在脉冲噪声环境中用于快衰信道估计的改进型算法

该文分析了在存在噪声干扰的情况下,进行估计快衰信道的方法。在无线通信系统中,快衰信道可以采用AR(Auto-Regressive)模型进行预测,而LS (Least Square)算法和自适应Kalman滤波器可以分别对AR模型的参数和信道的冲激响应进行估计,但是这两种算法对噪声干扰非常敏感。该文提出改进型的RLM算法和Kalman 滤波器,并在存在噪声的情况下,使用它们并行对AR参数和信道的冲激响应进行联合估计。仿真结果显示:相比于传统的算法,改进后的算法在联合估计信道时,提高了抵抗大脉冲干扰的能力,加快了待估的参数的收敛速度。     

Robustness of least-squares and subspace methods for blind channelidentification/equalization with respect to effective channelundermodeling/overmodeling

The least-squares and the subspace methods are two well-known approaches for blind channel identification/equalization. When the order of the channel is known, the algorithms are able to identify the channel, under the so-called length and zero conditions. Furthermore, in the noiseless case, the channel can be perfectly equalized. Less is known about the performance of these algorithms in the practically inevitable cases in which the channel possesses long tails of “small” impulse response terms. We study the performance of the mth-order least-squares and subspace methods using a perturbation analysis approach. We partition the true impulse response into the mth-order significant part and the tails. We show that the mth-order least-squares or subspace methods estimate an impulse response that is “close” to the mth-order significant part. The closeness depends on the diversity of the mth-order significant part and the size of the tails. Furthermore, we show that if we try to model not only the “large” terms but also some “small” ones, then the quality of our estimate may degrade dramatically; thus, we should avoid modeling “small” terms. Finally, we present simulations using measured microwave radio channels, highlighting potential advantages and shortcomings of the least-squares and subspace methods     

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.     

用于直接序列扩频系统的信道估计算法及改良

对于无线通信接收机设计说，信道估计单元一直是一个关键的模块。在WLAN（无线局域网）接收机的设计中，室内环境下无线信道的复杂性和不可预测性成为系统研究和分析的焦点。如何获得精确的信道估计，从而计算出准确的Rake接收机和均衡器的抽头系数，是关系着整个系统性能的重要因素。介绍了传统信道估计的方法和过程，并针对其缺点展开讨论，并提出了两种改良的信道估计算法。该算法能够大大地缩小估计误差，提高系统性能。     

Blind, Adaptive Channel Shortening Equalizer Algorithm Which Can Provide Shortened Channel State Information (BACS-SI)

Channel shortening equalization plays an important role in multicarrier modulation (MCM) systems. In this paper, we propose a blind channel shortening equalizer structure named blind, adaptive channel shortening equalizer which can provide the shortened channel state information (BACS-SI). The algorithm depends on the minimization of a cost function defined as the sum-squared difference of the autocorrelations of the shortened channel impulse response (CIR) and a target impulse response. The surface is proven to be multimodal; however, minima are shown to be related to each other in a certain way. A two-phase approach is proposed. In the first phase, the cost function is minimized by a stochastic gradient descent algorithm in order to find an arbitrary minimum. In the second phase using the relation between minima, genetic algorithms are employed to find the best minimum according to a fitness function. The algorithm can both successfully shorten the channel and also explicitly provides shortened CIR which is a necessary information for the proper operation of a MCM receiver, in contrast to many other algorithms proposed in the literature which cannot directly provide this information.      

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.     

Doubly-selective fading channel equalization: A comparison of the Kalman filter approach with the basis expansion model-based equalizers

In this paper, we exploit the Kalman filter as a time-varying linear minimum mean-square error equalizer for doubly-selective fading channels. We use a basis expansion model (BEM) to approximate the doubly-selective channel impulse response. Several time-varying linear equalizers have been proposed in the literature where both the channel and the equalizer impulse responses are approximated by complex exponential (CE) BEMs. Our proposed Kalman filter formulation does not rely on a specific BEM for the underlying channel, therefore, it can be applied to any BEM, including the CE-BEM and the discrete prolate spheroidal (DPS) BEM. Moreover, the Kalman filter relies solely on the channel model and therefore, does not incur any approximation error inherent in the CE-BEM representation of the equalizer. Through computer simulations, we show that compared to two of the existing algorithms, the proposed Kalman filter formulation yields the same or an improved bit error rate at a much lower computational cost, where the latter is measured in terms of the number of flops needed for the equalizer design and implementation.     

Blind adaptive channel estimation in ofdm systems

We consider the problem of blind channel estimation in zero padding OFDM systems, and propose blind adaptive algorithms in order to identify the impulse response of the multipath channel. In particular, we develop RLS and LMS schemes that exhibit rapid convergence combined with low computational complexity and numerical stability. Both versions are obtained by properly modifying the orthogonal iteration method used in numerical analysis for the computation of singular vectors. With a number of simulation experiments we demonstrate the satisfactory performance of our adaptive schemes under diverse signaling conditions     

Pilot-assisted channel estimation for the downlink of the UMTS-TDD component

The time-division duplex (TDD) component of the universal mobile telecommunications system (UMTS) employs synchronous code-division multiple-access techniques with orthogonal spreading codes to provide protection against cochannel interference. In the presence of multipath propagation, however, the code orthogonality is lost and multiaccess interference is generated at the receiver. In such conditions, an estimate of the channel impulse response is required for reliable detection. In this paper, we propose and compare two pilot-assisted schemes for channel estimation in the downlink of the UMTS-TDD system. Both algorithms also provide estimates of the users' energies, which are needed to perform multiuser detection. Theoretical analysis and computer simulations are used to assess the channel estimation performance in terms of mean-squared errors and bit-error rate. It is shown that the accuracy of the proposed estimators attains the Cramer-Rao bound at intermediate/high signal-to-noise ratios.     

Testing for the convergence of a linear decision directed equaliser

Adaptation algorithms for blind equalisation of communication channels suffer from the presence of local equilibria that may cause convergence to incorrect equaliser parameter settings. In this paper we consider an infinite impulse response (IIR) channel which is to be equalised by a linear transversal filter and a slicer connected in tandem, and use the correlation statistics of the sequence at the slicer output to determine if convergence to a desirable equilibrium has occurred. In particular, we show that if the input sequence to an IIR channel is binary, assuming values ±1, and its autocorrelation sequence is known a priori, the slicer output has the same autocorrelation sequence if, and only if, the slicer output is a possibly delayed and/or sign-inverted replica of the channel input. A Neyman-Pearson test is constructed, based on this result, to make a decision as to whether or not the equaliser has converged to an open-eye parameter setting. A method for estimating a lower bound on the equalisation delay that draws upon a classical correlation based impulse response estimation technique is discussed. Finally, simulation examples are presented to verify the theoretical results and to illustrate their application     

Perfect Blind-Channel Shortening for Multicarrier Systems

In multicarrier systems, when the order of a channel impulse response is larger than the length of the cyclic prefix (CP), there is a significant performance degradation due to interblock interference (IBI). This paper proposes a blind-channel shortening method in which the equalizer parameter vector is formed by the noise subspace of the received signal correlation matrix so that the output power is maximized. The proposed method can not only shorten the effective channel impulse response to within the CP length but also maximize the output signal-to-interference-and-noise ratio while eliminating the IBI. We point out that the performance depends on the choice of a decision delay and propose a simple method for determining the appropriate delay. We propose both a batch algorithm and an adaptive algorithm and show by simulation that they are superior to the conventional algorithms.     

Statistical analysis of some second-order methods for blind channelidentification/equalization with respect to channel undermodeling

Many second-order approaches have been proposed for blind FIR channel identification in single-input/multi-output context. In practical conditions, the measured impulse responses usually possess “small” leading and trailing terms, the second-order statistics are estimated from finite sample size, and there is additive white noise. This paper, based on a functional methodology, develops a statistical performance analysis of any second-order approach under these practical conditions. We study two channel models. In the first model, the channel tails are considered to be deterministic. We derive expressions for the asymptotic bias and covariance matrix (when the sample size tends to ∞) of the mth-order estimated significant part of the impulse response. In the second model, the tails are treated as zero mean Gaussian random variables. Expressions for the asymptotic covariance matrix of the estimated significant part of the impulse response are then derived when the sample size tends to ∞, and the variance of the tails tends to 0. Furthermore, some asymptotic statistics are given for the estimated zero-forcing equalizer, the combined channel-equalizer impulse response, and some byproducts, such as the open eye measure. This allows one to assess the influence of the limited sample size and the size of the tails, respectively, on the performance of identification and equalization of the algorithms under study. Closed-form expressions of these statistics are given for the least-squares, the subspace, the linear prediction, and the outer-product decomposition (OPD) methods, as examples. Finally, the accuracy of the asymptotic analysis is checked by numerical simulations; the results are found to be valid in a very large domain of the sample size and the size of the tails     

Deterministic linear prediction methods for blind channel estimation based on dual concept of zero-forcing equalization

This paper investigates a class of second-order blind channel estimation algorithms based on deterministic linear prediction, which includes double-sided as well as forward and backward single-sided, for single input multiple output (SIMO) finite impulse response (FIR) channels. By introducing the dual problem of well-known zero-forcing equalization concept, we first derive a double-sided deterministic linear prediction (D-DLP) algorithm that has, good channel estimation performance with the knowledge of exact channel order. By further exploiting the interference subspace cancellation technique and the triangular block-Toeplitz structure of a portion of the channel filtering matrix (upper-left or lower-right part), we obtain the forward and backward single-sided deterministic linear prediction (FS-DLP and BS-DLP) algorithms that can work in the absence of knowledge of channel order with a cost of relatively poor channel estimate. Moreover, a channel order estimation method is also studied based on results from both FS-DLP and BS-DLP. Simulation examples are finally presented to demonstrate the potential of the proposed methods.     

Fast coupled adaptation for sparse impulse responses using a partial haar transform

This work presents a novel scheme for identifying the impulse response of a sparse channel. The scheme consists of two adaptive filters operating sequentially. The first adaptive filter adapts using a partial Haar transform of the input and yields an estimate of the location of the peak of the sparse impulse response. The second adaptive filter is then centered about this estimate. Both filters are short in comparison to the delay uncertainty of the unknown channel. The principle advantage of this scheme is that two short adaptive filters can be used instead of one long adaptive filter, resulting in faster overall convergence and reduced computational complexity and storage. The scheme is analyzed in detail for a least mean squares (LMS) LMS-LMS type of structure, although it can be implemented using any combination of adaptive algorithms. Monte Carlo simulations are shown to be in good agreement with the theoretical model for the behavior of the peak estimating filter as well as for the mean square error (MSE) behavior of the second filter.     

Direct blind MMSE channel equalization based on second-orderstatistics

A family of new MMSE blind channel equalization algorithms based on second-order statistics are proposed. Instead of estimating the channel impulse response, we directly estimate the cross-correlation function needed in Wiener-Hopf filters. We develop several different schemes to estimate the cross-correlation vector, with which different Wiener filters are derived according to minimum mean square error (MMSE). Unlike many known sub-space methods, these equalization algorithms do not rely on signal and noise subspace separation and are consequently more robust to channel order estimation errors. Their implementation requires no adjustment for either single- or multiple-user systems. They can effectively equalize single-input multiple-output (SIMO) systems and can reduce the multiple-input multiple-output (MIMO) systems into a memoryless signal mixing system for source separation. The implementations of these algorithms on SIMO system are given, and simulation examples are provided to demonstrate their superior performance over some existing algorithms     

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     

Performance bounds for multistep prediction-based blindequalization

Blind equalization attempts to remove the interference caused by a communication channel without using any known training sequences. Blind equalizers may be implemented with linear prediction-error filters (PEFs). For many practical channel types, a suitable delay at the output of the equalizer allows for achieving a small estimation error. The delay cannot be controlled with one-step predictors. Consequently, multistep PEF-based algorithms have been suggested as a solution to the problem. The derivation of the existing algorithms is based on the assumption of a noiseless channel, which results in zero-forcing equalization. We consider the effects of additive noise at the output of the multistep PEF. Analytical error bounds for two PEF-based blind equalizers in the presence of noise are derived. The obtained results are verified with simulations. The effect of energy concentration in the channel impulse response on the error bound is also addressed     

Blind Beamforming Schemes in SC-FDMA Systems With Insufficient Cyclic Prefix and Carrier Frequency Offset

In cyclic prefix (CP)-based transmission systems, if the time duration of the cyclic extension is shorter than the channel impulse response duration, system performance is degraded due to the introduction of intersymbol interference (ISI) and intercarrier interference (ICI). In this paper, we propose a blind beamforming algorithm for single-carrier frequency-division multiple-access (SC-FDMA) systems under insufficient CP scenarios. In addition, we also consider the effects of carrier frequency offsets (CFOs) in the processing schemes. The simulation results are presented by employing an SC-FDMA uplink signal model to illustrate the efficacy of the proposed algorithms.      

Efficient Non-Pilot-Aided Channel Length Estimation for Digital Broadcasting Receivers

Channel estimation and equalization techniques are crucial for the ubiquitous broadcasting systems. Conventional receivers for most broadcasting or wireless standards preset the channel length to the maximal expected duration of the channel impulse response for the adopted channel estimation and equalization algorithms. The excessive channel length often significantly increases the implementational complexity of the wireless receivers and leads to the redundant information which would induce the additional estimation errors. Moreover, such a scheme does not allow the dynamic memory allocation for variable channel lengths. This could further increase the power consumption and reduce the battery life of a mobile device. The knowledge of the actual channel length would, in principle, help the system designers decrease the complexity of the channel estimators using maximum likelihood (ML) and minimum-mean-square-error (MMSE) algorithms. In this paper, we address this important channel length estimation problem and propose a novel autocorrelation-based algorithm to estimate the channel length without the need of pilots or training sequence. The associated threshold for the channel length estimation depends on the sample size, the signal-to-noise ratio and the leading/last channel coefficients. In addition, we provide the mean-square analysis on the effectiveness of the proposed non-pilot-aided channel length estimator through Monte Carlo simulations.      

Effect of multipath channel models to the recovery algorithms on compressed sensing in UWB channel estimation

Multipath arrivals in an Ultra-WideBand (UWB) channel have a long time intervals between clusters and rays where the signal takes on zero or negligible values. It is precisely the signal sparsity of the impulse response of the UWB channel that is exploited in this work aiming at UWB channel estimation based on Compressed Sensing (CS). However, these multipath arrivals mainly depend on the channel environments that generate different sparse levels (low-sparse or high-sparse) of the UWB channels. According to this basis, we have analyzed the two most basic recovery algorithms, one based on linear programming Basis Pursuit (BP), another using greedy method Orthogonal Matching Pursuit (OMP), and chosen the best recovery algorithm which are suitable to the sparse level for each type of channel environment. Besides, the results of this work is an open topic for further research aimed at creating a optimal algorithm specially for application of CS based UWB systems.