Channel Order Research Articles

Blind Channel Estimation and Equalization for Multiple FIR Channels

This paper deals with the problem of blind equalizations based on effective channel order determination for multiple FIR channels. Most popular order determination methods use the eigenvalue decomposition (EVD) technique with an overmodeled data correlation matrix. However, performing the EVD consumes huge computation resources. In this paper, we consider the channel with infinite small leading and tailing terms which is natural for measured microwave radio channels, and develop a computationally simple method for effective channel order determination. Based on multiple-shift property of a data correlation matrix, a new performance index is analyzed. The channel order is determined if the performance index is greater than a threshold. To select the threshold, we model the performance index as an -distributed random variable. For a specified confidence level, the threshold can be found from the table. This proposed method does not require EVD, the computation load is much lower than that of the EVD-based methods.

A Proof of the Identifiability of a Subspace-Based Blind Channel Estimation for OFDM Systems

Muquet et al. (2002) have proposed a subspace-based blind method for estimating the channel responses of cyclic-prefixed OFDM systems. Their proof for the channel identifiability uses the roots of channel transfer function and therefore depends on the channel order. When only an upper bound is known for the channel order, the proof fails. In this letter, a new proof for the identifiability is given which does not require knowledge of the precise channel order and can handle various choices of length of the OFDM block.

Subspace-Based Blind Multiuser Detection for Quasi-Synchronous MC-CDMA Systems

A subspace-based linear minimum mean-square error (MMSE) multiuser detector is proposed for quasi-synchronous multicarrier code-division multiple-access (MC-CDMA) systems. The proposed receiver is totally blind, i.e., it is both channel- and delay-independent and, unlike many subspace-based algorithms, requires only an upper bound (rather than the exact knowledge) of the channel order, without needing explicit delay estimation. The effectiveness of the proposed blind approach is tested by computer simulation results, which show that it assures satisfactory performances in severe near-far scenarios, while exhibiting a lower computational complexity in comparison with existing subspace-based methods.

A Semi-Blind Channel Estimation Method for Multiuser Multiantenna OFDM Systems

A subspace-based blind method is proposed for estimating the channel responses of a multiuser and multiantenna orthogonal frequency division multiplexing (OFDM) uplink system. It gives estimations to all channel responses subject to a scalar matrix ambiguity and does not need precise channel order information (only an upper bound for the orders is required). Furthermore, the scalar ambiguity matrix can be easily resolved by using only one pilot OFDM block, given that the number of users is smaller than the number of symbols in the pilot symbol block. Equalization methods are discussed based on the estimated channels. By using partial knowledge of the channels, a multipath subspace method is proposed that reduces the computational complexity. Simulations show that the methods are effective and robust.

Blind multipath channel equalization based on eigenvector decomposition

A new direct blind equalization algorithm is presented in this paper. It relies on the auto‐correlation matrix of the channel, and adopts its eigenvector decomposition for designing an equalizer, which exploits the correlation characteristics of the channel. The proposed equalization is insensitive to the inaccuracy of the channel order estimation, and its data sequence length required for estimating the channel's correlation matrix is shorter than that of the other eigenvector decomposition methods that assumed that the channel order was known or had been estimated. Simulation results show that this algorithm is capable of acquiring a good performance under lower SNR in a communication system employing 16‐QAM modulation.

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.

FIR channel estimation through generalized cumulant slice weighting

We study the problem of linear channel estimation with unknown channel input signals. Our work stems from the weighted slice algorithm, in which cumulant slices of different orders are linearly combined to produce an estimate of a single-input single-output channel. Aiming to improve the reliability of estimation, the new approach incorporates a certain matrix structure constraint into its weight computation criterion. It provides more reliable results for channels with weak leading coefficients. This generalized algorithm maintains the advantage of Fonollosa and Vidal's algorithm in handling the situation with channel order overestimation. Its natural extension to multiple-input multiple-output channel estimation is presented along with the channel identifiability conditions required.

A blind MIMO channel estimation method robust to order overestimation

A new second-order statistics (SOS)-based blind algorithm for MIMO channel estimation is proposed. It can give estimations of all channel impulse responses subject to a scalar matrix ambiguity which is intrinsic to all SOS-based blind methods. As a generalization of the blind identification algorithm for SIMO system in Gazzah et al. (IEEE Trans. Signal Process. 50(6) (2002)1449), this method is truly robust to channel order overestimation, i.e., it can accurately estimate the channels when only upper bounds for all MIMO channel orders are known.

Per-tone equalization for mimo ofdm systems

This paper focuses on multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with channel order larger than the cyclic prefix (CP) length. Writing the demodulating fast Fourier transform (FFT) as a sliding FFT followed by a downsampling operation, we show in this paper that by swapping the filtering operations of the MIMO channel and the sliding FFT, the data model for the temporally smoothened received signal of each individual tone of the MIMO OFDM system is very similar to the data model for the temporally smoothened received signal of a MIMO single-carrier (SC) system. As a result, to recover the data symbol vectors, the conventional equalization approach for MIMO SC systems can be applied to each individual tone of the MIMO OFDM system. This so-called per-tone equalization (PTEQ) approach for MIMO OFDM systems is an attractive alternative to the recently developed time-domain equalization (TEQ) approach for MIMO OFDM systems. In the second part of this paper, we focus on direct per-tone equalizer design and adapt an existing semi-blind equalizer design method for space-time block coding (STBC) SC systems to the corresponding semi-blind per-tone equalizer design method for STBC OFDM systems.

Blind and semi-blind equalization of CPM signals with the EMV algorithm

We apply the expectation-maximization Viterbi algorithm (EMVA) introduced in a previous paper to the blind or semi-blind maximum-likelihood equalization of continuous-phase modulated (CPM) signals transmitted over a noisy linear finite impulse response (FIR) channel. The EMVA is a computationally efficient technique for simultaneously performing system identification and signal detection whenever the transmission system admits a hidden Markov model (HMM) description. The convergence properties of the EMVA are examined and a method for monitoring the EMVA convergence rate online is presented. It is shown that the order of the FIR channel can be estimated by applying the order-incrementing (OI) and fixed-order (FO) methods proposed previously. A Cramer-Rao bound is derived for the channel impulse response, and it is shown via simulations that the EMVA approaches this bound as the SNR increases. Finally, an EMVA-based technique is described for estimating the error covariance matrix for the system parameters for the case of long observation blocks.

Projection minimization algorithm for blind channel equalizer

This paper presents a new direct blind channel equalizer by using spatial adaptive filtering technique. Two correlation matrices with time delay parameters d and d+1 are incorporated into design to guarantee the extraction of a d-delay signal. To reduce the system computation complexity of the algorithm, a projection minimization criterion is introduced. It is shown that the optimal equalizer weights can be found by searching the least dominant eigenvector of a generalized eigenvalue problem. The proposed algorithm has benefits of extracting the signals with delay not restricted to the first or the last of a received data. This paper also develops an optimal delay determination method for selecting the delay to reach the best performance. Several simulation examples demonstrate that the proposed algorithm has fast convergence speed and is robust to the channel order selection.

On the applicability to correlated sources of a blind channel equalization method robust to order overestimation

We consider the blind equalization problem in FIR multichannel models from the second-order statistics of the channel output, with a correlated channel input whose statistics are known to the receiver. The few algorithms that handle colored sources require exact knowledge of the channel order, a drawback since order determination is a difficult issue. Recently, Gazzah et al. (2002) have presented a channel estimator robust to order overestimation. Although their derivation assumed white sources, we show that it can be suitably modified in order to handle colored inputs. The algorithm is still able to blindly compute an FIR pre-equalizer such that the overall response reduces to an FIR transfer function which is known a priori by the receiver, up to a complex phase rotation. Therefore a post-equalizer can be designed in a blind, straightforward manner. The method remains robust to order overmodeling in the correlated source case.

Blind direct DFE estimation using multistep prediction

We propose a blind decision feedback equalizer (DFE) that is characterized by the fact that it does not require channel estimation. Because the output of the optimized multistep prediction error filter (PEF) can be represented as a product of the channel partial impulse response and the transmitted sequence, a backward multistep PEF can be used as the blind DFE feedforward filter. The corresponding feedback filter is obtained from the symbol-rate partial channel impulse response. The proposed algorithm has several advantages over existing blind channel estimation techniques, including stable performance without the necessity of exact channel order estimation.

An Evolutionary Approach for Joint Blind Multichannel Estimation and Order Detection

A joint blind order-detection and parameter-estimation algorithm for a single-input multiple-output (SIMO) channel is presented. Based on the subspace decomposition of the channel output, an objective function including channel order and channel parameters is proposed. The problem is resolved by using a specifically designed genetic algorithm (GA). In the proposed GA, we encode both the channel order and parameters into a single chromosome, so they can be estimated simultaneously. Novel GA operators and convergence criteria are used to guarantee correct and high convergence speed. Simulation results show that the proposed GA achieves satisfactory convergence speed and performance.

Blind MIMO system identification based on cumulant subspace decomposition

Blind identification of multiple-input multiple-output (MIMO) linear systems can be achieved by utilizing higher order statistics of the output signals. We study the blind identification of MIMO systems whose inputs are mutually independent, temporally white, non-Gaussian source signals. Based on sub-space analysis, we develop a new linear batch algorithm to identify MIMO systems from the common nullspace of a set of fourth-order cumulant matrices of the channel outputs. Given knowledge of the channel orders, the identifiability conditions required by the proposed algorithm are properly established. Like most subspace-based approaches, this new algorithm remains sensitive to channel order overestimation. Simulation results illustrate its performance for various channel models.

Blind linear channel estimation using genetic algorithm and SIMO model

In this paper, we propose to use genetic algorithm (GA) to solve the blind infinite-impulse-response (IIR) channel estimation problem. The contributions of this paper are three-fold: (1) We prove that by oversampling the output of a single-input–single-output IIR channel, one can build a single-input–multiple-output (SIMO) model in which the subchannels are IIR channels with the same Autoregressive (AR) order and coefficients. (2) Based on this SIMO model, we further develop a second-order statistics based objective function that includes the unknown model order and parameters whereas most of the existing work must assume the channel order is known in advance. (3) A GA is proposed to deal with this optimisation problem in that we encode the model order and parameters into one single chromosome. Therefore the order and parameters can be estimated simultaneously. Computer simulation results indicate the effectiveness of the proposed algorithms.

Blind ZF equalization with controlled delay robust to order over estimation

Blind channel identification and equalization aim at suppressing the need for training sequences and hence respond to the growing demand on bandwidth of modern and future communication systems. Techniques based on second order statistics show good performance but require accurate (but improbable) estimation of the channel order. An algorithm recently proposed by Gazzah et al. corrects this drawback while providing with only those zero-forcing (ZF) equalizers with minimum and maximum delays. However, in the presence of noise, these are not known to have the best performances. Inspired by this approach that processes shifted correlation matrices, we propose a new algorithm that computes ZF equalizers with any desired delay (as well as estimates of the channel response) while, at the same time, can handle over estimated values of the channel order, as justified theoretically and through simulations.

Channel order selection in blind deconvolution based on eigenvector characteristics and using normal modes in conjunction with multipath compression for source identification

Two related topics in blind deconvolution are presented. The first concerns channel order selection. Many blind deconvolution techniques assume the filter length to be known. One technique of filter length determination uses the dimension of a nullspace obtained by decomposing correlation matrices. Although the dimension is usually determined by calculations involving the eigenvalues, this alternative method relies on the known characteristics of eigenvectors among the subspaces. Multipath functions in underwater acoustics commonly have high kurtosis. The new method can give correct estimates on filter length for signal-to-noise ratios as low as 10 dB. The matrix methods described may not work as well when the sample length increases. However, the second topic shows how normal mode properties in conjunction with time compression in modeled multipath functions may be used to enhance blind deconvolution in a waveguide when the sample length is large. Given data from a vertical array of hydrophones, one may accurately obtain a source identification. The methods of the tracking and positioning of normal modes are incorporated with an input of a linear frequency-modulated pulse propagated through an ocean environment. [Research supported by ONR.]

Blind channel order estimation based on second-order statistics

For many existing blind channel estimation algorithms, accurate estimates of the channel order are a prerequisite. A novel scheme for blind channel order estimation using exclusively second-order statistics of the received signal is proposed, which can be embedded in channel estimation and is based on the examination of an indicator function constructed from initial channel estimates with overestimated order. It is demonstrated that significantly better order estimates can be obtained than by information-theoretic criteria like the minimum description length criterion.

Multiuser Channel Estimation from Higher-Order Statistical Matrix Pencil

This paper presents a new statistical approach to the blind estimation of linear multiple-input multiple-output (MIMO) channels with finite impulse response. A matrix pencil is constructed from a set of fourth-order cumulant matrices of the channel output signals. The MIMO channel impulse responses can then be efficiently estimated from the generalized eigendecomposition of this cumulant matrix pencil. Random weighting is applied in the matrix pencil construction to improve the reliability of the algorithm. The proposed new method requires a relaxed channel identifiability condition and is robust in the sense that it does not require the exact knowledge of the MIMO channel order.