Sampling-based soft equalization for frequency-selective MIMO channels

We consider the problem of channel equalization in broadband wireless multiple-input multiple-output (MIMO) systems over frequency-selective fading channels, based on the sequential Monte Carlo (SMC) sampling techniques for Bayesian inference. Built on the technique of importance sampling, the stochastic sampler generates weighted random MIMO symbol samples and uses resampling to rejuvenate the sample streams; whereas the deterministic sampler, a heuristic modification of the stochastic counterpart, recursively performs exploration and selection steps in a greedy manner in both space and time domains. Such a space-time sampling scheme is very effective in combating both intersymbol interference and cochannel interference caused by frequency-selective channel and multiple transmit and receiver antennas. The proposed sampling-based MIMO equalizers significantly outperform the decision-feedback MIMO equalizers with comparable computational complexity. More importantly, being soft-input soft-output in nature, these sampling-based MIMO equalizers can be employed as the first-stage soft demodulator in a turbo receiver for coded broadband MIMO systems. Such a turbo receiver successively improves the receiver performance through iterative equalization, channel re-estimation, and channel decoding. Finally, computer simulation results are provided to demonstrate the performance of the proposed sampling-based soft MIMO equalizers in both uncoded and turbo coded systems.     

Blind detection in MIMO systems via sequential Monte Carlo

We provide a novel sequential estimation and detection approach for multiple-input-multiple-output (MIMO) systems. The basic idea is to design a probabilistic approximation method for the computation of the maximum a posterior distribution (MAP) via the sequential Monte Carlo methods (SMC). The SMC method has two advantages over the other methods in that it is a blind method and can be computed in parallel. Furthermore, the SMC has characteristics of soft-input and soft-output in nature and, thus, it can be employed as the first stage demodulator in a turbo receiver for a coded MIMO system. Such a turbo receiver successively improves the receiver performance by iteratively exchanging the so-called extrinsic information with the MAP outer channel decoder. Finally, the performance of the proposed sequential Monte Carlo receiver is demonstrated through computer simulations for MIMO systems over single-path and multipath fading channels.     

A sequential Monte Carlo blind receiver for OFDM systems infrequency-selective fading channels

We consider the application of the sequential Monte Carlo (SMC) methodology to the problem of blind symbol detection in a wireless orthogonal frequency-division multiplexing (OFDM) system over a frequency-selective fading channel. Bayesian inference of the unknown data symbols in the presence of an unknown multipath fading channel is made only from the observations over one OFDM symbol duration. A novel blind SMC detector built on the techniques of importance sampling and resampling is developed for differentially encoded OFDM systems. The performance of different schemes of delayed-weight estimation methods is studied. Furthermore, being soft-input and soft-output in nature, the proposed SMC detector is employed as the first-stage demodulator in a turbo receiver for a coded OFDM system. Such a turbo receiver successively improves the receiver performance by iteratively exchanging the so-called extrinsic information with the maximum a posteriori (MAP) outer channel decoder. Finally, the performance of the proposed sequential Monte Carlo receiver is demonstrated through computer simulations     

Iterative (turbo) soft interference cancellation and decoding forcoded CDMA

The presence of both multiple-access interference (MAI) and intersymbol interference (ISI) constitutes a major impediment to reliable communications in multipath code-division multiple-access (CDMA) channels. In this paper, an iterative receiver structure is proposed for decoding multiuser information data in a convolutionally coded asynchronous multipath DS-CDMA system. The receiver performs two successive soft-output decisions, achieved by a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders, through an iterative process. At each iteration, extrinsic information is extracted from detection and decoding stages and is then used as a priori information in the next iteration, just as in turbo decoding. Given the multipath CDMA channel model, a direct implementation of a sliding-window SISO multiuser detector has a prohibitive computational complexity. A low-complexity SISO multiuser detector is developed based on a novel nonlinear interference suppression technique, which makes use of both soft interference cancellation and instantaneous linear minimum mean-square error filtering. The properties of such a nonlinear interference suppressor are examined, and an efficient recursive implementation is derived. Simulation results demonstrate that the proposed low complexity iterative receiver structure for interference suppression and decoding offers significant performance gain over the traditional noniterative receiver structure. Moreover, at high signal-to-noise ratio, the detrimental effects of MAI and ISI in the channel can almost be completely overcome by iterative processing, and single-user performance can be approached     

Low complexity soft-input soft-output block decision feedback equalization

A low complexity soft-input soft-output (SISO) block decision feedback equalizer (BDFE) is presented for turbo equalization. The proposed method employs a sub-optimum sequence-based detection, where the soft-output of the equalizer is calculated by evaluating an approximation of the sequence-based a posteriori probability (APP) of the data symbol. The sequence-based APP approximation is enabled by the adoption of both soft a priori information and soft decision feedback, and it leads to better performance and faster convergence compared to symbol-based detection methods as used by most other low complexity equalizers. The performance and convergence property of the proposed algorithm is analyzed by using extrinsic information transfer (EXIT) chart. Both analytical and simulation results show that the new equalizer can achieve a performance similar to that of trellis-based equalization algorithms, with a complexity similar to linear SISO minimum mean square error equalizers.     

Doubly Iterative Equalization of Continuous-Phase Modulation

In this paper, a doubly iterative receiver is proposed for joint turbo equalization, demodulation, and decoding of coded binary continuous-phase modulation (CPM) in multipath fading channels. The proposed receiver consists of three soft-input soft-output (SISO) blocks: a front-end soft-information-aided minimum mean square error (MMSE) equalizer followed by a CPM demodulator and a back-end channel decoder. The MMSE equalizer, combined with an a priori soft-interference canceler (SIC) and an a posteriori probability mapper, forms a SISO processor suitable for iterative processing that considers discrete-time CPM symbols which belong to a finite alphabet. The SISO CPM demodulator and the SISO channel decoder are both implemented by the a posteriori probability algorithm. The proposed doubly iterative receiver has a central demodulator coupled with both the front-end equalizer and the back-end channel decoder. A few back-end demodulation/decoding iterations are performed for each equalization iteration so as to improve the a priori information for the equalizer. As presented in the extrinsic information transfer (EXIT) chart analysis and simulation results for different multipath fading channels, this provides not only faster convergence to low bit error rates, but also lower computational complexity.     

Adaptive iterative detection for phase tracking in turbo-codedsystems

The problem of performing iterative detection (ID)-a technique originally introduced for the decoding of turbo codes-for systems having parametric uncertainty has received relatively little attention in the open literature. In this paper, the problem of adaptive ID (AID) for serial and parallel concatenated convolutional codes (SCCCs and PCCCs or turbo codes) in the presence of carrier-phase uncertainty is examined. Based on the theoretical framework of Anastasopoulos and Chugg, (see Proc. Int. Conf. Communications, p.177-181, 1999). and Colavolpe, Ferrari and Raheli (see IEEE Trans. Commun., vol.48, p.1488-98, 2000), adaptive soft inverse (ASI) algorithms are developed for two commonly used blocks in turbo codes, leading to the adaptive soft-input soft-output (A-SISO) and the adaptive soft demodulator (A-SODEM) algorithms. Based on these algorithms, practical AID receivers are presented. Several design options are proposed and compared and the impact of parametric uncertainty on previously established results for iterative detection with perfect channel state information (CSI) is assessed     

Graph-based detection algorithms for layered space-time architectures

We consider a unified framework to develop various graph-based detection algorithms for layered space-time architectures. We start with a factor graph representation for the communication channel, apply a belief propagation (BP) based algorithm for channel detection, and show that the detector achieves a near optimal performance even when number of receive antennas is smaller than number of transmit antennas. Based on this baseline algorithm, we further develop three different extensions of the BP detector that provide a good complexity/performance trade-off, which are especially useful for systems with a large number of antennas or when we encounter a frequency-selective fading channel with a long ISI span. Moreover, all the proposed detectors are soft-input soft-output in nature and they can be directly applied for use in turbo processing without any additional modifications. We study the performance of the new detectors via both simulations and convergence analysis using the measure of average mutual information.     

Soft-output sphere decoding: algorithms and VLSI implementation

Multiple-input multiple-output (MIMO) detection algorithms providing soft information for a subsequent channel decoder pose significant implementation challenges due to their high computational complexity. In this paper, we show how sphere decoding can be used as an efficient tool to implement soft-output MIMO detection with flexible trade-offs between computational complexity and (error rate) performance. In particular, we provide VLSI implementation results which demonstrate that single tree-search, sorted QR-decomposition, channel matrix regularization, log-likelihood ratio clipping, and imposing runtime constraints are the key ingredients for realizing soft-output MIMO detectors with near max-log performance at a chip area that is only 58% higher than that of the best-known hard-output sphere decoder VLSI implementation.     

Soft Bayesian recursive interference cancellation and turbodecoding for TDD-CDMA receivers

A novel receiver is proposed for CDMA links with recursive turbo coding, based on a soft-input soft-output multistage interference canceler (IC) and an iterative turbo decoder (TD). After performing IC and TD a first time, the coder state estimates available from the two soft-output Viterbi algorithms in the last TD iteration are exploited to calculate the data bits and the redundancy bits. These are employed for preliminary hard cancellation in the first iteration of a supplementary IC run, and then the TD is run again. An alternative solution with soft feedback is obtained by approximating the reliabilities of the redundancy bits with those of the coder state estimates, and using them for preliminary soft cancellation. Simulation results show the effectiveness of the proposed solutions     

An efficient decoding algorithm for block turbo codes

An efficient soft-input soft-output iterative decoding algorithm for block turbo codes (BTCs) is proposed. The proposed algorithm utilizes Kaneko's (1994) decoding algorithm for soft-input hard-output decoding. These hard outputs are converted to soft-decisions using reliability calculations. Three different schemes for reliability calculations incorporating different levels of approximation are suggested. The algorithm proposed here presents a major advantage over existing decoding algorithms for BTCs by providing ample flexibility in terms of performance-complexity tradeoff. This makes the algorithm well suited for wireless multimedia applications. The algorithm can be used for optimal as well as suboptimal decoding. The suboptimal versions of the algorithm can be developed by changing a single parameter (the number of error patterns to be generated). For any performance, the computational complexity of the proposed algorithm is less than the computational complexity of similar existing algorithms. Simulation results for the decoding algorithm for different two-dimensional BTCs over an additive white Gaussian noise channel are shown. A performance comparison of the proposed algorithm with similar existing algorithms is also presented     

An Iterative Receiver for Uplink of Coded MIMO DS-CDMA System Employing Layered Space-Time Transmission

We consider a coded multiple-input multiple-output (MIMO) DS-CDMA system using layered space-time transmission in multipath wireless channels, where space-time signals from multiple antennas of multiple users propagate through rich scattering multipath fading. We propose a receiver employing iterative joint detection and decoding with a reduced-complexity detector using linear minimum mean squared error filtering with a priori information and parallel soft-input soft-output (SISO) decoders. Computer simulation results show that the proposed receiver for multi-user MIMO transmission provides high-spectral efficiency and performance approaching to single-user bound. Furthermore, the reduced-complexity receiver outperforms an iterative soft decision-directed maximal ratio combining (DD-MRC) receiver, RAKE receiver as well as a conventional non-iterative receiver.     

频选衰落MIMO信道的Turbo均衡

针对Turbo编码频选慢衰落MIMO信道,提出基于滑窗式概率数据辅助(Probabilistic Data Association)的软输出判决反馈均衡和软输入软输出Turbo信道解码器间迭代处理的Turbo均衡算法。充分利用已获得的信息,实现信道均衡与信道解码的迭代更新,克服传统判决反馈均衡器误差传播的缺陷。仿真表明,该系统经3次迭代就可获得较为满意的符号间干扰消除效果。     

Iterative reduced-state multiuser detection for asynchronous coded CDMA

The conventional maximum a posteriori receiver for coded code-division multiple-access (CDMA) systems has exponential computational complexity in terms of the number of users and the memory of the channel code. In this letter, we propose a low-complexity soft-input soft-output (SISO) multiuser detector based on the reduced-state a posteriori probability algorithm. Per-survivor processing and soft interference cancellation are used to remove the residual past and future interference in the branch metric computation. The complexity of the proposed receiver is related to the reduced memory of the CDMA channel and can be adjusted according to the complexity/performance tradeoff. Simulation results show that for asynchronous convolutionally coded systems, the proposed receiver can achieve the near-single-user performance for moderate to high signal-to-noise ratios.     

Near-optimum decoding of product codes: block turbo codes

This paper describes an iterative decoding algorithm for any product code built using linear block codes. It is based on soft-input/soft-output decoders for decoding the component codes so that near-optimum performance is obtained at each iteration. This soft-input/soft-output decoder is a Chase decoder which delivers soft outputs instead of binary decisions. The soft output of the decoder is an estimation of the log-likelihood ratio (LLR) of the binary decisions given by the Chase decoder. The theoretical justifications of this algorithm are developed and the method used for computing the soft output is fully described. The iterative decoding of product codes is also known as the block turbo code (BTC) because the concept is quite similar to turbo codes based on iterative decoding of concatenated recursive convolutional codes. The performance of different Bose-Chaudhuri-Hocquenghem (BCH)-BTCs are given for the Gaussian and the Rayleigh channel. Performance on the Gaussian channel indicates that data transmission at 0.8 dB of Shannon's limit or more than 98% (R/C>0.98) of channel capacity can be achieved with high-code-rate BTC using only four iterations. For the Rayleigh channel, the slope of the bit-error rate (BER) curve is as steep as for the Gaussian channel without using channel state information     

Iterative tree search detection for MIMO wireless systems

This paper presents a reduced-complexity soft-input soft-output detection scheme, called iterative tree search detection, for multiple-input multiple-output wireless communication systems employing turbo processing at the receiver. In this scheme, a reduced search space is selected with the aid of the M-algorithm, and QAM signal constellations with block partitionable labels are used in order to make the detection complexity per bit almost independent of the modulation order, as well as asymptotically linear in the number of transmit antennas. Results from computer simulations are presented which demonstrate the capability of the scheme to approach optimal performance at considerably reduced complexity.     

一种基于16QAM调制系统的LDPC改进算法

对QAM调制系统进行分析,提出了一种简化状态软输入软输出APP算法。它基于LDPC和积算法思想,与其他简化状态SISO算法相比,具有更为一般的形式。该算法在解调输出时有效利用映射点之间的欧氏距离,计算出每一个编码比特的似然值,从而简化运算复杂度,并且利用判决反馈减小简化状态网格的Euclid距离损失。仿真表明,该方案能够有效利用QAM解调中的软输出,在高斯信道下,简化的译码算法比原有LDPC方案提高了0.25 dB增益。     

New SISO decoding algorithms

A new maximum a posteriori (MAP)-equivalent soft-input soft-output (SISO) algorithm is derived together with its simplified versions. The proposed SISO algorithms provide a good compromise between complexity and performance. Our simplest SISO algorithm has lower complexity than the log-MAP, the max-log-MAP, and the soft-output Viterbi (1998) algorithm SISO algorithms, and it is an equivalent max-log-MAP algorithm. When this algorithm is used, turbo codes with block length as short as 150 bits will outperform convolutional codes when compared on the basis of equal decoder complexity.     

A low-complexity sequential Monte Carlo algorithm for blind detection in MIMO systems

In statistical signal processing, the sequential Monte Carlo (SMC) method is powerful and can approach the theoretical optima. However, its computational complexity is usually very high, especially in multiple-input multiple-output (MIMO) systems. This paper presents a new low-complexity SMC (LC-SMC) algorithm for blind detection in MIMO systems, the main idea of which is to shrink the sampling space via channel estimation which is initialized using the first differentially modulated symbol and then updated using the Monte Carlo samples. Since the a posteriori probability of the transmitted symbols can be calculated separately by each transmit antenna, the proposed LC-SMC algorithm is not only computationally efficient, as compared to the original SMC whose complexity grows exponentially with the number of transmit antennas, but also makes blind turbo receiver more feasible for multilevel/phase modulations. Simulation results are presented to demonstrate the effectiveness of the LC-SMC algorithm.     

A Soft-Input Soft-Output Decorrelating Block Decision-Feedback Multiuser Detector for Turbo-Coded DS-CDMA Systems

Previously, a decorrelating decision-feedback multiuser detector for direct-sequence code-division multiple-access (DS-CDMA) systems normally produces only hard-decision outputs of users' data. In turbo-coded DS-CDMA systems, such a multiuser detector does not match well with the soft-input soft-output nature of a turbo-decoding algorithm, thereby resulting in some extent of performance loss. In this paper, a soft-input soft-output decorrelating block decision-feedback multiuser detector is proposed to perform joint multiuser detection and turbo decoding in an iterative manner. This multiuser detector partitions the received users' data into a number of blocks appropriately and then detects the users' data on a block-by-block basis, where the soft-decision outputs are generated based on the maximum a posteriori criterion and the decision outputs of a stronger block (with a higher energy) are fed back for use in making decisions of those weaker ones. Computer simulation results show that the proposed iterative multiuser detector with turbo decoding significantly improves the bit error rate performance of a DS-CDMA receiver.