Digital Precoding Research Articles

Hybrid RF-Baseband Precoding for Cooperative Multiuser Massive MIMO Systems With Limited RF Chains

Massive multiple-input multiple-output (massive MIMO) has been studied to improve the throughput in cellular communication systems via spatial degrees of freedom and array gain. However, in massive MIMO systems, due to the hardware cost considerations, it is infeasible to install a radio frequency (RF) chain for each antenna. To deploy massive MIMO within reasonable hardware cost, hybrid precoding is proposed in which the signal is processed by a low-dimensional digital baseband precoder and a high-dimensional analog RF precoder. On the other hand, cooperative transmission is another way to enhance system throughput, in which base stations (BSs) can jointly transmit to a user. In this paper, we first investigate the hybrid precoder design for cooperative multiuser massive MIMO systems. We propose hybrid precoding algorithms for two performance metrics: weighted sum rate and max-min fairness. We also propose a low complexity user pairing for both precoder designs. Numerical results show that the proposed hybrid precoding algorithms outperform existing hybrid precoding algorithms for non-cooperative transmissions, and perform closely compared with existing digital precoding algorithms for cooperative transmissions, when the number of users does not exceed the total number of RF chains of the BSs in cooperative (i.e., the largest possible channel rank). In summary, this paper provides a hybrid precoder design guideline for existing and developing cellular communication systems, including Long Term Evolution-Advanced and the fifth generation cellular systems.

Massive MIMO Channel Subspace Estimation From Low-Dimensional Projections

Massive MIMO is a variant of multiuser MIMO (Multi-Input Multi-Output) system, where the number of base-station antennas $M$ is very large and generally much larger than the number of spatially multiplexed data streams. Unfortunately, the front-end A/D conversion necessary to drive hundreds of antennas, with a signal bandwidth of 10 to 100 MHz, requires very large sampling bit-rate and power consumption. To reduce complexity, Hybrid Digital-Analog architectures have been proposed. Our work in this paper is motivated by one of such schemes named Joint Spatial Division and Multiplexing (JSDM), where the downlink precoder (resp., uplink linear receiver) is split into product of a baseband linear projection (digital) and an RF reconfigurable beamforming network (analog), such that only $m \ll M$ A/D converters and RF chains is needed. In JSDM, users are grouped according to similarity of their signal subspaces, and these groups are separated by the analog beamforming stage. Further multiplexing gain in each group is achieved using the digital precoder. Therefore, it is apparent that extracting the signal subspace of the $M$ -dim channel vectors from snapshots of $m$ -dim projections , with $m \ll M$ , plays a fundamental role in JSDM implementation. In this paper, we develop efficient subspace estimation algorithms that require sampling only $m=O(2 \sqrt{M})$ antennas and, for a given $p \ll M$ , return a $p$ -dim beamformer (subspace) that has a performance comparable with the best $p$ -dim beamformer designed from the full knowledge of the exact channel covariance matrix. We assess the performance of our proposed estimators both analytically and empirically via numerical simulations.

Channel Estimation and Hybrid Precoding for Millimeter-Wave MIMO Systems: A Low-Complexity Overall Solution

To enable multi-stream transmission and increase the achievable rate, a hybrid digital/analog precoding structure is usually adopted in millimeter-wave (mmWave) MIMO systems. However, it may require matrix operations with a scale of antenna size, which is generally large in mmWave communications. Moreover, the channel estimation is also rather time-consuming due to the large number of antennas at both Tx/Rx sides. In this paper, a low-complexity overall channel estimation and hybrid precoding approach is proposed. In the channel estimation phase, a hierarchical multi-beam search scheme is proposed to fast acquire $N_{\mathrm {S}}$ (the number of streams) multipath components (MPCs)/clusters with the highest powers. In the hybrid precoding phase, the analog and digital precodings are decoupled. The analog precoding is designed to steer along the $N_{\mathrm {S}}$ acquired MPCs/clusters at both Tx/Rx sides, shaping an $N_{\mathrm {S}}\times N_{\mathrm {S}}$ baseband effective channel, while the digital precoding is performed in the baseband with the reduced-scale effective channel. Performance evaluations show that, compared with the state-of-the-art scheme, while achieving a close or even better performance when the number of radio frequency chains or streams is small, both the time complexity of the channel estimation and the computational complexity of the hybrid precoding are reduced.

Artificial Noise Aided Hybrid Precoding Design for Secure mmWave MISO Systems with Partial Channel Knowledge

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.

毫米波大规模多用户MIMO的混合预编码研究

在毫米波大规模多输入多输出(MIMO)系统中，为了减小全数字预编码时硬件安装复杂度及安装费用，以及克服毫米波传输衰减大的问题，本文探讨一种线性混合预编码方法。首先分析了一个可渐近最优的线性模拟预编码方案，该方案可通过迭代处理就能实现。在此迭代模拟预编码基础上，本文进而在数字预编码方面考虑块对角化(BD)和最大比传输(MRT)两种线性方案，并在不同的参数下对MRT与BD进行仿真对比。仿真结果表明，在低信噪比和用户数少时，MRT性能优于BD，而在其它情况下，BD性能优于MRT。 In millimeter wave massive multiple-input multiple-output (MIMO) systems, in order to reduce installed hardware complexity and cost in full digital precoding, and to overcome the problem of large transmission loss in millimeter wave, this paper investigates a kind of hybrid precoding schemes with low complexity. This paper firstly analyzes a linear analog precoding scheme with asymptotically optimal performance, which can be implemented through iterative processing. Based on the iterative analog precoding scheme, this paper considers further the two linear digital precoding schemes with block diagonalization (BD) and maximum ratio transmission (MRT), respectively, and makes numerical comparison between the BD and the MRT for different kinds of parameters. The simulation results show that under the case with low SNR and a few users, the MRT has better performance than BD, and the BD has better performance than the MRT in the other cases.

Multiple-Beam Selection With Limited Feedback for Hybrid Beamforming in Massive MIMO Systems

Hybrid multiple-input multiple-output (MIMO) systems have been thought as a promising technology in future 5G. Compared with conventional digital MIMO systems, such a structure is equipped with fewer RF chains, which would reduce the computational complexity and hardware cost, and meanwhile additional analog beamforming is introduced to maintain the performance. However, scarce RF chains make channel state information acquisition difficult for analog beamforming. In this paper, we consider a practical hybrid beamforming, which includes zero-forcing (ZF) precoding in digital beamforming, and beam selection for analog beamforming. First, the statistic information of users (e.g., angle and distance) is utilized to construct an approximate channel for each user. Second, users individually evaluate the codebook and feedback the results, by which base station (BS) makes optimization and selects the final beams for analog beamforming. Finally, BS performs the digital baseband ZF precoding with the equivalent channel. In the process, we give two limited feedback methods for users, and two corresponding beam selection methods for BS. These methods are evaluated in the Rayleigh fading channels and mmWave channels. Simulation results show that our hybrid beamforming could approach performance of conventional digital precoding, and more RF chains could provide better performance. Moreover, proposed methods only require once feedback and effectively reduce the delay, and two feedback methods achieve a good tradeoff between performance and feedback cost.

Hybrid MMSE Precoding and Combining Designs for mmWave Multiuser Systems

Hybrid analog/digital precoding architectures are a low-complexity alternative for fully digital precoding in millimeter-wave (mmWave) MIMO wireless systems. This is motivated by the reduction in the number of radio frequency and mixed signal hardware components. Hybrid precoding involves a combination of analog and digital processing that enables both beamforming and spatial multiplexing gains in mmWave systems. This paper develops hybrid analog/digital precoding and combining designs for mmWave multiuser systems, based on the mean-squared error (MSE) criteria. In the first design with the analog combiners being determined at the users, the proposed hybrid minimum MSE (MMSE) precoder is realized by minimizing the sum-MSE of the data streams intended for the users. In the second design, both the hybrid precoder and combiners are jointly designed in an iterative manner to minimize a weighted sum-MSE cost function. By leveraging the sparse structure of mmWave channels, the MMSE precoding/combining design problems are then formulated as sparse reconstruction problems. An orthogonal matching pursuit-based algorithm is then developed to determine the MMSE precoder and combiners. Simulation results show the performance advantages of the proposed precoding/combining designs in various system settings.

Hybrid Precoding for mmWave Massive MIMO Systems With Partially Connected Structure

Hybrid precoding is widely studied in millimetre-wave (mmWave) massive MIMO systems due to low cost as well as low power consumption. In general, there are two kinds of hybrid precoding structures: one is fully connected structure (FCS), where each radio frequency (RF) chain is connected to all antennas, and the other is partially connected structure (PCS), where each RF chain is connected to a sub-array. In this paper, we investigate the optimal hybrid precoder design problem for mmWave massive MIMO systems based on PCS, since this kind of structure is more practical for antenna deployment. We first focus on the optimization of analog precoder (AP) and propose two AP design schemes for high signal-to-noise ratio (SNR) condition and low SNR condition, respectively. For each of the schemes, the original optimization problem is reformulated to single-stream optimal transmitter beamforming problem with per-antenna power constraint, which has an optimal solution. Then, the optimal digital precoder is obtained by water-filling algorithm after AP is determined. Moreover, upper bounds of the achievable data rate for the proposed schemes with closed-form expression are derived.

Low Complexity Hybrid Precoding Strategies for Millimeter Wave Communication Systems

Millimeter communication systems use large antenna arrays to provide good average received power and to take advantage of multi-stream MIMO communication. Unfortunately, due to power consumption in the analog front-end, it is impractical to perform beamforming and fully digital precoding at baseband. Hybrid precoding/combining architectures have been proposed to overcome this limitation. The hybrid structure splits the MIMO processing between the digital and analog domains, while keeping the performance close to that of the fully digital solution. In this paper, we introduce and analyze several algorithms that efficiently design hybrid precoders and combiners starting from the known optimum digital precoder/combiner, which can be computed when perfect channel state information is available. We propose several low complexity solutions which provide different trade-offs between performance and complexity. We show that the proposed iterative solutions perform better in terms of spectral efficiency and/or are faster than previous methods in the literature. All of them provide designs which perform close to the known optimal digital solution. Finally, we study the effects of quantizing the analog component of the hybrid design and show that even with coarse quantization, the average rate performance is good.

Hybrid Analog–Digital Precoding Revisited Under Realistic RF Modeling

In this letter, we revisit hybrid analog–digital precoding systems with emphasis on the modeling of their radio-frequency (RF) losses, to realistically evaluate their benefits in 5G system implementations. We focus on fully-connected analog beamforming networks (FC-ABFNs) and on discrete Fourier transform implementations, and decompose these as a bank of commonly used RF components. We then model their losses based on their S-parameters. Our results reveal that the performance and energy efficiency of hybrid precoding systems are severely affected once these, commonly ignored, losses are considered in the overall design. In this context, we also show that hybrid precoder designs similar to Butler matrices are capable of providing better performances than FC-ABFN for systems with a large number of RF chains.

Performance Evaluation of Analog Beamforming with Hardware Impairments for mmW Massive MIMO Communication in an Urban Scenario

The use of massive multiple-input multiple-output (MIMO) techniques for communication at millimeter-Wave (mmW) frequency bands has become a key enabler to meet the data rate demands of the upcoming fifth generation (5G) cellular systems. In particular, analog and hybrid beamforming solutions are receiving increasing attention as less expensive and more power efficient alternatives to fully digital precoding schemes. Despite their proven good performance in simple setups, their suitability for realistic cellular systems with many interfering base stations and users is still unclear. Furthermore, the performance of massive MIMO beamforming and precoding methods are in practice also affected by practical limitations and hardware constraints. In this sense, this paper assesses the performance of digital precoding and analog beamforming in an urban cellular system with an accurate mmW channel model under both ideal and realistic assumptions. The results show that analog beamforming can reach the performance of fully digital maximum ratio transmission under line of sight conditions and with a sufficient number of parallel radio-frequency (RF) chains, especially when the practical limitations of outdated channel information and per antenna power constraints are considered. This work also shows the impact of the phase shifter errors and combiner losses introduced by real phase shifter and combiner implementations over analog beamforming, where the former ones have minor impact on the performance, while the latter ones determine the optimum number of RF chains to be used in practice.

On the Number of RF Chains and Phase Shifters, and Scheduling Design With Hybrid Analog–Digital Beamforming

This paper considers hybrid beamforming (HB) for downlink multiuser massive multiple input multiple output (MIMO) systems with frequency selective channels. For this system, first we determine the required number of radio frequency (RF) chains and phase shifters (PSs) such that the proposed HB achieves the same performance as that of the digital beamforming (DB) which utilizes $N$ (number of transmitter antennas) RF chains. We show that the performance of the DB can be achieved with our HB just by utilizing $r_t$ RF chains and $2r_t(N-r_t + 1)$ PSs, where $r_t \leq N$ is the rank of the combined digital precoder matrices of all sub-carriers. Second, we provide a simple and novel approach to reduce the number of PSs with only a negligible performance degradation. Numerical results reveal that only $20-40$ PSs per RF chain are sufficient for practically relevant parameter settings. Finally, for the scenario where the deployed number of RF chains $(N_a)$ is less than $r_t$, we propose a simple user scheduling algorithm to select the best set of users in each sub-carrier. Simulation results validate theoretical expressions, and demonstrate the superiority of the proposed HB design over the existing HB designs in both flat fading and frequency selective channels.

Full-duplex communication for future wireless networks: Dynamic resource block allocation approach

In this paper, we discuss a full-duplex (FD) communication scenario, where multiple FD user equipments (UEs) share same spectrum resources (or resource blocks) simultaneously. The FD eNodeB deploys digital precoding and successive interference cancellation with optimal ordering algorithm, to allow coexistence of multiple UEs in downlink and uplink, respectively. The sharing of same resource blocks, results in co-channel interference (CCI), in downlink of a UE, from uplink signals of other UEs. To mitigate the interference, a smart antenna approach is adopted. The approach includes using multiple antennas at UEs to form directed beams towards eNodeB and nulls towards other UEs. However, the approach fails when the UEs due to their mobility align themselves in the same direction with respect to the eNodeB (eNB). In this paper, we propose a dynamic resource block allocation (DRBA) algorithm for avoiding CCI due to mobility of UEs, sharing the spectrum resource, in a FD communication scenario. The proposed algorithm shows significant improvement of the quality of service (QoS) of the communication links.

Subspace Estimation and Decomposition for Large Millimeter-Wave MIMO Systems

Channel estimation and precoding in hybrid analog-digital millimeter-wave (mmWave) MIMO systems is a fundamental problem that has yet to be addressed, before any of the promised gains can be harnessed. For that matter, we propose a method (based on the well-known Arnoldi iteration) exploiting channel reciprocity in TDD systems and the sparsity of the channel's eigenmodes, to estimate the right (resp. left) singular subspaces of the channel, at the BS (resp. MS). We first describe the algorithm in the context of conventional MIMO systems, and derive bounds on the estimation error in the presence of distortions at both BS and MS. We later identify obstacles that hinder the application of such an algorithm to the hybrid analog-digital architecture, and address them individually. In view of fulfilling the constraints imposed by the hybrid analog-digital architecture, we further propose an iterative algorithm for subspace decomposition, whereby the above estimated subspaces, are approximated by a cascade of analog and digital precoder / combiner. Finally, we evaluate the performance of our scheme against the perfect CSI, fully digital case (i.e., an equivalent conventional MIMO system), and conclude that similar performance can be achieved, especially at medium-to-high SNR (where the performance gap is less than 5%), however, with a drastically lower number of RF chains (4 to 8 times less).

Energy-Efficient Hybrid Analog and Digital Precoding for MmWave MIMO Systems With Large Antenna Arrays

Millimeter wave (mmWave) MIMO will likely use hybrid analog and digital precoding, which uses a small number of RF chains to avoid energy consumption associated with mixed signal components like analog-to-digital components not to mention baseband processing complexity. However, most hybrid precoding techniques consider a fully-connected architecture requiring a large number of phase shifters, which is also energyintensive. In this paper, we focus on the more energy-efficient hybrid precoding with sub-connected architecture, and propose a successive interference cancelation (SIC)-based hybrid precoding with near-optimal performance and low complexity. Inspired by the idea of SIC for multi-user signal detection, we first propose to decompose the total achievable rate optimization problem with non-convex constraints into a series of simple sub-rate optimization problems, each of which only considers one sub-antenna array. Then, we prove that maximizing the achievable sub-rate of each sub-antenna array is equivalent to simply seeking a precoding vector sufficiently close (in terms of Euclidean distance) to the unconstrained optimal solution. Finally, we propose a low-complexity algorithm to realize SICbased hybrid precoding, which can avoid the need for the singular value decomposition (SVD) and matrix inversion. Complexity evaluation shows that the complexity of SIC-based hybrid precoding is only about 10% as complex as that of the recently proposed spatially sparse precoding in typical mmWave MIMO systems. Simulation results verify the near-optimal performance of SIC-based hybrid precoding.

Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems

Millimeter wave (mmWave) communications has been regarded as a key enabling technology for 5G networks. In contrast to conventional multiple-input-multiple-output (MIMO) systems, precoding in mmWave MIMO cannot be performed entirely at baseband using digital precoders, as only a limited number of signal mixers and analog-to-digital converters (ADCs) can be supported considering their cost and power consumption. As a cost-effective alternative, a hybrid precoding transceiver architecture, combining a digital precoder and an analog precoder, has recently received considerable attention. However, the optimal design of such hybrid precoders has not been fully understood. In this paper, treating the hybrid precoder design as a matrix factorization problem, effective alternating minimization (AltMin) algorithms will be proposed for two different hybrid precoding structures, i.e., the fully-connected and partially-connected structures. In particular, for the fully-connected structure, an AltMin algorithm based on manifold optimization is proposed to approach the performance of the fully digital precoder, which, however, has a high complexity. Thus, a low-complexity AltMin algorithm is then proposed, by enforcing an orthogonal constraint on the digital precoder. Furthermore, for the partially-connected structure, an AltMin algorithm is also developed with the help of semidefinite relaxation. For practical implementation, the proposed AltMin algorithms are further extended to the broadband setting with orthogonal frequency division multiplexing (OFDM) modulation. Simulation results will demonstrate significant performance gains of the proposed AltMin algorithms over existing hybrid precoding algorithms. Moreover, based on the proposed algorithms, simulation comparisons between the two hybrid precoding structures will provide valuable design insights.

Energy-Efficient Transceiver Design for Hybrid Sub-Array Architecture MIMO Systems

Millimeter-wave (mmWave) communication operated in frequency bands between 30 and 300 GHz has attracted extensive attention due to the potential ability of offering orders of magnitude greater bandwidths combined with further gains via beamforming and spatial multiplexing from multi-element antenna arrays. mmwave system may exploit the hybrid analog and digital precoding to achieve simultaneously the diversity, array and multiplexing gain with a lower cost of implementation. Motivated by this, in this paper, we investigate the design of hybrid precoder and combiner with sub-connected architecture, where each radio frequency chain is connected to only a subset of base station antennas from the perspective of energy efficient transmission. The problem of interest is a non-convex and NP-hard problem that is difficult to solve directly. In order to address it, we resort to design a two-layer optimization method to solve the problem of interest by exploiting jointly the interference alignment and fractional programming. First, the analog precoder and combiner are optimized via the alternating-direction optimization method where the phase shifter can be easily adjusted with an analytical structure. Then, we optimize the digital precoder and combiner based on an effective multiple-input multiple-output channel coefficient. The convergence of the proposed algorithms is proved using the monotonic boundary theorem and fractional programming theory. Extensive simulation results are given to validate the effectiveness of the presented method and to evaluate the energy efficiency performance under various system configurations.

Limited Feedback Hybrid Precoding for Multi-User Millimeter Wave Systems

Antenna arrays will be an important ingredient in millimeter wave (mmWave) cellular systems. A natural application of antenna arrays is simultaneous transmission to multiple users. Unfortunately, the hardware constraints in mmWave systems make it difficult to apply conventional lower frequency multiuser MIMO precoding techniques at mmWave. This paper develops low complexity hybrid analog/digital precoding for downlink multiuser mmWave systems. Hybrid precoding involves a combination of analog and digital processing that is inspired by the power consumption of complete radio frequency and mixed signal hardware. The proposed algorithm configures hybrid precoders at the transmitter and analog combiners at multiple receivers with a small training and feedback overhead. The performance of the proposed algorithm is analyzed in the large dimensional regime and in single path channels. When the analog and digital precoding vectors are selected from quantized codebooks, the rate loss due to the joint quantization is characterized and insights are given into the performance of hybrid beamforming compared with analog-only beamforming solutions. Analytical and simulation results show that the proposed techniques offer higher sum rates compared with analog-only beamforming solutions, and approach the performance of the unconstrained digital beamforming with relatively small codebooks.

Joint Processing of Analog Fixed Beamforming and CSI-Based Precoding for Super High Bit Rate Massive MIMO Transmission Using Higher Frequency Bands

In order to tackle the rapidly increasing traffic, the 5th generation (5G) mobile communication system will introduce small cells using higher frequency bands with wider bandwidth to achieve super high bit rate transmission of several tens of Gbps. Massive multiple input multiple output (MIMO) beamforming (BF) is promising as one of the technologies that can compensate for larger path-loss in the higher frequency bands. Joint analog fixed BF and digital precoding have been proposed to reduce the cost of a Massive MIMO transceiver. However, the conventional scheme assumes the transmission of a few streams using well-known codebook-based precoding as the digital precoding, and both a selection method of the fixed BF weights and a digital precoder design, which are suitable for super high bit rate transmission using multiple streams, have not been studied. This paper proposes a joint fixed BF and CSI-based precoding (called FBCP) scheme for the 5G Massive MIMO systems. FBCP first selects the analog fixed BF weights based on a maximum total received power criterion, and then it calculates an eigenmode (EM) precoding matrix by exploiting CSI. This paper targets a 5G system achieving over 20Gbps in the 20GHz band as one example. Throughput performances of the Massive MIMO using the proposed FBCP are evaluated by link level simulations using adaptive modulation and coding and it is shown that the proposed FBCP with the optimum number of selected beams (baseband chains) can use higher level modulation, up to 256QAM, and higher coding rates and achieve throughputs close to 30Gbps while the cost and complexity can be reduced compared with the fully digital Massive MIMO.

Crosstalk Cancellation on High-Speed Interconnects Through a MIMO Linear Precoding

One of the main problems of multiple-input multiple-output (MIMO) high-speed interconnect (HSI) circuits that use single-ended signaling is crosstalk phenomena. Crosstalk is an unintentional coupling of the transmitted signals due to close spacing between transmission lines that distorts the information bearing symbols. A novel model for uniform or nonuniform multiconductor transmission line based on the S-parameters is proposed. It allows representation of an HSI as a MIMO channel. In addition, a linear precoding scheme stands on the aforementioned signal model and wireless digital precoding. The precoder generates eigen-beam patterns designed to avoid crosstalk. This research employs practical HSI circuits used in system-in-package at data rates of 2 Gb/s. Statistical link simulation results are presented to analyze and verify the performance and benefits in terms of signal integrity quality of the signal model and the linear precoder proposed.