Basis Expansion Model Research Articles

Time-varying channel estimation through optimal piece-wise time-invariant approximation for high-speed train wireless communications

The practical time-varying channel between a high-speed train (HST) and infrastructure has a single Doppler shift on each resolvable multipath in most cases. As a result, the HST channel can be modelled by only 2L parameters: L Doppler shifts and L complex channel gains. Based on this observation, we propose a novel channel estimation technique for orthogonal frequency-division multiplexing (OFDM) systems running on a HST, with the name PIece-wise Time-Invariant Approximation (PITIA). In PITIA, the HST channel is approximated by a bunch of time-invariant channels, whose channel impulse responses (CIRs) can be estimated through pilots. Variations of these CIR samples over time derive both Doppler shifts and complex channel gains, so the whole time-varying channel can be reconstructed. PITIA enjoys low computation complexity of O(NL) for N subcarriers. The optimal duration of time-invariant channels used to approximate HST channel is derived from both analytical analysis and simulations. Compared to basis expansion model (BEM) methods, PITIA uses fewer channel parameters with comparable modelling error, shows better normalized mean squared error (NMSE) performance under high-mobility and high signal-to-noise ratio (SNR) environments, and achieves comparable NMSE in low SNR regime.

Distributed Spectrum Estimation for Small Cell Networks Based on Sparse Diffusion Adaptation

The goal of this letter is to propose an adaptive and distributed approach to cooperative sensing for wireless small cell networks. The method uses a basis expansion model of the power spectral density (PSD) to be estimated, and exploits spectral sparsity to improve estimation accuracy and adaptation capabilities. An estimator of the model coefficients is developed based on sparse diffusion strategies, which are able to exploit and track sparsity while at the same time processing data in real-time and in a fully decentralized manner. Simulation results illustrate the advantages of the proposed sparsity-aware strategies for cooperative spectrum sensing applications.

A New Sparse Channel Estimation and Tracking Method for Time-Varying OFDM Systems

We propose a simple sparse channel estimation and tracking method for orthogonal frequency-division multiplexing (OFDM) systems based on a dynamic parametric channel model, where the channel is parameterized by a small number of distinct paths, each characterized by path delay and path gain, and all parameters are time varying. In the proposed method, we adaptively choose the delay grid and estimate each channel path delay iteratively. To further reduce the complexity, we also propose a tracking algorithm based on the fact that the changes in the channel path number and path delays are small over a few adjacent OFDM symbols. After the physical path delays are estimated, we then estimate the channel path gains by using the polynomial basis expansion model (P-BEM). Simulation results demonstrate the effectiveness of the proposed channel estimation and tracking method in dynamic environments. Compared with the compressive-sensing-based channel estimator using the orthogonal matching pursuit (OMP) algorithm, the new technique proposed here has much lower computational complexity while offering comparable performance.

Parallel Channel Estimator and Equalizer for Mobile OFDM Systems

Mobile OFDM refers to OFDM systems with fast moving transceivers, in contrast to traditional OFDM systems whose transceivers are stationary or have a low velocity. In this paper, we use the basis expansion model (BEM) to model time-varying OFDM channels. Using different BEM’s, we investigate various architectures to implement the least-squares (LS) channel estimation and its corresponding zero-forcing (ZF) channel equalization. The experimental results show that our implementation for mobile OFDM systems is capable of combatting the time variation of mobile OFDM channels, and more hardware resource utilization is necessary compared with a traditional OFDM design which fails in a time-varying scenario. For mobile OFDM systems, different BEM’s are available for the channel modeling. We observe that the so-called Critically sampled Complex-Exponential BEM (CCE-BEM) leads to the most efficient hardware architecture while still maintaining high modeling accuracy.

Channel Estimation for OFDM Systems over Doubly Selective Channels: A Distributed Compressive Sensing Based Approach

Channel estimation for an orthogonal frequency-division multiplexing (OFDM) broadband system over a doubly selective channel is very challenging. This is mainly due to the significant Doppler shift, which results in a time-frequency doubly-selective (DS) channel. The DS channel features a large number of channel coefficients, which introduces inter-carrier interference (ICI) and forces the need for allocating a large number of pilot subcarriers. To tackle this problem, in this paper we propose a novel channel estimation scheme based on distributed compressive sensing (DCS) theory. Taking advantage of the basis expansion model (BEM) and the channel sparsity in the delay domain, we transform the original DS channel into a novel two-dimensional channel model, where several jointly sparse BEM coefficient vectors become the estimation goal. Then a special decoupling form originating from a novel sparse pilot pattern is designed for such estimation, which results in an ICI-free structure and enables the DCS application to make joint estimation of these vectors accurately. Combined with a smoothing treatment process, the proposed scheme can achieve significantly higher estimation accuracy than the existing ones, although with a much smaller number of pilot subcarriers. Theoretical analysis and simulation results both confirm its performance merits.

The Super-Exponential Algorithm of Blind Equalization for Time-Varying Channel Based on Basis Expansion Model

Existing algorithms of blind equalization for time-varying channels are slow in convergence, easily interfered, and hard to pinpoint the location of pulsation in the frequency domain. In this paper we present a new blind equalization method that addresses the aforementioned issues. The new solution combines super-exponential algorithm with carrier frequency-offset estimation for time-varying channels. The time-varying channel taps described by the complex exponential basis expansion model (CE-BEM) are expressed as a superposition of time-varying complex exponential bases with time-invariant coefficients. We first employ a super-exponential algorithm to remove the inter-symbol interference caused by time-invariant coefficients. Then we estimate channel pulsation from equalized signals with a carrier frequency-offset estimation algorithm. Compared with existing ones, our solution converges faster with lower inter-symbol interference and easier specification of the pulsation in frequency domain. Simulation results prove the efficiency of the proposed algorithm.

An Improved Channel Estimation Method in OFDM System

In this paper, we will focus on channel estimation (CE) in orthogonal frequency-division multiplexing (OFDM) systems. The time-varying (TV) channelsare modeled by a basis expansion model (BEM). Due to the time-variation, the channel matrix in the frequency domain is no longer diagonal, but approximately banded.We use a pilot-aided algorithm for estimation of rapidly varying wireless channels in OFDM systems. Theperforms is goodwhen the channels vary on the scale of a single OFDM symbol duration, which occurs in mobile communication scenarios such as WiMAX, WAVE, and DVB-T.We recover Fourier coefficients of the channel taps by the pilot information.We then estimate the BEM coefficients of the channel taps from their respective Fourier coefficients using a recently developed inverse reconstruction method.We compare some BEM models in inverse methodsto find out the best ones in certain conditions.

Doubly-Selective Channel Estimation Using Superimposed Training and Weighted First-Order Statistics

Doubly-selective channel estimation using superimposed training and complex exponential basis expansion model is considered. By taking a weighted averaging operation of the received data, a weighted first-order statistical estimator is proposed, where the time-varying channel estimation is reduced to the simple average-based solution of time-invariant coefficients and the dominant effect of information-induced interference on channel estimation can be suppressed. To further improve the estimation performance with a limited training power, a joint iterative channel estimation and symbol detection scheme is developed where the detected symbol is exploited to enhance estimation performance instead of being viewed as interference. Theoretical analysis and simulation results show that the proposed scheme is superior to data-dependent superimposed training scheme and competitive with the conventional time-multiplexed training in terms of symbol error rate over doubly-selective channels.

Two‐step interference cancellation scheme in doubly selective channel estimation using superimposed training

Channel estimation for single-input–multiple-output systems over doubly selective channel using superimposed training and discrete prolate spheroidal basis expansion model is considered. To remove the interference from unknown data, a two-step interference cancellation scheme is proposed, where in the first step, a first-order statistics-based estimator with cyclic mean removal before transmission is proposed. In this step, only interference components corresponding to cyclic mean of data sequence are removed, which avoids the conflict between total interference elimination and symbol recovery. In the second step, a low complexity iterative interference cancellation scheme is proposed to further improve estimation performance with detected symbols at the receiver's end. Simulation results show that the proposed iterative scheme has the symbol error rate (SER) performance slightly inferior to that of the partially-data-dependent approach but with less computational complexity and outperforms the data-dependent scheme in terms of SER as well as mean-square error over doubly selective channels.

A Weighted First-Order Statistical Method for Time-Varying Channel and DC-offset Estimation Using Superimposed Training

Time-varying channel and dc-offset estimation using superimposed training and first-order statistics are considered. A weighted first-order statistics-based estimator using complex exponential basis expansion model (CE-BEM) is proposed, which explicitly exploits the cyclostationary characteristic of periodic training sequence and extends to time-varying channel estimation. By subtracting the cyclic mean from each data block, only partial unknown data interference is removed to make a tradeoff between interference cancellation and symbol recovery. A theoretical performance analysis is presented. Simulation results show that the proposed scheme has low computational complexity and exhibits good performance in terms of the symbol error rate.

Estimation of Fast-Fading Channels for Turbo Receivers With High-Order Modulation

This paper proposes an efficient, low-complexity, and near-optimal approach to pilot-assisted fast-fading channel estimation for single-carrier modulation with a turbo equalizer and a decoder. The proposed method is applicable to higher order modulation schemes, where the detector is sensitive to the estimation error. A doubly selective fast-fading channel is estimated using a fixed-lag Kalman filter (KF). The Kalman filtering is followed by a zero-phase low-pass filter, functioning as a smoother. A method for designing the smoother is introduced. Block processing is utilized to reduce the transient effects of the zero-phase filter (ZPF) at the edges of the symbol blocks. A first-order autoregressive (AR) model is fitted to the channel variations. For the case of 64-quadrature-amplitude modulation (QAM), a complex-exponential basis expansion model (CE-BEM) is exploited to capture the varying gains, and an AR(1) process is used to model the time evolution of the BEM coefficients. By virtue of the long memory of the smoother, the error-rate floor, which is commonly associated with low-order channel estimation models, is avoided. The potential for parallelism makes our approach well suited to multicore field implementations. The applicability of the method to 4-QAM, 16-QAM, and 64-QAM schemes is shown through simulation experiments.

Symmetric extension method for basis expansion models under fast‐varying channels

A symmetric extension method for basis expansion modelling (BEM) under a fast-varying channel is proposed. The conventional DFT BEM approach suffers from power leakage and results in a modelling error floor, especially at the channel boundaries. Proposed is a novel symmetric extension method to reduce the leakage power efficiently. Numerical results show that the performance of the proposed channel modelling method is robust under different normalised Doppler frequencies and the modelling errors at the channel boundaries can be eliminated substantially.

Low-Complexity ICI Cancellation Based on BEM for OFDM Systems over Doubly Selective Channels

One major challenge to implement orthogonal frequency division multiplexing (OFDM) systems over doubly selective channels is the non-negligible intercarrier interference (ICI), which significantly degrades the system performance. Existing solutions to cope with ICI include zero-forcing (ZF), minimum mean square error (MMSE) and other linear or nonlinear equalization methods. However, these schemes fail to achieve a satisfactory tradeoff between performance and computational complexity. To address this problem, in this paper we propose two novel nonlinear ICI cancellation techniques, which are referred to as parallel interference cancelation (PIC) and hybrid interference cancelation (HIC). Taking advantage of the special structure of basis expansion model (BEM) based channel matrices, our proposed schemes enjoy low computational complexity and are capable of cancelling ICI effectively. Moreover, since the proposed schemes can flexibly select different basis functions and be independent of the channel statistics, they are applicable to practical OFDM based systems such as DVB-T2 over doubly selective channels. Theoretical analysis and simulation results both confirm their performance-complexity advantages in comparison with some existing methods.

Modified clustered comb pilot-aided fast time-varying channel estimation for OFDM system

As high-speed railway is booming worldwide, the communication system with fast-time varying channel has drawn great attention. The comb pilot based linear minimum mean square error (LMMSE) channel estimator is proved to be an effective method for fast time-varying channel estimation. In this paper, the clustered comb pilot-aided channel estimation for orthogonal frequency-division multiplexing (OFDM) system is discussed, where the time varying channel is approximated by a basis expansion model (BEM). A modified clustered comb pilot structure is proposed and justified to improve the estimation performance compared with the clustered comb pilot proposed by Tang. Based on the complex-exponential BEM (CE-BEM) model, a suboptimal-pilot structure is proposed. In addition, optimal pilot length is analyzed and simulated with a predefined total number of pilots. The simulation results show that the modified clustered comb pilot can greatly reduce the estimation error especially with high Doppler spread. The suboptimal-pilot structure with guard pilot approximation is proven to be competitive. Optimal nonzero pilot lengths for different Doppler spread are obtained by simulation with a predefined channel order and fixed pilot subcarriers.

Doubly selective channel estimation for amplify-and-forward relay networks

In this article, doubly selective channel estimation is considered for 1amplify-and-forward-based relay networks. The complex exponential basis expansion model is chosen to describe the time-varying channel, from which the infinite channel parameters are mapped onto finite ones. Since direct estimation of these coefficients encounters high computational complexity and large spectral cost, we develop an efficient estimator that only targets at useful channel parameters that could guarantee the later data detection. The training sequence design that can minimize the channel estimation mean-square error is also proposed. Finally, numerical results are provided to corroborate the study.

Fast Time-Varying Channel Estimation Technique for LTE Uplink in HST Environment

A novel channel estimation technique is proposed for the time-division-duplex long-term evolution (TDD-LTE) single-carrier frequency-division multiple-access (SC-FDMA) system in the high-speed-train (HST) environment. In the new defined transform domain, the channel parameters of the two block pilots in the SC-FDMA subframe are first estimated, then the polynomial basis expansion model (P-BEM) is employed to estimate the channel parameters of the data symbols, and an autoregressive (AR) model is used to improve the estimation accuracy of the channel parameters of the data symbols out of the two block pilots. The symbol-by-symbol changes of the channel parameters can be effectively estimated by the proposed method. Simulation results show that the proposed method is robust to the fast time-varying channel in the HST scenario, and that the frame error rate (FER) performance of the system by using the proposed method can obtain a gain in the signal-to-noise ratio (SNR) of more than 10 dB compared with those of the available methods.

Time-Domain Block and Per-Tone Equalization for MIMO–OFDM in Shallow Underwater Acoustic Communication

Shallow underwater acoustic (UWA) channel exhibits rapid temporal variations, extensive multipath spreads, and severe frequency-dependent attenuations. So, high data rate communication with high spectral efficiency in this challenging medium requires efficient system design. Multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO---OFDM) is a promising solution for reliable transmission over highly dispersive channels. In this paper, we study the equalization of shallow UWA channels when a MIMO---OFDM transmission scheme is used. We address simultaneously the long multipath spread and rapid temporal variations of the channel. These features lead to interblock interference (IBI) along with intercarrier interference (ICI), thereby degrading the system performance. We describe the underwater channel using a general basis expansion model (BEM), and propose time-domain block equalization techniques to jointly eliminate the IBI and ICI. The block equalizers are derived based on minimum mean-square error and zero-forcing criteria. We also develop a novel approach to design two time-domain per-tone equalizers, which minimize bit error rate or mean-square error in each subcarrier. We simulate a typical shallow UWA channel to demonstrate the desirable performance of the proposed equalization techniques in Rayleigh and Rician fading channels.

Iterative Decomposed OFDM Channel Estimation Algorithm Over Highly Mobile Channels

In orthogonal frequency-division multiplexing systems, the temporal channel gains to estimate are much more than the observable data over highly mobile channels. The basis expansion model (BEM) has been employed to reduce the number of these channel parameters. In the absence of channel statistics, generalized complex-exponential BEM (GCE-BEM) is popular for its fast algebra operation and easy generation of basis matrix. However, there is still much potential for performance improvement by modeling error reduction. In this paper, the factors affecting the modeling error are analyzed and an iterative decomposed estimation algorithm is proposed to improve the modeling accuracy. The proposed algorithm decomposes each tap into the linear part and the non-linear part. The linear part with two parameters (the middle value and the slope) is initialized by estimation in linearly time-varying channel models. And the non-linear part is addressed by the conventional least-squares (LS) method based on GCE-BEM and then the slopes of the linear part are updated for the next iteration by two distinct slope update methods. The simulations show that the proposed algorithm outperforms the conventional estimation methods with significantly reduced modeling error under both high signal to noise ratio and Doppler shift conditions.

Joint channel and phase noise estimation in OFDM systems at very high speeds

In this paper, the problem of joint phase noise and channel estimation for OFDM systems over a fast time-varying frequency-selective channel is explored. Each channel tap time-variation within one OFDM symbol is approximated by a Basis Expansion Model (BEM). Joint estimation is performed on multiple OFDM symbols via the Extended Kalman Filtering in order to exploit the time-correlation of the parameters. The data symbols are estimated by means of an iterative pilot-based algorithm. It is shown that, with only 2 iterations, our algorithm outperforms the conventional one, and the performance approaches that of the ideal case for which the channel response and phase noise are known.

Turbo equalization of doubly selective channels

ABSTRACTIn this paper, turbo equalization for transmission over doubly selective channels is proposed. The maximum a posteriori probability (MAP) algorithm is used for channel detection as well as for channel decoding. The detection/decoding constituents can exchange soft information in an iterative manner resulting in the so‐called turbo equalization. The time‐varying multi‐path fading channel is modeled using the basis expansion model (BEM). In this BEM, the time‐varying channel is viewed as a bank of time‐invariant finite impulse response filters, and the time variation is captured by means of time‐varying complex exponential basis functions. Therefore, the time‐varying transition tables that characterize the time‐varying channel can also follow a similar BEM. The complexity of the MAP channel detector is rather prohibitive for practical applications. This motivates the search for lower‐complexity soft‐output channel detectors. For this purpose, soft‐output linear minimum‐mean square error (LMMSE)‐based channel detectors are proposed for single carrier as well as for multi‐carrier systems. With the use of Gaussian approximation, expressions for the a posteriori and extrinsic log‐likelihood ratios have been derived. The performance of the proposed turbo equalization schemes are evaluated using numerical simulations. Copyright © 2012 John Wiley & Sons, Ltd.