Joint channel estimation and equalisation of fast time‐varying frequency‐selective channels

The 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 very high velocities. We approach the problem by estimating the scattering function, which is assumed to be limited in 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 Kalman 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.

In this paper, a new joint timing and channel estimation scheme is proposed for orthogonal frequency division multiplexing and single carrier block transmission ultra-wideband (UWB) systems. In particular, a new preamble pattern is used for both coarse timing and channel estimation. Despite of the presence of coarse timing error, the estimated channel impulse response (CIR) is simply the cyclic shifted version of the real CIR, thanks to the unique structure of the preamble. Then a new method is proposed to search for the first channel tap in the CIR vector, which can be employed to fine tune the timing position and adjust the channel estimation for later data block detection. The proposed scheme has low complexity, saves preamble overhead by performing joint synchronization and channel estimation, and outperforms existing timing acquisition methods in the literature by a large margin in dense multipath UWB channels. Moreover, this paper presents an analysis of the effect of residual timing error on the performance of single carrier systems with frequency domain equalization.

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.

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.

Joint channel estimation and data detection under fading on reconfigurable fabric

A pilot-aided scheme is proposed for the joint estimation and tracking of channel impulse response (CIR), carrier frequency offset (CFO) and sampling frequency offset (SFO) in burst mode, multiple-input-multiple-output (MIMO), and orthogonal frequency division multiplexing(OFDM) systems. First, a received signal model that takes into account nonlinear CFO/SFO effects is formulated. Then, based on the derived signal model and the received multicarrier signal samples containing the pilot tones in the frequency domain, an objective function that includes MIMO CIR, CFO, and SFO is introduced to develop a vector recursive-least-square (RLS)-based joint channel estimation and synchronization algorithm. The analysis and simulation results show that, over the large ranges of the CFO and SFO values, the proposed estimation and tracking scheme offers fast convergence, high stability, and a near-optimum receiver performance that is remarkably close to the ideal performance in the case of perfect channel estimation and synchronization over quasi-static Rayleigh multipath fading channels.

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.

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.

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.

Multiple carrier frequency offsets and multipath channels estimation for coordinated multi-point FBMC systems

New parallel structures are proposed for joint data and channel estimation over frequency selective Rayleigh fading channels. Maximum likelihood sequence estimation (MLSE) is implemented using the per-survivor processing (PSP) method. The Kalman filter and the recursive least squares (RLS) algorithm are considered as estimation methods. A square-root implementation of the Kalman filter is discussed. The algorithm used for the measurement update in the Kalman filter results in significant simplicity, once it is used for realization of the RLS algorithm. Two parallel and pipelined architectures are introduced for the RLS algorithm, and an overall architecture is proposed to implement the MLSE receiver, combining the Viterbi decoder and the channel estimator.

In SFN (Single Frequency Network) broadcasting systems the equivalent CIR (Channel Impulse Response) can be very long but typically it has a sparse nature. This means that the equivalent CIR has several clusters of paths, each one associated to the CIR between a given transmitter and the receiver. These clusters have several multipath components and are typically well separated in time. In this paper we consider OFDM-based (Orthogonal Frequency Division Multiplexing) broadcasting systems with SFN operation and we propose an efficient channel estimation method that takes advantage of the sparse nature of the equivalent CIR. For this purpose, we employ low-power training sequences and we employ an iterative receiver with joint detection and channel estimation. The receiver can know the location of the different clusters that constitute the overall CIR or not. Our performance results show that we can have excellent performance, close to the performance with perfect channel estimation, even with employ low-power training blocks and also for the case where the receiver does not know the location of the different clusters that constitute the overall CIR.

In this paper, we consider a two-way relay system where two terminals exchange their information via an amplify-and-forward relay in a bi-directional manner. Due to the two-way relay protocol, signals from both terminals travel through different cascaded channels, and this makes synchronization and channel estimation much more complicated than those in conventional one-way relay systems. To cope with these problems, we propose a joint time synchronization and channel estimation scheme based on a specific training sequence arrangement, where each terminal's training sequence consists of a perfect sequence (with an ideal auto-correlation function) attached by an appropriate cyclic prefix and postfix. The proposed scheme relies on a first channel tap selection process, whose performance is highly dependent on the choice of a threshold to distinguish the signal outputs from noise. By analyzing some possible probability density functions of the correlator output, we derive optimal thresholds for selection of the first channel tap. With these thresholds, the proposed scheme provides better time synchronization performance than the maximum-likelihood approach for low signal-to-noise ratio (SNR) cases; both have similar performance for high SNR cases. It is also shown that the proposed scheme involves much less computational complexity than the maximum-likelihood approach.

Recently, a joint channel and angle-of-arrival (AoA) estimation scheme for pilot-assisted multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with digital arrays has been proposed; in that scheme, compressive sensing-based time-domain channel estimation is applied. In the scheme, it is assumed that each channel tap has only one AoA. However, in reality, one channel tap may contain responses from multiple paths with different AoAs. In this letter, we propose an improved approach to solve the aforementioned problem. The underlying concept is to transmit multiple OFDM symbols with different beamforming vectors, rendering the time-invariant channel equivalently time-variant. Subsequently, the correlation matrix, imbedded with AoA information, can be estimated. Finally, subspace-based algorithms, such as multiple signal classification (MUSIC), can be used for AoA estimation. The advantage of the proposed method is that the number of detectable AoAs is much larger than that in conventional MUSIC. The performance of the proposed method was also theoretically analyzed. Simulation results demonstrated that with a small number of OFDM symbols, both channel gains and AoAs could be satisfactorily estimated and the theoretical analysis results were accurate.

This letter considers a joint user activity, channel and data estimation problem in an uplink grant-free massive MIMO systems with low-precision analog-to-digital converters (ADCs). This joint estimation is firstly formalized as a non-overlapping group sparse problem, in which the components of compound channel follow independent conditional distribution. To address this problem, a new algorithm consists of the celebrated bilinear generalized approximate message passing (BiG-AMP) and loop belief propagation (LBP) is then proposed, where the strong connection of compound channel can be decoupled in LBP part. By exchanging the information between BiG-AMP part and LBP part, the proposed algorithm improves the performance of channel estimation compared with HyGAMP based method, in which the estimated payload data of proposed algorithm are utilized to aid channel estimation and it leads to relatively few pilot symbols to achieve equivalent channel and data estimation performances. The simulation results confirm that our proposed joint estimation algorithm improves the performance of the existing works in terms of user activity, channel and data estimation.