Multichannel MLSE equalizer with parametric FIR channelidentification

We propose a parametric finite impulse response (FIR) channel identification algorithm, apply the algorithm to a multichannel maximum likelihood sequential estimation (MLSE) equalizer using multiple antennas, and investigate the improvement in the overall bit error rate (BER) performance. By exploring the structure of the specular multipath channels, we are able to reduce the number of channel parameters to provide a better channel estimate for the MLSE equalizer. The analytic BER lower bounds of the proposed algorithm as well as those of several other conventional MLSE algorithms in the specular multipath Rayleigh-fading channels are derived. In the derivation, we consider the channel mismatch caused by the additive Gaussian noise and the finite-length channel approximation error. A handy-to-use simplified BER lower bound is also derived. Simulation results that illustrate the BER performance of the proposed algorithm in the global system for mobile communications (GSM) system are presented and compared to the analytic lower bounds     

Time-varying FIR equalization for doubly selective channels

We propose a time-varying (TV) finite impulse response (FIR) equalizer for doubly selective (time- and frequency-selective) channels. We use a basis expansion model (BEM) to approximate the doubly selective channel and to design the TV FIR equalizer. This allows us to turn a complicated equalization problem into an equivalent simpler equalization problem, containing only the BEM coefficients of both the doubly selective channel and the TV FIR equalizer. The minimum mean-square error (MMSE) as well as the zero-forcing (ZF) solutions are considered. Comparisons with the block linear equalizer (BLE) are made. The TV FIR equalization we propose here unifies and extends many previously proposed serial equalization approaches. In contrast to the BLE, the proposed TV FIR equalizer allows a flexible tradeoff between complexity and performance. Moreover, through computer simulations, we show that the performance of the proposed MMSE TV FIR equalizer comes close to the performance of the ZF and MMSE BLE, at a point where the design as well as the implementation complexity are much lower.     

一种脉冲噪声下的自适应均衡算法

由单层神经自适应滤波器和Chebyshev正交多项式滤波器级联构成一个均衡器,基于此均衡器结构,提出一种基于分数低阶统计量的自适应均衡算法(称为NC-NLMP算法).仿真结果表明,对线性信道和非线性信道,NC-NLMP算法的均衡性能均优于传统的FIR横向滤波器的自适应均衡算法和神经网络均衡算法;对于非线性信道,NC-NLMP算法的均衡性能远优于后两者;NC-NLMP算法对高斯噪声和稳定分布脉冲噪声都具有很好的均衡性能,对背景噪声韧性强.     

Near-Minimum Bit-Error Rate Equalizer Adaptation for PRML Systems

Receivers for partial response maximum-likelihood systems typically use a linear equalizer followed by a Viterbi detector. The equalizer tries to confine the channel intersymbol interference to a short span in order to limit the implementation complexity of the Viterbi detector. Equalization is usually made adaptive in order to compensate for channel variations. Conventional adaptation techniques, e.g., LMS, are, in general, suboptimal in terms of bit-error rate (BER). In this paper, we present a new equalizer adaptation algorithm that seeks to minimize the BER at the Viterbi detector output. The algorithm extracts information from the sequenced amplitude margin (SAM) histogram and incorporates a selection mechanism that focuses adaptation on particular data and noise realizations. The selection mechanism is based on the reliability of the add compare select (ACS) operations in the Viterbi detector. From a complexity standpoint, the algorithm is essentially as simple as the conventional LMS algorithm. Moreover, we present a further simplified version of the algorithm that does not require any hardware multiplications. Simulation results, for an idealized optical storage channel, confirm a substantial performance improvement relative to existing adaptation algorithms.     

Adaptive MLSE equalizers with parametric tracking for multipathfast-fading channels

We use the parametric channel identification algorithm proposed by Chen and Paulraj (see Proc. IEEE Vehicular Technology Conf., p.710-14, 1997) and by Chen, Kim and Liang (see IEEE Trans. Veh. Technol., p.1923-35, 1999) to adaptively track the fast-fading channels for the multichannel maximum likelihood sequence estimation (MLSE) equalizer using multiple antennas. Several commonly-used channel tracking schemes, decision-directed recursive least square (DD/RLS), per-survivor processing recursive least square (PSP/RLS) and other reduced-complexity MLSE algorithms are considered. An analytic lower bound for the multichannel MLSE equalizer with no channel mismatch in the time-varying specular multipath Rayleigh-fading channels is derived. Simulation results that illustrate the performance of the proposed algorithms working with various channel tracking schemes are presented, and then these results are compared with the analytic bit error rate (BER) lower bound and with the conventional MLSE equalizers directly tracking the finite impulse response (FIR) channel tap coefficients. We found that the proposed algorithm always performs better than the conventional adaptive MLSE algorithm, no matter what channel tracking scheme is used. However, which is the best tracking scheme to use depends on the scenario of the system     

A Modified Adaptive FIR Equalizer for Multipath Echo Cancellation in FM Transmission

Multipath propagation is a severe problem in conventional FM broadcasting since this phenomenon causes nonlinear distortions after demodulation. Several proposals for the correction of multipath corrupted FM signals were given in some recent papers, but up to now there exist no satisfactory solutions with sufficiently low hardware complexity for commercial application. The main idea of the present paper is to take advantage of some a priori knowledge of the multipath transfer function with the goal to develop a nonrecursive equalizer structure with minimum hardware expense. For adaptive adjustment of the equalizer, we use a recently introduced constant modulus algorithm (CMA) in a modified form. Instead of direct coefficient adjustment, we regard the parameters of the transmission channel as unknowns which are updated adaptively. The equalizer coefficients are uniquely defined by the channel parameters and can be determined in one step. The advantage of this method is a large improvement of the convergence behavior in comparison to existing solutions. The methods presented here are tested by means of an FM hardware system including FM transmitter, multipath simulation, FM demodulator, and an FIR multipath equalizer, which allows real-time investigations of the equalizer performance under well-defined multipath conditions.     

An FIR Equalizer Design for Nonlinear Channels Using Hybrid GA and LMI

In this paper, a finite impulse response (FIR) equalizer for nonlinear discrete-time channels is designed by employing a hybrid genetic algorithm (GA) and linear matrix inequality (LMI) approach from an H_∞ perspective. The GA technique is utilized to linearize the nonlinear channel model, and the approximate error can be viewed as a state uncertainty. Then, the design of the FIR equalizer is transformed into LMIs, and the coefficients of the FIR equalizer can be obtained by solving an LMI optimization problem. Finally, numerical examples are included to illustrate the effectiveness of the proposed methodology.     

Iterative joint optimization of minimal transmit redundancy FIR zero-forcing precoder-equalizer system for MIMO-ISI channel

An iterative joint finite-impulse response (FIR) zero-forcing (ZF) precoder-equalizer optimization algorithm for multiple-input multiple-output intersymbol interference (MIMO-ISI) channel is proposed. The existing joint precoder-equalizer design algorithms for MIMO-ISI channels require a guard period, which is longer than or equal to the channel order to avoid the interblock interference (IBI). This longer guard period is a kind of unnecessary redundancy consuming the valuable channel bandwidth. Based on space-time-modulated codes (STMC), this paper proposes the first algorithm for jointly optimizing the FIR precoder and equalizer without the guard-period constraint. Hence, the precoder-equalizer pairs obtained can achieve minimal transmit redundancy ISI-free communications for complex-valued signals. This greatly enhances the spectral efficiency for wide-band communications. The proposed algorithm is performed in an iterative basis. Sufficient conditions and convergence analysis of this algorithm are presented. The resultant precoder and equalizer are proved to be a least-square (LS) optimal solution for each other. The simulation results show that substantial performance gain is obtained with the proposed joint optimization algorithm.     

Adaptive Bayesian equalizer with decision feedback

A Bayesian solution is derived for digital communication channel equalization with decision feedback. This is an extension of the maximum a posteriori probability symbol-decision equalizer to include decision feedback. A novel scheme utilizing decision feedback that not only improves equalization performance but also reduces computational complexity greatly is proposed. It is shown that the Bayesian equalizer has a structure equivalent to that of the radial basis function network, the latter being a one-hidden-layer artificial neural network widely used in pattern classification and many other areas of signal processing. Two adaptive approaches are developed to realize the Bayesian solution. The maximum-likelihood Viterbi algorithm and the conventional decision feedback equalizer are used as two benchmarks to asses the performance of the Bayesian decision feedback equalizer     

A blind decision feedback equalizer incorporating fixed lagsmoothing

A new type of blind decision feedback equalizer (DFE) incorporating fixed lag smoothing is developed in this paper. The structure is motivated by the fact that if we make full use of the dependence of the observed data on a given transmitted symbol, delayed decisions may produce better estimates of that symbol. To this end, we use a hidden Markov model (HMM) suboptimal formulation that offers a good tradeoff between computational complexity and bit error rate (BER) performance. The proposed equalizer also provides estimates of the channel coefficients and operates adaptively (so that it can adapt to a fading channel for instance) by means of an online version of the expectation-maximization (EM) algorithm. The resulting equalizer structure takes the form of a linear feedback system including a quantizer, and hence, it is easily implemented. In fact, because of its feedback structure, the proposed equalizer shows some similarities with the well-known DFE. A full theoretical analysis of the initial version of the algorithm is not available, but a characterization of a simplified version is provided. We demonstrate that compared to the zero-forcing DFE (ZF-DFE), the algorithm yields many improvements. A large range of simulations on finite impulse response (FIR) channels and on typical fading GSM channel models illustrate the potential of the proposed equalizer     

A space-time-filtered Viterbi receiver for CCI/ISI reduction in TDMA systems

In this paper, we present a hybrid space-time-filtered Viterbi receiver using multiple antennas for co-channel interference (CCI) reduction and intersymbol interference (ISI) equalization in a slow Rayleigh fading channel. In this approach, a space-time filter is first applied at the antenna outputs to maximize the signal-to-interference-plus-noise ratio (SINR), and the scalar output is then sent to a Viterbi equalizer. We propose a closed-form solution to jointly determine the weight vector for the space-time filter and the channel vector for the Viterbi equalizer. We also examine the need for a whitening filter prior to the Viterbi equalizer and show that it only marginally improves the performance. Simulation results are provided to validate our approach and to compare the performance of our receiver with that of different existing receivers.     

Split soft-decision equalization for wireless channels with large delay spread

A novel split soft-decision equalizer (SSE) with near-optimum performance is proposed for wireless multipath channels with large delay spread. The concept of SSE is significantly different from the traditional notions of the Viterbi algorithm and decision-feedback equalizer. Instead of dealing with received sequence as a combined sequence, it splits the received sequence into its constituent paths. Using an iterative soft-decision algorithm, reliability of the soft decisions on each decomposed element is improved iteratively. The major advantage of SSE is the independence of computation complexity on channel time dispersion. Joint design of SSE with a soft-decision decoder is also considered in this paper. Performance analysis and simulation results show that performance of the proposed algorithm comes very close to that of the logarithmic maximum a posteriori decoder.     

A new adaptive equalizer with channel estimator for mobile radiocommunication

For unknown mobile radio channels with severe intersymbol interference (ISI), a maximum likelihood sequence estimator, such as a decision feedback equalizer (DFE) having both feedforward and feedback filters, needs to handle both precursors and postcursors. Consequently, such an equalizer is too complex to be practical. This paper presents a new reduced-state, soft decision feedback Viterbi equalizer (RSSDFVE) with a channel estimator and predictor. The RSSDFVE uses maximum likelihood sequence estimation (MLSE) to handle the precursors and truncates the overall postcursors with the soft decision of the MLSE to reduce the implementation complexity. A multiray fading channel model with a Doppler frequency shift is used in the simulation. For fast convergence, a channel estimator with fast start-up is proposed. The channel estimator obtains the sampled channel impulse response (CIR) from the training sequence and updates the RSSDFVE during the bursts in order to track changes of the fading channel. Simulation results show the RSSDFVE has nearly the same performance as the MLSE for time-invariant multipath fading channels and better performance than the DFE for time-variant multipath fading channels with less implementation complexity than the MLSE. The fast start-up (FS) channel estimator gives faster convergence than a Kalman channel estimator. The proposed RSSDFVE retains the MLSE structure to obtain good performance and only uses soft decisions to subtract the postcursor interference. It provides the best tradeoff between complexity and performance of any Viterbi equalizers     

维特比均衡算法

基于符号级维特比译码算法,将信道等效为一时变卷积编码器,提出了一种将信道均衡和信道译码相结合的技术——维特比均衡。重点研究了采用维特比均衡技术的单载波系统,并对比给出了采用频域均衡技术和维特比均衡技术,系统误码性能随信噪比的变化曲线及系统的计算复杂度。仿真结果表明：信道的等效脉冲响应滤波器长度较长时,维特比均衡技术明显改善了系统的误码性能,然而系统的复杂度也随之增加。     

Adaptive maximum-likelihood sequence estimation by means ofcombined equalization and decoding in fading environments

This paper proposes an adaptive maximum-likelihood sequence estimation (MLSE) by means of combined equalization and decoding, i.e., adaptive combined MLSE, which employs separate channel estimation for respective states in the Viterbi algorithm. First, an approximate metric including channel estimation is derived analytically for this proposed adaptive combined MLSE. Secondly, procedures to accomplish blind equalization are investigated for the proposed MLSE. Finally, its excellent BER performance on fast time-varying fading channels is confirmed by computer simulation, when the proposed MLSE operates as a blind equalizer     

Adaptive minimum bit-error rate equalization for binary signaling

We consider the design and adaptation of a linear equalizer with a finite number of coefficients in the context of a classical linear intersymbol-interference channel with Gaussian noise and a memoryless decision device. If the number of equalizer coefficients is sufficient, the popular minimum mean-squared-error (MMSE) linear equalizer closely approximates the optimal linear equalizer that directly minimizes bit-error rate (BER). However, when the number of equalizer coefficients is insufficient to approximate the channel inverse, the minimum-BER equalizer can outperform the MMSE equalizer by as much as 16 dB in certain cases. We propose a simple stochastic adaptive algorithm for realizing the minimum-BER equalizer. Compared to the least-mean-square algorithm, the proposed algorithm can provide a substantial reduction in BER with no increase in complexity     

Blind channel estimation via combining autocorrelation and blind phase estimation

Symbol spaced blind channel estimation methods are presented which can essentially use the results of any existing blind equalization method to provide a blind channel estimate of the channel. Blind equalizer's task is reduced to only phase equalization (or identification) as the channel autocorrelation is used to obtain the amplitude response of the channel. Hence, when coupled with simple algorithms such as the constant modulus algorithm (CMA) these methods at baud rate processing provide alternatives to blind channel estimation algorithms that use explicit higher order statistics (HOS) or second-order statistics (subspace) based fractionally-spaced/multichannel algorithms. The proposed methods use finite impulse response (FIR) filter linear receiver equalizer or matched filter receiver based infinite impulse response+FIR linear cascade equalizer configurations to obtain blind channel estimates. It is shown that the utilization of channel autocorrelation information together with blind phase identification of the CMA is very effective to obtain blind channel estimation. The idea of combining estimated channel autocorrelation with blind phase estimation can further be extended to improve the HOS based blind channel estimators in a way that the quality of estimates are improved.     

A 2.5- to 3.5-Gb/s Adaptive FIR Equalizer With Continuous-Time Wide-Bandwidth Delay Line in 0.25-$muhbox m$CMOS

This paper presents an adaptive finite impulse response (FIR) equalizer with continuous-time wide-bandwidth delay line in CMOS 0.25-$muhbox m$process for 2.5-Gb/s to 3.5-Gb/s data communications. To achieve wide bandwidth, fractionally spaced structure is used and an inverter with active-inductor load design is proposed as the delay cell of the tap delay line. Close loop adaptation of the fractionally spaced FIR equalizer is demonstrated using a low-power and area-efficient pulse extraction method as on-chip error detector. Measurement results show that the proposed adaptive equalizer achieves over 75% horizontal eye opening when the channel loss at the half-data-rate frequency varies from 4 dB to 21 dB at 2.5-Gb/s data rate. At 3.5-Gb/s data rate, the equalizer achieves 68% horizontal eye opening when the channel loss is about 9.3 dB at the half-data-rate frequency. The adaptive equalizer including the FIR filter and the error detector occupies 0.095$hbox mm^2$die area and dissipates 95 mW at 2.5-Gb/s data rate from 2.5-V voltage supply.     

A Routing and Interface Assignment Algorithm for Multi-Channel Multi-Interface <Emphasis Type="Italic">Ad Hoc</Emphasis> Networks

In this paper, we present a routing and interface assignment algorithm for multi-channel multi-interface (MCMI) wireless ad hoc networks. An MCMI network consists of nodes that have more than one interface, and more than one channel available for transmission. The proposed algorithm takes into account both the number of hops between the source to the destination nodes, and the effects of adjacent hop interference. The algorithm has two decoupled steps: route selection and interface assignment. The step of route selection finds the path that has the minimum lower bound among all possible routes between the source and the destination while the step of interface assignment assigns an interface to a channel on each hop on that path. The interface assignment is based on the use of the Viterbi algorithm. The use of decoupled steps makes the algorithm computationally efficient, while the use of the lower bound metrics in route selection and the Viterbi algorithm in interface assignment helps improving the global optimality of the routing. Computer simulation and examples are used to demonstrate the effectiveness and performance of the proposed technique. Comparisons are made to other existing routing techniques in the area of dynamical spectrum access.     

Optimum open eye equalizer design for nonminimum phase channels

This paper contains results on the design of optimum equalizers to eliminate intersymbol interference (ISI) in linear nonminimum phase channels conveying binary signals. The optimization is with respect to an open eye condition with a delay d. For causal stable channels with n _c nonminimum phase zeros, we argue that this problem requires only the consideration of the n_c-tap FIR modified channel that has all the n_c nonminimum phase zeros of the original channel. We show that if this modified channel can be equalized to yield an equalized system that is open eye with delay d, then the optimizing equalizer is, in fact, (d-n_c)-tap FIR with all zeros outside the unit circle. We also give a simple necessary and sufficient condition to determine if for a particular d, a given channel can be equalized to achieve an equalized response that is open eye with delay d