Channel Identification Algorithm Research Articles

An Improved Multipath Channel Identification Algorithm Using Mulichannel Linear Prediction

Blind channel identification exploits the measurable channel output signal and some a priori knowledge of the statistics of the channel input signal. However, in many scenarios, more side information is available. In digital communication systems, the pulseshaping filter in the transmitter and the antialiasing filter in the receiver are often known to the receiver. Exploitation of this prior knowledge can simplify the channel identification problem. In this paper, we provide a thorough theoretical analysis on the linear prediction (LP)-based multipath identification approach. The analysis shows that the order overdetermination greatly deteriorates the performance of the LP multipath identification approach. This article, then, proposes an effective approach to detect the order of the multipath channel and alleviate the performance degradation attributed to the channel overmodeling. The obtained results demonstrate that the proposed approach offers substantial performance gain.

Iterative LBG clustering for SIMO channel identification

This paper deals with the problem of channel identification for Single Input Multiple Output (SIMO) slow fading channels using clustering algorithms. Due to the intrinsic memory of the discrete-time model of the channel, over short observation periods, the received data vectors of the SIMO model are spread in clusters because of the AWGN noise. Each cluster is practically centered around the ideal channel output labels without noise and the noisy received vectors are distributed according to a multivariate Gaussian distribution. Starting from the Markov SIMO channel model, simultaneous maximum-likelihood estimation of the input vector and the channel coefficients reduce to one of obtaining the values of this pair that minimizes the sum of the Euclidean norms between the received and the estimated output vectors. Viterbi algorithm can be used for this purpose provided the trellis diagram of the Markov model can be labeled with the noiseless channel outputs. The problem of identification of the ideal channel outputs, which is the focus of this paper, is then equivalent to designing a Vector Quantizer (VQ) from a training set corresponding to the observed noisy channel outputs. The Linde-Buzo-Gray (LBG)-type clustering algorithms [1] could be used to obtain the noiseless channel output labels from the noisy received vectors. One problem with the use of such algorithms for blind time-varying channel identification is the codebook initialization. This paper looks at two critical issues with regards to the use of VQ for channel identification. The first has to deal with the applicability of this technique in general; we present theoretical results for the conditions under which the technique may be applicable. The second aims at overcoming the codebook initialization problem by proposing a novel approach which attempts to make the first phase of the channel estimation faster than the classical codebook initialization methods. Sample simulation results are provided confirming the effectiveness of the proposed initialization technique.

Linear prediction based multipath channel identification algorithm

In digital communication systems, the pulse-shaping filter in the transmitter and the anti-aliasing filter in the receiver are often known. In this brief, this a priori knowledge is exploited to simplify the channel identification problem. The multipath identification problem is formulated as a homogeneous linear equation, in which a matrix is formed from the optimal linear predictor. Instead of solving directly the underlying linear equation, the estimate is obtained by finding the minor eigenvector of a matrix. The presented analysis shows that the performance of the proposed approach degrades significantly when the order is over estimated. An effective approach is then proposed to remove the redundant components in the estimated multipath channel vector. The obtained results show that the proposed approach is able to enhance the performance of the linear programming approach significantly when the order is over estimated.

A fast blind SIMO channel identification algorithm for sparse sources

We address the blind identification of single-input-multiple output (SIMO) finite impulse response systems when the input signal is sparse. The problem is equivalent to underdetermined blind source separation (BSS), but with temporal correlation among the sources. Exploiting the sparse character of the input signal, the algorithm solves three different problems: first, to estimate the directions of the columns of the channel matrix; second, to estimate the L/sub 2/-norm of the columns; and finally, to find the correct ordering of the columns of the mixing matrix. The last step is not required for the blind source separation (BSS) problem, since any permutation of the columns is admissible for BSS. The performance and computational cost of the algorithm in a noiseless situation is compared against subspace-based techniques.

Space-Time Coded MC-CDMA: Blind Channel Estimation, Identifiability, and Receiver Design

Integrating the strengths of multicarrier (MC) modulation and code division multiple access (CDMA), MC-CDMA systems are of great interest for future broadband transmissions. This paper considers the problem of channel identification and signal combining/detection schemes for MC-CDMA systems equipped with multiple transmit antennas and space-time (ST) coding. In particular, a subspace-based blind channel identification algorithm is presented. Identifiability conditions are examined and specified which guarantee unique and perfect (up to a scalar) channel estimation when knowledge of the noise subspace is available. Several popular single-user based signal combining schemes, namely the maximum ratio combining (MRC) and the equal gain combining (EGC), which are often utilized in conventional single-transmit-antenna-based MC-CDMA systems, are extended to the current ST-coded MC-CDMA (STC-MC-CDMA) system to perform joint combining and decoding. In addition, a linear multiuser minimum mean square error (MMSE) detection scheme is also presented, which is shown to outperform the MRC and EGC at some increased computational complexity. Numerical examples are presented to evaluate and compare the proposed channel identification and signal detection/combining techniques.

An improved least squares blind channel identification algorithm for linearly and affinely precoded communication systems

Certain linear and affine precoders introduce enough algebraic redundancy to enable the receiver to identify a. single-input single-output finite-impulse response channel without making any statistical assumptions on the source sequence. However, quite surprisingly, the traditional steepest descent least squares algorithm for estimating the channel often fails to converge, even in the absence of noise. This article explains why this is the case and derives a novel steepest descent algorithm on complex projective space that is guaranteed to converge. The complex projective space formulation also provides a standard framework for understanding different performance measures proposed in the literature.

A blind multichannel identification algorithm robust to order overestimation

Active research in blind single input multiple output (SIMO) channel identification has led to a variety of second-order statistics-based algorithms, particularly the subspace (SS) and the linear prediction (LP) approaches. The SS algorithm shows good performance when the channel output is corrupted by noise and available for a finite time duration. However, its performance is subject to exact knowledge of the channel order, which is not guaranteed by current order detection techniques. On the other hand, the linear prediction algorithm is sensitive to observation noise, whereas its robustness to channel order overestimation is not always verified when the channel statistics are estimated. We propose a new second-order statistics-based blind channel identification algorithm that is truly robust to channel order overestimation, i.e., it is able to accurately estimate the channel impulse response from a finite number of noisy channel measurements when the assumed order is arbitrarily greater than the exact channel order. Another interesting feature is that the identification performance can be enhanced by increasing a certain smoothing factor. Moreover, the proposed algorithm proves to clearly outperform the LP algorithm. These facts are justified theoretically and verified through simulations.

Adaptive multi-channel least mean square and Newton algorithms for blind channel identification

The problem of identifying a single-input multiple-output FIR system without a training signal, the so-called blind system identification, is addressed and two multi-channel adaptive approaches, least mean square and Newton algorithms, are proposed. In contrast to the existing batch blind channel identification schemes, the proposed algorithms construct an error signal based on the cross relations between different channels in a novel, systematic way. The corresponding cost (error) function is easy to manipulate and facilitates the use of adaptive filtering methods for an efficient blind channel identification scheme. It is theoretically shown and empirically demonstrated by numerical studies that the proposed algorithms converge in the mean to the desired channel impulse responses for an identifiable system.

Convergence of stochastic-approximation-based algorithms for blind channel identification

We develop adaptive algorithms for multichannel (single-input-multiple-output, or SIMO) blind identification with both statistic and deterministic models. In these algorithms, the estimates are continuously improved while receiving new signals. Therefore, the algorithms can track the channel continuously and thus are amenable to real applications such as wireless communications. At each step, only a small amount of computation is involved. The algorithms are based on stochastic-approximation methods. The convergence properties of these algorithms are proved. Simulation examples are presented to show the performance of the algorithms.

Blind channel identification based on the geometry of the received signal constellation

We study the geometric properties of the constellation of the points z(k)=[x(k),x(k-1)]/sup T/ formed by an ISI corrupted M-ary PAM source transmitted through a narrowband channel. We show that in the absence of noise, the convex hull of the constellation contains all the information pertaining to the channel taps. In particular, the edges of the convex hull can be used to recover the channel uniquely (up to the sign). These results provide a set of geometric identifiability conditions leading to a novel clustering-based channel identification algorithm.

Blind channel identification and equalization in OFDM-based multiantenna systems

Wireless systems employing multiple antennas at the transmitter and the receiver have been shown to have the potential of achieving extraordinary bit rates. Orthogonal frequency division multiplexing (OFDM) significantly reduces the receiver complexity in multiantenna broadband systems. We introduce an algorithm for blind channel identification and equalization in OFDM-based multiantenna systems. Our approach uses second-order cyclostationary statistics, employs antenna precoding, and yields unique channel estimates (up to a phase rotation for each transmit antenna). Furthermore, it requires only an upper bound on the channel order, it does not impose restrictions on channel zeros, and it exhibits low sensitivity to stationary noise. We present simulation results demonstrating the channel estimator and the corresponding multichannel equalizer performance.

Adaptive blind channel identification algorithm based on linear prediction for SIMO FIR systems

An adaptive algorithm for blind identification of single-input multiple-output (SIMO) FIR systems is proposed. It is based on the one-step forward linear prediction (LP) technique and can be implemented by an RLS adaptation. Unlike most second-order statistics (SOS)-based approaches, the proposed solution does not require the computation of the correlation matrix or its inverse explicitly. The obtained results demonstrate that the proposed approach is able to deliver better performance compared with the typical batch algorithm. It is also observed that the proposed algorithm can tolerate the appearance of near common zeros among the subchannels.

Blind channel identification via stochastic approximation: constant step-size algorithms

This work is devoted to the study of a class of recursive algorithms for blind channel identification. Using weak convergence methods, the convergence of the algorithm is obtained and the rate of convergence is ascertained. The technique discussed can also be used in the analysis of rates of convergence for decreasing step-size algorithms.

Error correcting least-squares Subspace algorithm for blind identification and equalization

A subspace based blind channel identification algorithm using only the fact that the received signal can be oversampled is proposed. No direct use is made in this algorithm of either the statistics of the input sequence or even of the fact that the symbols are from a finite set and therefore this algorithm can be used to identify even channels in which arbitrary symbols are sent. Using this algorithm as a base and using the extra information which becomes available when the transmitted symbols are from a known finite set, the EC-LS-Subspace algorithm is derived. The EC-LS-Subspace algorithm operates directly on the data domain and therefore avoids the problems associated with other algorithms which use the statistical information contained in the received signal directly. In the noiseless case, if some conditions are met, it is possible for the proposed Basic Subspace algorithm to identify the channel exactly using an observation interval of just ( J+2) T, if the length of the impulse response of a channel is JT, T being the symbol interval. In the noisy case, simulations have shown that the channel can be identified accurately by using a very small observation interval (comparable to ( J+2) T).

Adaptive Bayesian decision feedback equaliser for alpha-stable noise environments

In some communication systems the channel noise is known to be non-Gaussian due, largely, to impulsive phenomena. The performance of signal processing algorithms designed under the Gaussian assumption may degrade seriously in such environments. In this paper we investigate the problem of adaptive channel equalisation in an impulsive noise environment. The impulsive interfering noise is modelled as an α-stable process. We first derive the optimum Bayesian decision feedback equaliser and present a novel analytical framework for the evaluation of systems in infinite variance environments. A family of generalised adaptive channel identification algorithms for this infinite variance noise environment is also presented. The combination of a Bayesian equaliser and a channel estimator operating as an adaptive channel equaliser is experimentally studied and its performance is compared with that of a traditional system designed under the Gaussian assumption. The experimental data suggest that the proposed combination of equaliser and channel estimator outperforms the traditionally designed adaptive equaliser in terms of error probability. We finally provide some useful approximations concerning the practical implementation of an α-stable adaptive equaliser.

Adaptive MLSE equalizers with parametric tracking for multipath fast-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 cumulant matrix subspace algorithm for blind single FIR channel identification

Blind identification of discrete-time single-user FIR channels with nonminimum phase is studied here. Exploiting higher order cumulants of output signals of unknown channels, a new closed-form solution to the FIR channel impulse response is derived. The algorithm is simple and fast. It relies only on nullspace decomposition of some cumulant matrices. This method neither involves the difficult task of iterative global minimization of nonunimodal cost functions, nor does it require overparametrization, which poses consistency difficulties. It can be used either as the final channel estimate or as a good initial point in nonlinear cumulant matching techniques. The application of this identification method is broad and not limited to the use of any fixed-order cumulants. Its application in identifying data communication systems shows great potential and promise.

Noncoherent adaptive channel identification algorithms for noncoherent sequence estimation

In this letter, two novel noncoherent adaptive algorithms for channel identification are introduced. The proposed noncoherent least-mean-square (LMS) and noncoherent recursive least squares (RLS) algorithms can be combined easily with noncoherent sequence estimation (NSE) for M-ary differential phase-shift keying signals transmitted over intersymbol interference (ISI) channels. It is shown that the resulting adaptive noncoherent receivers are very robust against carrier phase variations. For zero frequency offset, the convergence speed and the steady-state error of the noncoherent adaptive algorithms are similar to those of conventional LMS and RLS algorithms. However, the conventional algorithms diverge even for relatively small frequency offsets, whereas the proposed noncoherent algorithms converge for relatively large frequency offsets. Simulations confirm the good performance of NSE combined with noncoherent adaptive channel estimation in time-variant (fading) ISI channels.

Blind channel identification and equalization using periodic modulation precoders: performance analysis

The paper deals with blind identification and equalization of communication channels within the so-called modulation induced cyclostationarity (MIC) framework, where the input symbol stream is modulated by a P periodic precoder with the purpose of inducing cyclostationarity in the transmit sequence. By exploiting the cyclostationarity induced by the periodic precoder, a subspace-based channel identification algorithm that is resilient to the location of channel zeros, channel order overestimation errors, and color of additive stationary noise, is developed. The asymptotic performance of the subspace-based identification approach is analyzed and compared with the asymptotic lower bound provided by the nonlinear cyclic correlation matching approach. Criteria for optimally designing the periodic precoder are also presented. The performance of MMSE-FIR and MMSE-DFE equalizers is quantified for the proposed cyclostationarity-induced framework in terms of the MMSE. Although cyclostationarity-inducing transmitters present several advantages relative to their stationary counterparts from a channel estimation viewpoint, it is shown that from an equalization viewpoint, MIC-based systems exhibit a slightly increased MMSE/BER when compared with the stationary case.

A stochastic subspace algorithm for blind channel identification in noise fields with unknown spatial covariance

In this paper, the blind channel identification problem is formulated in a stochastic state space framework. Starting from a state space model, we introduce a preprocessing step based on two orthogonal subspace projections, derived from the theory of Van Overschee and De Moor (Subspace Identification for Linear Systems: Theory, Implementation, Applications, Kluwer Academic Publishers, Dordrecht, 1996). Using these orthogonal projections, we present an algorithm for blind channel estimation which is robust to the spatial color of the noise.