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.     

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.     

An approximate MAP-based iterative receiver for MIMO channels using modified sphere detection

For coded multiple-input multiple-output spatial multiplexing (MIMO-SM) systems, the iterative receiver consisting of the MIMO detector and decoding can provide near optimal performance. While the sphere detection (SD) technique can be employed to implement the MIMO maximum likelihood (ML) detection with a lower complexity, some modifications of the SD have been proposed to provide a soft-decision for iterative receivers. In the paper, we propose an alternative approach that is based on a quadratic cost function to find the maximum a-posteriori (MAP) solution for the MIMO detection. Using the proposed approach, the MAP detection with the soft-decision can be straightforwardly implemented by the SD technique. Compared to the existing approach, in the new scheme, the soft-decision is well defined and it avoids a numerical instability in computing a soft-decision (which is an approximation of the log likelihood ratio (LLR)). Through simulation results, it is shown that the performance of the proposed scheme is comparable to that of the existing approach.     

BPSK通信系统的部分最优MIMO检测算法

在BPSK调制下,基于最大似然（Maximum Likelihood,ML）准则的MIMO检测器是一个二进制二次规划问题,其计算复杂度随着天线数的增多呈指数增加,当天线数较多时,其计算量太大,无法满足实时通信的要求。本文提出了一种新的MIMO检测算法。使用新算法,可以在很小的计算开销下,求解出ML检测器的部分全局最优解,然后,将优先检测出的部分最优解从原二进制二次规划问题中剔除得到一个相对小规模问题,最后使用传统的次最优检测算法对该小规模问题进行求解。这样,新算法不仅可以得到比传统的次最优检测器更低的误码率,计算量又远小于ML最优检测器。本文的仿真结果验证了新算法的有效性。      

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。     

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.     

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。     

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.     

ML Approaching MIMO Detection Based on Orthogonal Projection

A detection algorithm for spatially multiplexed multiple input multiple output (MIMO) systems is proposed. The receiver first estimates the MIMO channel and rearranges the layers according to the measured SNRs. To determine the candidate vectors, an orthogonal projection combined with the M-algorithm is used. Without performing the exhaustive full search of the maximum likelihood (ML) method, the proposed algorithm can reach the performance which is closely akin to the ML method. The computational complexity markedly decreases: 0.66% over the ML method in terms of the number of real multiplications.     

MIMO系统中k-best球形译码算法研究

通过对广度优先策略中有恒定复杂度的层排序k-best球译码算法进行分析,提出一种每节点保留可变扩展节点的层排序k-best球形译码算法(k-best SDA Ⅱ),在64QAM调制及每层保留8节点的实数SDA模型下,通过仿真的方法得出了保留恒定扩展节点的k-best SDA当每节点保留扩展节点数大于等于2时,性能基本不变(k-best SDA Ⅰ);而改进的k-best SDA Ⅱ则对k-best SDA Ⅰ在性能与复杂度上作了比较好的折中,前者计算复杂度大约减少了28%,而性能的损失基本可以忽略.     

V-BLAST系统中一种近似最佳列表检测算法

针对V-BLAST系统,提出一种近似最佳列表检测算法。该列表检测算法通过调节列表维数参数在检测性能和计算复杂度之间实现了较好的折衷。此外,给出了一种不同于OSIC算法的检测排序方法,进一步提高了检测性能。仿真和复杂度比较结果表明,在不相关和空间相关性较强的信道下,该列表检测算法均显著优于OSIC算法,甚至接近ML算法的性能,实现了性能和复杂度较好的折衷,是一种实用的选择。      

On the partial MAP detection with applications to MIMO channels

We investigate a multidimensional detection problem with a partial information of the a posteriori probability, which is referred to as the partial maximum a posteriori probability (MAP) detection problem. We show that the maximum likelihood (ML) detection of a higher dimension can be reduced to the ML detection of a lower dimension with cancellation under a certain condition through the formulation of the partial MAP detection problem. Using this, we can propose a computationally efficient algorithm to apply to the detection problem for multiple input multiple output (MIMO) channels including multiple transmit and multiple receive antenna (MTMR) channels and intersymbol interference (ISI) channels. It is shown that the proposed method has less error propagation effect, and its performance is close to that of the full ML detection with a lower computational complexity.     

Combined simplified maximum likelihood and sphere decoding algorithm for MIMO system

In this article, a new system model for sphere decoding （SD） algorithm is introduced. For the 2 × 2 multipleinput multiple-out （MIMO） system, a simplified maximum likelihood （SML） decoding algorithm is proposed based on the new model. The SML algorithm achieves optimal maximum likelihood （ML） performance, and drastically reduces the complexity as compared to the conventional SD algorithm. The improved algorithm is presented by combining the sphere decoding algorithm based on Schnorr-Euchner strategy （SE-SD） with the SML algorithm when the number of transmit antennas exceeds 2. Compared to conventional SD, the proposed algorithm has low complexity especially at low signal to noise ratio （SNR）. It is shown by simulation that the proposed algorithm has performance very close to conventional SD.     

Soft quasi-maximum-likelihood detection for multiple-antenna wireless channels

The paper addresses soft maximum-likelihood (ML) detection for multiple-antenna wireless communication channels. We propose a soft quasi-ML detector that maximizes the log-likelihood function by deploying a semi-definite relaxation (SDR). Given perfect channel state information at the receiver, the quasi-ML SDR detector closely approximates the performance of the optimal ML detector in both coded and uncoded multiple-input, multiple-output (MIMO) channels with quadrature phase-shift keying (QPSK) modulation and frequency-flat Rayleigh fading. The complexity of the quasi-ML SDR detector is much less than that of the optimal ML detector, thus offering more favorable performance/complexity characteristics. In contrast to the existing sphere decoder, the new quasi-ML detector enjoys guaranteed polynomial worst-case complexity. The two detectors exhibit quite comparable performance in a variety of ergodic QPSK MIMO channels, but the complexity of the quasi-ML detector scales better with increasing number of transmit and receive antennas, especially in the region of low signal-to-noise ratio (SNR).     

基于动态分组的球形译码算法

在MIMO信号检测中,采用最大似然算法可以使系统的误码率最低,但最大似然算法要搜索整个信号空间,计算速度相当慢。球形译码算法性能最接近最大似然算法,它通过减少需要比较的信号点可大大降低计算量。提出了动态分组的球形译码算法,对传统球形译码算法进行了改进。仿真结果表明,所提算法可以根据M IMO系统的需要进行动态调整,可在小信噪比时降低误码率,大信噪比时提高译码速率。     

Efficient detection algorithms for MIMO channels: a geometrical approach to approximate ML detection

It is well known that suboptimal detection schemes for multiple-input multiple-output (MIMO) spatial multiplexing systems (equalization-based schemes as well as ing-and-cancelling schemes) are unable to exploit all of the available diversity, and thus, their performance is inferior to ML detection. Motivated by experimental evidence that this inferior performance is primarily caused by the inability of suboptimal schemes to deal with "bad" (i.e., poorly conditioned) channel realizations, we study the decision regions of suboptimal schemes for bad channels. Based on a simplified model for bad channels, we then develop two computationally efficient detection algorithms that are robust to bad channels. In particular, the novel sphere-projection algorithm (SPA) is a simple add-on to standard suboptimal detectors that is able to achieve near-ML performance and significantly increased diversity gains. The SPA's computational complexity is comparable with that of ing-and-cancelling detectors and only a fraction of that of the Fincke-Phost sphere-decoding algorithm for ML detection.     

MIMO雷达搜索模式下的射频隐身算法

为提高MIMO雷达在电子战中的生存能力,分析了雷达各参数与其搜索性能及射频隐身性能的关系,建立了MIMO雷达搜索模式下的射频隐身性能优化模型,其中射频隐身性能综合考虑了MIMO雷达的截获因子及搜索帧周期。在此基础上,给出了一种MIMO雷达搜索模式下的射频隐身优化算法,该算法通过自适应地控制雷达系统天线划分的子阵数、信号占空比、波束驻留时间以及搜索帧周期,在满足雷达系统检测性能及搜索时间资源约束的要求下,优化雷达系统的射频隐身性能。仿真结果表明,MIMO雷达采用搜索模式下的射频隐身算法,能在保证检测性能的条件下,相比非射频隐身的搜索状态,获得更好的射频隐身性能。     

大规模MIMO系统基于分布式压缩感知的信号检测算法研究

随着通信技术的不断发展,人们对通信速率的要求越来越高,大规模MIMO(Multiple-Input Multiple-Output)技术因其能够大大提高系统的频谱效率,成为通信技术领域的研究热点.在大规模空间调制MIMO中,原本最佳的检测方法——最大似然(Maximum likelihood,ML)检测算法由于算法复杂度过高,不再适用.而适用于小规模空间调制MIMO系统的低复杂度的检测算法在大规模系统中性能会很差.本文利用空间调制信号的结构化稀疏性,提出了基于分布式压缩感知(Distributed Compressed Sensing,DCS)的信号检测算法,同时参照已有文献,利用分组传输和信号交织来进一步提高信号检测性能.最后我们通过仿真验证了此方案能够较好地逼近最大似然检测算法性能.     

On maximum-likelihood detection and the search for the closest lattice point

Maximum-likelihood (ML) decoding algorithms for Gaussian multiple-input multiple-output (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using number-theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr-Euchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near-ML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.     

一种新的用于多天线系统的快速球形解码算法

本文提出了一种实现多输入—多输出(MIMO)无线系统最大似然(ML)信号检测的快速球形解码器框架,在本框架内,算法不需要确定半径参数,同时,在算法的搜索阶段只需要访问最少的树节点数,从而降低算法的复杂度。另外,当我们采用一种直接的Schnorr-Euchner枚举(SEE)方法时,本球解码框架可用于复数MIMO系统。仿真结果显示,和其它球形解码器相比,本解码器能大大提升最大似然(ML)检测的速度。