MIMO Detection Research Articles

Research of a reliable constraint algorithm on MIMO signal detection

For common nonlinear QR decomposition detection algorithm in MIMO system, this paper proposes reliability constraints QR algorithm (RC-QR algorithm) with low complexity. The reliability of soft estimates is judged by shadow area constraint method. Besides, constellation points are introduced as the candidate points. Then the optimal candidate point is chosen from multiple candidate points for feedback. Relative to conventional QR DE composition algorithm, the RC-QR algorithm can significantly improve system interference and greatly reduce error propagation in decision feedback by increasing the algorithm complexity only by a small amount. The simulation results show that the performance of our algorithm improves very obviously when the antenna configuration is 4 × 4 or 6 × 6. When bit error rate is 5 × 1,000, 6 dB signal to noise ratio can be saved. Meanwhile, RC-QR algorithm can flexibly balance bit error rate detection performance and operation complexity through controlling constraint threshold and the quantity of candidate points.

Efficient MIMO Preprocessor With Sorting-Relaxed QR Decomposition and Modified Greedy LLL Algorithm

This paper proposes a high-efficient preprocessing algorithm for $16\times 16$ MIMO detections. The proposed algorithm combines a sorting-relaxed QR decomposition (SRQRD) and a modified greedy LLL (MGLLL) algorithm. First, SRQRD is conducted to decompose the channel matrices. This decomposition adopts a relaxed sorting strategy together with a paralleled Givens Rotation (GR) array scheme, which can reduce the processing latency by 60% compared with conventional sorted QR decomposition (SQRD). Then, an MGLLL algorithm is conducted to improve detection performance further. The MGLLL algorithm adopts a paralleled selection criterion, and only process the most urgent iterations. Thus the processing latency and column swaps can be reduced by 50% and 75%, respectively, compared with the standard LLL algorithm. Finally, the bit-error-rate (BER) performance of this preprocessing algorithm is evaluated using two MIMO detectors. Results indicate that this preprocessor suffers a negligible performance degradation compared with the combination of the standard LLL algorithm and SQRD. Based on this preprocessing algorithm, a pipelined hardware architecture is also designed in this paper. A series of systolic coordinated-rotation-digital-computer (CORDIC) arrays are utilized, and highly-pipelined circuits are designed, helping this architecture achieve high frequency performance. This architecture is implemented using 65-nm CMOS technology, which can work at a maximum frequency of 625 MHz to process channel matrices every 16 clock cycles. The latency is 0.9 us. Comparisons indicate that this preprocessor outperforms other similar designs in terms of latency, throughput, and gate-efficiency.

Efficient initialisation of iterative linear massive MIMO detectors using a stair matrix

Several approximate matrix inversion methods have been used in linear massive MIMO uplink detectors where their convergence rate, performance, and complexity are greatly affected by the initial solution. In this Letter, the authors exploit a stair matrix, instead of a diagonal matrix, in initialising iterative linear minimum mean square error massive MIMO detector based on several approximate matrix inversion methods, namely, the Gauss-Seidel, successive over relaxation, Richardson iteration, and Newton iteration methods. Numerical results show a significant performance enhancement without a burden of extra complexity using a stair matrix over a diagonal matrix in all methods.

Efficient Method for Three Loop MMSE-SIC based Iterative MIMO Systems

Iterative decoding is one of the promising methods to improve the performance of MIMO systems. In iterative processing channel decoder and MIMO detector share the information in order to enhance the overall system performance. However, iterative processing requires a lot of computations therefore it is considered as a computationally complex approach due to complex detection schemes involving iterative processing. There are several promising detection methods that require further improvements and they can be candidates in order to practically implement iterative processing. In this paper, the propose method to improve the efficiency of three loop-based minimum mean squared errors with soft interference cancellation (MMSE-SIC) method by reducing its complexity with a single inverse operation. Simulation results are given in order to provide detail analysis of the proposed MMSE-SIC based approach for iterative detection and decoding (IDD).

On Design of Protograph LDPC Codes for Large-Scale MIMO Systems

Protograph low-density parity-check (LDPC) codes and large-scale multi-input multi-output (LS-MIMO) systems have achieved great interest with various practical applications. However, how to effectively evaluate and design protograph LDPC codes for LS-MIMO systems remains a challenging yet critical problem, especially for low-latency applications. To solve that design challenge, the protograph extrinsic information transfer chart (PEXIT) algorithm for LS-MIMO systems, so-called LS-MIMO-PEXIT algorithm, is first derived based on the mutual information functions of messages that are passed on the joint MIMO detection and LDPC decoding graph. The proposed LS-MIMO-PEXIT algorithm plays a vital role in the optimization process of designing new protograph LDPC codes, tailored for LS-MIMO communications systems. Experiment results demonstrate that the analytical results based on the LS-MIMO-PEXIT algorithm are in good agreement with the simulation results under various input constraints, including the coding rate, the number of decoding iterations, and the LS-MIMO configuration. On top of that, the new protograph LDPC codes designed using our LS-MIMO-PEXIT algorithm achieve a coding gain from 0.2 dB at a low coding rate to 0.4 dB at a high coding rate in comparison with the state-of-the-art protograph codes in the literature. Additionally, we incorporate the practical design experience and the theoretical analysis of mutual functions into a two-step procedure to search for protograph LDPC codes that do not have error-floor behavior at frame error rate (FER) or bit error rate (BER) as low as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> or 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> , respectively. Together with the coding gain, the error-floor-free feature of the proposed protograph LDPC codes is vitally important for future wireless networks where the ultra-reliability is one of the critical requirements.

A Symmetric Successive Overrelaxation (SSOR) based Gauss-Seidel Massive MIMO Detection Algorithm

With an increasing number of antennas and users, the complexity increases dramatically, in order to simplify the process. In this paper, We propose existed algorithms discussing their principles and their advantages as well as the comparison between each method and then we provide the possible improvement in theory changing steps in iteration process to avoid the matrix inversion, by introducing a pre-conditioned gradient (PCG) method and further improved Jacobi method and using Neumann-series terms to estimate an approximate matrix inversion and the Gauss-Seidel (GS) method with a diagonal-approximate initial solution to the method and biconjugate gradient stabilized (BICGSTAB) method and above all of the methods are based on the minimum mean square error (MMSE) detector including the application in multi-user MIMO system. Another approach is from a signal detector based on symmetric successive over relaxation (SSOR) method without matrix inversion and Neumann series based on the zero forcing signal detector. The third algorithm uses a modified version of the conjugate gradient least square (CGLS). These methods are mainly replacing the inversion process into iteration process to reduce the complexity of the algorithm not only replacing the stages but optimizing the speed from setting the initial solution as well as the improvement using the Neumann-series to replace the iteration part. Finally, we proposed a symmetric successive overrelaxation (SSOR) based Gauss-Seidel for massive MIMO detection.

On Low-Complexity Lattice Reduction Algorithms for Large-Scale MIMO Detection: The Blessing of Sequential Reduction

Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for large-scale problems, this paper investigates a new framework called sequential reduction (SR), which aims to reduce the lengths of all basis vectors. The performance upper bounds of the strongest reduction in SR are given when the lattice dimension is no larger than 4. The proposed new framework enables the implementation of a hash-based low-complexity lattice reduction algorithm, which becomes especially tempting when applied to large-scale MIMO detection. Simulation results show that, compared to other reduction algorithms, the hash-based SR algorithm exhibits the lowest complexity while maintaining comparable error performance.

Adjustable threshold LAS massive MIMO detection under imperfect CSI and spatial correlation

In this paper, a likelihood ascent search (LAS) detector with adjustable threshold (ρ-LAS) is proposed for uplink (UL) massive multiple-input-multiple-output (M-MIMO) systems. The performance-complexity tradeoff for the ρ-LAS-based detector is extensively analyzed and compared with the conventional LAS M-MIMO detector by means of Monte Carlo simulations (MCS). Adjusting a threshold associated with the likelihood function, for each system and channel scenario, we found that the ρ-LAS is able to achieve better performance than the conventional LAS detector without complexity increment. Considering practical scenarios deteriorated by antenna correlation and imperfect channel state information (CSI) in M-MIMO systems, ρ-LAS detector has proven to be superior than the LAS detector in terms of performance while requires a fixed but very marginal additional number of computations. In addition, ρ-LAS provided a much better performance-complexity tradeoff in scenario with medium signal-to-noise ratio (SNR) and high number of antennas, a common operation scenario in M-MIMO systems. Finally, the ρ-LAS M-MIMO and three representative M-MIMO detection methods, namely the polynomial expansion (PE), the dual band Newton inversion (DBNI) and the iterative sequential detector (ISD), are compared. The results indicate a substantial performance-complexity tradeoff improvement for our proposed ρ-LAS detector.

A 2.92-Gb/s/W and 0.43-Gb/s/MG Flexible and Scalable CGRA-Based Baseband Processor for Massive MIMO Detection

Communication systems’ development requires service customization in aspects, such as standards, multiple-input multiple-output (MIMO) scales, and algorithms. The existing hardware designs for massive MIMO detection have difficulty in achieving both high flexibility and scalability with high hardware efficiency. This article proposes a baseband processor based on a dynamic coarse-grained reconfigurable array (CGRA) for massive MIMO detection. To efficiently support various algorithm features and requirements, three optimization techniques are proposed to achieve high flexibility and scalability. First, an on-demand matrix–vector systolic array is proposed to enable flexible and scalable matrix and vector operations, reducing memory accesses by 82%. Second, distributed multi-interaction data storage is designed for flexible data access and reusability. Finally, a continuable adaptive context information format is proposed to support different bit widths, operations, and extensions of MIMO systems, reducing context information by 67%. These techniques achieve the improvements of 1.33 $\times $ , 1.34 $\times $ , and 1.29 $\times $ in energy efficiency and 1.21 $\times $ , 1.18 $\times $ , and 1.18 $\times $ in area efficiency, evaluated by removing one technique at a time from the proposed architecture. Fabricated in a 28-nm CMOS technology, the chip achieves high flexibility and scalability in supporting various detection algorithms; various MIMO scales, such as $4\,\,\times $ 4, 32 $\times $ 32, and 128 $\times $ 8; and baseband processing tasks, such as filtering and fast Fourier transformation. When benchmarked on various detection algorithms, the processor achieves 1.64–2.92-Gb/s/W energy efficiency and 0.25–0.43-Gb/s/MG area efficiency, which are 2.78–28.54 $\times $ and 2.05–14.43 $\times $ those of state-of-the-art programmable designs, respectively. To our knowledge, this is the first flexible and scalable CGRA-based baseband processor for massive MIMO detection.

Performance enhancement based on machine learning scheme for space multiplexing 2[formula omitted]2 MIMO VLC system employing joint IQ independent component analysis

With the increasing demand for Visible Light Communication (VLC) bandwidth, the space-multiplexing technique has been widely utilized to enhance the capability of the VLC system. In this paper, we proposed a novel MIMO detection scheme to decompose the superposed signals in a 2×2 multiple-input-multiple-output (MIMO) VLC system. With the help of the proposed machine learning scheme, two received optical signals can be separated into two independent parallel signals. By simulation, the unmixing matrix can be quickly converged by iterations. Extensive experiments demonstrate an average BER of 6.191×10−4 is achieved at a bitrate of 750 Mbps over a 1.3-m line of sight (LOS) in the 2×2 MIMO scenario. Finally, to evaluate the performance of the algorithm, the Q factor yielded a gain of about 2.5 dB compared with the traditional Alamouti Space–Time Block Coding (STBC) scheme.

A computationally efficient detector for MIMO systems

&lt;p&gt;In this work, a newly designed multiple-input multiple-output (MIMO) detector for implementation on software-defined-radio platforms is proposed and its performance and complexity are studied. In particular, we are interested in proposing and evaluating a MIMO detector that provides the optimal trade-off between the decoding complexity and bit error rate (BER) performance as compared to the state of the art detectors. The proposed MIMO decoding technique appears to find the optimal compromise between competing interests encountered in the implementation of advanced MIMO detectors in practical hardware systems where it i) exhibits deterministic decoding complexity, i.e., deterministic latency, ii) enjoys a good complexity–performance trade-off, i.e., it keeps the complexity considerably lower than that of the maximum likelihood detectors with almost optimal performance, iii) allows fully parameterizable performance to complexity trade-off where the performance (or complexity) of the MIMO detector can be adaptively adjusted without the requirement of changing the implementation, iv) enjoys simple implementation and fully supports parallel processing, and v) allows simple and efficient extension to soft-bit output generation for support of turbo decoding. From the simulation results, the proposed MIMO decoding technique shows a substantially improved complexity–performance trade-off as compared to the state of the art techniques.&lt;/p&gt;

Markov Chain Monte Carlo Methods for Lattice Gaussian Sampling: Convergence Analysis and Enhancement

Sampling from lattice Gaussian distribution has emerged as an important problem in coding, decoding, and cryptography. In this paper, the classic Gibbs algorithm from Markov chain Monte Carlo (MCMC) methods is demonstrated to be geometrically ergodic for lattice Gaussian sampling, which means that the Markov chain arising from it converges exponentially fast to the stationary distribution. Meanwhile, the exponential convergence rate of the Markov chain is also derived through the spectral radius of the forward operator. Then, a comprehensive analysis of the convergence rate is carried out, and two sampling schemes are proposed to further enhance the convergence performance. The first one, referred to as a Metropolis-within-Gibbs (MWG) algorithm, improves the convergence by refining the state space of the univariate sampling. The second is a blocked strategy of the Gibbs algorithm, which performs sampling over multivariates at each Markov move, and is shown to yield a better convergence rate than the traditional univariate sampling. In order to perform blocked sampling efficiently, the Gibbs–Klein (GK) algorithm is proposed, which samples block by block using the Kleins algorithm. Furthermore, the validity of the GK algorithm is demonstrated by showing its ergodicity. Simulation results based on MIMO detections are presented to confirm the convergence gain brought by the proposed Gibbs sampling schemes.

A Novel Iterative Discrete Estimation Algorithm for Low-Complexity Signal Detection in Uplink Massive MIMO Systems

In this paper, a novel iterative discrete estimation (IDE) algorithm, which is called the modified IDE (MIDE), is proposed to reduce the computational complexity in MIMO detection in uplink massive MIMO systems. MIDE is a revision of the alternating direction method of multipliers (ADMM)-based algorithm, in which a self-updating method is designed with the damping factor estimated and updated at each iteration based on the Euclidean distance between the iterative solutions of the IDE-based algorithm in order to accelerate the algorithm’s convergence. Compared to the existing ADMM-based detection algorithm, the overall computational complexity of the proposed MIDE algorithm is reduced from O N t 3 + O N r N t 2 to O N t 2 + O N r N t in terms of the number of complex-valued multiplications, where Ntand Nr are the number of users and the number of receiving antennas at the base station (BS), respectively. Simulation results show that the proposed MIDE algorithm performs better in terms of the bit error rate (BER) than some recently-proposed approximation algorithms in MIMO detection of uplink massive MIMO systems.

Lattice-Reduction-Aided Gibbs Algorithm for Lattice Gaussian Sampling: Convergence Enhancement and Decoding Optimization

Sampling from the lattice Gaussian distribution has emerged as an important problem in coding, decoding, and cryptography. In this paper, lattice reduction technique is adopted to Gibbs sampler for lattice Gaussian sampling. First, with respect to lattice Gaussian distribution, we show the convergence rate of systematic scan Gibbs sampling is characterized by the Hirschfeld-Gebelein-Renyi maximal correlation among the multivariate of being sampled. Then, Lattice-reduction-aided Gibbs algorithm is proposed to sample from an equivalent lattice Gaussian distribution but with less correlated multivariate, thus leading to a better Markov mixing. After that, we extend the proposed lattice-reduction-aided Gibbs sampling to lattice decoding, where the choice of the standard deviation for the sampling is fully investigated. A customized solution that suits for each specific decoding case by Euclidean distance is given, which results in a better tradeoff between Markov mixing and sampler decoding. Based on it, a startup mechanism is also proposed for Gibbs sampler decoding, where decoding complexity can be reduced without performance loss. Moreover, the recycling Gibbs sampling that exploits the potential of samples is also considered to improve the decoding performance in lattice decoding. Simulation results based on large-scale uncoded multiple-input multiple-output detection are presented to confirm the performance gain and complexity reduction.

A Novel Efficient Sphere Decoding with Reed-Solomon Code in MIMO Detection

An optimal receiver recovering transmitted signals across a noisy communication channel employs an efficient impact as Sphere Decoding (SD) benchmark to reduce the probability of error. This system can employ a coding strategy for information security where the data symbol space forms a scant lattice. The sparsity structure is resolved through channel code. In this article, motivated by this idea, we present novel efficient detection-decoding combinational techniques using Reed-Solomon (RS) decoding followed by the single tree search (STS) algorithm in SD detection. The simulation results determine that the proposed method of improving the performance of 1.6 dB at the bit error rate (BER) of has a significant impact.

Lattice reduction aided pre-processor for large scale MIMO detection

Linear detectors such as Minimum Mean Square Error (MMSE), Zero Forcing are applied for large scale MIMO detection because of their low computational cost, but has the least performance. In this paper, improvement in the performance of lattice Reduction aided- linear detectors for large scale MIMO is analyzed. Lattice reduction is performed using Seysen's Algorithm (SA). SA finds the reduced basis with minimum number of iterations compared to the commonly used Lenstra, Lenstra, and Lovász (LLL) algorithm. Also, SA based reduction of channel matrix, outperforms the existing LLL algorithm based reduction for sub optimal linear detectors in terms of bit error rate (BER) and computational complexity. The simplified VLSI architecture of SA is implemented in hardware using 45 nm technology

High throughput K best MIMO detector using modified final selector based carry select adder

The VLSI architecture of novel K best detector using Carry Select Adder (CSA) with Modified Final Selector Unit (MFSU) is proposed for wireless communication applications. The challenge in K best detector design is to utilize less number of levels with high throughput. To overcome this limitation, pipelining technique is exploited in expansion and minimization block. This architecture also includes the sorter block which provides these signals in a proper format and then the processing element processed the signals from the sorter block and determines the best signal. This proposed design can achieve high throughput with the clock frequency as 311.6 MHz. The proposed K best detector is synthesized and simulated using Xilinx ISE and it is coded in Verilog HDL. When compared to ISCAS’13, DATE’11, KB-HPED, KB-VPED, K best detector with CSA, the proposed novel K best detector with MFSU based CSA reduces the number of slices by 11.89%, 9.85%, 8.29%, 6.12%, 3.56% and reduces the number of 4 input LUTs by 9.38%, 0.1%, 8.10%, 3.15%, 1.9% respectively. The proposed technique reduces the energy consumption by 33.33%, 16.5% and 5.18% compared to KB-HPED, KB-VPED and KB with CSA.

Iterative Gaussian-Approximated Message Passing Receiver for MIMO-SCMA System

Sparse code multiple access (SCMA) and multiple-input multiple-output (MIMO) are viewed as two key techniques to address the high spectral efficiency requirements for the 5G wireless system. However, the complexity of standard message passing algorithm (MPA) for the MIMO-SCMA detection yet increases exponentially with the degree of resource nodes $d_f$ and the number of transmit antennas $N_t$ . In this paper, to tackle this problem, we design two types of low-complexity MPA over the MIMO-SCMA extended factor graph to perform joint multiuser and MIMO detection. The main idea of the proposed algorithms is approximating the discrete interferences at function nodes (FNs) as the continuous Gaussian messages so that the traversal enumeration at the FN update can be avoided. The symbol level Gaussian approximated MPA (GAMPA-S) updates the symbol likelihood during the detector's inner-loop iterations which is similar to the standard MPA, and this algorithm is compatible to any SCMA codebooks. The bit level Gaussian approximated MPA (GAMPA-B) updates the bit likelihood ratio which shows lower complexity compared to the GAMPA-S. However, the GAMPA-B requires that the SCMA codebooks can satisfy the bit significance expansion property. In the receiver, the proposed detectors are combined with users’ decoders to form the outer-loop structure, in which a critical damping factor (DF) is designed to compress the amplitude of extrinsic information exchanged between the detector and decoders. The extrinsic information transform chart is introduced to optimize the DF. Consequently, the complexity of the proposed receiver just increases linearly with $d_f$ and $N_t$ while its performance is comparable or even better than the conventional receiver. This would effectively boost the practical use of MIMO-SCMA techniques.

Performance evaluation of 2 × 2 MIMO–OFDM‐based radio‐over‐fibre system using Alamouti coding and Hammerstein equaliser

Radio-over-fibre (RoF) systems consist of two subsystems including optical subsystem and wireless radio frequency subsystem. It is shown that by using multiple-input multiple-output (MIMO) and orthogonal frequency-division multiplexing (OFDM) systems, the RoF transmission can be improved in frequency-selective channels. In this study, two different configurations of MIMO–OFDM-based RoF systems are compared for the long-term evolution standard under different non-linearity levels, bandwidths, and fading channel conditions. Using the total degradations (TD) criterion, an appropriate quiescent point is determined to decrease the impact of non-linearity level, and hence the performances of different MIMO detection methods are compared. Bit error rate results demonstrate that by using Hammerstein type equaliser, the system performance is improved under different conditions including different fading channels, Doppler frequencies, bandwidths, and output back off levels. Results demonstrate that with an appropriate structure for MIMO–OFDM–RoF systems, a suitable quiescent point can be found for all scenarios by employing Alamouti coding and Hammerstein equaliser.

Enhancement of K-Best Sphere Detection algorithm Performance in MIMO Systems

Due to the rapid development of our life toward a life with high-quality communication systems, which require large data rates for transfer such as Long Term Evolution (LTE), Worldwide Interoperability for Microwave Access(WiMAX), and Wireless Fidelity (WiFi) which use Multiple Input - Multiple Output (MIMO) systems. Therefore, become necessary to interest in MIMO system parts especially the MIMO detector (MIMOD). A good detector system must have two important goals, low Computational Complexity (CC) and good Symbol Error Rate (SER) performance). To achieve that two important goals, our work divided into two parts. The first part, by using an unequal power transmission (UEPT) scheme in instead of equal power transmission (EPT) scheme to get a good SER. The second part, how to reduced CC, this achieved by changing the Euclidean Distance (ED) by using Manhattan Distance (MD). The simulation results show us a slight improvement in the SER performance of about 1.1 dB as average gain and a good reduction in CC about 24% as average reduction in visited nodes when using the UEPT with MD against using EPT with ED.