Analog Precoding Research Articles

Low-Complexity Hybrid Precoding Algorithm Based on Log-Det Expansion for GenSM-Aided MmWave MIMO System

Generalized spatial modulation (GenSM) aided millimeter wave (mmWave) multiple-input multiple-output (MIMO) system has been recently considered as a new efficient technique due to the combination of numerous antennas and reduced number of radio frequency (RF) chains. However, the present hybrid precoding schemes for GenSM-aided system are still troubled by high computational complexity and performance loss in spectral efficiency (SE). In this paper we propose low-complexity hybrid precoding schemes based on Martin's expansion for logarithmic determinant (log-det) form in analytical SE lower bound. Digital and analog precoders are herein optimized separately, which means complicated alternating minimization iteration is omitted. Besides, we can adjust algorithmic complexity adaptively corresponding to different demand levels for users. Finally the numerical simulations show that the proposed methods outperform other GenSM-aided mmWave MIMO schemes and can achieve a better tradeoff between complexity and SE.

Constructive Interference-Based Symbol-Level Precoding Design for Millimeter-Wave Massive Multiuser MIMO Systems With Hardware-Efficient Hybrid Precoding Architecture

This study considers the constructive interference-based symbol-level precoding design problem in millimeter-wave massive multiuser multiple-input multiple-output systems with hybrid analog-and-digital precoding architecture. In contrast to traditional hybrid precoding architecture in which the analog part is implemented by infinite-resolution phase shifters, analog precoders are achieved in this study using low-cost and energy-efficient switches and inverters. Our objective is to design a hybrid precoder that minimizes the Euclidean distance between the hybrid precoder and the optimal fully digital precoder. However, such a design problem is difficult due to the intricate coupling of digital and analog precoder variables. Thus, we apply the alternating minimization (AltMin) framework to decouple the considered problem into digital and analog precoder design problems and then solve for digital and analog precoders in an alternating manner. By adopting the AltMin framework, we obtain a closed-form solution for digital precoder. Nevertheless, solving the analog precoder design problem incurs combinatorial complexity, which we address by proposing a coordinate descent algorithm to sequentially update each element of the analog precoder with a closed-form expression. Simulation results reveal that the application of the proposed algorithm for the proposed hardware-efficient hybrid precoding architecture provides the desired balance among symbol error rate performance, power consumption, and hardware cost.

Improved Hybrid Beamforming for mmWave Multi-User Massive MIMO

Massive multiple input multiple output (MIMO) has become essential for the increase of capacity as the millimeter-wave (mmWave) communication is considered. Also, hybrid beamforming systems have been studied since full-digital beamforming is impractical due to high cost and power consumption of the radio frequency (RF) chains. This paper proposes a hybrid beamforming scheme to improve the spectral efficiency for multi-user MIMO (MU-MIMO) systems. In a frequency selective fading environment, hybrid beamforming schemes suffer from performance degradation since the analog precoder performs the same precoding for all subcarriers. To mitigate performance degradation, this paper uses the average channel covariance matrix for all subcarriers and considers an iterative algorithm to design analog precoder using approximation techniques. The analog precoder is iteratively updated for each column until it converges. The proposed scheme can reduce errors in the approximating process of the overall spectral efficiency. This scheme can be applied to fully-connected and partially-connected structures. The simulation results show that spectral efficiency performance for the proposed scheme is better than the conventional schemes. The proposed scheme can achieve similar performance with full-digital beamforming by using a sufficiently large number of RF chains. Also, this paper shows that the proposed scheme outperforms other schemes in the frequency selective fading environment. This performance improvement can be achieved in both structures.

Performance Enhancement of MmWave MIMO Systems Using Deep Learning Framework

In order to obtain beamforming gains and prevent high pathloss in millimeter wave (mmWave) systems, large number of antennas is employed. Digital precoders are difficult to implement with many antennas because of hardware constraints, while analog precoders have limited performance. In this paper, hybrid precoding based on a deep learning framework, HybridPrecodingNet, is proposed, which uses large-scale information to predict the parameters of hybrid precoders and decoders. The statistics of the channel covariance matrix are applied to design the hybrid precoders and decoders. The proposed HybridPrecodingNet at the receiver is applied for the channel estimation and design of hybrid decoders. In our proposed framework, the structure of HybridPrecodingNet is trained to learn how to optimize the hybrid precoder and decoder for maximum spectral efficiency. Comparison between different precoding techniques is provided. Results show that HybridPrecodingNet approaches the sub-optimal solution and gives significant spectral efficiency enhancement.

Hybrid Precoding Algorithm for Millimeter‐Wave Massive MIMO Systems with Subconnection Structures

In mmWave massive MIMO systems, traditional digital precoding is difficult to be implemented because of the high cost and energy consumption of RF chains. Fortunately, the hybrid precoding which combines digital precoding and analog precoding not only solves this problem successfully, but also improves the performance of the system effectively. However, due to the constant mode constraint introduced by the phase shifter in the analog domain, it is difficult to solve the hybrid precoding directly. There is a solution which divides the total optimization problem into two stages to solve, that is, first fix the digital precoding matrix, solve the analog precoding matrix, and then optimize the digital precoding matrix according to the obtained analog precoding matrix. In this paper, a high energy‐efficient hybrid precoding scheme is proposed for the subconnection structure. In the first stage, the optimization problem can be decomposed into a series of subproblems by means of the independent submatrix structure of the analog precoding matrix. When the optimized analog precoding matrix is obtained, the digital precoding matrix can be solved by the minimum mean error (MMSE). Finally, the digital precoding matrix is normalized to satisfy the constraint conditions. The simulation results demonstrate that the performance of the proposed algorithm is close to that of fully digital precoding based on subconnection structure and better than that of the existing algorithms. In addition, this paper presents the simulation analysis of the algorithm performance under imperfect channel state information. Simulation results show that when the estimation accuracy of channel state information is 0.8, the spectral efficiency of the proposed algorithm can already be maintained at a good level.

Hybrid Beamforming With Deep Learning for Large-Scale Antenna Arrays

The emergence of highly directional beamforming technology makes millimeter wave frequency band communication possible in future wireless communication networks. Based on the multipath characteristics of millimeter wave frequency communication, a high-precision multipath channel estimation algorithm based on signal subspace is proposed. In the mobile terminal, an iterative heuristic radio frequency combination algorithm based on spatial points is proposed. The analog precoding at the base station uses deep learning to accelerate the calculation, and then the multi-user communication is modeled to design the digital precoding. The simulation results show that the multi-channel estimation algorithm can estimate 4 paths with an error of no more than 0.3 rad. The proposed DL algorithm takes only 20% of the time when it is close to the 87% spectral efficiency of the traditional algorithm.

Hierarchical Energy Efficient Hybrid Precoding for Configurable Sub-Connected MIMO Systems

This paper proposed a configurable sub-connected architecture with a framework that dynamically activates the near-optimal subset of antennas and RF chains to implement energy-efficient hybrid precoding in millimeter wave multiple-input multiple-output system. Since the exhaust search is computational intractable, we propose a two-stage hybrid precoding algorithm, where the digital precoder is designed to eliminate the inter-user interference by zero-forcing rule. Specifically, in the first stage, we introduce an extended cross-entropy algorithm that adaptively updates the probability distribution of potential states in the analog precoder matrix, which can generate a solution that is close to the optimal with a sufficiently high probability. In the second stage, a QR-based subset selection algorithm is proposed to pick the near-optimal subset of the RF chains to further cut down on the energy cost. Simulation results show that proposed extend-CE algorithm gets favorable performance in terms of energy efficiency, and QR-based RF chain selection can achieve a near-optimal performance. Other hybrid precoding algorithms can also be incorporated into the proposed RF chain selection algorithm.

Hybrid Beamforming for Sum Rate Maximization in Wideband Multi-User MIMO Relay Systems

Hybrid precoding has a great potential to achieve near-optimal performance with few radio-frequency (RF) chains in comparison to the number of antennas. This paper proposes a novel hybrid beamforming solution for sum rate maximization in a wideband multi-user multi-input multi-output (MU-MIMO) relay system. The problem at hand is non-convex and hence mathematically intractable due to the constant modulus constraints associated with the analog beamforming design at communicating nodes shared by all sub-carriers. Furthermore, relaying in MU-MIMO systems under frequency-selective channels is also a challenging task as it requires complicated signal processing. To address this problem, source analog beamformer, relay RF combiner and phase-only processing component at each destination are obtained by deriving the common RF processing matrix which enables beamforming gain over all sub-carriers. This process involves reconstruction loss minimization for designing the required analog beamforming vectors having ability to maximize end-to-end signal-to-interference plus noise ratio (SINR). The relay analog precoder is designed by maximizing the received power at each destination through gain maximization of the equivalent baseband channel over the allocated frequency spectrum. To reduce the computational complexity of the iterative approach used to find the relay RF precoding matrix, the closed form expression is derived for achieving the desired objective. Finally, digital baseband processing components are obtained from the equivalent baseband channels by suppressing the interference among transmitted signals indirectly. Simulation results for different system configurations reveal that the proposed algorithm can achieve near-optimal performance.

Hybrid Multi-User Precoding with Manifold Discriminative Learning for Millimeter-Wave Massive MIMO Systems

In large-array millimeter-wave (mmWave) systems, hybrid multi-user precoding is one of the most attractive research topics. This paper first presents a low-dimensional manifolds architecture for the analog precoder. An objective function is formulated to maximize the Energy Efficiency (EE) in consideration of the insertion loss for hybrid multi-user precoder. The optimal scheme is intractable to achieve, so that we present a user clustering hybrid precoding scheme. By modeling each user set as a manifold, we formulate the problem as clustering-oriented multi-manifolds learning. We discuss the effect of non-ideal factors on the EE performance. Through proper user clustering, the hybrid multi-user precoding is investigated for the sum-rate maximization problem by manifold quasi conjugate gradient methods. The high signal to interference plus noise ratio (SINR) is achieved and the computational complexity is reduced by avoiding the conventional schemes to deal with high-dimensional channel parameters. Performance evaluations show that the proposed scheme can obtain near-optimal sum-rate and considerably higher spectral efficiency than some existing solutions.

Dynamically Subarray‐Connected Hybrid Precoding Scheme for Multiuser Millimeter‐Wave Massive MIMO Systems

Hybrid precoding is widely used in millimeter wave (mmWave) massive multiple‐input multiple‐output (MIMO) systems. However, most prior work on hybrid precoding focused on the fully connected hybrid architectures and the subconnected but fixed architectures in which each radio frequency (RF) chain is connected to a specific subset of the antennas. The limited work shows that dynamic subarray architectures address the tradeoff between achievable spectral efficiency and energy efficiency of mmWave massive MIMO systems. Nevertheless, in the multiuser hybrid precoding systems, the existing dynamic subarray schemes ignore the fairness of users and the problem of user selection. In this paper, we propose a novel multiuser hybrid precoding scheme for dynamic subarray architectures. Firstly, we select a multiuser set among all users according to the analog effective channel information of the base station (BS) and then design the subset of the antennas to each RF by the fairness antenna‐partitioning algorithm. Finally, the optimal analog precoding vector is designed according to each subarray, and the digital precoding is designed by the minimum mean‐squared error (MMSE) criterion. The simulation results show that the performance advantages of the proposed multiuser hybrid precoding scheme for dynamic subarray architectures.

Broadband Hybrid Precoding Scheme Based on Cyclic Delay in Terahertz Communications

The terahertz communication system with traditional hybrid precoding structure has the problem of beam diffusion. This problem leads to the serious loss of achievable rate and offsets the performance gain caused by bandwidth increase, so a broadband hybrid precoding scheme based on cyclic delay is proposed in this paper. Firstly, a broadband hybrid precoding framework based on cyclic delay is constructed. A delay element is placed at each antenna of the traditional full-connected hybrid precoding structure. Thus, a frequency-dependent phase shift is accomplished to compensate the beam diffusion. Then, the unit delay of delay element at each antenna is determined by maximizing the array gain of the sub-carriers, but there is a problem that the unit delay is not uniform. Finally, through the design of analog precoding, the unity of the unit delay can be realized, while maximizing the array gain of each sub-carrier. The simulation results show that the proposed scheme can achieve 100% array gain at any sub-carrier, and is suitable for solving the problem of beam diffusion under different bandwidth and different number of transmit antennas. Compared with the existing schemes, the achievable rate of the proposed scheme is very close to that of the full-digital precoding scheme, and has the advantage of high energy efficiency.

Hybrid Precoding Design for Secure Generalized Spatial Modulation With Finite-Alphabet Inputs

Technically, the security performance of generalized spatial modulation (GenSM) networks can be enhanced by dynamically adjusting the precoder allocated to the legitimate signal as communication channel varies. For this purpose, our paper proposes a secure transmission strategy upon designing both digital and analog precoders for hybrid GenSM systems, where an eavesdropper is taken into account. The concept of the hybrid GenSM system has arose to improve the spatial multiplexing (SMX) gain for remedying the shortcoming of the limited number of radio frequency chains in traditional GenSM systems. However, this may lead to a great deal of security degradation since the SMX gain of the unintended receiver will be also improved. To this end, we develop a secrecy enhancement scheme by devising both analog and digital precoders for hybrid GenSM networks. Specifically, we derive an efficiently closed-form alternative to the original secrecy rate (SR) expression for reducing the excessive computational complexity of the joint optimization problem over the hybrid precoder. Then, by using this alternative as our cost function, an iterative algorithm is proposed. In particular, we elaborately conceive a pair of concave maximization problems in order to optimize the digital and analog precoders, respectively. Our proposed strategy not only utilizes semi-positive definite relaxing technique over the analog precoder but also invokes a lower bound of the alternative to further simplify the optimization over the vectored digital precoder. Subsequently, both the convergence and computational complexity of the proposed alternating iteration algorithm are analyzed. Compared to existing designs, our proposed strategy strikes a compelling role in balancing the SR performance and complexity. Finally, our simulation results confirm the efficiency of the proposed algorithm in terms of the SR performance achieved.

System Energy-Efficient Hybrid Beamforming for mmWave Multi-User Systems

This paper develops energy-efficient hybrid beamforming designs for mmWave multi-user systems where analog precoding is realized by switches and phase shifters such that radio frequency (RF) chain to transmit antenna connections can be switched off for energy saving. By explicitly considering the effect of each connection on the required power for baseband and RF signal processing, we describe the total power consumption in a sparsity form of the analog precoding matrix. However, these sparsity terms and sparsity-modulus constraints of the analog precoding make the system energy-efficiency maximization problem non-convex and challenging to solve. To tackle this problem, we first transform it into a subtractive-form weighted sum rate and power problem. A compressed sensing-based re-weighted quadratic-form relaxation method is employed to deal with the sparsity parts and the sparsity-modulus constraints. We then exploit alternating minimization of the mean-squared error to solve the equivalent problem where the digital precoding vectors and the analog precoding matrix are updated sequentially. The energy efficiency upper bound and a heuristic algorithm are also examined for comparison purposes. Numerical results confirm the superior performances of the proposed algorithm over benchmark energy-efficiency hybrid precoding algorithms and heuristic one.

Hybrid Analog-Digital Precoder Design for Securing Cognitive Millimeter Wave Networks

Millimeter wave (mmWave) communications and cognitive radio technologies constitute key technologies of improving the spectral efficiency of communications. Hence, we conceive a hybrid secure precoder for enhancing the physical layer security of a cognitive mmWave wiretap channel, where a secondary transmitter broadcasts confidential information signals to multiple secondary users under the interference temperature constraint of the primary user (PU). The optimization problem is formulated as jointly optimizing the analog and digital precoder for maximizing the minimum secrecy rate of all the secondary users under practical constraints. In particular, our design satisfies the constraint on the maximum interference power received by multiple PUs, as well as the secondary users’ minimum quality-of-service (Qos), and the unit-modulus constraint on the analog precoder. Due to the non-convexity of the resultant objective function and owing to the coupling between the analog and digital precoder, the optimization problem formulated is nonconvex and nonlinear, hence it is very challenging to solve directly. Hence, we first transform it into a tractable form, and develop a penalty dual decomposition (PDD) based iterative algorithm to locate its Karush-Kuhn-Tucker (KKT) solution. Finally, we generalize the proposed PDD algorithm to a secure hybrid precoder design relying on practical finite-resolution phase shifters and show that the proposed PDD algorithm can be straightforwardly adapted to handle the scenario, where each PU is equipped with multiple antennas and the CSI of multiple eavesdroppers (Eves) is imperfectly known. Our simulation results validate the efficiency of the proposed iterative algorithm.

Precoding and Transmit Antenna Subarray Selection for Secure Hybrid Spatial Modulation

Spatial modulation (SM) is a particularly important form of multiple-input multiple-output (MIMO), which uses both modulation symbols and antenna indices to carry information. In this paper, to avoid the high cost and circuit complexity of SM, we consider the hybrid SM system with a hybrid precoding transmitter architecture, combining a digital precoder and an analog precoder. In such a system, we carried out secure hybrid precoding and transmit antenna subarray selection (TASS) methods. Two hybrid precoding methods, called maximizing approximate secrecy rate (SR) via gradient ascent (Max-ASR-GA) and maximizing approximate SR via alternating direction method of multipliers (Max-ASR-ADMM), are proposed to improve the SR performance. As for TASS, a high-performance method of maximizing the approximate SR (Max-ASR) is first presented. To reduce its high complexity, two low-complexity TASS methods, namely maximizing eigenvalue (Max-EV) and maximizing product of signal-to-interference-plus-noise ratio and artificial noise-to-signal-plus-noise ratio (Max-P-SINR-ANSNR), are proposed. Simulation results demonstrate that the proposed Max-ASR-GA and Max-ASR-ADMM hybrid precoders harvest substantial SR performance gains over existing method. For TASS, the proposed three methods Max-ASR, Max-EV, and Max-P-SINR-ANSNR perform better than existing leakage method. Particularly, the proposed Max-EV and Max-P-SINR-ANSNR are of low-complexity at the expense of a little performance loss compared with Max-ASR.

Deep double-pilot-based hybrid precoding in UAV-enabled mmWave massive MIMO

Unmanned aerial vehicle (UAV)-enabled communication system provides flexibility and reliability compared to conventional ones. Millimeter wave (mmWave) and massive multiple-input–multiple-output (MIMO) have widely been researched since recent years, which are promising techniques for the next and even the later generation communication system. Hybrid precoding, as a method to reduce the high cost in hardware and power brought by massive antenna array, develops fiercely and is often combined to deep learning, a kind of popular optimization tool, which brings an overwhelming performance. On the other hand, there are not so many attentions about the hybrid precoding in time-varying mmWave massive MIMO, which is necessary to be considered in a UAV-enabled communication scenario because the performance will degrade seriously if the channel changed while the transmitter and receiver use the precoding matrix corresponding to the expired channel, yet. In this paper, we propose a double-pilot-based hybrid precoding system, which completes analog precoding and digital precoding separately—predicting the previous one using deep learning structure and updating equivalent channel frequently for the post one by enhancing the frequency of equivalent channel estimation.

BD-UCD-Based Nonlinear Hybrid Precoding for Millimeter Wave Massive Multiuser MIMO Systems

In this letter, we investigate the downlink hybrid precoding design for time-division duplexing (TDD) millimeter wave (mmWave) massive multiuser MIMO (MU-MIMO) systems, aiming to enhance both the sum spectral efficiency (SSE) and the bit error rate (BER) performance. First, we propose a joint analog precoding and combining design via Gram-Schmidt orthogonalization to maximize the beamforming gain while mitigating the inter-user interference. Then, by exploiting the uplink-downlink duality, we propose a block diagonal uniform channel decomposition (BD-UCD) based digital precoding and combining scheme to further improve the SSE and BER performance. Furthermore, Tomlinson–Harashima precoding (THP) is utilized to eliminate both the inter-user interference and the inter-stream interference. Simulation results demonstrate that the proposed BD-UCD-based nonlinear hybrid precoding scheme performs close to the fully-digital BD-UCD scheme and outperforms the other existing hybrid precoding schemes in terms of SSE and BER performance.

Dynamic Hybrid Precoding Relying on Twin- Resolution Phase Shifters in Millimeter- Wave Communication Systems

Hybrid analog/digital precoding in millimeter-wave (mmWave) multi-input multi-ouput (MIMO) systems is capable of achieving the near-optimal full-digital performance at reduced hardware cost and power consumption compared to its full-RF digital counterpart. However, having numerous phase shifters is still costly, especially when the phase shifters are of high resolution. In this paper, we propose a novel twin-resolution phase-shifter network for mmWave MIMO systems, which reduces the power consumption of an entirely high-resolution network, whilst mitigating the severe array gain reduction of an entirely low-resolution network. The connections between the twin phase shifters having different resolutions and the antennas are either fixed or dynamically configured. In the latter, we jointly design the phase-shifter network and the hybrid precoding matrix, where the phase of each entry in the analog precoding matrix can be dynamically designed according to the required resolution. This method is slightly modified for the fixed network's hybrid precoding matrix. Furthermore, we extend the proposed method to multi-user MIMO systems and provide its performance analysis. Our simulation results show that the proposed dynamic hybrid precoding method strikes an attractive performance vs. power consumption trade-off.

Signal Shaping for Non-Uniform Beamspace Modulated mmWave Hybrid MIMO Communications

This paper investigates adaptive signal shaping methods for millimeter wave (mmWave) multiple-input multiple-output (MIMO) communications based on the maximizing the minimum Euclidean distance (MMED) criterion. In this work, we utilize the indices of analog precoders to carry information and optimize the symbol vector sets used for each analog precoder activation state. Specifically, we firstly propose a joint optimization based signal shaping (JOSS) approach, in which the symbol vector sets used for all analog precoder activation states are jointly optimized by solving a series of quadratically constrained quadratic programming (QCQP) problems. JOSS exhibits good performance, however, with a high computational complexity. To reduce the computational complexity, we then propose a full precoding based signal shaping (FPSS) method and a diagonal precoding based signal shaping (DPSS) method, where the full or diagonal digital precoders for all analog precoder activation states are optimized by solving two small-scale QCQP problems. Simulation results show that the proposed signal shaping methods can provide considerable performance gain in reliability in comparison with existing mmWave transmission solutions.

Analog Versus Hybrid Precoding for Multiuser Massive MIMO With Quantized CSI Feedback

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 characterize the conditions in closed form with respect to signal-to-noise ratio (SNR), the number of users and the number of feedback bits. Numerical results verify the derived conclusions on both Rayleigh channels and mmWave channels.