Large Multiple-input Multiple-output Systems Research Articles

Time domain turbo equalization based on vector approximate message passing for multiple-input multiple-output underwater acoustic communications.

This paper proposes a high-performance receiver for underwater acoustic communications based on time reversal processing for multiple-input multiple-output (MIMO) systems. The receiver employs the vector approximate message passing (VAMP) algorithm as a soft equalizer in turbo equalization. By performing self-iteration between the inner soft slicer and the inner soft equalizer, the VAMP algorithm achieves near-optimal performance. Furthermore, an iterative channel-estimation-based soft successive interference cancellation method is incorporated to suppress co-channel interference in the MIMO system. Additionally, the introduction of passive time reversal technology can combine multiple channels into a single channel, which greatly reduces the computational complexity of the MIMO system, especially for large MIMO systems. The effectiveness of the proposed receiver is verified using experimental data collected in Songhua Lake, China in 2019. The results demonstrate that the proposed receiver significantly reduces the complexity of the traditional parallel-VAMP receiver without sacrificing performance and outperforms other receivers of the same type. Moreover, our experimental results also verify that the VAMP-turbo outperforms the generalized approximate message passing (GAMP)-turbo in terms of bit error rate and convergence performance.

Performance analysis of a millimeter wave MIMO channel estimation method in an embedded multi-core processor

The emerging Multi-Processor System-on-Chip (MPSoC) technology, which combines heterogeneous computing with the high performance of field programmable gate arrays (FPGA), is a promising platform for a large number of applications, including wireless communications and vehicular technology. In this specific application context, when multiple-input multiple-output (MIMO) scenarios are considered, the system usually has to manage a large number of communication links among sensors and antennas involving different vehicles and users. Millimeter wave (mmWave) communications are one of the key technology enablers toward achieving high data rates in beyond 5G systems (B5G). Communication at these frequency bands usually involves the use of large antenna arrays, often requiring high computational resources. One of the candidate platforms able to manage a huge number of communications is the Xilinx Zynq UltraScale+ EG Heterogeneous MPSoC, which is composed of a dual-core Cortex-R5, a quad-core ARM Cortex-A53, a graphics processing unit (GPU) and a high-end FPGA. This work analyzes the computational performance that requires a recent mmWave MIMO channel estimation algorithm in a platform of this kind. As a first approach, we will focus our work on the performance that can be achieved via the quad-core ARM Cortex-A53. To this end, we will use the libraries for numerical algebra (BLAS and LAPACK). The results show that our reference implementation is able to manage a large MIMO communication system with 256 antennas without exhausting platform resources.

Gibbs Sampling Detection for Large MIMO and MTC Uplinks with Adaptive Modulation.

Wireless networks beyond 5G will mostly be serving myriads of sensors and other machine-type communications (MTC), with each device having different requirements in respect to latency, error rate, energy consumption, spectral efficiency or other specifications. Multiple-input multiple-output (MIMO) systems remain a central technology towards 6G, and in cases where massive antenna arrays or cell-free networks are not possible to deploy and only moderately large antenna arrays are allowed, the detection problem at the base-station cannot rely on zero-forcing or matched filters and more complex detection schemes have to be used. The main challenge is to find low complexity, hardware feasible methods that are able to attain near optimal performance. Randomized algorithms based on Gibbs sampling (GS) were proven to perform very close to the optimal detection, even for moderately large antenna arrays, while yielding an acceptable number of operations. However, their performance is highly dependent on the chosen “temperature” parameter (TP). In this paper, we propose and study an optimized variant of the GS method, denoted by triple mixed GS, and where three distinct values for the TP are considered. The method exhibits faster convergence rates than the existing ones in the literature, hence requiring fewer iterations to achieve a target bit error rate. The proposed detector is suitable for symmetric large MIMO systems, however the proposed fixed complexity detector is highly suitable to spectrally efficient adaptively modulated MIMO (AM-MIMO) systems where different types of devices upload information at different bit rates or have different requirements regarding spectral efficiency. The proposed receiver is shown to attain quasi-optimal performance in both scenarios.

Application of Deep Learning to Sphere Decoding for Large MIMO Systems

Although the sphere decoder (SD) is a powerful detector for multiple-input multiple-output (MIMO) systems, it has become computationally prohibitive in massive MIMO systems, where a large number of antennas are employed. To overcome this challenge, we propose fast deep learning (DL)-aided SD (FDL-SD) and fast DL-aided $K$-best SD (KSD, FDL-KSD) algorithms. Therein, the major application of DL is to generate a highly reliable initial candidate to accelerate the search in SD and KSD in conjunction with candidate/layer ordering and early rejection. Compared to existing DL-aided SD schemes, our proposed schemes are more advantageous in both offline training and online application phases. Specifically, unlike existing DL-aided SD schemes, they do not require performing the conventional SD in the training phase. For a $24 \times 24$ MIMO system with QPSK, the proposed FDL-SD achieves a complexity reduction of more than $90\%$ without any performance loss compared to conventional SD schemes. For a $32 \times 32$ MIMO system with QPSK, the proposed FDL-KSD only requires $K = 32$ to attain the performance of the conventional KSD with $K=256$, where $K$ is the number of survival paths in KSD. This implies a dramatic improvement in the performance--complexity tradeoff of the proposed FDL-KSD scheme.

Early Neighbor Rejection-Aided Tabu Search Detection for Large MIMO Systems

In this study, a low complexity tabu search (TS) algorithm for multiple-input multiple-output (MIMO) systems is proposed. To reduce the computational complexity of the TS algorithm, early neighbor rejection (ENR) and layer ordering schemes are employed. In the proposed ENR-aided TS (ENR-TS) algorithm, the least promising k neighbors are excluded from the neighbor set in each layer, which reduces the computational complexity of neighbor examination in each TS iteration. For efficient computation of the neighbors’ metrics, the ENR scheme can be incorporated into QR decomposition-aided TS (ENR-QR-TS). To further reduce the complexity and improve the performance of the ENR-QR-TS scheme, a layer ordering scheme is employed. The layer ordering scheme determines the order in which layers are detected based on their expected metrics, which reduces the risk of excluding likely neighbors in early layers. The simulation results show that the ENR-TS achieves nearly the same performance as the conventional TS while providing up to 82% complexity reduction.

Beamforming and combining for multi‐user large MIMO communication system

A beamforming and combining method for a multi-user large multiple-input multiple-output (MIMO) system is proposed, in this study. A transmitter is equipped with a very large number of antennas to serve many users. At the transmitter, a group of antennas is allocated to each user. For a particular group of antennas, a specific beamforming vector is employed at the transmitter for transmission of a signal of a specific user. At the user end, a distinct combining vector is utilised for detecting the transmitted signal. In the proposed scheme, first, the interference due to unwanted signals of undesired users is nullified by using the concept of null space. Then the method of maximum ratio transmission is used to calculate the beamforming vector. The calculation of combining vector depends upon the maximum eigenvalue criterion. The analytical performance of the proposed method is discussed in terms of symbol error rate (SER). An expression of SER is derived by using the moment generating function approach. It is shown by simulations and analysis that the proposed scheme performs better if more antennas are equipped either at the transmitter or users.

Groupwise Neighbor Examination for Tabu Search Detection in Large MIMO Systems

In the conventional tabu search (TS) detection algorithm for multiple-input multiple-output (MIMO) systems, the metrics of all neighboring vectors are computed to determine the best one to move to. This strategy requires high computational complexity, especially in large MIMO systems with high-order modulation schemes such as 16- and 64-QAM signaling. This paper proposes a novel reduced-complexity TS detection algorithm called neighbor-grouped TS (NG-TS), which divides the neighbors into groups and finds the best neighbor by using a simplified cost function. Furthermore, based on the complexity analysis of NG-TS, we propose a channel ordering scheme that further reduces its complexity. Simulation results show that the proposed NG-TS with channel ordering can achieve up to 85% complexity reduction with respect to the conventional TS algorithm with no performance loss in both low- and higher-order modulation schemes.

QR-Decomposition-Aided Tabu Search Detection for Large MIMO Systems

In the conventional tabu search (TS) detection algorithm for multiple-input multiple-output (MIMO) systems, the cost metrics of all neighboring vectors are computed to determine the best neighbor. This can require an excessively high computational complexity, especially in large MIMO systems because the number of neighboring vectors and the dimension per vector are large. In this study, we propose an improved TS algorithm based on the QR decomposition of the channel matrix (QR-TS), which allows for finding the best neighbor with a significantly lower complexity compared with the conventional TS algorithm. Specifically, QR-TS does not compute all metrics by early rejecting unpromising neighbors, which reduces the computational load of TS without causing any performance loss. To further optimize the QR-TS algorithm, we investigate novel ordering schemes, namely the transmit-ordering (Tx-ordering) and receive-ordering (Rx-ordering), which can considerably reduce the complexity of QR-TS. Simulation results show that QR-TS reduces the complexity approximately by a factor of two compared with the conventional TS. Furthermore, when both Tx-ordering and Rx-ordering are applied, QR-TS requires approximately $60\%\text{ -- }90\%$ less complexity compared with the conventional TS scheme. The proposed algorithms are suitable for both low-order and high-order modulation, and can achieve a significant complexity reduction compared to the Schnorr–Euchner and $K\text{-}$ best sphere decoders in large MIMO systems.

A near maximum likelihood performance modified firefly algorithm for large MIMO detection

Abstract To meet the ever-growing demand for high data rates, employing a large number of antennas at both the transmitter and receiver is a necessity for future advanced wireless systems. Multiple-input multiple-output (MIMO) systems, which are equipped with multiple antennas, provide high data rates with high spectral efficiency. However, the design of an efficient, robust and non-erroneous detection algorithm is a huge challenge in large MIMO systems. In this paper, a stochastic bio-inspired meta-heuristic algorithm is proposed for large MIMO detection. The proposed algorithm is motivated by the bioluminescence of fireflies and uses a probabilistic metric to update solutions in the search space. Robustness of the proposed algorithm is verified under channel estimation errors at the receiver. Simulation results reveal that the proposed algorithm outperforms unordered congestion control ant colony optimization, congestion control ant colony optimization, standard particle swarm optimization, binary particle swarm optimization, memetic particle swarm optimization, firefly algorithm, firefly algorithm with neighborhood attraction, minimum mean square error and successive interference cancellation based MIMO detection techniques in terms of bit error rate (BER) performance. The proposed algorithm achieves near maximum likelihood BER performance with lower computational complexity. This makes the proposed algorithm an appropriate candidate for reliable detection in future large MIMO systems.

Imperfect CSI‐based large MIMO systems

The authors address the problem of channel estimation and data detection in a large multiple-input multiple-output (MIMO) systems in Rayleigh fading environment. A method of channel estimation and data detection is proposed in large MIMO systems. The channel matrix is decomposed in N d /2 × N s /2 channel matrices; where N d and N s are the number of antennas at the destination and source, respectively. The pilot signals are clubbed with data symbols encoded in N d /2 × N s /2 orthogonal space-time block codes (OSTBC), and then by using the properties of null matrix, channel estimation is performed. A decoder of OSTBC data is derived by assuming the perfect channel state information (CSI) at the destination; then perfect CSI is replaced by estimated CSI in the decision metric. The expression for the moment generating function (MGF) of the received signal-to-noise ratio at the destination node is derived for the proposed scheme. Using the MGF expressions, they obtain the analytical symbol error rate for the proposed channel estimation-based decoders for general OSTBCs with M-ary phase-shift keying modulation symbols.

Distance Hardening in Large MIMO Systems

Asymptotic analysis plays an important role in the performance evaluation and technology design of large multiple-input multiple-output (MIMO) systems. This paper investigates an asymptotic property of large MIMO systems, called distance hardening . It involves distance metrics defined in terms of many factors, such as the channel matrix and the difference matrix of two arbitrary transmitted codewords. The asymptotic property is revealed by the use of the Chernoff bounding method and expressed in an analogous way to the well-known channel hardening. More specifically, we first derive Chernoff bounds on the tail probabilities of distance metrics, in which we are interested. Then, we formulate the asymptotic property based on a generalized definition of the hardening phenomena by referring to a formal definition of the channel hardening. The distance hardening is shown to have implications for space-time code design, MIMO detection, and millimeter wave MIMO systems. Numerical simulations are conducted to verify our theoretical development.

Bit-Level Reduced Neighborhood Search for Low-Complexity Detection in Large MIMO Systems

Neighborhood search algorithms (NSAs) reduce the detection complexity in a multiple-input multiple-output (MIMO) system equipped with a large number of antennas. These algorithms iteratively search for the optimal maximal likelihood (ML) vector in a chosen neighborhood and therefore, their performance depends on the probability that the desired solution vector belongs to the neighborhood. An efficient choice of neighborhood vectors which are likely to reduce the ML cost, can in-turn reduce the complexity of the NSAs. To enable this, we propose a novel MIMO detection framework by representing the transmit symbols as a polynomial function of its constituent bits. We use this framework to propose: 1) a bit-level extension for the minimum mean squared error detector to initialize neighborhood search and 2) a metric-based selection criteria to reduce the neighborhood size. Combining the two ideas, we re-frame the NSAs, namely, likelihood ascent search and reactive tabu search, and numerically show that the proposed approach significantly reduces the complexity without affecting the bit error rate.

A Space-Time Transmission Scheme for Large MIMO Systems

In this letter, we propose a space-time transmission scheme (STTS) for large multiple-input multiple-output (MIMO) communication systems. These systems are primarily used to transmit a huge amount of data. The existing space-time block codes (STBCs) are not suitable for these systems due to the fact that these STBCs require very large channel coherence time (more than the number of transmit antennas), render poor data rate (less than one), and aim at full spatial diversity. In a practical large MIMO system with one thousand transmit and one thousand receive antennas, the diversity order of ${10}^{{6}}$ can be achieved; however, such a high value of diversity order is not required in practical systems. Therefore, an STTS with good data rate, parsimoniously utilized temporal dimensions, and symbol-wise decoding is essentially required for practical large MIMO systems. In this letter, we emphasize design of a new STTS by relaxing the constraint of achieving full spatial diversity. In the proposed STTS, the data rate of the large MIMO system is increased at the expense of the reduction in spatial diversity order. An approximate expression of symbol error rate of the proposed system is obtained-based on the moment generating function of the instantaneous received signal-to-noise ratio. Further, it is shown that the diversity order of the proposed STTS-based system is one less than the number of receive antennas.

Likelihood-Based Tree Search for Low Complexity Detection in Large MIMO Systems

A recently reported result on large/massive multiple-input multiple-output (MIMO) detection shows the utility of the branch and bound (BB)-based tree search approach for this problem. We can consider strong branching for improving upon this approach. However, that will require the solution of a large number of quadratic programs (QPs). We propose a likelihood based branching criteria to reduce the number of QPs required to be solved. We combine this branching criteria with a node selection strategy to achieve a better error performance than the reported BB approach, that too at a lower computational complexity. Simulation results show that the proposed algorithm outperforms the available detection algorithms for large MIMO systems.

An Unconstrained Likelihood Ascent Based Detection Algorithm for Large MIMO Systems

Neighborhood search algorithms have been proposed for detection in large multiple-input multiple-output systems. They iteratively search for the best vector in a fixed neighborhood. A better way could be to look for an update which is not restricted to a fixed neighborhood. Motivated by this, we formulate a problem to maximize the reduction in maximum likelihood (ML) cost and use it to derive an expression for updating the current solution. Using this update and a likelihood function regarding the locations of errors, we propose an unconstrained likelihood ascent search (ULAS) algorithm. ULAS seeks to provide the maximum reduction in ML cost by finding an update which is not restricted to be in a fixed neighborhood. Using simulations, the proposed algorithm has been shown to provide better error performance for uncoded systems than existing algorithms, at lower complexity. We also show that ULAS is amenable to lattice reduction, which helps in obtaining two variants leading to further improvements in performance.

OSTBC Transmission in Large MIMO Systems

We address the problem of orthogonal space-time block code (OSTBC) transmission in a large multiple-input multiple-output (MIMO) system in Rayleigh fading environment. Because there are hundreds of antennas at the transmitter, a very large dimension OSTBC is required in the case of massive MIMO system. Full rate OSTBC is available only for two transmit antenna-based system with complex symbols. Recently, an implementation of OSTBC for 32 transmit and 32 receive antennas is presented for real symbols. In this letter, we present a scheme of OSTBC transmission for practical large MIMO systems by embedding the OSTBCs of small dimensions with good rate. At the receiving end, the decoding of the OSTBCs is performed by utilizing the concept of null space. It is shown by simulation and analysis that the code rate can be improved at the cost of degraded performance; however, the performance of large MIMO system is not an issue because of the availability of very large antennas at the transmitter and receiver. The expression for the moment generating function (MGF) of the received signal-to-noise ratio at the receiver node is derived for the proposed OSTBC-based scheme. Using the MGF expression, we obtain the analytical symbol error rate for the proposed scheme with M-ary phase-shift keying modulation symbols.

On the Throughput of Large MIMO Beamforming Systems With Channel Aging

We study the problem of throughput optimization in large multiple-input multiple-output (MIMO) beamforming systems with channel aging, as the number of transmit and receive antennas is increased. We quantify the effective channel coherence time in terms of the intertraining interval, which is the time after which the channel state information needs to be reestimated to avoid loss in performance due to outdated channel estimates. Conventional wisdom suggests that the coherence time of large MIMO systems should decrease with increasing number of antennas, because the system has a large number of independently varying channel coefficients. On the contrary, we show that the effective channel coherence time increases with the number of antennas. We optimize the throughput with respect to the symbol and pilot energies, the number of antennas, frame duration, and target SNR. This analysis brings out the important fact that the effective channel coherence time critically depends on the underlying signaling scheme, and not only on the temporal correlation coefficient of the wireless channel.

An MCMC–MIMO Detector as a Stochastic Linear System Solver Using Successive Overrelexation

In this paper, we consider a Markov chain Monte Carlo (MCMC) algorithm using Gibbs sampling for signal detection in multiple input multiple output (MIMO) or code division multiple access (CDMA) systems. It is shown that the MCMC detector can be seen as a stochastic linear system solver. Based on this point of view, we generalize the MCMC detector using a relaxation factor that can improve the convergence rate. For the MCMC detector, since a faster convergence rate implies a lower computational complexity, it is important to have a faster convergence rate especially for large MIMO systems, which can also be achieved by optimizing the temperature parameter. While the optimal temperature parameter heavily depends on the signal-to-noise ratio (SNR), it is shown that a good relaxation factor can be found for wide range of the SNR and other parameters.

A Review of Compressive Sensing Detection for Spatial Modulation in Massive MIMO System

Multiple Input Multiple Output (MIMO) low complexity receiver which utilizes the compressive sensing detection for Spatial Modulation in large scale MIMO system in order to reduce the system complexity. In conventional MIMO system; huge amount of antennas is used at both ends to exploit the multipath propagation. This system maximizes the throughput performance and data rates are increased but only at the cost of high hardware complexity and increased power-consumption. Spatial Modulation Matching Pursuit (SMMP) is the proposed enhanced CS technique used for the improvement of detection performance. Hence, this paper reviews recent research findings concerning normalized Compressive Sensing (CS) detection algorithm, used for Spatial Modulation (SM) in massive MIMO, to lowers the signal processing complexity, which in result improves the energy efficiency of system against that of conventional MIMO system.This strategy is achieved by involving additional structures and sparsity in which a single transmitter antenna or a subset of it is turned on at each case to transmit a certain data. The subset of antenna which is turned on for transmission depends on approaching data bits. Therefore, the total increase in the spectral efficiency of the system is given as base-two logarithm of whole antennas at the transmitter. It reduces the signal processing load at base station and doesn’t depend upon any synchronization between transmitters. The Spatial Modulation Matching Pursuit used prevents the Inter Channel Interference (ICI) of the system which in result improves the Bit Error Rate (BER) performance than the typical MIMO system.

Non-reciprocity compensation correction and antenna selection for optical large MIMO system

This paper exploits an optical large multiple input multiple output (MIMO) system. We first establish the non-reciprocity compensation correction factor to solve the channel non-reciprocity problem. Then we propose an antenna selection algorithm with the goal of realizing maximum energy efficiency (EE) when satisfying the outage EE. The simulation results prove that this non-reciprocity compensation correction factor can compensate beam energy attenuation gap and spatial correlation gap between uplink and downlink effectively, and this antenna selection algorithm can economize the number of transmit antennas and achieve high EE performance. Finally, we apply direct current- biased optical orthogonal frequency division multiplexing (DCO-OFDM) modulation in our system and prove that it can improve the bit error rate (BER) compared with on-off keying (OOK) modulation, so the DCO-OFDM modulation can resist atmospheric turbulence effectively.