A simple low-complexity algorithm for generalized spatial modulation

Generalized spatial modulation (GSM) is an extension of spatial modulation which is significant for the next generation communication systems. Optimal detection process for the GSM is the maximum-likelihood (ML) detection which jointly detects the antenna combinations and transmitted symbols. However, the receiver is much more complicated than SM due to inter-antenna interference and/or increased number of combinations. Therefore, the computational complexity of the ML detection grows with the number of transmit antennas and the signal constellation size. In this letter, we introduce a novel and simple detection algorithm which uses sub-optimal method based on the least squares solution to detect likely antenna combinations. Once the antenna indices are detected, ML detection is utilized to identify the transmitted symbols. For obtaining near-ML performance while keeping lower complexity than ML detection, sphere decoding is applied. Our proposed algorithm reduces the search complexity while achieving a near optimum solution. Computer simulation results show that the proposed algorithm performs close to the optimal (ML) detection resulting in a significant reduction of computational complexity.     

An application of univariate marginal distribution algorithm in MIMO communication systems

The paper discusses a sequence detector based on univariate marginal distribution algorithm (UMDA) that jointly estimates the symbols transmitted in a multiple input multiple output (MIMO) communication system. While an optimal maximum likelihood detection using an exhaustive search method is prohibitively complex, it has been shown that sphere decoder (SD) achieves the optimal bit error rate (BER) performance with polynomial time complexity for smaller array sizes. However, the worst‐case complexity of SD is exponential in the problem dimensions, this brings in question its practical implementation for larger number of spatial layers and for higher‐order signal constellation. The proposed detector shows promising results for this overly difficult and complicated operating environment, confirmed through simulation results. A performance comparison of the UMDA detector with SD is presented for higher‐order complex MIMO architectures with limited average transmit power. The proposed detector achieves substantial performance gain for higher‐order systems attaining a near optimal BER performance with reduced computational complexity as compared with SD. Copyright © 2009 John Wiley & Sons, Ltd.     

An MBER–BLAST algorithm for OFDM–SDMA communication using particle swarm optimization

A multiple antenna‐aided, minimum bit error rate–Bell Laboratories‐layered space–time (MBER–BLAST) multiuser detection algorithm is proposed for uplink orthogonal frequency division multiplexing–space division multiple access (OFDM–SDMA) communication to increase the capacity of the system. The proposed algorithm overcomes the limitations of the conventional detectors when the number of users exceed the number of receiver antennas. A particle swarm optimization (PSO) algorithm is employed for finding the optimum weight vectors for MBER detector. PSO is well suited for physically realizable, real‐time applications, where low complexity and fast convergence are of absolute importance, while an optimum maximum likelihood (ML) detection using an exhaustive search method is prohibitively complex. The proposed algorithm outperforms the MBER detector and is capable of achieving performance close to that attained by ML detector at a significantly lower complexity, especially under high user loads. Simulation results show that MBER–BLAST detector promises substantially improved performance compared with the existing systems and offers a good performance–complexity trade‐off. It supports a large number of users by exploiting the capacity advantages of multiple antenna systems in rich scattering environments. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance Analysis of Layer Pruning on Sphere Decoding in MIMO Systems

Sphere decoding (SD) for multiple‐input and multiple‐output systems is a well‐recognized approach for achieving near‐maximum likelihood performance with reduced complexity. SD is a tree search process, whereby a large number of nodes can be searched in an effort to find an estimation of a transmitted symbol vector. In this paper, a simple and generalized approach called layer pruning is proposed to achieve complexity reduction in SD. Pruning a layer from a search process reduces the total number of nodes in a sphere search. The symbols corresponding to the pruned layer are obtained by adopting a QRM‐MLD receiver. Simulation results show that the proposed method reduces the number of nodes to be searched for decoding the transmitted symbols by maintaining negligible performance loss. The proposed technique reduces the complexity by 35% to 42% in the low and medium signal‐to‐noise ratio regime. To demonstrate the potential of our method, we compare the results with another well‐known method — namely, probabilistic tree pruning SD.     

广义空间调制系统的正则化OMP检测算法

在广义空间调制（GSM）系统中,最大似然（ML）检测可以取得最优的检测性能,然而其计算复杂度随激活天线数的增加急剧增长。针对这一问题,提出了一种基于稀疏重构理论的低复杂度检测算法——正则化正交匹配追踪（ROMP）算法。该算法首先根据信道矩阵和当前残差的内积选取多个候选激活天线索引,接着对候选天线索引按正则化标准进行可靠性验证,剔除错误索引,缩小信号的搜索空间,最后通过求解最小二乘问题估计信号。仿真结果表明,与经典的正交匹配追踪（OMP）算法相比,所提算法以少许复杂度的增加为代价极大提升了检测性能,能够在检测性能与复杂度之间取得更好的折中。     

MIMO系统中局域化最大似然信号检测算法

提出了一种MIM0系统中低复杂度的局域化最大似然信号检测算法，该方法通过调整信号有效搜索域大小，在计算复杂度与系统性能之间折衷．实验结果表明：该信号检测算法明显降低了高阶QAM调制的计算复杂度，在QPSK和16QAM调制时，当系统性能接近最大似然算法时计算量仅为其很小一部分。     

正交空间调制的低复杂度检测算法

针对正交空间调制(QSM)系统中激活天线数的不确定性、最大似然(ML)检测算法复杂度极高的缺点,提出了一种低复杂度检测算法.首先,该算法基于压缩感知(CS)信号重构理论,对系统模型进行重构,使固定激活天线系统中的低复杂度算法可以在新的系统模型中使用;然后,借鉴正交匹配追踪(OMP)算法的思想,选出一个激活天线备选集;最后,通过ML算法搜索备选集,选出激活天线和调制符号.仿真结果显示,相比ML检测算法,所提算法在性能丢失较小的情况下,降低了约90％的复杂度.     

Optimal low-complexity detection for space division multiple access wireless systems

A symbol detector for wireless systems using space division multiple access (SDMA) and orthogonal frequency division multiplexing (OFDM) is derived. The detector uses a sphere decoder (SD) and has much less computational complexity than the naive maximum likelihood (ML) detector. We also show how to detect non-constant modulus signals with constrained least squares (CLS) receiver, which is designed for constant modulus (unitary) signals. The new detector outperforms existing suboptimal detectors for both uncoded and coded systems.     

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.     

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     

Genetic algorithm assisted joint multiuser symbol detection andfading channel estimation for synchronous CDMA systems

A novel multiuser code division multiple access (CDMA) receiver based on genetic algorithms is considered, which jointly estimates the transmitted symbols and fading channel coefficients of all the users. Using exhaustive search, the maximum likelihood (ML) receiver in synchronous CDMA systems has a computational complexity that is exponentially increasing with the number of users and, hence, is not a viable detection solution. Genetic algorithms (GAs) are well known for their robustness in solving complex optimization problems. Based on the ML rule, GAs are developed in order to jointly estimate the users' channel impulse response coefficients as well as the differentially encoded transmitted bit sequences on the basis of the statistics provided by a bank of matched filters at the receiver. Using computer simulations, we showed that the proposed receiver can achieve a near-optimum bit-error-rate (BER) performance upon assuming perfect channel estimation at a significantly lower computational complexity than that required by the ML optimum multiuser detector. Furthermore, channel estimation can be performed jointly with symbol detection without incurring any additional computational complexity and without requiring training symbols. Hence, our proposed joint channel estimator and symbol detector is capable of offering a higher throughput and a shorter detection delay than that of explicitly trained CDMA multiuser detectors     

4×4 V-BLAST系统分组最大似然检测算法

对于V-BLAST系统的检测,最大似然(ML)算法有着最优的性能却也有最大的计算复杂度;经典的排序连续干扰抵消(OSIC)算法复杂度较低,但数值稳定性差,且性能与ML差距较大.因此,本文基于检测性能和计算复杂度折中的思想,针对4×4 V-BLAST系统提出了一种分组最大似然(Group ML,GML)检测算法,在保证较好检测性能的基础上,通过将四维ML检测器分成两组二维ML检测器来降低计算复杂度.此外,本文还提出了一种简化的最大似然(Simpli-fled ML,SML)检测算法,通过将每组中的二维ML检测器的搜索空间从二维降至一维,进一步降低了计算复杂度,并证明其与ML算法具有一致的性能.仿真表明,在误符号率为10~(-3)时GML算法相比OSIC算法有约7dB的性能提升.经分析知.GML算法复杂度与ML-OSIC算法相比在高阶调制方式下有着显著的降低,易于硬件实现.     

Performance analysis for MIMO systems with lattice-reduction aided linear equalization

Multi-input multi-output (MIMO) systems equipped with multiple antennas have well documented merits in combating fading and enhancing data rates. MIMO V-BLAST transmission is a widely adopted method to achieve high spectral efficiency and low-complexity implementation. When the maximum likelihood (ML) or near-ML detector is employed, receive diversity is collected for MIMO V-BLAST systems to enhance the performance. However, because of its exponential complexity, ML detector may be infeasible for practical systems when the number of antennas and/or the constellation size is large. On the other hand, linear equalizers have much lower complexity but come with inferior performance. In this paper, we analytically quantify the diversity order of linear detectors for MIMO V-BLAST systems. Then, we adopt low-complexity complex lattice-reduction (LR) aided linear equalizers for V-BLAST systems to improve the performance and prove that LR-aided linear equalizers collect the same diversity order as that exploited by the ML detector but with much lower complexity. Relative to the existing real LR-aided equalizers, we illustrate that the complex LR further reduces the complexity while keeping the same performance. Simulation results corroborate our theoretical claims.     

A Statistical Pruning Strategy for Schnorr-Euchner Sphere Decoding

The high computational complexity of maximum likelihood (ML) decoding can impact many applications such as code division multiple access (CDMA) and multiple-input multiple-output (MIMO) systems. The sphere decoder (SD) as an efficient ML decoder has therefore received significant attention in the wireless research community. This letter presents a new statistical method to reduce the complexity of the Schnorr and Euchner sphere decoder (SESD). The method uses a set of bounds, which are computed using the conditional probability based on the minimum metric of the current solution. A lookup tabic for the bounds can be computed offline. The proposed method is effective for any number of antennas with complexity savings about 50% or more over the conventional SD approach.     

广义空间调制系统的低复杂度检测算法

针对广义空间调制( GSM)系统接收端最大似然( ML)检测算法计算复杂度极高的缺点,提出了一种基于压缩感知( CS)信号重构理论的低复杂度信号检测算法。首先,在多输入多输出( MI-MO)信道模型下,通过改进正交匹配追踪( OMP)算法,得到一个激活天线索引备选集;然后,利用ML算法在该备选集中进行遍历搜索,检测出激活天线索引和星座调制符号。仿真结果表明所提算法的检测性能接近于ML算法,且复杂度约为ML算法的2%。因此,所提算法在保证检测性能的同时也大大降低了计算复杂度,实现了检测性能与复杂度之间的平衡。     

基于深度学习的多模OFDM索引调制检测器

本文提出了一种基于深度学习（Deep Learning, DL）的多模正交频分复用索引调制（Multi-Mode Orthogonal Frequency Division Multiplexing with Index Modulation, MM-OFDM-IM）检测器。在该检测器中包括两个子卷积神经网络（Sub-Convolutional Neural Network, SCNN）并行对MM-OFDM-IM信号的索引位和载波位进行检测,接收符号在经过迫零（Zero Force, ZF）均衡后再预处理生成二维矩阵,同时输入到子卷积网络中学习信号的内在特征。经过离线训练,该检测器可以实现MM-OFDM-IM符号的在线检测。仿真结果表明,该检测器在瑞利衰落信道条件下能以较低的计算复杂度获得近似最大似然（Maximum Likelihood, ML）检测性能。通过对已训练后的模型进行剪枝操作,能在保证检测误码率（Bit Error Rate, BER）的前提下大幅度减少模型的参数量,达到了性能与计算复杂度的有效平衡。     

Hybrid SNR-Adaptive Multiuser Detectors for SDMA-OFDM Systems

Multiuser detection (MUD) and channel estimation techniques in space-division multiple-access aided orthogonal frequency-division multiplexing systems recently has received intensive interest in receiver design technologies. The maximum likelihood (ML) MUD that provides optimal performance has the cost of a dramatically increased computational complexity. The minimum mean-squared error (MMSE) MUD exhibits poor performance, although it achieves lower computational complexity. With almost the same complexity, an MMSE with successive interference cancellation (SIC) scheme achieves a better bit error rate performance than a linear MMSE multiuser detector. In this paper, hybrid ML-MMSE with SIC adaptive multiuser detection based on the joint channel estimation method is suggested for signal detection. The simulation results show that the proposed method achieves good performance close to the optimal ML performance at low SNR values and a low computational complexity at high SNR values.     

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.     

Efficient Hybrid Linear Massive MIMO Detector Using Gauss–Seidel And Successive Over-Relaxation

The initial solution of a massive multiple-input multiple-output (M-MIMO) detector for uplink (UL) is greatly influence the balance between the bit error rate (BER) performance and the computational complexity. Although the maximum likelihood (ML) detector obtains the best BER performance, it has an extremely high computational complexity. Iterative linear minimum mean square error (MMSE) detector based on the Gauss–Seidel (GS), the successive over-relaxation (SOR), and the Jacobi (JA), obtains a good performance-complexity profile when the base station (BS)-to-user-antenna-ratio (BUAR) is large. However, when the BUAR is small, the system suffers from a considerable performance loss. In this paper, a hybrid detector based on the joint GS and SOR methods is proposed where the initial solution is determined by the first iteration of GS method. Numerical results show a considerable complexity reduction and performance enhancement using the proposed GS-SOR method over all methods when the BUAR is small.

     

一种低复杂度空间调制球形译码检测算法

现有的空间调制系统球形译码（Sphere-Decoding,SD）检测算法虽然能够较大地降低最大似然（Maximum-Likelihood,ML）检测算法的计算复杂度,但由于其更新半径比较松散、收敛较慢,计算复杂度降低的水平仍十分有限,尤其是在高阶调制系统下.针对上述问题,采用统计分布的思想对现有算法更新半径中的冗余项进行估计,提出了两种改进的球形译码检测算法.理论分析与仿真结果表明,改进算法在达到最优检测性能的同时,极大地降低了传统球形译码的计算复杂度,具有较好的理论和实际应用意义.