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.     

Lattice-reduction aided equalization for OFDM systems

Orthogonal Frequency Division Multiplexing (OFDM) is an effective technique to deal with frequency-selective channels since it facilitates low complexity equalization and decoding. Many existing OFDM designs successfully exploit the multipath diversity offered by frequency-selective channels. However, most of them require maximum likelihood (ML) or near-ML detection at the receiver, which is of high complexity. On the other hand, empirical results have shown that linear detectors have low complexity but offer inferior performance. In this paper, we analytically quantify the diversity orders of linear equalizers for linear precoded OFDM systems, and prove that they are unable to collect full diversity. To improve the performance of linear equalizers, we further propose to use a lattice reduction (LR) technique to help collect diversity. The LR-aided linear equalizers are shown to achieve maximum diversity order (i.e., the one collected by the ML detector), but with low complexity that is comparable to that of conventional linear equalizers. The theoretical findings are corroborated by simulation results.     

Layered space-time codes over Ricean fading channels by reducing the correlation of spatial shaping pulses

In this paper, an asynchronous layered space-time architecture is proposed to realize the spatial multiplexing over the Ricean multiple-input multiple-output (MIMO) channels. Based on reducing the correlation of spatial shaping pulses between the multiplexed streams, this approach can be used to solve the problem of detection in the ill-conditioned channel matrix. It is shown that at the receiver, the reduction of the correlation enables the requirement on the number of the receive antennas to be removed by the zero forcing (ZF) detector compared with the conventional synchronous layered space-time architecture. First, this paper presents how to exploit the correlation of spatial shaping pulses between the multiplexed streams. Then deriving the exact closed-form expression of error rate for the proposed scheme, this paper finds that the maximum possible diversity gain can be achieved based on the independent layered architecture by the ZF detector at the cost of limited multiplexing gain.     

FSO MIMO系统中分层空时码检测算法

多输入多输出(MIMO)系统可以有效提高频谱效率和系统容量。基于MIMO系统重点研究了无线光通信垂直分层空时系统(V-BLAST)检测算法。首先分析了最大似然、线性迫零、最小均方误差以及排序干扰抵消等典型的传统检测算法,基于OOK调制和4PPM调制对采用不同检测算法的系统差错性能进行了仿真对比,最后对Turbo码与BLAST技术相结合构成的新系统采用了软输入软输出(SISO)迭代检测译码方案。仿真结果表明,分层空时检测算法中性能最优的是ML,其次是SISO-MAP,ZF算法性能最差;Turbo-BLAST系统可以有效提高无线光通信系统的抗干扰性能。     

Implementation of a High Throughput Soft MIMO Detector on GPU

Multiple-input multiple-output (MIMO) significantly increases the throughput of a communication system by employing multiple antennas at the transmitter and the receiver. To extract maximum performance from a MIMO system, a computationally intensive search based detector is needed. To meet the challenge of MIMO detection, typical suboptimal MIMO detectors are ASIC or FPGA designs. We aim to show that a MIMO detector on Graphic processor unit (GPU), a low-cost parallel programmable co-processor, can achieve high throughput and can serve as an alternative to ASIC/FPGA designs. However, careful architecture aware software design is needed to leverage the performance offered by GPU. We propose a novel soft MIMO detection algorithm, multi-pass trellis traversal (MTT), and show that we can achieve ASIC/FPGA-like performance and handle different configurations in software on GPU. The proposed design can be used to accelerate wireless physical layer simulations and to offload MIMO detection processing in wireless testbed platforms.     

LR-Aided MIMO Detectors under Correlated and Imperfectly Estimated Channels

In this contribution, lattice reduction (LR) technique is applied to improve the multiple-input multiple-output (MIMO) detector performance under correlated channels and imperfect channel estimation constrains. Zero-forcing, minimum mean squared error, ordered successive interference cancellation and sphere decoding (SD) detectors are analysed taking into consideration (a) different correlated fading channel indexes, (b) increasing spectral efficiency, by combining number of transmit antennas and modulation formats, and (c) channel coefficient error estimations. Analysis of correlated channel effects over the MIMO system performance equipped with different LR-aided detectors are carried out, indicating the robustness of those detectors and the SD–MIMO detector deficiency to deal with such channel condition. Besides, computational complexities are compared aiming to determine the best LR–MIMO detection scheme under the perspective of performance-complexity tradeoff.     

Generalized feedback detection for spatial multiplexing multi-antenna systems

We present a unified detection framework for spatial multiplexing multiple-input multiple-output (MIMO) systems by generalizing Heller's classical feedback decoding algorithm for convolutional codes. The resulting generalized feedback detector (GFD) is characterized by three parameters: window size, step size and branch factor. Many existing MIMO detectors are turned out to be special cases of the GFD. Moreover, different parameter choices can provide various performance-complexity tradeoffs. The connection between MIMO detectors and tree search algorithms is also established. To reduce redundant computations in the GFD, a shared computation technique is proposed by using a tree data structure. Using a union bound based analysis of the symbol error rates, the diversity order and signal-to-noise ratio (SNR) gain are derived analytically as functions of the three parameters; for example, the diversity order of the GFD varies between 1 and N. The complexity of the GFD varies between those of the maximum-likelihood (ML) detector and the zero-forcing decision feedback detector (ZF-DFD). Extensive computer simulation results are also provided.     

Implementation of an SDR platform using GPU and its application to a 2?��?2 MIMO WiMAX system

Conventional communication systems have been implemented using digital signal processors (DSPs) and/or field programmable gate arrays (FPGAs), especially for software defined radio (SDR) functionality. We propose a scheme that uses a graphics processing unit (GPU) in place of the conventional DSPs or FPGAs for the implementation of an SDR-based communication system. The GPU, a high-speed parallel processor with multiple arithmetic logic units, is adopted for the signal processing of the physical layer required for the parallel processing in an SDR system. The compute unified device architecture (CUDA) based on the C language provides a software development kit (SDK) for the modem application of the GPU. Therefore we utilize the CUDA SDK to implement the real-time modem function. This paper presents an implementation of a 2 × 2 multiple-input multiple-output (MIMO) WiMAX system employing a GPU as the real-time modem. By installing a radio frequency module on top of the GPU modem, we implement a real-time transmission system for video data. The performance of the proposed GPU-based system is demonstrated by comparing its operation time against that of the conventional DSP-based system.     

Spatial diversity in radars-models and detection performance

Inspired by recent advances in multiple-input multiple-output (MIMO) communications, this proposal introduces the statistical MIMO radar concept. To the authors' knowledge, this is the first time that the statistical MIMO is being proposed for radar. The fundamental difference between statistical MIMO and other radar array systems is that the latter seek to maximize the coherent processing gain, while statistical MIMO radar capitalizes on the diversity of target scattering to improve radar performance. Coherent processing is made possible by highly correlated signals at the receiver array, whereas in statistical MIMO radar, the signals received by the array elements are uncorrelated. Radar targets generally consist of many small elemental scatterers that are fused by the radar waveform and the processing at the receiver, to result in echoes with fluctuating amplitude and phase. It is well known that in conventional radar, slow fluctuations of the target radar cross section (RCS) result in target fades that degrade radar performance. By spacing the antenna elements at the transmitter and at the receiver such that the target angular spread is manifested, the MIMO radar can exploit the spatial diversity of target scatterers opening the way to a variety of new techniques that can improve radar performance. This paper focuses on the application of the target spatial diversity to improve detection performance. The optimal detector in the Neyman-Pearson sense is developed and analyzed for the statistical MIMO radar. It is shown that the optimal detector consists of noncoherent processing of the receiver sensors' outputs and that for cases of practical interest, detection performance is superior to that obtained through coherent processing. An optimal detector invariant to the signal and noise levels is also developed and analyzed. In this case as well, statistical MIMO radar provides great improvements over other types of array radars.     

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.     

基于V-BLAST的特征波束形成技术在大规模MIMO中的运用

为了获得较高的频谱效率及较低的误码率,提出了大规模MIMO系统中基于V-BLAST的特征波束形成技术(the Eigen-Beamforming combined with V-BLAST,V-BLAST&E-BF),利用大规模天线形成多个特征波束,在这些特征波束上传输多个码流,既可以获得阵列增益又可以获得复用增益.仿真结果表明:提出的方案较MF预编码和传统特征波束形成技术具有较好的性能,并且在接收端无须进行传统V-BLAST的检测算法(如MMSE检测、ZF检测)亦可分离出信号.     

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.     

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.     

具有未知参数的多输入多输出雷达弱目标检测

针对弱目标检测算法的特点,提出了一种新的多输入多输出(MIMO)雷达检测器。在经典线性模型的基础上,通过最大似然法对未知统计特性的噪声量进行了估计。利用所得到的估计量,分别推导了在信道完全不相关和信道任意相关条件下虚警概率和检测概率的闭合表达式,对具有未知参数的MIMO雷达在任意信道环境下的检测算法进行了分析和比较,有效地解决了具有未知统计特性的噪声的MI-MO雷达目标检测问题。仿真结果证实了该方法的有效性。     

Target spatial and frequency scattering diversity property for diversity MIMO radar

Statistical multiple-input multiple-output (MIMO) radar, e.g., frequency diversity MIMO radar (FDMR) and spatial diversity MIMO radar (SDMR), can exploit signal diversity to improve target detection performance. The statistical property of target echo signals received in diversity channels is an important concern in designing signal processing algorithms for an FDMR and an SDMR, which is studied in this paper by using a round shaped scatterers centre target model. A uniform formula is derived to estimate the correlation coefficients of target echo signals in diversity channels for both an FDMR and an SDMR. The theoretical correlation coefficients are testified by numerical experiments.     

Full-rate full-diversity 2 × 2 space-time codes of reduced decoder complexity

Multiple-input multiple-output (MIMO) techniques have become an essential part of broadband wireless communications systems. For example, the recently developed IEEE 802.16e specifications for broadband wireless access include three MIMO profiles employing 2times2 space-time codes (STCs) and two of those are mandatory on the downlink of Mobile WiMAX systems. Conventional approaches to STC design are based on performance criteria such as coding gain, diversity gain, multiplexing gain, and ignore the decoder complexity. In this paper, we take an alternative approach and present a full-rate full-diversity 2times2 STC design leading to substantially lower complexity of the optimum detector than existing schemes. This makes the implementation of high performance full-rate codes realistic in practical 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.     

Computationally Efficient Lattice Reduction Aided Detection for MIMO‐OFDM Systems under Correlated Fading Channels

We analyze the relationship between channel coherence bandwidth and two complexity‐reduced lattice reduction aided detection (LRAD) algorithms for multiple‐input multiple‐output (MIMO) orthogonal frequency division multiplexing (OFDM) systems in correlated fading channels. In both the adaptive LR algorithm and the fixed interval LR algorithm, we exploit the inherent feature of unimodular transformation matrix P that remains the same for the adjacent highly correlated subcarriers. Complexity simulations demonstrate that the adaptive LR algorithm could eliminate up to approximately 90 percent of the multiplications and 95 percent of the divisions of the brute‐force LR algorithm with large coherence bandwidth. The results also show that the adaptive algorithm with both optimum and globally suboptimum initial interval settings could significantly reduce the LR complexity, compared with the brute‐force LR and fixed interval LR algorithms, while maintaining the system performance.     

V-BLAST光MIMO系统检测算法分析

为了降低系统光多输入多输出(MIMO)系统的复杂度,提高系统的性能,介绍了迫零(ZF)检测算法、最小均方误差(MMSE)检测算法、最大似然(ML)检测算法在垂直分层空时编码(V-BLAST)光MIMO空时系统中的应用。从理论上对算法性能和复杂度进行研究,然后在MATLAB建立仿真模型,对多模光纤的传输函数进行仿真,结果表明在多模光纤链路中,ZF算法性能较低;MMSE算法较ZF算法有所改进;ML算法通过比较接收符号和原发送的符号之间的相似度,从而获得原符号的最小差错概率,其性能最好。     

Exploration of Soft-Output MIMO Detector Implementations on Massive Parallel Processors

Emerging Software Defined Radio (SDR) baseband platforms are based on multiple processors with massive parallelism. Although the computational power of these platforms would theoretically enable SDR solutions with advanced wireless signal processing, existing work implements still rather basic algorithms. For instance, current Multiple-Input Multiple-Output (MIMO) detector implementations are typically based on simple linear hard-output and not on advanced near-Maximum Likelihood (ML) soft-output detection. However, only the latter enables to exploit the full potential of MIMO technology. In this work, we explore the feasibility of advanced soft-output near-ML MIMO detectors on massive parallel processors. Although such detectors are considered to be very challenging due to their high computational complexity, we combine architecture-friendly algorithm design, application specific instructions and instruction-level/data-level parallelism explorations to make SDR solutions feasible. We show that, by applying the proposed combination of techniques, it is possible to obtain SDR implementations which can deliver data rates that are sufficient for future wireless systems. For example, a 2 × 4 Coarse Grain Array (CGA) processor with 16-way Single Instruction Multiple Data (SIMD) can deliver 192/368 Mbps throughput for 2 × 2 64/16-QAM transmissions. Finally, we estimate the area and power consumption of the programmable solution and compare it against a traditional Application Specific Integrated Circuit (ASIC) approach. This enables us to draw conclusions from the cost perspective.