Low-complexity iterative decoding with decision-aided equalizationfor magnetic recording channels

Turbo codes are applied to magnetic recoding channels by treating the channel as a rate-one convolutional code that requires a soft a posteriori probability (APP) detector for channel inputs. The complexity of conventional APP detectors, such as the BCJR algorithm or the soft-output Viterbi algorithm (SOVA), grows exponentially with the channel memory length. This paper derives a new APP module for binary intersymbol interference (ISI) channels based on minimum mean squared error (MMSE) decision-aided equalization (DAE), whose complexity grows linearly with the channel memory length, and it shows that the MMSE DAE is also optimal by the maximum a posteriori probability (MAP) criterion. The performance of the DAE is analyzed, and an implementable turbo-DAE structure is proposed. The reduction of channel APP detection complexity reaches 95% for a five-tap ISI channel when the DAE is applied. Simulations performed on partial response channels show close to optimum performance for this turbo-DAE structure. Error propagation of the DAE is also studied, and two fixed-delay solutions are proposed based on combining the DAE with the BCJR algorithm     

On the application of factor graphs and the sum-product algorithm to ISI channels

In this paper, based on the application of the sum-product (SP) algorithm to factor graphs (FGs) representing the joint a posteriori probability (APP) of the transmitted symbols, we propose new iterative soft-input soft-output (SISO) detection schemes for intersymbol interference (ISI) channels. We have verified by computer simulations that the SP algorithm converges to a good approximation of the exact marginal APPs of the transmitted symbols if the FG has girth at least 6. For ISI channels whose corresponding FG has girth 4, the application of a stretching technique allows us to obtain an equivalent girth-6 graph. For sparse ISI channels, the proposed algorithms have advantages in terms of complexity over optimal detection schemes based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. They also allow a parallel implementation of the receiver and the possibility of a more efficient complexity reduction. The application to joint detection and decoding of low-density parity-check (LDPC) codes is also considered and results are shown for some partial-response magnetic channels. Also in these cases, we show that the proposed algorithms have a limited performance loss with respect to that can be obtained when the optimal "serial" BCJR algorithm is used for detection. Therefore, for their parallel implementation, they represent a favorable alternative to the modified "parallel" BCJR algorithm proposed in the literature for the application to magnetic channels.     

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.     

Decision-feedback soft-input/soft-output multiuser detector foriterative decoding of coded CDMA

The optimal decoding scheme for a code-division multiple-access (CDMA) system that employs convolutional codes results in a prohibitive computational complexity. To reduce the computational complexity, an iterative receiver structure was proposed for decoding multiuser data in a convolutional coded CDMA system. At each iteration, extrinsic information is exchanged between a soft-input/soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders. However, a direct implementation of the full-complexity SISO multiuser detector also has the exponential computational complexity in terms of the number of users. This paper proposes a low-complexity SISO multiuser detector based on tentative hard decisions that are made and fed back from the channel decoders in the previous iteration. The computational complexity of the proposed detector is linear in terms of the number of users and can be adjusted according to the complexity/performance tradeoff. Simulation results show that even with this simple feedback scheme, the performance of the coded multiuser system approaches that of the single-user system for moderate to high signal-to-noise ratios (SNRs)     

基于SISO的LDPC码盲译码算法研究

针对传统BP译码算法需要初始条件的缺点,本文提出了一种基于软输入软输出(SISO)的LDPC码盲译码算法,所提算法采用类似BP迭代译码算法步骤,通过对距离信息进行迭代处理,实现无需接收信号的信噪比和信道状态即可译码;同时,还将所提盲译码算法推广到多进制LDPC码的译码应用中。本文所提盲译码算法在初始状态难以确定以及接收信号信噪比难以估计的通信信道中具有重要价值。仿真结果表明,所提算法不论是在AWGN信道还是在瑞利衰落信道上都能取得优良的性能,不论是与标准BP译码算法还是与分层BP译码算法相比,在性能相近的情况下,计算复杂度都有所降低。     

Iterative decoding of convolutionally encoded signals overmultipath Rayleigh fading channels

We analyze and compare several strategies for iteratively decoding trellis-encoded signals over channels with memory. Soft-in/soft-out extensions of reduced-complexity trellis search algorithms such as delayed decision-feedback sequence estimating (DDFSE) or parallel decision-feedback decoding (PDFD) algorithms are used instead of conventional BCJR and min-log-BCJR algorithms. It has been shown that for long channel impulse responses and/or high modulation orders where the BCJR algorithm becomes prohibitively complex, the proposed algorithms offer very good performance with low complexity. The problem of channel estimation in practical implementation of turbo detection schemes is studied in the second part. Two methods of channel reestimation are proposed: one based on the expectation-maximization (EM) algorithm and the second on a simple Bootstrap technique. Both algorithms are shown to dramatically improve the performance of the classical pseudo inverse channel estimation performed initially on a training sequence     

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     

A new class of soft MIMO demodulation algorithms

We propose a new class of soft-input soft-output demodulation schemes for multiple-input multiple-output (MIMO) channels, based on the sequential Monte Carlo (SMC) framework under both stochastic and deterministic settings. The stochastic SMC sampler generates MIMO symbol samples based on importance sampling and resampling techniques, whereas the deterministic SMC approach recursively performs exploration and selection steps in a greedy manner. By exploiting the artificial sequential structure of the existing simple Bell-Labs layered space-time (BLAST) detection method based on ing and cancellation, the proposed algorithms achieve an error probability performance that is orders of magnitude better than the traditional BLAST detection schemes while maintaining a low computational complexity. In fact, the new methods offer performance comparable with that of the sphere decoding algorithm without attendant increase in complexity. More importantly, being soft-input soft-output in nature, both the stochastic and deterministic SMC detectors can be employed as the first-stage demodulator in a turbo receiver in coded MIMO systems. Such a turbo receiver successively improves the receiver performance by iteratively exchanging the so-called extrinsic information between the soft outer channel decoder and the inner soft MIMO demodulator under both known channel state and unknown channel state scenarios. Computer simulation results are provided to demonstrate the performance of the proposed algorithms.     

Bayesian Monte Carlo multiuser receiver for space-time codedmulticarrier CDMA systems

We consider the design of optimal multiuser receivers for space-time block coded (STBC) multicarrier code-division multiple-access (MC-CDMA) systems in unknown frequency-selective fading channels. Under a Bayesian framework, the proposed multiuser receiver is based on the Gibbs sampler, a Markov chain Monte Carlo (MCMC) method for numerically computing the marginal a posteriori probabilities of different users' data symbols. By exploiting the orthogonality property of the STBC and the multicarrier modulation, the computational complexity of the receiver is significantly reduced. Furthermore, being a soft-input soft-output algorithm, the Bayesian Monte Carlo multiuser detector is capable of exchanging the so-called extrinsic information with the maximum a posteriori (MAP) outer channel code decoders of all users, and successively improving the overall receiver performance. Several practical issues, such as testing the convergence of the Gibbs sampler in fading channel applications, resolving the phase ambiguity as well as the antenna ambiguity, and adapting the proposed receiver to multirate MC-CDMA systems, are also discussed. Finally, the performance of the Bayesian Monte Carlo multiuser receiver is demonstrated through computer simulations     

A low-complexity SISO multiuser detector for iterative decoding of asynchronous CDMA systems with convolutional codes

The optimal decoding scheme for asynchronous code-division multiple-access (CDMA) systems that employ convolutional codes results in a prohibitive computational complexity. To reduce the computational complexity, an iterative receiver structure was proposed for decoding multiuser data in a convolutional coded CDMA system. At each iteration, extrinsic information is exchanged between a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders. A direct implementation of the optimal SISO multiuser detector, however, has exponential computational complexity in terms of the number of users which is still prohibitive for channels with a medium to large number of users. This paper presents a low-complexity SISO multiuser detector using the decision-feedback scheme, of which tentative hard decisions are made and fed back to the SISO multiuser from the previous decoding output. In the proposed scheme, the log-likelihood ratios (LLR) as well as the tentative hard decisions of code bits are fed back from the SISO decoders. The hard decisions are used to constrain the trellis of the SISO multiuser detector and the LLRs are used to provide a priori information on the code bits. The detector provides good performance/complexity tradeoffs. The computational complexity of the detector can be set to be as low as linear in the number of users. Simulations show that the performance of the low-complexity SISO multiuser detector approaches that of the single-user system for moderate to high signal-to-noise ratios even for a large number of users.     

Application of Sequential Estimation Algorithm Based on Branch Metric to Frequency-Selective Channel Equalization

In this work, a sequential estimation algorithm based on branch metric is used as channel equalizer to combat intersymbol interference in frequency-selective wireless communication channels. The bit error rate (BER) and computational complexity of the algorithm are compared with those of the maximum likelihood sequence estimation (MLSE), the recursive least squares (RLS) algorithm, the Fano sequential algorithm, the stack sequential algorithm, list-type MAP equalizer, soft-output sequential algorithm (SOSA) and maximum-likelihood soft-decision sequential decoding algorithm (MLSDA). The BER results have shown that whilst the sequential estimation algorithm has a close performance to the MLSE using the Viterbi algorithm, its performance is better than the other algorithms. Beside, the sequential estimation algorithm is the best in terms of computational complexity among the algorithms mentioned above, so it performs the channel equalization faster. Especially in M-ary modulated systems, the equalization speed of the algorithm increases exponentially when compared to those of the other algorithms.     

Soft-Output BEAST Decoding With Application to Product Codes

A Bidirectional Efficient Algorithm for Searching code Trees (BEAST) is proposed for efficient soft-output decoding of block codes and concatenated block codes. BEAST operates on trees corresponding to the minimal trellis of a block code and finds a list of the most probable codewords. The complexity of the BEAST search is significantly lower than the complexity of trellis-based algorithms, such as the Viterbi algorithm and its list generalizations. The outputs of BEAST, a list of best codewords and their metrics, are used to obtain approximate a posteriori probabilities (APPs) of the transmitted symbols, yielding a soft-input soft-output (SISO) symbol decoder referred to as the BEAST-APP decoder. This decoder is employed as a component decoder in iterative schemes for decoding of product and incomplete product codes. Its performance and convergence behavior are investigated using extrinsic information transfer (EXIT) charts and compared to existing decoding schemes. It is shown that the BEAST-APP decoder achieves performances close to the Bahl–Cocke–Jelinek–Raviv (BCJR) decoder with a substantially lower computational complexity.      

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.     

Turbo equalization with sequential sequence estimation overmultipath fading channels

We investigate the performance of a turbo equalization scheme over frequency-selective fading channels, where a soft-output sequential algorithm is employed as the estimation algorithm. The advantage of this scheme comes from the low computational complexity of the sequential algorithm, which is only linearly dependent on the channel memory length. Simulation results of an 8-PSK trellis-coded modulation (TCM) system show that the performance of this scheme suffers approximately 2-dB loss compared with that of the turbo max-log maximum a posteriori (MAP) probability equalizer after 5 iterations     

A new framework for soft decision equalization in frequency selective MIMO channels

We introduce a novel framework for soft-input, soft-output (SISO) equalization in frequency selective multipleinput multiple-output (MIMO) channels based on the well-known belief propagation (BP) algorithm. As in the BP equalizer, we model the multipath channels using factor graphs (FGs) where the transmitted and received signals are represented by the function and variable nodes respectively. The edges connecting the function and variable nodes illustrate the dependencies of the multipath channel and soft decisions are developed by exchanging information on these edges iteratively. We incorporate powerful techniques such as groupwise iterative multiuser detection (IMUD), probabilistic data association (PDA) and sphere decoding (SD) in order to reduce the computational complexity of BP equalizer with relatively small degradation in performance. The computational complexity of this new reduced-complexity BP (RCBP) equalizer grows linearly with block size and memory length of the channel. The proposed framework has a flexible structure that allows for parallel as well as serial detection. We will illustrate through simulations that the RCBP equalizer can even handle overloaded scenarios where the channel matrix is rank deficient, and it can achieve excellent performance by applying iterative equalization using the low-density parity check codes (LDPC).     

On the symmetric information rate of two-dimensional finite-state ISI channels

We derive a pair of bounds (upper and lower) on the symmetric information rate of a two-dimensional finite-state intersymbol interference (ISI) channel model. For channels with small impulse response support, they can be estimated via a modified forward recursion of the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. The convergence of the bounds is also analyzed. To relax the constraint on the size of the impulse response, a new upper bound is proposed which allows the tradeoff of the computational complexity and the tightness of the bound. These bounds are further extended to d-dimensional (d>2) ISI channels.     

A Study of the Technique of Linear Multiuser

The technique of linear multiuser detection in DS-CDMA systems is studied in this paper. The purpose is to find a receiver structure with good performance and moderate complexity, so that the receiver can efficiently suppress multiple-access interference(MAI) and multipath interference and has good near-far resistant ability, which may improve the system's capability while reducing the requirement for power control. The main work of the dissertation can be summarized as follows: the performance of MMSE multiuser detector in synchronous/asynchronous DS-CDMA systems over different channels is analyzed in chapter 2 of the dissertation. Using matrix method, we analyze the relation between performance measurement and spreading code correlation matrix, Signal-Interference-Ratio(SIR) and near-far factor, and prove that the performance of MMSE detector is better than that of the decorrelating detector. For fading channel, we analyze the performance of MMSE detector in DS-SS system firstly. Results show that the detector can efficiently suppress multipath interference. Extending to synchronous/asynchronous DS-CDMA systems over fading channels, we propose a simple linear detector structure that accomplishes despreading, detection and combining. Thus, the receiver is easy for implementation. Based on the proposed notion of combined spreading codes, we prove that the synchronous/asynchronous CDMA system is equivalent to the synchronous CDMA system over AWGN channel with double users. Therefore, the MMSE detector can efficiently suppress MAI and multipath interference in steady state, and has good near-far resistant ability. In chapter 3, we study the adaptive algorithm based on MMSE criterion. Firstly, the approach to the blind algorithm based on subspace is analyzed. We improve the algorithm in the part of channel estimation, which decreases the computational complexity while guaranteeing the performance. Meanwhile, we point out that CMOE-RLS algorithm is essentially an algorithm based on subspace approach. Also, it is shown from simulation that PASTd subspace tracking algorithm is not applicable for multiuser detection. Secondly, we propose an adaptive algorithm based on pilot channel, called PCA/PCRA. The algorithm does not require channel estimation, and has a rapid convergence rate. The steady state performance can be achieved by increasing the transmitting power in pilot channel. Computational complexity is only O(N2). Therefore, PCA/PCRA is suitable for the engineering application. The cost is that a pilot channel is needed for each user in the system. In chapter 4, constant algorithms for multiuser detection are studied. Firstly, we analyze the capture performance of CMA, and point out there exist many local stationary points. Initializations to guarantee CMA converges to the desired point are discussed. Results show that the convergence of CMA is decided by constant, step-size, spreading code correlation matrix and near-far factor. Secondly, we propose the constrained constant algorithm (C-CMA) for multiuser detection. It is shown that when the constant is greater than the triple power of the desired user, C-CMA globally converges to the desired point. Simulations illustrate that C-CMA has a rapid convergence rate and the steady state performance is good. However, great step-size can also reult in dispersion for the algorithm. Since C-CMA is a variable step-size CMOE-LMS algorithm, we propose a variable step-size constraint algorithm (VSCA). VSCA has the advantages of both CMOE-LMS and C-CMA such as robust, rapid convergence rate and good steady state performance. Thus, VSCA is suitable for engineering application. But the improper selection of step-size coefficients may degrade performance seriously. The computational complexity of the above constant algorithms is only O(N). In Section 5, the cyclostationarity of spreading signals is analyzed in the first part. We prove that spreading signals are ergodic cyclostationary signals with a cyclic period that is equal to the period of spreading code. Methods for processing cyclostationary signals are then given. It is shown that this method can mitigate the interference from a stationary noise for channel estimation. But the computational complexity for cyclostationary correlation is high, which prevents its application in implementation. In the second part, we discuss the application of oversampling technique in spreading communication systems. Although the oversampling can improve the performance of the linear multiuser detector, the improvement is trivial. On the contrary, oversampling increases the computational complexity of the weight vector greatly, which prevents its application in implementation. Additionally, we prove that FSE plus despreading or despreading pus FSE is equivalent to the linear detector with different lengths of delay line. However, the two kinds of structure have lower computational complexity.     

A rate-k/n heuristic soft-output Viterbi algorithm (SOVA) that ispostdetector-compatible

A soft-output Viterbi algorithm (SOVA) that can be used on trellis-coded modulation (TCM), rate-k/n convolutional codes, and intersymbol interference (ISI) channels is proposed. The algorithm utilizes the postdetector architecture proposed by Berrou et al. (1993) to achieve low computational complexity. By starting with Battail's (1987) generalized revision algorithm and rereferencing the “relative values” to the surviving path to each state, substantial simplifications are made possible. By comparing the revision operations dictated by the simplified revision equation for a rate-1/n convolutional code to the operations mandated by the rate-1/n postdetector algorithm presented by Berrou et al., it is possible to deduce the additional modifications necessary to produce a rate-k/n postdetector algorithm. Computer simulations suggest that the derived rate-k/n algorithm produces reasonably good a posteriori input probability estimates for rate-k/n convolutional codes and trellis codes. The algorithm may also be used for soft-output Viterbi equalization (SOVE) provided that the channel impairments are not too severe     

60GHz 室内信道下一种快速天线选择算法

传统的基于信道容量最大化准则的天线选择算法虽然使信道容量达到了最大化,但是计算复杂度很高。针对计算复杂度高的问题, 提出了一种基于Doolittle-QR 分解的低复杂度天线选择算法。该算法基于Doolittle-QR 分解,可以快速选择出使系统容量最大化的天线。与传统的天线选择算法相比,该算法的计算复杂度不仅有效地降低了, 而且容量性能相近。在60GHz 室内信道下,仿真实验结果表明, 该算法具有良好的容量性能,优于随机天线选择算法,接近最优天线选择算法。     

非理想信道估计下的软输出MMSE V-BLAST检测算法

针对信道编码MIMO系统,该文推导出了实际信道估计下的软输出MMSE V-BLAST检测算法,该算法同时考虑了信道估计误差和判决误差传播的影响。仿真结果显示该文所提算法在几乎没有增加复杂度的情况下,可以极大地降低残余误码平层,获得显著的性能增益;所提算法对信道估计误差方差的估计可靠性不敏感,因而具有实际应用价值。