Reliability feedback–aided low‐complexity detection in uplink massive MIMO systems

Massive multiple‐input multiple‐output (MIMO) plays a crucial role in realizing the demand for higher data rates and improved quality of service for 5G and beyond communication systems. Reliable detection of transmitted information bits from all the users is one of the challenging tasks for practical implementation of massive‐MIMO systems. The conventional linear detectors such as zero forcing (ZF) and minimum mean square error (MMSE) achieve near‐optimal bit error rate (BER) performance. However, ZF and MMSE require large dimensional matrix inversion which induces high computational complexity for symbol detection in such systems. This motivates for devising alternate low‐complexity near‐optimal detection algorithms for uplink massive‐MIMO systems. In this work, we propose an ordered sequential detection algorithm that exploits the concept of reliability feedback for achieving near‐optimal performance in uplink massive‐MIMO systems. In the proposed algorithm, symbol corresponding to each user is detected in an ordered sequence by canceling the interference from all the other users, followed by reliability feedback‐based decision. Incorporation of the sequence ordering and the reliability feedback‐based decision enhances the interference cancellation, which reduces the error propagation in sequential detection, and thus, improves the BER performance. Simulation results show that the proposed algorithm significantly outperforms recently reported massive‐MIMO detection techniques in terms of BER performance. In addition, the computational complexity of the proposed algorithm is substantially lower than that of the existing algorithms for the same BER. This indicates that the proposed algorithm exhibits a desirable trade‐off between the complexity and the performance for massive‐MIMO systems.     

Zero forcing based sphere decoder for generalized spatial modulation systems

To reduce the number of radio frequency (RF) chains in multiple input multiple output (MIMO) systems, generalized spatial modulation (GSM) techniques have been proposed in the literature. In this paper, we propose a zero‐forcing (ZF)‐based detector, which performs an initial pruning of the search tree that will be considered as the initial condition in a sphere decoding (SD) algorithm. The proposed method significantly reduces the computational complexity of GSM systems while achieving a near maximum likelihood (ML) performance. We analyze the performance of the proposed method and provide an analytic performance difference between the proposed method and the ML detector. Simulation results show that the performance of the proposed method is very close to that of the ML detector, while achieving a significant computational complexity reduction in comparison with the conventional SD method, in terms of the number of visited nodes. We also present some simulations to assess the accuracy of our theoretical results.     

Low‐Power Channel‐Adaptive Reconfigurable 4×4 QRM‐MLD MIMO Detector

This paper presents a low‐complexity channel‐adaptive reconfigurable QR‐decomposition and M‐algorithm‐based maximum likelihood detection (QRM‐MLD) multiple‐input and multiple‐output (MIMO) detector. Two novel design approaches for low‐power QRM‐MLD hardware are proposed in this work. First, an approximate survivor metric (ASM) generation technique is presented to achieve considerable computational complexity reduction with minor BER degradation. A reconfigurable QRM‐MLD MIMO detector (where the M‐value represents the number of survival branches in a stage) for dynamically adapting to time‐varying channels is also proposed in this work. The proposed reconfigurable QRM‐MLD MIMO detector is implemented using a Samsung 65 nm CMOS process. The experimental results show that our ASM‐based QRM‐MLD MIMO detector shows a maximum throughput of 288 Mbps with a normalized power efficiency of 10.18 Mbps/mW in the case of MIMO with 64‐QAM. Under time‐varying channel conditions, the proposed reconfigurable MIMO detector also achieves average power savings of up to 35% while maintaining a required BER performance.     

Adaptive joint maximum‐likelihood detection and minimum‐mean‐square error with successive interference canceler over spatially correlated multiple‐input multiple‐output channels

We develop an efficient hard detector for multiple‐input multiple‐output (MIMO) channels, which adaptively combines maximum‐likelihood detection (MLD) and minimum‐mean‐square error with a successive interference canceler together. Unlike the conventional joint combination scheme, which may suffer from considerable degradation in bit‐error‐rate (BER) performance over correlated channels and where only one data stream is detected by MLD, our proposed scheme adaptively controls the number of data streams to be detected by MLD based on an analytical characterization of reliability for the detection. Simulation results illustrate that near‐optimal BER performance can be obtained at much lower computational complexity by the proposed method as compared with existing techniques, regardless of the spatial correlation of the MIMO channels. Copyright © 2012 John Wiley & Sons, Ltd.     

Low complexity scalable MIMO sphere detection through antenna detection reordering

This paper describes a novel low complexity scalable multiple-input multiple-output (MIMO) detector that does not require preprocessing and the optimal squared l ²-norm computations to achieve good bit error (BER) performance. Unlike existing detectors such as Flexsphere that use preprocessing before MIMO detection to improve performance, the proposed detector instead performs multiple search passes, where each search pass detects the transmit stream with a different permuted detection order. In addition, to reduce the number of multipliers required in the design, we use l ¹-norm in place of the optimal squared l ²-norm. To ameliorate the BER performance loss due to l ¹-norm, we propose squaring then scaling the l ¹-norm. By changing the number of parallel search passes and using norm scaling, we show that this design achieves comparable performance to Flexsphere with reduced resource requirement or achieves BER performance close to exhaustive search with increased resource requirement.     

GPU Acceleration of a Configurable N-Way MIMO Detector for Wireless Systems

Multiple-input multiple-output (MIMO) wireless is an enabling technology for high spectral efficiency and has been adopted in many modern wireless communication standards, such as 3GPP-LTE and IEEE 802.11n. However, (optimal) maximum a-posteriori (MAP) detection suffers from excessively high computational complexity, which prevents its deployment in practical systems. Hence, many algorithms have been proposed in the literature that trade-off performance versus detection complexity. In this paper, we propose a flexible N-Way MIMO detector that achieves excellent error-rate performance and high throughput on graphics processing units (GPUs). The proposed detector includes the required QR decomposition step and a tree-search detector, which exploits the massive parallelism available in GPUs. The proposed algorithm performs multiple tree searches in parallel, which leads to excellent error-rate performance at low computational complexity on different GPU architectures, such as Nvidia Fermi and Kepler. We highlight the flexibility of the proposed detector and demonstrate that it achieves higher throughput than existing GPU-based MIMO detectors while achieving the same or better error-rate performance.     

Symbol detection in spatial multiplexing system using particle swarm optimization meta-heuristics

Symbol detection in multi-input multi-output (MIMO) communication systems using different particle swarm optimization (PSO) algorithms is presented. This approach is particularly attractive as particle swarm intelligence is well suited for real-time applications, where low complexity and fast convergence is of absolute importance. While an optimal maximum likelihood (ML) detection using an exhaustive search method is prohibitively complex, PSO-assisted MIMO detection algorithms give near-optimal bit error rate (BER) performance with a significant reduction in ML complexity. The simulation results show that the proposed detectors give an acceptable BER performance and computational complexity trade-off in comparison with ML detection. These detection techniques show promising results for MIMO systems using high-order modulation schemes and more transmitting antennas where conventional ML detector becomes computationally non-practical to use. Hence, the proposed detectors are best suited for high-speed multi-antenna wireless communication systems. Copyright © 2008 John Wiley & Sons, Ltd.     

Linear and widely linear filtering applied to iterative detection of generalized MIMO signals

To suppress the co-antenna interference in multiple input multiple output (MIMO) systems, an iterative receiver with a linear detector for complex symbols is investigated. We show that the considered generalized MIMO system, i.e., a system that transmits complex conjugate repetitions in addition to the pure data, requires the application of a widely linear (wl) detector. Awl detector consists of four real filters which are represented by two complex filters for the received signal and its complex conjugate, respectively. Furthermore, we present approximations of the detector that significantly reduce computational complexity with only little loss in frame-error rate performance. Simulation results show that the proposed MIMO system achieves large gains over standard solutions.     

Efficient Near‐Optimal Detection with Generalized Sphere Decoder for Blind MU‐MIMO Systems

In this letter, we propose an efficient near‐optimal detection scheme (that makes use of a generalized sphere decoder (GSD)) for blind multi‐user multiple‐input multiple‐output (MU‐MIMO) systems. In practical MU‐MIMO systems, a receiver suffers from interference because the precoding matrix, the result of the precoding technique used, is quantized with limited feedback and is thus imperfect. The proposed scheme can achieve near‐optimal performance with low complexity by using a GSD to detect several additional interference signals. In addition, the proposed scheme is suitable for use in blind systems.     

The Error Probability of the Fixed-Complexity Sphere Decoder

The fixed-complexity sphere decoder (FSD) has been previously proposed for multiple-input multiple-output (MIMO) detection in order to overcome the two main drawbacks of the sphere decoder (SD), namely its variable complexity and its sequential structure. Although the FSD has shown remarkable quasi-maximum-likelihood (ML) performance and has resulted in a highly optimized real-time implementation, no analytical study of its performance existed for an arbitrary MIMO system. Herein, the error probability of the FSD is analyzed, proving that it achieves the same diversity as the maximum-likelihood detector (MLD) independent of the constellation used. In addition, it can also asymptotically yield ML performance in the high-signal-to-noise ratio (SNR) regime. Those two results, together with its fixed complexity, make the FSD a very promising algorithm for uncoded MIMO detection.     

MMSE准则下近似最优MIMO分组并行检测算法

在采用多天线高阶QAM的MIMO通信系统中,现有基于信道分组并行检测算法虽然接近最优检测性能但以牺牲计算效率为代价.针对这一问题,本文提出一种MMSE准则下基于信道分组的并行检测算法,不但有效降低计算复杂度,而且仍保证检测性能.该算法采用MMSE准则下格归约算法改进分组后条件较好子信道矩阵特性,并在消除参考信号基础上利用改进的子信道矩阵对剩余信号以非线性方式进行检测.仿真结果表明:对4×4和6×6MIMO系统,该算法检测性能达到最优,对于8×8 MIMO系统,比最优算法所需信噪比提高约1dB.复杂度分析表明:相比现有信道分组检测算法,相同检测性能下该算法在6×6 MIMO系统中复杂度降低90%以上,在8×8 MIMO系统中复杂度降低98%以上.     

Implementation of parallel lattice reduction-aided MIMO detector using graphics processing unit

Since H. Yao proposed the lattice reduction (LR)-aided detection algorithm for the MIMO detector, one can exploit the diversity gain provided by the LR method to achieve performance comparable to the maximum likelihood (ML) algorithm but with complexity close to the simple linear detection algorithms such as zero forcing (ZF), minimum mean squared error, and successive interference cancellation, etc. In this paper, in order to reduce the processing time of the LR-aided detector, a graphics processing unit (GPU) has been proposed as the main modem processor in such a way that the detections can be performed in parallel using multiple threads in the GPU. A 2X2 multiple input multiple output (MIMO) WiMAX system has been implemented using a GPU to verify that various MIMO detection algorithms such as ZF, ML, and LR-aided methods can be processed in real-time. From the experimental results, we show that GPUs can realize a 2X2 WiMAX MIMO system adopting an LR-aided detector in real-time. We achieve a processing time of 2.75?ms which meets the downlink duration specification of 3?ms. BER performance of experimental tests also indicates that the LR-aided MIMO detector can fully exploit diversity gain as well as ML detector.     

Performance analysis of uplink spatial multiplexing MIMO MT‐CDMA over multipath fading channels

In this paper, we consider multiple‐input multiple‐output (MIMO) multi‐tone code division multiple access (MT‐CDMA) uplink transmission over multipath fading channels. The zero‐forcing vertical Bell Laboratories layered space‐time architecture (ZF V‐BLAST) algorithm and maximum ratio combining scheme are applied at the receiver. The average bit error rate (BER) expression is derived provided that the number of receive antennas is not less than that of transmit antennas. The BER expression is verified by simulations. Numerical results show that the numbers of transmit and receive antennas have significant effects on the BER performance of the considered system. Spatial and path diversity show different capabilities to improve the BER performance. The MIMO MT‐CDMA system based on the ZF V‐BLAST algorithm is capable of achieving a better BER performance and a higher capacity than the conventional MT‐CDMA system. Copyright © 2011 John Wiley & Sons, Ltd.     

A new complex sphere detector with SE enumeration

Multiple-Input Multiple-Output (MIMO) techniques are promising in wireless communication systems for its high spectral efficiency. Sphere Detector (SD) is favoured in MIMO detection to achieve Maximum-Likelihood (ML) performance. In this paper, we proposed a new SD method for MIMO-Orthogonal Frequency Division Multiplexing (OFDM) systems based on IEEE802.11n, which uses Singular Value Decomposition (SVD) in complex domain to reduce the computation complexity. Furthermore, a new Schnorr-Euchner (SE) enumeration algorithm is also discussed in detail. The computer simulation result shows that the computational complexity and the number of visited nodes can be reduced significantly compared with conventional SD detectors with the same Bit Error Rate (BER) performance.     

适用于大规模MIMO系统的低复杂度RZF-SOR预编码算法

在大规模多输入多输出(MIMO)系统中,为了降低传统预编码算法的复杂度,在原有正则化迫零(RZF)预编码算法的基础上,提出用超松驰迭代(SOR)法代替矩阵求逆的高复杂度运算,得到一种改进算法RZF-SOR,并应用随机矩阵原理得出其最优相关参数的近似表达式和取值的必要条件.实验仿真表明,提出的RZF-SOR预编码算法与RZF预编码相比有效地降低了一个数量级的复杂度,在很小的迭代次数下达到接近于RZF预编码的误码率性能,并且优于基于Neumann级数预编码算法的误码率性能.     

A Low-Complexity Detector for Large MIMO Systems and Multicarrier CDMA Systems

We consider large MIMO systems, where by 'large' we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a low-complexity detector which achieves uncoded near-exponential diversity performance for hundreds of antennas (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average per-bit complexity of just O(N_tN_r), where N_t and N_r denote the number of transmit and receive antennas, respectively. With an outer turbo code, the proposed detector achieves good coded bit error performance as well. For example, in a 600 transmit and 600 receive antennas V-BLAST system with a high spectral efficiency of 450 bps/Hz (using BPSK and rate-3/4 turbo code), our simulation results show that the proposed detector performs to within about 7 dB from capacity. This practical feasibility of the proposed high-performance, low-complexity detector could potentially trigger wide interest in the theory and implementation of large MIMO systems. We also illustrate the applicability of the proposed detector in the low-complexity detection of high-rate, non-orthogonal space-time block codes and large multicarrier CDMA (MC-CDMA) systems. In large MC-CDMA systems with hundreds of users, the proposed detector is shown to achieve near single-user performance at an average per-bit complexity linear in number of users, which is quite appealing for its use in practical CDMA systems.     

短波通信多组空时编码中等效MIMO模型ZF解码

面向短波通信提出了多组空时编码( MGSTC )的一种等效多输入多输出( MIMO )模型迫零( ZF)解码算法。该算法以降低运算复杂度为目的,将原多时隙MIMO系统拆分为多个多时隙单输入多输出( SIMO)系统并分别等效为多个新的单时隙MIMO系统模型,通过各自左乘等效信道矩阵的共轭转置后进行最大比合并( MRC)以及ZF解码获得发送信号估计值,避免了球形解码( SD)中对高阶矩阵的QR分解。仿真结果表明,与虚拟MIMO模型SD解码算法相比,等效MIMO模型ZF解码算法在误码率( BER)性能1 dB损耗的情况下,运算量降低一个数量级以上。     

Network‐coded MIMO‐NOMA systems with FEC codes in two‐way relay networks

This paper assumes two users and a two‐way relay network with the combination of 2×2 multi‐input multi‐output (MIMO) and nonorthogonal multiple access (NOMA). To achieve network reliability without sacrificing network throughput, network‐coded MIMO‐NOMA schemes with convolutional, Reed‐Solomon (RS), and turbo codes are applied. Messages from two users at the relay node are network‐coded and combined in NOMA scheme. Interleaved differential encoding with redundancy (R‐RIDE) scheme is proposed together with MIMO‐NOMA system. Quadrature phase‐shift keying (QPSK) modulation technique is used. Bit error rate (BER) versus signal‐to‐noise ratio (SNR) (dB) and average mutual information (AMI) (bps/Hz) versus SNR (dB) in NOMA and MIMO‐NOMA schemes are evaluated and presented. From the simulated results, the combination of MIMO‐NOMA system with the proposed R‐RIDE‐Turbo network‐coded scheme in two‐way relay networks has better BER and higher AMI performance than conventional coded NOMA system. Furthermore, R‐RIDE‐Turbo scheme in MIMO‐NOMA system outperforms the other coded schemes in both MIMO‐NOMA and NOMA systems.     

Quasi-maximum-likelihood multiuser detection using semi-definiterelaxation with application to synchronous CDMA

The maximum-likelihood (ML) multiuser detector is well known to exhibit better bit-error-rate (BER) performance than many other multiuser detectors. Unfortunately, ML detection (MLD) is a nondeterministic polynomial-time hard (NP-hard) problem, for which there is no known algorithm that can find the optimal solution with polynomial-time complexity (in the number of users). A polynomial-time approximation method called semi-definite (SD) relaxation is applied to the MLD problem with antipodal data transmission. SD relaxation is an accurate approximation method for certain NP-hard problems. The SD relaxation ML (SDR-ML) detector is efficient in that its complexity is of the order of K^3.5, where K is the number of users. We illustrate the potential of the SDR-ML detector by showing that some existing detectors, such as the decorrelator and the linear-minimum-mean-square-error detector, can be interpreted as degenerate forms of the SDR-ML detector. Simulation results indicate that the BER performance of the SDR-ML detector is better than that of these existing detectors and is close to that of the true ML detector, even when the cross-correlations between users are strong or the near-far effect is significant     

VLSI Architecture for MIMO Soft-Input Soft-Output Sphere Detection

Achieving good detection performance while incurring low complexity is known to be one of the major challenges in multiple-input multiple-output (MIMO) communications based on spatial multiplexing. The tuple search detector (TSD) was recently introduced, improving this trade-off with regard to other tree-search-based algorithms (e.g. single tree search or list sphere detector). Motivated by the tremendous gain achievable through the turbo principle and based on a previously developed soft-output (SO) TSD implementation, this work presents the first soft-input soft-output (SISO) TSD realization, scalable in constellation size and number of antennas and mapped to a highly parallel and pipelined VLSI architecture. The proposed SISO-TSD VLSI realization is instantiated for 4 × 4 MIMO transmission and 64-QAM constellation in 65-nm CMOS technology. For a given BER?complexity trade-off, the throughput ranges from 57.3 Mbps (iterative detection-decoding with 3 iterations) to 403.6 Mbps (non-iterative detection-decoding) at a clock frequency of 454 MHz. The BER?complexity trade-off can be moreover adjusted according to transmission conditions, reaching >1 Gbps in high SNR scenarios. A silicon area of 0.14 mm² (97.7 kGEs) is occupied by the SISO-TSD core, reporting low power dissipation (58.2 mW – 73.9 mW) under typical case operating conditions. The proposed detector implementation achieves hence high throughput with reasonable hardware complexity, representing a very competitive strategy with regard to relevant state-of-the-art realizations.