基于最大缩短信噪比算法的对称时域均衡器的设计

本文首先分析最大缩短信噪比(MSSNR)算法的原理,然后证实基于该算法的时域均衡器有对称性的特性,并通过仿真验证。最后提出改进算法,即对称的最大缩短信噪比算法,该算法能有效强化均衡器的对称性,使运算量大大减少,复杂度降低。     

Second-order statistical approaches to channel shortening in multicarrier systems

In multicarrier systems with a cyclic prefix, interblock interference can be limited by shortening the channel impulse response using time-domain equalizers. In this paper, we present two blind channel-shortening algorithms that exploit the second-order statistics of the channel outputs. The equalizer parameter vector is chosen from a space that forces the length constraint on the effective channel impulse response. The first algorithm is less sensitive to channel-order estimation errors, whereas the second one is simpler to implement. Furthermore, we show that the two algorithms are equivalent for noiseless channels. Simulation examples are provided to demonstrate their superior performance over some existing algorithms.     

Minimum-Mean-Output-Energy Blind Adaptive Channel Shortening for Multicarrier SIMO Transceivers

In this paper, we propose a blind adaptive channel-shortening method for designing finite-impulse response time-domain equalizers (TEQs) in single-input multiple-output systems employing multicarrier modulations. The proposed algorithm, which relies on a constrained minimization of the mean-output-energy at the TEQ output, does not require a priori knowledge of the channel impulse response or transmission of training sequences, and admits an effective and computationally efficient adaptive implementation. Moreover, the proposed TEQ is narrowband-interference resistant and its synthesis only requires an upper bound (rather than the exact knowledge) of the channel order. Numerical simulations are provided to illustrate the advantages of the proposed technique over a recently developed blind channel shortener.     

Adaptive bit rate maximizing time-domain equalizer design for DMT-based systems

The classical discrete multitone receiver as used in, e.g., digital subscriber line (DSL) modems, combines a channel shortening time-domain equalizer (TEQ) with one-tap frequency-domain equalizers (FEQs). In a previous paper, the authors proposed a nonlinear bit rate maximizing (BM) TEQ design criterion and they have shown that the resulting BM-TEQ and the closely related BM per-group equalizers (PGEQs) approach the performance of the so-called per-tone equalizer (PTEQ). The PTEQ is an attractive alternative that provides a separate complex-valued equalizer for each active tone. In this paper, the authors show that the BM-TEQ and BM-PGEQ, despite their nonlinear cost criterion, can be designed adaptively, based on a recursive Levenberg-Marquardt algorithm. This adaptive BM-TEQ/BM-PGEQ makes use of the same second-order statistics as the earlier presented recursive least-squares (RLS)-based adaptive PTEQ. A complete range of adaptive BM equalizers then opens up: the RLS-based adaptive PTEQ design is computationally efficient but involves a large number of equalizer taps; the adaptive BM-TEQ has a minimal number of equalizer taps at the expense of a larger design complexity; the adaptive BM-PGEQ has a similar design complexity as the BM-TEQ and an intermediate number of equalizer taps between the BM-TEQ and the PTEQ. These adaptive equalizers allow us to track variations of transmission channel and noise, which are typical of a DSL environment.     

Time-Domain Block and Per-Tone Equalization for MIMO–OFDM in Shallow Underwater Acoustic Communication

Shallow underwater acoustic (UWA) channel exhibits rapid temporal variations, extensive multipath spreads, and severe frequency-dependent attenuations. So, high data rate communication with high spectral efficiency in this challenging medium requires efficient system design. Multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO–OFDM) is a promising solution for reliable transmission over highly dispersive channels. In this paper, we study the equalization of shallow UWA channels when a MIMO–OFDM transmission scheme is used. We address simultaneously the long multipath spread and rapid temporal variations of the channel. These features lead to interblock interference (IBI) along with intercarrier interference (ICI), thereby degrading the system performance. We describe the underwater channel using a general basis expansion model (BEM), and propose time-domain block equalization techniques to jointly eliminate the IBI and ICI. The block equalizers are derived based on minimum mean-square error and zero-forcing criteria. We also develop a novel approach to design two time-domain per-tone equalizers, which minimize bit error rate or mean-square error in each subcarrier. We simulate a typical shallow UWA channel to demonstrate the desirable performance of the proposed equalization techniques in Rayleigh and Rician fading channels.     

办公室环境下的超宽带信道测量与建模

依据广泛的频域信道测量数据,提出了符合中国超宽带(UWB)技术频率使用规定的办公室室内信道模型。信道总体模型采用修正Saleh-Valenzuela(S-V)模型。在信道测量信号的后处理中,使用过渡带为高斯滚降特性的类高斯窗来提取符合中国超宽带频谱规范的测量信号。利用CLEAN算法从时域测量数据中提取高分辨率的离散信道响应,并为信道时域测量信号提出了一种基于小波分析的自动分簇算法,统计提取出了大尺度和小尺度信道模型参数。结果表明:提出的办公室超宽带信道模型和实测数据具有相近的时延扩展特性和平均多径数量,可以比IEEE802.15.4a信道模型更好地反映中国办公室环境下的UWB信道特性。     

L’égalisation numérique en communications

This tutorial contribution explains how digital equalization permits very high transmission rates, even with severe channels, by adaptive (real time) correction of the distortion. Equalizers are in general digital filters. Transversal equalizers are only suitable for mild channels. In data transmission, where symbols have discrete levels, severe channels can be equalized by adding a recursive path that is filled in with detected symbols. Engineers have realized optimal equalizers for more than twenty years thanks to the adaptive tracking of the channel time variations, at a very low computational cost. However adaptation requires the periodic transmission of a training sequence deprived of information content. This supervised learning technique is acceptable only in an end-to-end communication system. The most recent equalization methods are usable in multiuser systems such as networks, broadcasted communications, etc., because they employ self-learning or unsupervised equalization. Then adaptation is controlled by the very information data flow. It only takes advantage of an a priori statistical knowledge on the emitted data, e.g. their whiteness, a property that is ensured thanks to jamming. Let us conjecture that all equalizers will be self-learning in a near future.     

On convergence analysis of fractionally spaced adaptive blindequalizers

In this paper, we study the convergence analysis of fractionally spaced adaptive blind equalizers. We show that based on the trivial and nontrivial nullspaces of a channel convolution matrix, all equilibria can be classified as channel dependent equilibria (CDE) or algorithm dependent equilibria (ADE). Because oversampling provides channel diversity, the nullspace of the channel convolution matrix is affected. We show that fractionally spaced equalizers (FSEs) do not possess any CDE if a length-zero condition is satisfied. The convergence behavior of these FSE are clearly determined by the specific choice of cost function alone. We characterize the global convergence ability of several popular algorithms simply based on their ADE. We also present an FSE implementation of the super-exponential algorithm. We show that the FSE implementation does not introduce any nonideal approximation. Simulation results are also presented to illustrate the robustness and the improved performance of FSE under the super-exponential algorithm     

Convergence analysis of the stop-and-go blind equalizationalgorithm

Unlike traditional trained channel equalizers, not much work has been done to theoretically characterize the convergence properties of blind channel equalizers due to their inherent nonlinearity. It is only recently that convergence properties of some well-known algorithms such as the generalised Sato algorithm (GSA) and the constant modulus algorithm (CMA) have been analytically derived. In this paper, the convergence properties of the stop-and-go algorithm proposed by Picchi and Prati (1987) are analyzed. The derived mean squared error and the coefficient trajectories are compared with simulation results to verify the validity of the analytical results     

Global convergence of fractionally spaced Godard (CMA) adaptiveequalizers

The Godard (1980) or constant modulus algorithm (CMA) equalizer is perhaps the best known and the most popular scheme for blind adaptive channel equalization. Most published works on blind equalization convergence analysis are confined to T-spaced equalizers with real-valued inputs. The common belief is that analysis of fractionally spaced equalizers (FSEss) with complex inputs is a straightforward extension with similar results. This belief is, in fact, untrue. We present a convergence analysis of Godard/CMA FSEs that proves the important advantages provided by the FSE structure. We show that an FSE allows the exploitation of the channel diversity that supports two important conclusions of great practical significance: (1) a finite-length channel satisfying a length-and-zero condition allows Godard/CMA FSE to be globally convergent, and (2) the linear FSE filter length need not be longer than the channel delay spread. Computer simulation demonstrates the performance improvement provided by the adaptive Godard FSE     

一种基于间接Volterra学习算法的前置补偿器

非线性补偿技术对于的非线性通过补偿信道的非线性特性来提高通信信道的性能越来越重要,非线性补偿器可分为2大类:均衡器和前置补偿器。前者位于非线性信道的输出端而后者则位于非线性信道的输入端。在前置补偿器的基础上,提出一种新的基于Volterra级数前置补偿器,它利用间接学习算法来解决一类前置补偿问题——即信道的特性预先是未知的。这一点P阶逆算法是无法做到的,然后又以正交幅度调制信号(16QAM)验证这种新算法的性能优于P阶逆算法。     

OFDM电力线通信系统的时域信道估计方法

针对G3-PLC协议,提出了两种改进的时域信道估计方法。为达到时域降噪效果,采用了预置电力线信道最大时延的方法,但这使得相关的时频变换矩阵不满秩,无法直接采用最小二乘准则估计其时域特性。因此,文中提出一种基于修正变换矩阵的时域LS算法,解决了矩阵不可逆问题。同时进一步提出了一种无需信道统计特性的时域线性最小均方误差算法,大幅降低了复杂度。仿真结果表明,修正的时域LS算法和简化的时域LMMSE算法均性能良好。     

Turbo Coding with Equalization in WCDMA Downlink

In this paper, the performance of turbo coding in WCDMA downlink is considered in conjunction with receivers using two adaptive channel equalizers. Bit error and frame error rates are compared to the performance of the conventional Rake receiver. Special consideration is given to the cases with two receive antennas, the efficiency of the channel interleaver, the number of iterations in decoding, the performance with various numbers of users, the influence of mobile receiver velocity as well as to the effect of power control. The simulation results show that turbo coding, combined with power control and channel equalizers is a very efficient way to implement reliable data transmissions in WCDMA downlink. The results in the paper also verify that the adaptive channel equalizers is a very promising technique to improve the receiver performance and increase the user capacity.     

Design of Sparse Filters for Channel Shortening

Channel shortening equalizers are used in acoustics to reduce reverberation, in error control decoding to reduce complexity, and in communication receivers to reduce inter-symbol interference. The cascade of a channel and channel shortening equalizer ideally produces an overall impulse response that has most of its energy compacted into fewer adjacent samples. Once designed, channel shortening equalizers filter the received signal on a per-sample basis and need to be adapted or re-designed if the channel impulse response changes significantly. In this paper, we evaluate sparse filters as channel shortening equalizers. Unlike conventional dense filters, sparse filters have a small number of non-contiguous non-zero coefficients. Our contributions include (1) proposing optimal and sub-optimal low complexity algorithms for sparse shortening filter design, and (2) evaluating impulse response energy compaction vs. design and implementation stage computational complexity tradeoffs for the proposed algorithms. We apply the proposed equalizer design procedures to (1) asymmetric digital subscriber line channels and (2) underwater acoustic communication channels. Our simulation results utilize measured channel impulse responses and show that sparse filters are able to achieve the same channel energy compaction with half as many coefficients as dense filters.     

Blind equalization based on prediction and polycepstra principles

The polycepstra and prediction equalization algorithm (POPREA) is proposed for blind equalization of nonminimum phase channels. The algorithm equalizes the amplitude and phase of the channel independently by employing linear prediction and tricepstrum principles, respectively. It guarantees convergence to a global solution. The tracking and cancellation of phase due to carrier frequency offset is carried out independently of equalization. It is demonstrated, by means of computer simulations, that the proposed POPREA is able to open the eye pattern of QAM signal constellations faster than existing polyspectra-based equalizers. The complexity of the algorithm is high but comparable to that of polyspectra equalizers     

Channel equalization for block transmission systems

In a block transmission system the information symbols are arranged in the form of blocks separated by known symbols. Such a system is suitable for communication over time-dispersive channels subject to fast time-variations, e,g., the HF channel. The known reliable receiver for this system is the nonlinear data-directed estimator (NDDE). This paper presents appropriate equalization methods for this system. A nonstationary innovations representation based on Cholesky factorization is used in order to define a noise whitener and a maximum-likelihood block detector. Also block linear equalizers and block decision-feedback equalizers are derived. For each type we give the zero-forcing and the minimum-mean-squared-error versions. Performance evaluations and comparisons are given. We show that they perform better than conventional equalizers. As compared to the NDDE, the derived block decision-feedback equalizers perform better and are much less complex. Whereas the NDDE uses the Levinson algorithm to solve M/2 Toeplitz systems of decreasing order (where M is the number of symbols per block), the derived equalizers need to process only one Toeplitz system. Moreover, the Schur algorithm, proposed for Cholesky factorization allows us to further reduce the complexity     

Fast recovery equalization techniques for DTV signals

Blind equalizers do not require any training sequence for the initial startup period but rather perform equalization blindly on the data directly. In this paper, a general approach for designing such equalizers for 8-VSB transmission systems is presented. The candidate algorithms considered here include Godard's algorithm (Godard 1980), Sato's algorithm (Sato 1975), the G-pseudo error algorithm using Sato's function and the G-pseudo error algorithm using Godard's function. This paper analyzes these algorithms for the 8-VSB transmission format and recommends the most suitable algorithm. The performance comparison parameters include MSE, convergence characteristics, computational load and accuracy of estimating the channel     

Set-membership adaptive equalization and an updator-sharedimplementation for multiple channel communications systems

This paper considers the problems of channel estimation and adaptive equalization in the novel framework of set-membership parameter estimation. Channel estimation using a class of set-membership identification algorithms known as optimal bounding ellipsoid (OBE) algorithms and their extension to tracking time-varying channels are described. Simulation results show that the OBE channel estimators outperform the least-mean-square (LMS) algorithm and perform comparably with the RLS and the Kalman filter. The concept of set-membership equalization is introduced along with the notion of a feasible equalizer. Necessary and sufficient conditions are derived for the existence of feasible equalizers in the case of linear equalization for a linear FIR additive noise channel. An adaptive OBE algorithm is shown to provide a set of estimated feasible equalizers. The selective update feature of the OBE algorithms is exploited to devise an updator-shared scheme in a multiple channel environment, referred to as updator-shared parallel adaptive equalization (USHAPE). U-SHAPE is shown to reduce the hardware complexity significantly. Procedures to compute the minimum number of updating processors required for a specified quality of service are presented     

Reconstruction of oversampled band-limited signals fromΣΔ encoded binary sequences

Considers the application of ΣΔ modulators to analog-to-digital conversion. The authors have previously shown that for constant input signals, optimal nonlinear decoding can achieve large gains in signal-to-noise ratio (SNR) over linear decoding. The present paper shows a similar result for band-limited input signals. The new nonlinear decoding algorithm is based on projections onto convex sets (POCS), and alternates between a time-domain operation and a band limitation to find a signal invariant under both. The time-domain operation results in a quadratic programming problem. The band limitation can be based on singular value decomposition of a certain matrix. The authors show simulation results for the SNR performance of a POCS-based decoder and a linear decoder for the single loop, double loop and two-stage ΣΔ modulators and for a specific fourth-order interpolative modulator. Depending on the modulator and the oversampling ratio, improvements in SNR of up to 10-20 dB can be achieved     

Efficient reinitialization of the prewhitened constant modulusalgorithm

We present a reinitialization scheme for blind equalizers adapted via the constant modulus algorithm (CMA) when an all-pole prefilter is included to whiten the received signal. The mechanism exploits the special structure of the minimum mean squared error (MMSE) equalizers and their relation with CMA equalizers. A heuristic rule for blind determination of the best equalization delay is also provided. Using these guidelines, the equalizer is capable of finding the optimal setting in an online and computationally efficient fashion. In particular, estimation and inversion of the channel output autocorrelation matrix is not needed, in contrast with previous approaches