Large-scale Multiple-input Multiple-output Systems Research Articles

Nested Variational Chain and Its Application in Massive MIMO Detection for High-Order Constellations.

Multiple input multiple output (MIMO) technology necessitates detection methods with high performance and low complexity; however, the detection problem becomes severe when high-order constellations are employed. Variational approximation-based algorithms prove to deal with this problem efficiently, especially for high-order MIMO systems. Two typical algorithms named Gaussian tree approximation (GTA) and expectation consistency (EC) attempt to approximate the true likelihood function under discrete finite-set constraints with a new distribution by minimizing the Kullback-Leibler (KL) divergence. As the KL divergence is not a true distance measure, 'exclusive' and 'inclusive' KL divergences are utilized by GTA and EC, respctively, demonstrating different performances. In this paper, we further combine the two asymmetric KL divergences in a nested way by proposing a generic algorithm framework named nested variational chain. Acting as an initial application, a MIMO detection algorithm named Gaussian tree approximation expectation consistency (GTA-EC) can thus be presented along with its alternative version for better understanding. With less computational burden compared to its counterparts, GTA-EC is able to provide better detection performance and diversity gain, especially for large-scale high-order MIMO systems.

Toward Extra Large-Scale MIMO: New Channel Properties and Low-Cost Designs

Extra large-scale multiple-input multiple-output (MIMO) has been recognized as one of the potential development directions of massive MIMO. By employing even more antennas than massive MIMO in the fifth-generation era, extra large-scale MIMO can further exploit the spatial domain resources and enable ultra high data rates, low latency communications as well as emerging applications, such as sensing and localization, in sixth-generation mobile communication systems. However, with the increase of the size of the antenna array, and the decrease of the distance between a user and the array, new channel properties, that did not manifest in conventional massive MIMO, start to kick in. Most importantly, existing research strategies pertaining to massive MIMO cannot be directly applied or simply extended to fit the extra large-scale MIMO case. Moreover, increasing the number of antennas will inevitably boost the total cost, which refers to not only the high hardware cost, but also the burden of vast processing and computations as well as the substantial training overhead. In this paper, we make a survey on the state-of-the-art on the new channel properties of and low-cost designs for extra large-scale MIMO systems. Particularly, we pursue a mathematical analysis to explain why the new features appear and illustrate how they affect the system model. Furthermore, we summarize and compare the low-cost designs from various perspectives and give our suggestions from a practical deployment point of view.

BP-algorithm based on factor diagram about massive MIMO system

In order to meet the growing demand for high-speed mobile data business, there has been a constant concern for the fifth-generation mobile communication system. 5G large-scale Multiple Input Multiple Output (MIMO) technique has significantly improved the system spectral efficiency and energy efficiency. In order to study the signal detection method under the large-scale MIMO system and improve the existing methods, the article describes the background of signal detection. It introduces the development of the belief propagation (BP) algorithm. There are four main BP algorithms: Original-BP algorithm, RDF-BP algorithm, EBRDF-BP algorithm, and GAI-BP algorithm. One algorithm is proposed based on these fundamental algorithms to improve the whole detection performance. This algorithm reduces complexity while not increasing the error rate too much, which means that it has certain feasibility and practicability.

Low Complexity, Pairwise Layered Tabu Search for Large Scale MIMO Detection

This paper presents a low complexity pairwise layered tabu search based detection algorithm for a large-scale multiple-input multiple-output system. The proposed algorithm can compute two layers simultaneously and reduce the effective number of tabu searches. An efficient Gram matrix and matched filtered output update strategy is developed to reuse the computations from past visited layers. Also, a precomputation technique is adapted to reduce the redundancy in computation within tabu search iterations. Complexity analysis shows that the upper bound of initialization complexity in the proposed algorithm reduces from \(O(N_t^4)\) to \(O(N_t^3)\). The detection performance of the proposed detector is almost the same as the conventional complex version of LTS for 64QAM and 16QAM modulations. However, the proposed detector outperforms the conventional system for 4QAM modulation, especially in \(16 \times 16\) and \(8 \times 8\) MIMO. Simulation results show that the percent of complexity reduction in the proposed method is approximately 75% for \(64 \times 64\), 64QAM and 85% for \(64 \times 64\) 16QAM systems to achieve a BER of \(10^{-3}\). Moreover, we have proposed three layer-wise iteration allocation strategies that can further reduce the upper bound of complexity with minor degradation in detection performance.

Energy-Efficient Resource Allocation of Wireless Energy Transfer for the Internet of Everything in Digital Twins

The work aims to improve the stability of wireless energy transfer (WET) in the Internet of Things (IoT), prolong the service life of wireless devices, and promote green communication. Based on a digital twins (DTs) IoT environment, we depict how to optimize the energy efficiency of large-scale multiple-input multiple-output (MIMO) systems under WET technology. The large-scale distributed antenna array is applied to the wireless sensor network. MIMO can produce extremely narrow beams so that the system reduces interference to other users. Our MIMO system's energy efficiency optimization uses fractional planning and the block coordinate descent algorithm. The simulation results show that the algorithm has the best throughput performance when the maximum transmission power reaches 19 dBm. The total energy consumption of the proposed resource allocation algorithm is only about 9 percent higher than that of the power minimization algorithm. In the case of different maximum transfer powers, the number of iterations in which the proposed algorithm is required to converge is within four. Changes in the number of users cannot affect the convergence performance of the proposed algorithm. After the antenna selection mechanism is introduced, the average power of the energy received by the user is improved notably compared to the case of simply using the largescale distributed antenna array. The research results can reference large-scale MIMO systems' energy efficiency optimization problems under WET conditions in the DTs IoT environment.

Toward Optimally Efficient Search With Deep Learning for Large-Scale MIMO Systems

This paper investigates the optimal signal detection problem with a particular interest in large-scale multiple-input multiple-output (MIMO) systems. The problem is NP-hard and can be solved optimally by searching the shortest path on the decision tree. Unfortunately, the existing optimal search algorithms often involve prohibitively high complexities, which indicates that they are infeasible in large-scale MIMO systems. To address this issue, we propose a general heuristic search algorithm, namely, hyper-accelerated tree search (HATS) algorithm. The proposed algorithm employs a deep neural network (DNN) to estimate the optimal heuristic, and then use the estimated heuristic to speed up the underlying memory-bounded search algorithm. This idea is inspired by the fact that the underlying heuristic search algorithm reaches the optimal efficiency with the optimal heuristic function. Simulation results show that the proposed algorithm reaches almost the optimal bit error rate (BER) performance in large-scale systems, while the memory size can be bounded. In the meanwhile, it visits nearly the fewest tree nodes. This indicates that the proposed algorithm reaches almost the optimal efficiency in practical scenarios, and thereby it is applicable for large-scale systems. Besides, the code for this paper is available at \url{https://github.com/skypitcher/hats}.

Randomized Iterative Methods for Low-Complexity Large-Scale MIMO Detection

In this paper, we introduce a randomized iterative method for signal detection in uplink large-scale multiple-input multiple-output (MIMO) systems, which not only achieves a low computational complexity but also enjoys a global and exponentially fast convergence. First of all, by adopting the random sampling into the iterations, the randomized iterative detection algorithm (RIDA) is proposed for large-scale MIMO systems. We show that RIDA converges exponentially fast in terms of mean squared error (MSE). Furthermore, this global convergence <i>always</i> holds, and does not depend on the standard requirements such as <inline-formula><tex-math notation="LaTeX"><?TeX $N\gg K$?></tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX"><?TeX $N$?></tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX"><?TeX $K$?></tex-math></inline-formula> denote the numbers of antennas at the sides of base station and users. This broadly extends the applications of low-complexity detection in uplink large-scale MIMO systems. Then, based on a new conditional sampling, optimization and enhancements are given to further improve both the convergence and efficiency of RIDA, resulting in the modified randomized iterative detection algorithm (MRIDA). Meanwhile, with respect to MRIDA, further complexity reduction by exploiting the matrix structure is given while its implementation by deep neural networks (DNN) is also presented for a better detection performance.

Applications of a Quantum Linear System Algorithm to Linear MIMO Detections

A linear system can be solved more efficiently by quantum computing. However, previously known quantum algorithms provide only a quantum state as the solution; consequently, we cannot obtain the value of each component of the solution. We propose a method to extract the component values of the solution, and we present an application to linear multiple-input multiple-output (MIMO) detections. In the proposed algorithm, we demonstrate a concrete method that applies a quantum linear system algorithm (QLSA) when the components of a solution have binary variables, quaternary variables, or roots of a complex number. Whereas the conventional method requires an additional process to read out the values of the components, the proposed algorithm does not need any post-procedure. Instead, our method uses a QLSA iteratively, and the number of uses is logarithmic in the size of the linear system. Thus, our method maintains the runtime with the quantum advantage, but the conventional approach increases the runtime significantly. Furthermore, the application of the proposed method shows that quantum computing can collaborate with communication systems for large-scale MIMO systems.

Low-complexity sparse-aware multiuser detection for large-scale MIMO systems

Sparse-aware (SA) detectors have attracted a lot attention due to its significant performance and low-complexity, in particular for large-scale multiple-input multiple-output (MIMO) systems. Similar to the conventional multiuser detectors, the nonlinear or compressive sensing based SA detectors provide the better performance but are not appropriate for the overdetermined multiuser MIMO systems in sense of power and time consumption. The linear SA detector provides a more elegant tradeoff between performance and complexity compared to the nonlinear ones. However, the major limitation of the linear SA detector is that, as the zero-forcing or minimum mean square error detector, it was derived by relaxing the finite-alphabet constraints, and therefore its performance is still sub-optimal. In this paper, we propose a novel SA detector, named single-dimensional search-based SA (SDSB-SA) detector, for overdetermined uplink MIMO systems. The proposed SDSB-SA detector adheres to the finite-alphabet constraints so that it outperforms the conventional linear SA detector, in particular, in high SNR regime. Meanwhile, the proposed detector follows a single-dimensional search manner, so it has a very low computational complexity which is feasible for light-ware Internet of Thing devices for ultra-reliable low-latency communication. Numerical results show that the the proposed SDSB-SA detector provides a relatively better tradeoff between the performance and complexity compared with several existing detectors.

Optimized Uniform Scalar Quantizers of Ternary ADCs for Large-Scale MIMO Communications

Large-scale multiple-input multiple-output (LS-MIMO), a promising technology for the future wireless networks to boost the network capacity, unavoidably faces hardware cost and power consumption issues due to a large number of high-resolution power-hungry analog-to-digital converters (ADCs) at the receiver side. The low-resolution ADCs have recently been proven to be an effective solution to cut down the system cost. This paper studies the LS-MIMO communication systems where three-level ADCs, so-called Ternary ADCs (T-ADCs), are employed to achieve better energy efficiency in some LS-MIMO configurations. The truncation limit of the uniform scalar quantizer of the T-ADCs is optimized to minimize the quantization distortion on the LS-MIMO received signal, and thus its performance approaches that of the well-known Lloyd-Max algorithm while offering lower complexity and better robustness. Furthermore, our proposed solution is independent of the number of antennas. The LS-MIMO systems' performance with the proposed T-ADCs is substantially improved over the conventional 3- σ uniform scalar quantizer in three different performance metrics - achievable rates, iterative decoding thresholds of pragmatic protograph low-density parity-check codes (LDPC), and the frame error rate (FER)/bit error rate (BER). Our energy efficiency investigation reveals that proposed T-ADCs attain better energy efficiency than that of the 1-bit ADCs and 2-bit ADCs when the ratio between the receiving antennas and the transmitting antennas is low and medium as the power consumption of ADCs and the transmission power are better balanced in comparison with one-bit ADCs and two-bit ADCs.

A channel estimation algorithm for large-scale MIMO system using block sparsity adaptive matching pursuit

A new adaptive channel estimation algorithm for large-scale multiple input multiple output (MIMO) systems is proposed by combining the block sparsity adaptive matching pursuit (BSAMP) technique with adaptive beamforming. Firstly, the structure model based on continuous constant is optimised randomly, and it is used alternately with the basic denoising optimisation scheme to find the sparse characteristic channel. Then the sparse matrix is optimised based on adaptive beamforming to enhance the channel sparsity. Furthermore, based on BSAMP technology, using the joint sparsity of large-scale MIMO system subchannels, we set threshold and find the maximum backward difference position to select the atoms of the support set quickly and preliminarily. At the same time, the energy dispersion caused by the non-orthogonality of the observation matrix is considered to improve the estimation performance of the algorithm. Finally, the atoms are filtered by regularisation to improve the stability of the algorithm. Simulation results show that the algorithm can recover large-scale MIMO channel information with unknown sparsity quickly and accurately, and the average running time is only 0.12 s.

Joint Detection and Decoding of Mixed-ADC Large-Scale MIMO Communication Systems With Protograph LDPC Codes

Nowadays, large-scale multiple-input multiple-output (LS-MIMO) with low-resolution analog-to-digital converters (ADCs) is a favorable transmission scheme for 5G and beyond wireless networks to reduce the power consumption of the radio frequency chains and to increase the network capacity. This paper derives the joint message-passing detection and decoding algorithm based on the double-layer graph for LS-MIMO communication systems with mixed-ADCs. The new protograph extrinsic information chart (PEXIT) algorithm is developed to analytically evaluate the performance of protograph low-density parity-check code under various mixed-ADC combinations and LS-MIMO configuration scenarios. The simulation results validate the accuracy of the proposed algorithm. Furthermore, our experiments show that the mixed-ADC system can achieve a significant power gain even when only one received antenna is equipped with high-resolution ADCs. It is observed that 4-bit or 5-bit resolution is an optimal choice for the high-resolution receive antennas. Interestingly, mixed-ADC systems with Ternay-ADCs generally provide significant gains at the cost of the increase in the average resolution by a fraction of a bit. There are specific scenarios where the Ternary-ADC-based system outperforms the 1-bit-ADC based system at the same or lower average resolution. In the particular case of 16 ×16 MIMO configuration where the number of low-resolution antennas is N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> = 12 and the number of high-resolution antennas is N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> = 4, the Ternary-ADC based system can obtain a power gain of about 2 dB at the frame error rate (FER) or bit error rate (BER) level of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> .

Non-iterative Coordinated Beamforming for Multicell MIMO Heterogeneous Networks

In this paper, we present a novel non-iterative coordinated beamforming algorithm for overlaid multicell coordinated beamforming systems where a macro base station acts as an anchor and computes the beamforming vectors. We propose beamforming vector design that improves the received signal-to-interference-plus-noise-ratio while reducing the computational complexity. We also show its asymptotic behaviors with respect to the number of antennas, confirming that the proposed solutions are useful for large-scale multiple-input multiple-output systems in heterogeneous and small cell networks.

Asymptotic Analysis of Full-Duplex Large-Scale MIMO Systems With Low-Resolution ADCs/DACs Over Rician Fading Channels

In this article, the uplink rate and downlink achievable rates of full-duplex (FD) large-scale multiple-input–multiple-output (MIMO) systems with low-resolution analog-to-digital converters/digital-to-analog converters (ADCs/DACs) over the Rician fading channels are investigated. By utilizing the maximum ratio combining/maximum ratio transmission processing, the approximate achievable rates of uplink and downlink with imperfect channel state information environments are presented. Then, the effects of the loop interference (LI), quantization error, and interuser interference (IUI) are evaluated based on the derived rates. According to the derived results, we find that interference and noise can be wiped out by using proper power scaling law, more antennas and bigger Rician factor. The numerical results show that deploying more base station antennas can effectively eliminate the LI, IUI, and noise caused by the FD mode. We also find that the approximate achievable rates of uplink and downlink will converge to a constant as the number of quantized bits tends to infinity. Moreover, performance of an FD large-scale MIMO system is found in close relationship with the quantization bits number, which, however, is insignificant when the ADCs/DACs quantization bits are increased. Thus, the use of low-resolution ADCs/DACs is verified sufficient in a large-scale MIMO system.

Transmit Signal Design for Large-Scale MIMO System With 1-bit DACs

Deploying low-resolution (e.g. one-bit) digital-to-analog converters (DACs) is of great importance in the multiple-input multiple-output (MIMO) system equipped with a large-scale antenna array since such a hardware architecture brings low-cost and circuit power saving for each antenna. In this paper, the problem of transmit signal design in a large-scale MIMO system with 1-bit DACs is investigated. To ensure directional transmission, we propose to design the transmit signal by minimizing the weighted mean-squared error (MSE) between the formed beampattern and a given one. The resulting design problem, which involves a nonconvex fourth-order objective and a set of nonconvex discrete constraints, is NP-hard, and therefore, an alternating minimization (AM) method is devised. In order to obtain a high-quality 1-bit solution, we propose a continuous and differentiable function to approximate the 1-bit signal, such that the problem with discrete 1-bit constraint is recast to an unconstrained optimization problem with a penalty term, which can be effectively solved via the limited-memory Broyden, Fletcher, Goldfarb, and Shanno (L-BFGS) approach. Moreover, it is found that a closed-form solution can be obtained when equal weights are applied. In addition, low-complexity schemes are developed based on the fast Fourier transform (FFT). The numerical simulations are conducted to demonstrate the effectiveness and superiority of the proposed method.

ROD-based hybrid TH precoding and combining for mmWave large-scale MIMO systems

Hybrid precoding is one of key techniques for millimeter wave (mmWave) large-scale multiple-input multiple-output (MIMO) systems. This paper considers a nonlinear hybrid precoding architecture which consists of a nonlinear unit, a reductive digital precoder and a constant modulus radio frequency (RF) precoder, and presents a novel hybrid Tomlinson-Harashima (TH) precoding and combining algorithm. Firstly, due to the intractability of the sum rates maximization problem for such a nonlinear hybrid precoding architecture, a tractable three-stage optimization problem is constructed through the lower bound of the sum rates, which allows the digital precoding matrix, the RF precoding matrix and the RF combining matrix to be optimized sequentially and independently. Then, in order to solve the three-stage optimization problem effectively, a novel row orthogonal decomposition (ROD) is defined. Based on the ROD, it is interesting that the necessary and sufficient condition of the optimal digital precoding matrix can be obtained, and a near-optimal RF precoding matrix can be derived. Finally, the optimization of the RF combining matrix is reformulated as a unimodular quadratic programming and solved by a generalized power method. Theoretical analyses and simulations indicate that the proposed ROD-based hybrid TH precoding and combining algorithm can offer a higher sum rates and a lower bit error rate with a comparable complexity in comparison to the previous works.

Performance Analysis of Protograph LDPC Codes Over Large-Scale MIMO Channels With Low-Resolution ADCs

Protograph LDPC (P-LDPC) codes and large-scale multiple-input multiple-output (LS-MIMO) are cornerstones of 5G and future wireless systems, thanks to their powerful error-correcting capability and high spectral efficiency. To alleviate the high complexity in signal detection/decoding that dramatically grows with the number of antennas (in the order of tens or even hundreds), low-resolution analog-to-digital converters (ADCs) and joint detection and decoding using factor graph have recently attracted paramount interest. Unlike high-resolution ADCs, by using a small number of bits to quantize the received signal, low-resolution ADCs help reduce the hardware cost and power consumption of the RF circuit of practical LS-MIMO transceivers. Such a very much desirable reduction comes at the cost of additional quantization noise, introduced by low-resolution ADCs. This work aims to provide a unified framework to analyze the impact of the low-resolution ADCs on the performance of P-LDPC codes in practical LS-MIMO systems. It is worth noting that the previous analytical tools that have been used to evaluate the performance of P-LDPC codes do not account for the quantization noise effect of the low-resolution ADCs and the fact that the covariance of quantization noise depends on the fading channels. This article addresses this shortcoming by first leveraging the additive quantization noise model. We then derive the expression of extrinsic information for the belief-propagation LS-MIMO detector. The mutual information functions, which are the core elements of our proposed protograph extrinsic information transfer (PEXIT) algorithm, are analyzed for LS-MIMO communication systems. Our proposed PEXIT algorithm allows us to analyze and predict the impact of the low-resolution ADCs on the performance of P-LDPC codes, considering various input parameters, including the LS-MIMO configuration, the code rate, and the maximum number of decoding iterations, and the code structure. Based on our extensive analytical and simulation results, we found that the performance of 3-bit and 4-bit ADC systems only have a small gap to that of the unquantized systems. Especially when the 5-bit ADC scheme is applied, the performance loss is negligible. This finding sheds light on the practical design of LS-MIMO systems using P-LDPC codes.

Accurate Analytical BER Performance for ZF Receivers Under Imperfect Channel in Low-SNR Region for Large Receiving Antennas

Most analytical work for zero-forcing (ZF) receivers are conducted for small-scale multiple-input multiple-output (MIMO) systems in large signal-to-noise ratio (SNR) region and under small channel estimation error conditions. Using large receiving antennas, systems are expected to work in the low-SNR region and under large channel estimation error. In these conditions, we observe an obvious mismatch between the existing analytical results and the simulations. In this letter, we derive an accurate analytical bit error rate (BER) expression for ZF receivers under imperfect channel estimation. We show that our results match nicely with the simulations in small-scale and large-scale MIMO systems, even when large channel estimation error presents.

Low-Complexity Multi-User Detection for MBM in Uplink Large-Scale MIMO Systems

Media-based modulation (MBM) is a novel modulation scheme, which embeds information in different channel fading realizations created by changing the status of radio frequency mirrors. In this letter, we investigate the problem of multi-user MBM signal detection in a large-scale multiple-input multiple-output system, where the base station is equipped with a large number of antennas and several users use MBM for uplink transmission. We propose an iterative interference cancellation-based algorithm. The basic idea is to treat the multi-user interference as noise and cancel it iteratively. Computer simulation results show that the proposed algorithm has good performance with low complexity.

An ADMM Approach for PAPR Reduction for Large-Scale MIMO-OFDM Systems

We consider the problem of peak-to-average power ratio (PAPR) reduction for orthogonal frequency-division multiplexing based large-scale multiple-input multiple-output systems. A novel perturbation-assisted scheme is developed to reduce the PAPRs of the transmitted signals by exploiting the redundant degrees-of-freedom inherent in the large-scale antenna array. Specifically, we introduce carefully devised perturbation signals to the frequency-domain precoded signals, with the aim of reducing the PAPRs of their time-domain counterpart signals. Meanwhile, the additive perturbation signal associated with each tone is constrained to lie in the null-space of its associated channel matrix, such that it does not cause any multiuser interference and out-of-band radiations. Such a problem is formulated as convex optimization problems, and two efficient algorithms, referred to as PROXINF-ADMM1 and PROXINF-ADMM2, are developed by resorting to the variable splitting and alterative direction method of multipliers techniques. Simulation results show that the proposed method has a fast convergence rate and achieves substantial PAPR reduction within only tens of iterations.