Iterative Joint Detection, Decoding, and Channel Estimation in Turbo-Coded MIMO-OFDM

An iterative receiver for a multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) system is considered to jointly decode the transmitted bits and estimate the channel state. The receiver consists of a list detector, a turbo decoder, and a channel estimator that is based on the space-alternating generalized expectation-maximization (SAGE) algorithm. This paper proposes a way to improve the convergence of the iterative detection and decoding by using a priori information to also recalculate the candidate list, aside from the log-likelihood ratios (LLRs) of the coded bits. A new list parallel interference cancellation (PIC) detector is derived to approximate an a posteriori probability (APP) algorithm with reduced complexity and minimal losses of performance. Furthermore, the organization of spectrally efficient decision-directed (DD) SAGE channel estimation under a constrained number of detector-decoder iterations is optimized by computer simulations, and the SAGE algorithm itself is modified for nonconstant envelope constellations. The list recalculation is shown to improve convergence. It is also shown that the list PIC detector with good initialization outperforms the K-best list sphere detector (LSD) in the case of small list sizes, whereas the complexities of the algorithms are of the same order. Despite the low preamble density and fast-fading channel, the proposed iterative receiver shows robust performance.     

Iterative Multiuser Detection and Decoding for DS-CDMA System With Space-Time Linear Dispersion

This paper considers a $Q$-ary orthogonal direct-sequence code-division multiple-access (DS-CDMA) system with high-rate space-time linear dispersion codes (LDCs) in time-varying Rayleigh fading multiple-input–multiple-output (MIMO) channels. We propose a joint multiuser detection, LDC decoding, $Q$-ary demodulation, and channel-decoding algorithm and apply the turbo processing principle to improve system performance in an iterative fashion. The proposed iterative scheme demonstrates faster convergence and superior performance compared with the V-BLAST-based DS-CDMA system and is shown to approach the single-user performance bound. We also show that the CDMA system is able to exploit the time diversity offered by the LDCs in rapid-fading channels.      

On the Suboptimality of Iterative Decoding for Turbo-Like and LDPC Codes With Cycles in Their Graph Representation

Performance of Multicarrier CDMA With Successive Interference Cancellation in a Multipath Fading Channel A high-capacity, low-complexity, and robust system design for a successive interference cancellation (SIC) system is developed and analyzed. Multicarrier code-division multiple access (MC-CDMA) is used to suppress multipath and to overcome the multipath channel estimation problem in single-carrier SIC systems. In addition, an optimal power control algorithm for MC-CDMA with SIC is derived, allowing analytical bit-error rate expressions to be found for an uncoded system. Low-rate forward error-correcting codes are then added to the system to achieve robustness. It is found that the capacity of the coded system approaches the additive white Gaussian noise capacity for SIC, even in a fading multipath channel with channel estimation error. This indicates that MC-CDMA is very attractive for systems employing SIC.     

Iterative Group-Blind Multiuser Detection and Decoding With Signal Rank Estimation for Coded CDMA Systems

In this paper, a turbo receiver structure is proposed for the uplink of coded code-division multiple-access (CDMA) systems in the presence of unknown users. The proposed receiver consists of two stages following each other. The first stage performs soft interference cancellation and group-blind linear minimum mean square error (MMSE) filtering, and the second stage performs channel decoding. The proposed group-blind linear MMSE filter suppresses the residual multiple-access interference (MAI) from known users based on the spreading sequences and the channel characteristics of these users while suppressing the interference from other unknown users using a subspace-based blind method. The proposed receiver is suitable for suppressing intercell interference in heavily loaded CDMA systems. Since the knowledge of the number of unknown users is crucial for the proposed receiver structure, a novel estimator is also proposed to estimate the number of unknown users in the system by exploiting the statistical properties of the received signal. Simulation results demonstrate that the proposed estimator can provide the number of unknown users with high accuracy; in addition, the proposed group-blind receiver integrated with the new estimator can significantly outperform the conventional turbo multiuser detector in the presence of unknown users.      

基于置信传播和波束搜索的LDPC联合译码算法

当置信传播算法BP（Belief Propagation）应用于LDPC短码时,由于传递消息的不独立性,使得译码性能与最大似然译码有较大差距。考虑到LDPC码分布的稀疏性,以及在BP失败译码中仅有少量错误位的统计事实,提出了一种波束搜索算法,把它级联于BP算法来对失败译码进行后处理。在付出一定计算复杂性的代价下,以期提高整体的译码性能。在波束搜索算法的实现中,译码伴随式的信息以及码字位的可靠性信息被融合进对搜索个体的代价函数中。它的目标是在给定的波束宽度下,寻找到失败译码对应的错误样式,从而纠错的目的。仿真结果表明对LDPC短码,此联合算法在译码性能与计算复杂度之间取得较好的折衷。     

Adaptive Parallel and Iterative QRDM Detection Algorithms for MIMO Multiplexing Systems

QR-decomposition with M-algorithm (QRDM) achieves quasi-ML performance in multiple-input multiple-output (MIMO) multiplexing systems. Nevertheless, QRDM performs avoidable computations because of its systematic search strategy and its failure to consider the channel and noise conditions. Another drawback is that QRDM is sequential, which limits pipelining capabilities. In this paper, we propose quasi-ML adaptive parallel QRDM (APQRDM) and adaptive iterative QRDM (AIQRDM) algorithms based on set grouping. In set grouping, the tree-search stage of the QRDM algorithm is divided into partial detection phases (PDPs). These are processed in parallel and iteratively in the proposed APQRDM and AIQRDM algorithms, respectively. Therefore, when the tree-search stage of the QRDM algorithm is divided into G PDPs, the latency of the proposed APQRDM algorithm and the hardware requirements of the proposed AIQRDM algorithm are reduced by a factor of G compared to the QRDM algorithm. Moreover, simulation results show that in 4?×?4 MIMO system, and at E _b /N ₀ of 12?dB, APQRDM decreases the average computational complexity to approximately 43% that of the conventional QRDM. Also, at E _b /N ₀ of 0?dB, AIQRDM algorithm reduces the computational complexity to about 54%, and the average number of metric comparisons to approximately 10%, compared to the conventional QRDM.     

Performance Comparison of MLSE and Iterative Equalization in FEC Systems for PMD Channels With Respect to Implementation Complexity

Advanced electronic signal processing for high-bit-rate lightwave systems has become available recently. Adaptive receiver concepts are proposed to mitigate dynamic changes in the optical channel response. In particular, two different approaches are under discussion: independent equalization and decoding, e.g., by maximum-likelihood sequence estimation followed by a separate error-correction decoder, and a combined approach by iterative decoding of the channel correlations and the error-correction code. The authors compare the two concepts with respect to their mitigation capabilities in the presence of polarization mode dispersion. Special attention is paid to hardware implementation aspects, since the application of the concepts is severely limited by memory and signal processing requirements     

A 0.18-$muhbox m$CMOS Analog Min-Sum Iterative Decoder for a (32,8) Low-Density Parity-Check (LDPC) Code

Current-mode circuits are presented for implementing analog min-sum (MS) iterative decoders. These decoders are used to efficiently decode the best known error correcting codes such as low-density parity-check (LDPC) codes and turbo codes. The proposed circuits are devised based on current mirrors, and thus, in any fabrication technology that accurate current mirrors can be designed, analog MS decoders can be implemented. The functionality of the proposed circuits is verified by implementing an analog MS decoder for a (32,8) LDPC code in a 0.18-mum CMOS technology. This decoder is the first reported analog MS decoder. For low signal to noise ratios where the circuit imperfections are dominated by the noise of the channel, the measured error correcting performance of this chip in steady-state condition surpasses that of the conventional floating-point discrete-time synchronous MS decoder. When data throughput is 6 Mb/s, loss in the coding gain compared to the conventional MS decoder at BER of 10^-3 is about 0.3 dB and power consumption is about 5 mW. This is the first time that an analog decoder has been successfully tested for an LDPC code, though a short one     

Combine LDPC Codes Over GF(q) With q-ary Modulations for Bandwidth Efficient Transmission

Low-density parity-check (LDPC) codes are playing more and more important role in digital broadcasting standards due to their excellent error correction performance. In this paper, we study the combination of LDPC codes over GF(q) with q-ary modulations for bandwidth efficient transmission over AWGN channel and consider the design of the codes. Specifically, we develop the concept of quasi-regular codes, and propose an improved Monte Carlo method to optimize the quasi-regular codes. To justify the performance of our proposed scheme, simulation results are presented and analysed.     

一种新的谐波检测算法及其对比研究

本文通过详细的数学推导证明了瞬时无功功率理论的数学本质是三维时变向量空间中的正交变换和反变换,在不同正交向量坐标基下,可以检测任意次、任意序的有功或无功电流。通过与传统FFT算法相比,证明二者在数学本质上是一致的,低通滤波器和积分器是二者实时性能差异的根源。据此文中提出了一种采用LPF的FFT改进算法用于谐波提取。     

On MSE Exit Chart Analysis and Real Time DSP Implementation for Iterative (Turbo) Detection

We investigate the use of the mean square error (MSE) transfer characteristics to examine the convergence behaviour of the iterative (turbo) multiuser detector for coded code-division multiple-access (CDMA) systems. Both MSE and mutual information (MI) based extrinsic information transfer (MSE-EXIT and MI-EXIT) chart techniques reveal the same asymptotic and convergence behaviours. An improved low complexity version of the soft interference cancellation MMSE (SIC-MMSE) detection scheme is also proposed for CDMA systems utilizing BPSK modulation. Herein, under fixed-point data representation and computation constraint a real time DSP implementation (using TMS320C6416) is suggested. EXIT charts reveal that fixed-point implementation is feasible at possibly no performance degradation. Based on the measured number of cycles of different constituent sub-functions of the proposed receiver, a data transmission rate of up to 186 Kb/s can be reached for a 5-users load and a processing gain of 7 in an AWGN channel.     

Filterbank Decompositions for (Non)-Systematic Reed–Solomon Codes With Applications to Soft Decoding

This paper focuses on Reed-Solomon (RS) codes, which are the most widespread classical error correcting codes. Recently, we have shown that an finite-impulse response (FIR) critically subsampled filterbank representation can be derived for some RS codes. However, this work only addresses RS codes with a non-coprime codeword and dataword length, seriously limiting its practical usability. In this paper, an alternative purely algebraic method is presented to construct such a filterbank. Apart from providing additional insight into the algebraic structure of (non-systematic) RS codes, this method is suited to eliminate the non-coprimeness constraint mentioned before. Using this filterbank decomposition, a RS code is broken into smaller subcodes that can subsequently be used to build a soft-in soft-out (SISO) RS decoder. It is shown how any RS code, written as an FIR filterbank, can be SISO decoded using the filterbank based decoder. Owing to the importance of systematic RS codes, it is shown that any systematic RS code can be decoded using the FIR filterbank decomposition. This leads to better decoding performance in addition with a slightly lower complexity. A further extension towards systematic RS codes is also presented in this paper resulting in an infinite-impulse response critically subsampled filterbank representation.     

Decoding With Expected Length and Threshold Approximated (DELTA): A Near-ML Scheme for Multiple-Input–Multiple-Output Systems

In this paper, we propose a near maximum likelihood (ML) scheme for the decoding of multiple-input–multiple-output (MIMO) systems. By employing the metric-first search method, Schnorr–Euchner enumeration, and branch-length thresholds in a single frame systematically, the proposed technique provides efficiency that is higher than those of other conventional near-ML decoding schemes. From simulation results, it is confirmed that the proposed scheme has computational complexity lower than those of other near-ML decoders while maintaining the bit error rate (BER) very close to the ML performance. The proposed scheme, in addition, possesses the capability of allowing flexible tradeoffs between the computational complexity and BER performance.      

基于BM算法的RS（18,10）译码的软件实现和性能分析

使用MATLAB软件设计了GF（2^8）上的加法、乘法、求逆运算模块,并以这些模块为基础,编写了RS（18,10）的采用串行的时域Berlekamp-Massye（BM）算法、钱搜索算法、forney算法的译码的软件实现。各个算法模块均采用硬件可以容易实现的算法,为硬件开发验证和调试提供了强有力的辅助手段,并对该码进行了性能分析。     

Multiuser Space–Time Algorithms for Synchronization, Channel Estimation, and Data Detection in an Interference Monitoring System for UMTS/TDD Networks

We present multiuser space-time receiver algorithms for synchronization, channel estimation, and data detection in the downlink of a universal mobile telecommunications system (UMTS)/time-division duplex (TDD) cellular communication system with multiple receive antennas. These algorithms were designed for use in a network monitoring device that analyzes the interference situation present, thereby allowing the operators to improve their networks. For interference analysis, we decode the broadcast channels (BCHs) of surrounding base stations. To cope with the widely differing power levels of signals received from different base stations, we combine multiuser space-time signal processing techniques with reestimation and successive cancellation schemes. Simulation results demonstrate that our algorithms enable reliable BCH data detection even at low SINR.     

A New Stacked Two-Dimensional Spectral Iterative Technique (SIT) for Analyzing Microwave Power Deposition in Biological Media

Conventional numerical methods for analyzing power deposition in biological media have been restricted to bodies which are relatively small electrically. A new, stacked-two-dimensional-spectral-iterative-technique (SIT), presented below, does not involve the generation and inversion of a matrix and is capable of analyzing larger bodies. It is based on modeling the body by a set of planar parallel slabs and utilizing the simple (convolution-type) relationship between a current distribution on any slab and the field due to this current. This invertible relationship is conveniently formulated in the transform domain in a strictly algebraic fashion. The interactions between the various slabs are also simple and algebraic in the spectral domain. The solution is generated in an iterative manner by applying these relationships sequentially over the slabs until convergence is achieved. Discussion on convergence and numerical examples are given.