Minimum mean squared error equalization using a priori information

A number of important advances have been made in the area of joint equalization and decoding of data transmitted over intersymbol interference (ISI) channels. Turbo equalization is an iterative approach to this problem, in which a maximum a posteriori probability (MAP) equalizer and a MAP decoder exchange soft information in the form of prior probabilities over the transmitted symbols. A number of reduced-complexity methods for turbo equalization have been introduced in which MAP equalization is replaced with suboptimal, low-complexity approaches. We explore a number of low-complexity soft-input/soft-output (SISO) equalization algorithms based on the minimum mean square error (MMSE) criterion. This includes the extension of existing approaches to general signal constellations and the derivation of a novel approach requiring less complexity than the MMSE-optimal solution. All approaches are qualitatively analyzed by observing the mean-square error averaged over a sequence of equalized data. We show that for the turbo equalization application, the MMSE-based SISO equalizers perform well compared with a MAP equalizer while providing a tremendous complexity reduction     

MLSE and MAP Equalization for Transmission Over Doubly Selective Channels

In this paper, equalization for transmission over doubly selective channels is discussed. The symbol-by-symbol maximum a posteriori probability (MAP) equalizer and the maximum-likelihood sequence estimation (MLSE) are discussed. The doubly selective channel is modeled using the basis expansion model (BEM). Using the BEM allows for an easy and low-complexity mechanism for constructing the channel trellis to implement the MLSE and the MAP equalizer. The MLSE and the MAP equalizer are implemented for single-carrier transmission and for multicarrier transmission implemented using orthogonal frequency-division multiplexing (OFDM). In this scenario, a complexity-diversity tradeoff can be observed. In addition, we propose a joint estimation and equalization technique for doubly selective channels. In this joint estimation and equalization technique, the channel state information (CSI) is obtained in an iterative manner. Simulation results show that the performance of the joint channel estimation and equalization approaches the performance when perfect CSI is available at the receiver.     

Double turbo equalization of continuous phase modulation with frequency domain processing

In this paper, a doubly-iterative linear receiver, equipped with a soft-information aided frequency domain minimum mean-squared error (MMSE) equalizer, is proposed for the combined equalization and decoding of coded continuous phase modulation (CPM) signals over long multipath fading channels. In the proposed receiver architecture, the front-end frequency domain equalizer (FDE) is followed by the soft-input, softoutput (SISO) CPM demodulator and channel decoder modules. The receiver employs double turbo processing by performing back-end demodulation/decoding iterations per each equalization iteration to improve the a priori information for the front-end FDE. As presented by the computational complexity analysis and simulations, this process provides not only a significant reduction in the overall computational complexity, but also a performance improvement over the previously proposed iterative and noniterative MMSE receivers.     

Joint MAP equalization and channel estimation forfrequency-selective and frequency-flat fast-fading channels

This paper presents a new fractionally-spaced maximum a posteriori (MAP) equalizer for data transmission over frequency-selective fading channels. The technique is applicable to any standard modulation technique. The MAP equalizer uses an expanded hypothesis trellis for the purpose of joint channel estimation and equalization. The fading channel is estimated by coupling minimum mean square error techniques with the (fixed size) expanded trellis. The new MAP equalizer is also presented in an iterative (turbo) receiver structure. Both uncoded and conventionally coded systems (including iterative processing) are studied. Even on frequency-flat fading channels, the proposed receiver outperforms conventional techniques. Simulations demonstrate the performance of the proposed equalizer     

Belief Propagation over SISO/MIMO Frequency Selective Fading Channels

In this letter, we propose an iterative belief propagation (BP) channel detector (equalizer) over single-input single- output (SISO) and multiple-input multiple-output (MIMO) frequency selective fading channels as an alternative to the typically used maximum a-posteriori (MAP) or maximum likelihood (ML) detectors. The proposed detector has a parallel structure, resulting in fast hardware implementations. Moreover, BP detector is less complex than the MAP detector and it has a short decoding delay. We analyze the bit error rate and the mutual information and show that, over frequency selective fading channels, the proposed BP detector achieves a near-optimal performance, even in the presence of the length 4 cycles in the corresponding channel factor graph.     

MIMO OFDM系统中的Turbo子载波均衡

在MIMO OFDM系统中,为了对抗同天线干扰及由于保护间隔不足而引起的码间干扰和载波间干扰,该文给出了一种基于MMSE的Turbo子载波均衡器。在该算法中,软输入软输出(SISO)的子载波均衡器与软输入软输出(SISO)解码器通过迭代进行软信息交换。仿真结果表明,与非迭代的子载波均衡器相比,该文给出的Turbo子载波均衡器能够有效利用时间和空间分集,使系统性能得到了改善。     

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.     

MIMO-CDMA系统的分数间隔空频均衡接收方案

该文提出了两种适用于宽带单载波多用户MIMO-CDMA系统下行链路的分数间隔空频均衡接收方案,并进行了理论推导。第1种接收方案采用分数间隔空频均衡器对MIMO频率选择性衰落信道进行均衡,从而恢复了扩频码的正交性,减小了码间干扰和共道干扰。第2种方案在假设接收端已知各用户扩频码的前提下,将分数间隔空频均衡器与频域并行干扰消除器结合,能够进一步消除天线间干扰,提高系统性能。仿真结果表明,这两种分数间隔空频均衡接收方案都比传统的频域均衡接收方案在性能上有很大的提高,并且复杂度也比较低。     

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).     

Space–Time Turbo Equalization With Successive Interference Cancellation for Frequency-Selective MIMO Channels

This paper addresses the issue of iterative space–time equalization for multiple-input–multiple-output (MIMO) frequency-selective fading channels. A new soft equalization concept based on successive interference cancellation (SIC) is introduced for a space–time bit-interleaved coded modulation (STBICM) transmission. The proposed equalizer allows us to separate intersymbol interference (ISI) and multiantenna interference (MAI) functions. Soft ISI is successively suppressed using a low-complexity suboptimum minimum mean square error (MMSE) criterion. The decoupling of ISI and MAI offers more flexibility in the design of the whole space–time equalizer. Different multiantenna detection criteria can be considered, ranging from simple detectors to the optimal maximum a posteriori (MAP) criterion. In particular, we introduce two soft equalizers, which are called SIC/SIC and SIC/MAP, and we show that they can provide a good performance-to-complexity tradeoff for many system configurations, as compared with other turbo equalization schemes. This paper also introduces an MMSE-based iterative channel state information (CSI) estimation algorithm and shows that attractive performance can be achieved when the proposed soft SIC space–time equalizer iterates with the MMSE-based CSI estimator.      

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.     

Equalization for OFDM over doubly selective channels

In this paper, we propose a time-domain as well as a frequency-domain per-tone equalization for orthogonal frequency-division multiplexing (OFDM) over doubly selective channels. We consider the most general case, where the channel delay spread is larger than the cyclic prefix (CP), which results in interblock interference (IBI). IBI in conjunction with the Doppler effect destroys the orthogonality between subcarriers and, hence, results in severe intercarrier interference (ICI). In this paper, we propose a time-varying finite-impulse-response (TV-FIR) time-domain equalizer (TEQ) to restore the orthogonality between subcarriers, and hence to eliminate ICI/IBI. Due to the fact that the TEQ optimizes the performance over all subcarriers in a joint fashion, it has a poor performance. An optimal frequency-domain per-tone equalizer (PTEQ) is then obtained by transferring the TEQ operation to the frequency domain. Through computer simulations, we demonstrate the performance of the proposed equalization techniques.     

单载波通信系统的迭代频域合成均衡算法

为提高符号间干扰(ISI)信道条件下信号接收的可靠性,该文研究单载波通信系统的多天线空间分集接收问题,提出一种迭代频域合成均衡算法。该算法推导先验信息条件下合成均衡器的频域传输函数,并借助快速傅里叶变换(FFT)实现合成均衡器系数和均衡滤波的高效计算。仿真结果表明,相比时域算法,该算法能够在不损失性能的前提下,大幅降低运算复杂度。与单载波频域均衡(SC-FDE)算法相比,该算法不需要在数据传输的结构中插入循环前缀(CP),提高频谱利用率,能够直接应用于现有单载波通信系统。     

瑞利衰落信道下的Turbo均衡

Turbo均衡是一种将Turbo原理和均衡技术结合起来的技术。他通过反复均衡和信道译码来提高接收机性能。针时瑞利衰落信道，采用基于线性滤波器的软输入／软输出均衡器来消除码间干扰，其系数由最小均方误差准则确定。译码器采用最大后验概率算法时卷积码译码。考虑到瑞利衰落信道为随机信道，用非相干检测时信道进行估计。接收机通过联合均衡和译码以充分利用已经获得的信息，实现信道估计及信道均衡与信道译码的迭代更新。仿真结果表明其性能不仅远远优于非迭代系统．而且在信噪比高于4dB时几乎可以完全消除符号间干扰的影响，与MAPSE相比其复杂度大大降低。     

分数阶傅立叶变换OFDM系统自适应均衡算法

由于子载波间干扰(ICI)的影响,传统OFDM系统均衡方法在快速衰落的信道环境下性能有较大下降.本文提出了一种基于分数阶傅立叶变换的OFDM系统自适应均衡方法,它用分数阶傅立叶变换代替傅立叶变换进行子载波调制与解调,同时在分数阶傅立叶域对接收信号进行自适应均衡.文中给出了最优分数阶傅立叶变换阶次的选取方法,和分数阶傅立叶域最小均方算法的步骤.分析和数值仿真结果表明,最优分数阶傅立叶域的自适应均衡算法较传统频域方法有更好的均衡效果,并且复杂度不高.     

Iterative estimation of doubly selective channels with ICI suppression for OFDM using KL-BEM

Channel estimation for orthogonnl frequency division multiplexing(OFDM)systems operating over doubly selective channels is complicated by the existence of intercarrier interference(ICI).This paper extends the idea of estimating time-variant channel impulse response(CIR)via time-averaged CIR.proposed by Hijazi,and proposes a low-complexity channel estimation scheme with ICI suppression based on Karhnnen-Loeve basis expansion model(KL-BEM),which is in a more general form.In the proposed scheme,the KL-BEM coefficients are obtained through their numerical relationship with the time-averaged CIR.The estimation performance is improved by adopting an expectation-maximization(EM)-based iterative structure combined with a low-complexity ICI equalizer and canceller.Theoretical analysis and simulation results show that the proposed scheme achieves superior performance over the original one with lower computational complexity.     

Soft input soft output Kalman equalizer for MIMO frequency selective fading channels

We consider the Kalman filter for equalization of a multiple-input multiple-output (MIMO), frequency selective, quasi-static fading channel. More specifically, we consider a coded system, where the incoming bit stream is convolutionally encoded, interleaved and then spatially multiplexed across the transmit antennas. Each substream is modulated into M-ary symbols before being transmitted over a frequency selective channel. At the receiver, we propose to use the Kalman filter as a low complexity MIMO equalizer, as opposed to the trellis based maximum a-posteriori (MAP) equalizer whose computational complexity grows exponentially with the channel memory, the number of transmit antennas and the spectral efficiency (bits/s/Hz) of the system. We modify the structure of the Kalman filter and enable it to process the a-priori (soft) information provided by the channel decoder, thereby allowing us to perform iterative (turbo) equalization on the received sequence. The iterative equalizer structure is designed for general M-ary constellations. We also propose a low complexity version of the above algorithm whose performance is comparable to its full complexity counterpart, but which achieves a significant complexity reduction. We demonstrate via simulations that for higher order constellations, when sufficient number of receive antennas are available (e.g. for a 2 transmitter, 3 receiver system, QPSK), the performance of the proposed algorithms after 4 iterations is within 1.5 dB of the non-iterative MAP algorithm with close to an order of magnitude complexity reduction. By objectively quantifying the complexity of all the considered algorithms we show that the complexity reduction for the proposed schemes becomes increasingly significant for practical systems with moderate to large constellation sizes and a large number of transmit antennas     

一种快变信道中的正交频分复用系统均衡算法

当信道参数随时间的快速变化时,正交频分复用通信系统(OFDM)子载波间的正交性遭到破坏,出现了载波间的相互干扰(ICI),传统的单抽头频域均衡不再适用。虽然可采用最小均方误差(MMSE)均衡来补偿信道失真,但其计算量太大。为此,常用的方法是:先对接收信号进行ICI消除,恢复载波间的正交性,然后再进行单抽头频域或均衡。现有文献对ICI的分析均在频域进行,在此基础上提出的ICI消除与均衡算法存在计算量大或频谱利用率低的缺点。本文对ICI的产生机理和性质进行了时域和频域两方面的分析,利用现有OFDM标准中的空闲子载波信息,提出了一种ICI消除与均衡算法。理论分析和计算机仿真结果表明:该算法具有ICI消除效果好、计算量小和频谱利用率高等优点。     

基于Rimoldi分解的连续相位调制信号Turbo频域均衡算法

针对高阶部分响应连续相位调制(CPM)信号均衡中存在的复杂度高和性能较差等问题,该文从Rimoldi分解的角度出发,设计了一种新的适用于倾斜相位CPM信号的发射帧结构,并在此基础上结合单载波频域均衡(FDE)和Turbo均衡的思想,提出了一种适用于高阶CPM信号的Turbo频域均衡算法。该算法通过将信号均衡转化到频域进行处理,避免了时域均衡算法在计算均衡器系数时存在的大矩阵求逆问题,同时使用Turbo均衡的软信息迭代处理来改善系统的性能。理论分析和仿真结果表明,对于四阶部分响应CPM信号,在存在严重符号间干扰的多径衰落信道的条件下,该算法与现有的基于符号的频域均衡算法相比,在保持较低复杂度的同时,具有大约1.5 dB的性能增益。     

Novel semi-blind ICI equalization algorithm for wireless OFDM systems

Intercarrier interference is deemed as one of the crucial problems in the wireless orthogonal frequency division multiplexing (OFDM) systems. The conventional ICI mitigation schemes involve the frequency-domain channel estimation or the additional coding, both of which require the spectral overhead and hence lead to the significant throughput reduction. Besides, the OFDM receivers using the ICI estimation rely on a large-dimensional matrix inverter with high computational complexity especially for many subcarriers such as digital video broadcasting (DVB) systems and wireless metropolitan-area networks (WMAN). To the best of our knowledge, no semi-blind ICI equalization has been addressed in the existing literature. Thus, in this paper, we propose a novel semi-blind ICI equalization scheme using the joint multiple matrix diagonalization (JMMD) algorithm to greatly reduce the intercarrier interference in OFDM. However, the well-known phase and permutation indeterminacies emerge in all blind equalization schemes. Hence we also design a few OFDM pilot blocks and propose an iterative identification method to determine the corresponding phase and permutation variants in our semi-blind scheme. Our semi-blind ICI equalization algorithm integrating the JMMD with the additional pilot-based iterative identification is very promising for the future high-throughput OFDM systems. Through Monte Carlo simulations, the QPSK-OFDM system with our proposed semi-blind ICI equalizer can achieve significantly better performance with symbol error rate reduction in several orders-of-magnitude. For the 16QAM-OFDM system, our scheme can also improve the performance over the plain OFDM system to some extent.