Block channel equalization in the frequency domain

In this paper, channel equalization algorithms processing two samples of the received signal per channel symbol and operating in the frequency domain are described in a unifying framework. First, minimum mean-square error linear and decision-feedback equalizers are derived, and a synthesis technique based on the well-known Levinson-Durbin algorithm is proposed for the latter. Then, iterative linear and decision-feedback equalization algorithms for turbo processing are devised. Performance results for both uncoded and coded phase-shift keying transmissions show the efficacy of the proposed equalization techniques and their superiority over other existing frequency-domain equalization strategies.     

Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners.     

Joint frequency-domain differential detection and equalization for DS-CDMA signal transmissions in a frequency-selective fading channel

It has been revealed that direct sequence code-division multiple access (DS-CDMA) can achieve a good bit-error rate (BER) performance, comparable to multicarrier CDMA (MC-CDMA), by using coherent frequency-domain equalization (FDE) instead of coherent Rake combining. However, coherent FDE requires accurate channel estimation. Pilot-assisted channel estimation is a practical solution, but its accuracy is sensitive to the Doppler spread. In this paper, a frequency-domain differential encoding and detection scheme is proposed for a DS-CDMA mobile radio. Joint frequency-domain differential detection and equalization (FDDDE) based on minimum mean-square error (MMSE) criterion is presented, where a simple decision feedback filter is used to provide a reliable reference signal for MMSE-FDDDE. Also presented is an approximate BER analysis. It is confirmed by both approximate BER analysis and computer simulation that MMSE-FDDDE provides good BER performance close to the coherent MMSE-FDE and shows high robustness against the Doppler spread; it outperforms coherent MMSE-FDE for large Doppler spreads. The proposed MMSE-FDDDE can also be applied to MC-CDMA. A performance comparison between uncoded DS- and MC-CDMA shows that DS-CDMA with MMSE-FDDDE achieves better BER performance than MC-CDMA with MMSE-FDDDE for small spreading factors.     

Turbo equalization: adaptive equalization and channel decodingjointly optimized

This paper deals with a receiver scheme where adaptive equalization and channel decoding are jointly optimized in an iterative process. This receiver scheme is well suited for transmissions over a frequency-selective channel with large delay spread and for high spectral efficiency modulations. A low-complexity soft-input soft-output M-ary channel decoder is proposed. Turbo equalization allows intersymbol interference to be reduced drastically. For most time-invariant discrete channels, the turbo-equalizer performance is close to the coded Gaussian channel performance, even for low signal-to-noise ratios. Finally, results over a time-varying frequency-selective channel proves the excellent behavior of the turbo equalizer     

Protocol-aided channel equalization in wireless ATM

We study the equalization problem in time division multiple access wireless asynchronous transfer mode (ATM) systems. Aiming at minimizing the overhead associated with equalization, we propose a protocol-aided channel equalization (PACE) approach for wireless ATM. Specifically, the medium access control (MAC) and data link control (DLC) protocols are exploited to provide known ATM cell headers to the receiver at the base station. A blind channel estimation-decision feedback equalizer (BCE-DFE) algorithm is developed for uplink data transmissions. There are two advantages of the BCE-DFE algorithm: the elimination of training symbols for uplink data bursts and the removal of channel estimation error propagation suffered by conventional block equalization schemes. Simulation results show the BCE-DFE has a robust performance for wireless ATM uplink data transmissions over fast time-varying channels     

Baud-rate channel equalization in nanometer technologies

Chip design technology has been accelerating the advances of the communication technology in the past decades because a chip with larger computing capacity can support a communication system of higher transmission bandwidth. Since the communication transceivers are now in the multigiga bits/second range, the computing bandwidth requirement for a transceiver has grown into several hundreds of giga-FLOPs second range. To support such big computing tasks on a chip, nanometer technology and pure baud-rate computing without pipelining and oversampling overheads will be much more important. Meanwhile, baud-rate computing does not require extra-digital control for the digital-signal processing functions. This can greatly reduce the power consumption and chip area of a VLSI system. Yet, there are several design issues, such as the output signal-to-noise ratio, algorithmic mapping for computing model, and the critical path for the datapath design of the VLSI computing function, which need to be resolved under small silicon area requirements A novel baud-rate channel equalization architecture based on training coefficient relaxation techniques is presented in this paper to resolve these issues in nanotechnology such as 130- and 90-nm technologies. This design paradigm clearly demonstrates its advantage to enable multiport transceiver system-on-a-chip designs in nanometer technology. Trends for the baud-rate computing in smaller geometry are also explained.     

Single-user channel estimation and equalization

There has been much interest in blind (self-recovering) channel estimation and blind equalization where no training sequences are available or used. In multipoint networks, whenever a link from the server to one of the tributary stations is interrupted, it is clearly not feasible (or desirable) for the server to start sending a training sequence to re-establish a particular link. In digital communications over fading/multipath channels, a restart is required following a temporary path interruption due to severe fading. During on-line transmission impairment monitoring, the training sequences are obviously not supplied by the transmitter. Consequently, the importance of blind channel compensation research is also strongly supported by practical needs. We present a comprehensive summary of research development on single-user channel estimation and equalization, focusing on both training-based and blind approaches. Our emphasis is on linear time-invariant channels.     

Nonparametric trellis equalization in the presence of non-Gaussian interference

We consider the problem of trellis equalization of the intersymbol interference channel in the presence of thermal noise and cochannel interference (CCI). Conventional maximum-likelihood sequence estimation (MLSE) and maximum a posteriori probability (MAP) trellis equalizers treat the sum of noise and interference as additive white Gaussian noise, while CCI is generally a colored non-Gaussian process. We propose a novel nonparametric approach based on the estimation of the probability density function of the noise-plus-interference. Given the availability of a limited volume of data, the density is estimated by kernel-smoothing techniques. The use of a whitening filter in the presence of temporally colored disturbance is also addressed. Simulation results are provided for the global system for mobile communications (GSM), showing a significant performance improvement with respect to the equalizer based on the Gaussian assumption. Major advantages of the proposed strategy are its intrinsic robustness and general applicability to those cases where accurate modeling of the interference is difficult or a model is not available.     

面向ASIC设计的单载波超宽带信道均衡研究

单载波超宽带通信系统的均衡在芯片实现中面临高吞吐率、高性能和低复杂度三方面问题。该文首先比较了最大似然均衡（MLSE）、线性均衡（LE）、判决反馈均衡（DFE）及单载波频域均衡（SC-FDE）在性能、复杂度及高速化实现上的优缺点,并综合考虑SC-UWB系统这一特殊的应用场景最终选择了DFE。然后针对DFE算法中的三个关键参数——前馈阶数Nf,反馈阶数Nb及判决延迟D,提出了一种实际系统中有效且实用的参数优化设计策略,最后仿真证明了优化策略的实用性和有效性。     

Decision feedback equalization of the indoor radio channel

The measured multipath profiles from five different indoor areas are used for the performance analysis of a binary phase shift keying (BPSK) modem with a decision feedback equalizer (DFE). The performance from the measured multipath profiles is compared with the performance predictions based on a computer simulated channel model. Both average probability of error and probability of outage are calculated for a DFE with three fractionally spaced forward and three feedback taps. An equivalent delay power spectrum function, determined from the ensemble of the measured channel impulse responses, is defined. Using this function, analytical lower bounds on the average probability of error and the probability of outage of the BPSK/DFE modem with an infinite number of feedback taps and three forward taps are determined and compared with the results based on measured data and the computer generated channel impulse responses     

基于FPGA的信道估计和信道均衡的实现

信道估计与信道均衡是自组网物理层关键技术;本文提出了一种改进的LMMSE信道估计算法;然后设计并实现了基于FPGA硬件平台的信道估计与均衡模块;结果表明,该模块算法复杂度低,占用硬件资源少,估计精度符合预期,满足应用需求.     

Adaptive asymptotic Bayesian equalization using a signal space partitioning technique

The Bayesian solution is known to be optimal for symbol-by-symbol equalizers; however, its computational complexity is usually very high. The signal space partitioning technique has been proposed to reduce complexity. It was shown that the decision boundary of the equalizer consists of a set of hyperplanes. The disadvantage of existing approaches is that the number of hyperplanes cannot be controlled. In addition, a state-search process, that is not efficient for time-varying channels, is required to find these hyperplanes. In this paper, we propose a new algorithm to remedy these problems. We propose an approximate Bayesian criterion that allows the number of hyperplanes to be arbitrarily set. As a consequence, a tradeoff can be made between performance and computational complexity. In many cases, the resulting performance loss is small, whereas the computational complexity reduction can be large. The proposed equalizer consists of a set of parallel linear discriminant functions and a maximum operation. An adaptive method using stochastic gradient descent has been developed to identify the functions. The proposed algorithm is thus inherently applicable to time-varying channels. The computational complexity of this adaptive algorithm is low and suitable for real-world implementation.     

无人机数据链信道均衡技术仿真研究

信道均衡技术是无线通信中解决码间干扰的关键技术.选取LMS,RLS和CMA常用的均衡算法以及信道均衡器的结构作为研究对象,通过对三种均衡算法的收敛性能的仿真分析,以及结合无人机信道模型对常用的两种均衡结构的误码性能进行的仿真,所得结果对于后期基于FPGA实现高速的信道均衡器时算法和结构的选择具有参考的价值.     

Blind channel identification and equalization withmodulation-induced cyclostationarity

Recent results have pointed out the importance of inducing cyclostationarity at the transmitter for blind identification and equalization of communication channels. This paper addresses blind channel identification and equalization relying on the modulation-induced cyclostationarity, without introducing redundancy at the transmitter. It is shown that single-input single-output channels can be identified uniquely from output second-order cyclic statistics, irrespective of the location of channel zeros, color of additive stationary noise, or channel order overestimation errors, provided that the period of modulation-induced cyclostationarity is greater than half the channel length. Linear, closed-form, nonlinear correlation matching, and subspace-based approaches are developed for channel estimation and are tested using simulations. Necessary and sufficient blind channel identifiability conditions are presented. A Wiener cyclic equalizer is also proposed     

Combined multiuser signal classification and blind equalization

A multiuser automatic modulation classifier (MAMC) is an important signal processing component of a multiantenna cognitive radio (CR) receiver that helps the radio in identifying modulation format employed by multiple users in a frequency band simultaneously. In a typical wireless communication, transmitted signals are subjected to multipath fading and interference from other users. Multipath fading not only affects symbol detection performance but also affects the performance of the automatic modulation classifier. A multi input multi output (MIMO) blind equalizer is another important component of a multiantenna CR receiver that improves symbol detection performance by reducing inter symbol interference and inter user interference. In a CR scenario it is preferable to consider the performance of the AMC also while adapting the parameters of the blind equalizer. In this paper we propose MIMO blind equalizers that improves the performance of both multiuser symbol detection and cumulants based MAMC. Computer simulations are provided to illustrate this concept and the proposed algorithm.     

Nonminimum phase channel equalization using noncausal filters

The Viterbi algorithm is the optimum method for detection of a data sequence in the presence of intersymbol interference and additive white Gaussian noise. Since its computational complexity is very large, several simplifications and alternative methods have been proposed, most of which are more effective when dealing with minimum phase channels. We present a novel technique for the equalization of nonminimum phase channels that employs noncausal all-pass filters operating in reversed time. The impulse response of the equalized channel approximates a minimum phase sequence with higher energy concentration at its left-hand end than at the right-hand end. The method can be modified to obtain a desired impulse response with few nonzero samples with only minor variations in noise level, providing significant complexity reduction in the Viterbi algorithm for detection. In addition, a twopass decoding strategy is developed, leading to significant improvement in performance with little increase in computational cost. Simulation results are included to verify the advantages of the proposed techniques     

Least squares approach to blind channel equalization

We present a least squares (LS) algorithm for blind channel equalization based on a reformulation of the Godard algorithm. A transformation for the equalizer parameters is considered to convert the nonlinear LS problem inherent in the Godard algorithm to a linear LS problem. Unlike the Godard (1980) algorithm, the proposed LS approach does not suffer from ill-convergence to closed-eye local minima. Methods for extracting the equalizer parameters from their transformed version are developed. Offline and recursive implementations of the LS algorithm are presented. The algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis-a-vis the Godard algorithm. The channel input correlation does not impose any restriction on the application of the algorithm, as long as a weak sufficient-excitation condition is satisfied. Simulation examples are presented to demonstrate the LS approach and to compare it with the Godard algorithm     

Unbiased blind adaptive channel identification and equalization

The blind adaptive equalization and identification of communication channels is a problem of important current theoretical and practical concerns. Previously proposed solutions for this problem exploit the diversity induced by sensor arrays or time oversampling, leading to the so-called second-order algebraic/statistical techniques. The prediction error method is one of them, perhaps the most appealing in practice, due to its inherent robustness to ill-defined channel lengths as well as for its simple adaptive implementation. Unfortunately, the performance of prediction error methods is known to be severely limited in noisy environments, which calls for the development of noise (bias) removal techniques. We present a low-cost algorithm that solves this problem and allows the adaptive estimation of unbiased linear predictors in additive noise with arbitrary autocorrelation. This algorithm does not require the knowledge of the noise variance and relies on a new constrained prediction cost function. The technique can be applied in other noisy prediction problems. Global convergence is established analytically. The performance of the denoising technique is evaluated over GSM test channels     

Optimal design for channel equalization via the filterbank approach

Channel equalization is investigated via the filterbank approach. A necessary and sufficient condition is established for perfect reconstruction (PR) of the transmitter-receiver filterbanks. If the PR condition holds, then all causal and stable receiver filterbanks that achieve PR are parameterized. It is further shown that the receiver filterbank for optimal channel equalization has the form of state estimator and is a modified Kalman filter. The design algorithm for optimal channel equalizers is developed. A simulation example is worked out to illustrate the proposed design algorithm.