Joint channel estimation and equalization for fast time-variant multipath channels

This paper presents a method for joint channel and data estimation for transmission over frequency-selective and time-variant channels. Hereby, fast time-variant channels can be tracked, which is important for mobile communications at high velocities. We approach the problem by estimating the scattering function, which depends on delay and Doppler frequency. At the transmitter, a short training sequence is inserted at the beginning of the data block. This sequence is used for initializing a recursive estimation filter, which carries out the joint channel and data estimation adaptively. After the training sequence hypothetical data symbols are considered to extend the persecuted paths in the data tree.

Channel state information (CSI) is required at the transmitter for achieving the maximum potentials of multiple-input multiple-output (MIMO) systems. In fast time-variant vehicular communications channels high data rate feedback lines are required in a frequency division duplex (FDD) transceiver for updating the transmitter with the rapidly changing CSI. Even with high data rate feedback lines, the delay caused by channel estimation and feedback may lead to outdated CSI at the transmitter. To reduce both the feedback load and CSI delay, this paper presents a reduced rank autoregressive (AR) channel predictor based on low dimensional discrete prolate spheroidal (DPS) sequences. The new subframe-wise DPS basis expansion model (DPS-BEM) channel predictor properly exploits the channel's restriction to low dimensional subspaces for reducing the prediction error and the computational complexity. The proposed channel predictor can be applied for updating the precoding matrix in time-variant MIMO systems. Simulation results demonstrate that the proposed channel predictor outperforms the DPS based minimum energy (ME) predictor at different Doppler frequencies and has better performance than the conventional Wiener predictor for slower time-variant channels and almost similar performance for very fast time-variant channels with reduced amount of computational complexity.

This paper is concerned with the challenging and timely problem of joint channel estimation, equalization, and data detection for uplink orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency selective and very rapidly time varying channels. The resulting algorithm is based on the space alternating generalized expectation maximization (SAGE) technique which is particularly well suited to multicarrier signal formats leading to a receiver structure that also incorporates interchannel interference (ICI) cancelation. In order to reduce the computational complexity of the algorithm, band-limited, discrete cosine orthogonal basis functions are employed to represent the rapidly time-varying fading channel by the discrete cosine serial expansion coefficients. It is shown that, depending on the normalized Doppler frequency, only a small number of expansion coefficients is sufficient to approximate the channel perfectly and there is no need to know the correlation function of the input signal. In this way, the resulting reduced dimensional channel coefficients are estimated and the data symbols detected iteratively with tractable complexity. The proposed SAGE joint detection algorithm updates the data sequences serially and the channel parameters are updated in parallel, leading to a receiver structure that also incorporates ICI cancelation. Computer simulations show that the cosine transformation represents the time-varying channel very effectively and the proposed algorithm has excellent symbol error rate and channel estimation performance even with a very small number of channel expansion coefficients employed in the algorithm, resulting in substantial reduction of the computational complexity.

This paper addresses joint channel and data estimation for transmission over frequency‐selective and time‐varying channels based on a Doppler‐variant channel impulse response (CIR). A discrete spreading function (DSF), which corresponds to the Doppler Fourier series of the time‐varying channel taps, is introduced. The spectral leakage associated with the Fourier series representation is reduced by oversampling in Doppler‐direction. This approach, however, requires joint channel estimation and equalisation (JCE). Therefore, a recursive least squares (RLS) algorithm for the DSF estimation is combined with the data detection in a reduced state diagram. Furthermore, an enhanced metric, previously introduced in De Broeck et al. (Proceedings of Second International Workshop on Multi‐Carrier Spread‐Spectrum, 1999; published by Kluwer Academic Publishers: Dordrecht, 2000) for time‐invariant channels, is applied here for path selection. The performance of this metric is investigated here for time‐varying and frequency‐selective (TV‐FS) channels. The performance of the proposed approach is compared with the JCE algorithm which uses RLS estimation of a CIR by simulations. Copyright © 2007 John Wiley & Sons, Ltd.

This paper is concerned with the challenging and timely problem of joint channel estimation and equalization for orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency selective and very rapidly time varying channels. The resulting algorithm is based on the space alternating generalized expectation maximization—maximum a posteriori probability (SAGE-MAP) technique which is particularly well suited to multicarrier signal formats. The algorithm is implemented in the time-domain which enables one to use the Gaussian approximation of the transmitted OFDM samples. Consequently, the averaging process of the nonpilot data symbols becomes analytically possible resulting in a feasible and computationally efficient channel estimation algorithm leading to a receiver structure that yields also an equalized output from which the data symbols are detected with excellent symbol error rate (SER) performance. Based on this Gaussian approximation the exact Bayesian Cramér Rao lower bound (CRLB) as well as the convergence rate of the algorithm are derived analytically. To reduce the computational complexity of the algorithm, discrete Legendre orthogonal basis functions are employed to represent the rapidly time-varying fading channel. It is shown that, depending on the normalized Doppler frequency, only a small number of expansion coefficients is sufficient to approximate the channel very well and there is no need to know the correlation function of the input signal. The computational complexity of the algorithm is shown to be <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\sim}O(NL)$</tex></formula> per detected data symbol and per SAGE-MAP algorithm cycle where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$N$</tex></formula> is the number of OFDM subcarriers and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$L$</tex></formula> is the number of multipath components.

High-speed railway communication implemented based on Long-Term Evolution-Railway (LTE-R) Platform has strict requirements for quality of services to support high data-rate transmission for numerous mobile users. In such environment, there often exists inter-carrier interference. In this paper, we exploit a robust channel estimation method in the time domain for very fast time-varying LTE-railway channels, and then, we propose an effective and adaptive frequency-domain equalizer that can offer a tradeoff between performance and computational complexity. The simulation results show the robustness of our proposed method compared with previous ones. The computational complexity of the proposed method retain at a decent number by exploiting specified properties of channel matrices.

Joint channel estimation and data detection under fading on reconfigurable fabric

The problem of joint channel estimation, equalization, and multiuser detection for a multiantenna DS/CDMA system operating over a frequency-selective fading channel and adopting long aperiodic spreading codes is considered in this paper. First of all, we present several channel estimation and multiuser data detection schemes suited for multiantenna long-code DS/CDMA systems. Then, a multipass strategy, wherein the data detection and the channel estimation procedures exchange information in a recursive fashion, is introduced and analyzed for the proposed scenario. Remarkably, this strategy provides, at the price of some attendant computational complexity increase, excellent performance even when very short training sequences are transmitted, and thus couples together the conflicting advantages of both trained and blind systems, that is, good performance and no wasted bandwidth, respectively. Space-time coded systems are also considered, and it is shown that the multipass strategy provides excellent results for such systems also. Likewise, it is also shown that excellent performance is achieved also when each user adopts the same spreading code for all of its transmit antennas. The validity of the proposed procedure is corroborated by both simulation results and analytical findings. In particular, it is shown that adopting the multipass strategy results in a remarkable reduction of the channel estimation mean-square error and of the optimal length of the training sequence.

This paper considers joint active user detection (AUD) and channel estimation (CE) for massive connectivity scenarios with sporadic traffic. The state-of-art method under a Bayesian framework to perform joint AUD and CE in such scenarios is approximate message passing (AMP). However, the existing theoretical analysis of AMP-based joint AUD and CE can only be performed with a given fixed point of the AMP state evolution function, lacking the analysis of AMP phase transition and Bayes-optimality. In this paper, we propose a novel theoretical framework to analyze the performance of the joint AUD and CE problem by adopting the replica method in the Bayes-optimal condition. Specifically, our analysis is based on a general channel model, which reduces to particular channel models in multiple typical MIMO communication scenarios. Our theoretical framework allows ones to measure the optimality and phase transition of AMP-based joint AUD and CE as well as to predict the corresponding performance metrics under our model. To reify our proposed theoretical framework, we analyze two typical scenarios from the massive random access literature, i.e., the isotropic channel scenario and the spatially correlated channel scenario. Accordingly, our performance analysis produces some novel results for both the isotropic Raleigh channel and spatially correlated channel case.

Orthogonal frequency division multiplexing (OFDM) systems suffer performance degradation in fast fading channels due to intercarrier interference (ICI). Combining frequency domain equalization and bit-interleaved coded modulation (BICM), the iterative receiver is able to harvest both temporal and frequency diversity. In order to perform coherent detection and estimation, channel state information (CSI) is indispensable. Being able to accurately and effectively acquire CSI in the fast time-varying channel is critical. Conventional frequency domain channel estimation (CE) methods have an irreducible error floor at high normalized Doppler frequency fdTs, since ICI corrupts the orthogonality among subcarriers. Considering that the fast time-varying channel is also a source of temporal diversity, CE ought to take place in the pre-FFT time domain. Realizing channel variations in time are often smooth, this paper proposes a time domain channel estimator using pilot symbol assisted modulation (PSAM) with complexity O(N), where N is the FFT size. Simulation results demonstrate that a PSAM system with channel estimation provides excellent trade-off between performance, complexity and spectral efficiency.

The channel estimation and equalization for EDGE system with time-varying and frequency-selective fading channels are discussed. It is shown that the fast fading channel during a selected slot in the EDGE system can be modeled as a linear function of time, and a linear least-squares algorithm is proposed to estimate the fading channel. For typical channel profiles of the EDGE system, the channel impulse response is not in its minimum phase form, thus cannot be directly used in computationally efficient equalizers, such as delayed decision feedback sequence estimation or reduced state sequence estimation. To overcome this problem, a Cholesky decomposition-based method is introduced to transform the estimated channel impulse response into its minimum phase form. The simulation results show that the proposed algorithms can effectively combat the time-varying and frequency-selective channel fading with Doppler frequency being in a wide range up to 300 Hz.

Joint data and channel estimation for mobile communication receivers can be realized by employing a Viterbi detector along with channel estimators which estimate the channel impulse response. The behavior of the channel estimator has a strong impact on the overall error rate performance of the receiver. Kalman filtering is an optimum channel estimation technique which can lead to significant improvement in the receiver bit error rate (BER) performance. However, a Kalman filter is a complex algorithm and is sensitive to roundoff errors. Square-root implementation methods are required for robustness against numerical errors. Real-time computation of the Kalman estimator in a mobile communication receiver calls for parallel and pipelined structures to take advantage of the inherent parallelism in the algorithm. In this paper different implementation methods are considered for measurement update and time update equations of the Kalman filter. The unit-lower-triangular-diagonal (LD) correction algorithm is used for the time update equations, and systolic array structures are proposed for its implementation. For the overall implementation of joint data and channel estimation, parallel structures are proposed to perform both the Viterbi algorithm and channel estimation. Simulation results show the numerical stability of different implementation techniques and the number of bits required in the digital computations with different estimators.

Accurate channel state information is the foundation of the receiver design for power line communication (PLC) system. However, the presence of impulsive noise makes the problem more complex. As traditional impulsive noise mitigation methods are based on the assumption that the channel state information is known in advance, which limits their applications. In this paper, by exploiting the parametric sparsity, we propose a joint channel and impulsive noise estimation scheme based on compressed sensing theory for narrowband PLC systems. Observing the strong coherence of measurements matrix, we adopt the sparse Bayesian learning (SBL) to solve the compressed sensing problem. Simulation results verify our proposed algorithm has smaller mean square error and bit error rate.

To improve the performance of the optimal pilot sequences over multiple OFDM symbols in fast time-varying channels, this letter proposes a novel channel estimation method using virtual pilot tones in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. Assuming that the superimposed virtual pilot tones at the data locations over the specific sub-carriers are transmitted from all transmit antennas, the corresponding virtual received pilot signals at the same locations are obtained from the neighboring real received pilot signals over the same sub-carriers by Wiener filter. Based on the least squares (LS) channel estimation, the channel parameters can be obtained from the combination of the virtual and real received pilot signals over one OFDM symbol. Simulation results show that the proposed channel estimation method greatly outperforms the previous method for the optimal pilot sequences over multiple OFDM symbols in fast time-varying channels, as well as approaches the method for the comb-type optimal pilot sequences in performance.

Non pilot data-aided carrier and sampling frequency offsets estimation in fast time-varying channel