aided hybrid precoder outperforms the existing hybrid precoder design. Effect of finite-resolution phase shifters on the proposed precoder is also investigated.

Generalized triangular decomposition (GTD) has been found to be useful in the field of signal processing, but the feasibility of the related hardware has not yet been established. This paper presents (for the first time) a GTD processor architecture with a parallel algorithm. The proposed parallel GTD algorithm achieves an increase in speed of up to 1.66 times, compared to the speed of its conventional sequential counterpart for an 8 ×8 matrix. For hardware implementation, the proposed reconfigurable architecture is capable of computing singular value decomposition (SVD), geometric mean decomposition (GMD), and GTD for matrix sizes from 1 ×1 to 8 ×8. The proposed GTD processor is composed of 16 processing cores in a heterogeneous systolic array. Computations are distributed over area-efficient coordinate rotation digital computers (CORDICs) to achieve a high throughput. To establish the validity of the concept, a GTD processor was designed and implemented. The latency constraint of 16 μs specified in the 802.11ac standard is adopted for the hardware realization. The proposed design achieves a maximum throughput of 83.3k matrices/s for an 8 ×8 matrix at 112.4 MHz. The estimated power and core area are 172.7 mW and 1.96 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , respectively, based on standard 90 nm CMOS technology.

In this paper, a new approach, based on the generalized triangular decomposition (GTD), is proposed for simultaneous wireless information and power transfer (SWIPT) in the spatial domain for a point-to-point multiple-input multiple-output (MIMO) system. The proposed approach takes advantage of the GTD structure to allow the transmitter to use the strongest eigenchannel jointly for energy harvesting and information exchange while these transmissions can be separated at the receiver. The optimal structure of the GTD that maximizes the total information rate constrained by a given power allocation and a required amount of energy harvesting is derived. An algorithm is developed that minimizes the total transmitted power for given information rate and energy harvesting constraints with a limited total power at the transmitter. Both theoretical and simulation results show that our proposed GTD based SWIPT outperforms singular value decomposition (SVD) based SWIPT. This is due to the flexibility introduced by the GTD to increase the energy harvested via interstream interference.

Hybrid precoding is a cost-effective approach to support directional transmissions for millimeter-wave (mmWave) communications, but its precoder design is highly complicated. In this paper, we propose a new hybrid precoder implementation, namely the double phase shifter (DPS) implementation, which enables highly tractable hybrid precoder design. Efficient algorithms are then developed for two popular hybrid precoder structures, i.e., the fully- and partially-connected structures. For the fully-connected one, the RF-only pre-coding and hybrid precoding problems are formulated as a least absolute shrinkage and selection operator problem and a low-rank matrix approximation problem, respectively. In this way, computationally efficient algorithms are provided to approach the performance of the fully digital one with a small number of radio frequency (RF) chains. On the other hand, the hybrid precoder design in the partially-connected structure is identified as an eigenvalue problem. To enhance the performance of this cost-effective structure, dynamic mapping from RF chains to antennas is further proposed, for which a greedy algorithm and a modified K-means algorithm are developed. Simulation results demonstrate the performance gains of the proposed hybrid precoding algorithms over existing ones. It shows that, with the proposed DPS implementation, the fully-connected structure enjoys both satisfactory performance and low design complexity while the partially-connected one serves as an economic solution with low hardware complexity.

The orthogonal matching pursuit (OMP) algorithm is widely used because of its simple algorithmic structure, the linear magnitude of its computational complexity and other advantages. Algorithms of improved and extended OMP types are continually emerging. To make the OMP algorithm more suitable for the new transmission requirements of the fifth-generation (5G) network, the orthogonal matching pursuit with multiple users (OMP_mu) algorithm is proposed for cell-free massive multi-input multi-output (MIMO) networks with multiuser spatial index modulation. The OMP_mu algorithm considers the constraint condition for the sparsity of each user on the basis of each iterative search in the OMP algorithm until all users meet the constraint. The simulation results show that compared with the original OMP algorithm, the OMP_mu algorithm has a greatly improved demodulation performance. Compared with the orthogonal matching pursuit step-by-step (OMP_step) algorithm, which takes the user sparsity constraint condition into account in two steps, the OMP_mu algorithm greatly reduces the operation time and number of iterations while achieving a slightly better performance. The OMP_mu algorithm provides an effective reference for the application of spatial index modulation in cell-free massive MIMO networks.