Complex Exponential Basis Expansion Model Research Articles

Time-Varying Channel Estimation Based on Distributed Compressed Sensing for OFDM Systems.

For orthogonal frequency division multiplexing (OFDM) systems in high-mobility scenarios, the estimation of time-varying multipath channels not only has a large error, which affects system performance, but also requires plenty of pilots, resulting in low spectral efficiency. To address these issues, we propose a time-varying multipath channel estimation method based on distributed compressed sensing and a multi-symbol complex exponential basis expansion model (MS-CE-BEM) by exploiting the temporal correlation and the joint delay sparsity of wideband wireless channels within the duration of multiple OFDM symbols. Furthermore, in the proposed method, a sparse pilot pattern with the self-cancellation of pilot intercarrier interference (ICI) is adopted to reduce the input parameter error of the MS-CE-BEM, and a symmetrical extension technique is introduced to reduce the modeling error. Simulation results show that, compared with existing methods, this proposed method has superior performances in channel estimation and spectrum utilization for sparse time-varying channels.

Near-Optimal BEM OTFS Receiver With Low Pilot Overhead for High-Mobility Communications

In this paper, a new receiver design based on basis expansion model (BEM) orthogonal time frequency space (OTFS) is presented for high-mobility communications with Doppler-spread channel. By deriving an analytical BEM OTFS system model, a low-order generalized complex exponential BEM (GCE-BEM) aided rough channel estimation is proposed at the initial stage with low pilot overhead, followed by equalization. Then, the refinement of channel estimation and equalization is conducted iteratively, in which a high-resolution GCE-BEM model with a large BEM order is adopted and the detected data symbols are exploited as pseudo-pilots, leading to higher estimation accuracy. Simulation results show that the proposed BEM OTFS receiver significantly outperforms the existing OTFS receivers in terms of the mean square error (MSE) of channel estimation and bit error rate (BER), while featuring low pilot overhead. Results also show the near-optimal performance of the novel solution, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , achieved BER is very close to the case of perfect channel estimation. The theoretical lower bound on MSE of channel estimation is derived to verify the effectiveness of the proposed BEM OTFS receiver, which is shown to be close to simulation results.

Adaptive blind equalization of fast time‐varying channel with frequency estimation in impulsive noise environment

In this paper, a novel source signal recovery method for fast time-varying channels described by complex exponential-basis expansion model (CE-BEM) in the impulsive noise environment is proposed. This method consists of two phases. The first phase is the equalization of fast time-varying channels, in this phase, a novel algorithm FSE-FLOS-CMA is proposed. The convergence performance of this newly proposed algorithm is much better than that of existing fractionally spaced equalizer-constant modulus algorithm (FSE-CMA) in impulsive noise environment. In the second phase, a novel frequency estimation method is proposed. The estimated frequency in impulsive noise environment is obtained by calculating a specific p-order fractional low-order cyclic moment of the equalized signal. Simulation results show that the proposed FSE-FLOS-CMA and frequency estimation method can effectively estimate the source signals transmitted through the fast time-varying channels in impulsive noise environment.

BEM-PSP for Single-Carrier and SC-FDMA Communication Over a Doubly Selective Fading Channel

In this paper, we consider pilot-aided channel estimation and equalization for single-carrier and single-carrier frequency division multiple-access (SC-FDMA) transmission over doubly-selective channels (DSC). To reduce the channel estimation (CE) parameters, the DSC is modelled using a complex-exponential basis expansion model (CX-BEM) with non-uniform BEM frequencies. We optimize the CX-BEM basis functions using CE error minimization as the objective. As a result, the channel modelling error is greatly reduced. Next, we propose a BEM-based per-survivor processing (PSP) technique and combine it with a decision-directed channel estimator to obtain a channel-tracking equalizer at the receiver. The resultant BEM-PSP receiver significantly improves the channel estimation mean square error (MSE) and the bit error rates (BER) performance in fast fading multi-path channel, thanks to the channel tracking capability embedded within its Viterbi equalizer. Finally, we employ cross-frame channel interpolation, and power distribution between the data and pilot symbols to further improve the system performance at high fading rates. Extensive simulation results show that our BEM-PSP receiver outperforms many existing methods and approaches close to an ideal receiver with perfectly known CSI under various fading scenarios.

Pilot Design for BEM-Based Channel Estimation in Doubly Selective Channel

This paper investigates pilot design for enhanced channel estimation in single carrier communication systems over doubly-selective channels (DSC). Our contribution is twofold: first, we propose to use Huffman sequences as pilot clusters with low peak-to-average power ratio (PAPR), yet with good channel estimation performance when periodic pilot placement is adopted; second, we propose a low-complexity pilot placement strategy based on the analysis of the complex-exponential basis expansion model (CE-BEM) of the DSC. The latter leads to improved channel estimation performance with useful insights for pilot placement.

Novel Adaptive Distributed Compressed Sensing Algorithm for Estimating Channels in Doubly-Selective Fading OFDM Systems

Doubly-selective (DS) fading channel is often occurred in many orthogonal frequency division multiplexing (OFDM) communication systems, such as high-speed rail communication systems and underwater acoustic (UWA) wireless networks. It is challenging to provide an accurate and fast estimation over the doubly-selective channel, due to the strong Doppler shift. This paper addresses the doubly selective channel estimation problem based on complex exponential basis expansion model (CE-BEM) in OFDM systems from the perspective of distributed compressive sensing (DCS). We propose a novel DCS-based improved sparsity adaptive matching pursuit (DCS-IMSAMP) algorithm. The advantage of the proposed algorithm is that it can exploit the joint channel sparsity information using dynamic threshold, variable step size and tailoring mechanism. Simulation results show that the proposed algorithm achieves 5dB performance gain with faster operation speed, in comparison with traditional DCS-based sparsity adaptive matching pursuit (DCS-SAMP) algorithm.

Compressed Sensing-Based Sparsity Adaptive Doubly Selective Channel Estimation for Massive MIMO Systems

By exploiting the sparsity of the channel in the delay and angle domains, compressed sensing (CS) algorithms can be used for channel estimation of massive multiple-input multiple-output (MIMO) systems to reduce pilot overhead. Due to the Doppler frequency shift, however, the intercarrier interference (ICI) and the rapid change of the channel state result in the poor estimation effect of doubly selective (DS) channel. In this paper, we propose the block sparsity adaptive matching pursuit (B-SAMP) algorithm to solve this problem. Firstly, the complex exponential basis expansion model (CE-BEM) is used to convert numerous channel tap coefficients into BEM parameter vectors and then the sparsity adaptive channel estimation scheme based on compressed sensing is proposed. Specifically, the ICI-free model is obtained by using the proposed equally placed pilot group scheme, and the B-SAMP algorithm is proposed by using the spatio-temporal common sparsity of the channel to complete the estimation of DS channel. Finally, a linear smoothing method is used to reduce the error caused by CE-BEM, thereby further improving the accuracy of the estimation. The simulation results show that the proposed method not only improves the estimation accuracy compared with the existing scheme but also requires fewer pilots.

Low-Complexity Equalization of Orthogonal Signal-Division Multiplexing in Doubly-Selective Channels

Orthogonal signal-division multiplexing (OSDM) is a generalized modulation scheme to bridge the gap between orthogonal frequency-division multiplexing (OFDM) and single-carrier frequency-domain equalization. It allows significantly more flexibility in system design; however, over doubly-selective channels, it suffers from a special signal distortion structure, namely inter-vector interference, which is analogous to inter-carrier interference in conventional OFDM. To analyze its effect, in this paper, the complex exponential basis expansion model (CE-BEM) is used to approximate the doubly-selective channel. We show that the composite channel matrix of OSDM systems is cyclically block banded in this case, and the blocks in its main band can be further diagonalized. By exploiting this unique matrix structure, low-complexity block and serial OSDM equalization algorithms are then proposed. These two equalization algorithms are based on block LDLH factorization and block iterative matrix inversion, respectively, both of which are implemented in a transformed domain to avoid direct inversion of large matrices. In addition, a CE-BEM channel estimation method is designed for OSDM systems, which uses frequency-shifted Chu sequences as pilots to ease the computation. Numerical simulations are finally provided to justify the validity of our channel equalization and estimation algorithms.

High mobility channel estimation method based on improved basis expansion model

In this paper, the problem of high mobility channel estimation in the Long-Term Evolution for Railway (LTE-R) communication system is investigated. By using a Basis Expansion Model (BEM), the channel impulse response is modeled as the sum of several basis functions multiplied by coefficients. By estimating the basis function coefficients, the fast time-varying channel can be approximated. In order to reduce the estimation error resulting from the high frequency basis function, the Generalized Complex Exponential BEM (GCE-BEM) is modified to form an Improved GCE-BEM (IGCE-BEM) by adding a correction coefficient to the basis function. Moreover, an Improved Baseline Tilting (IBT) method is proposed to reduce the Gibbs effect. In addition, linear interpolation, Gauss interpolation, and three-order Hermite interpolation are adopted to obtain the channel impulse response at non pilot locations based on the channel estimation results at pilot positions. The simulation results show that the IGCE-BEM outperforms the CE-BEM and GCE-BEM in terms of the Normalized Mean Squared Error (NMSE). The IBT method is better than the BT method in reducing the Gibbs effect. In addition, combined with the IBT, the IGCE-BEM also has low NMSE under high moving speed and high noise power. The performance of the three-order Hermite interpolation method is higher than that of the linear interpolation and Gauss interpolation approaches.

Dynamic Clutter Suppression and Multitarget Detection in a DVB-T-Based Passive Radar

This paper examines the problem of suppressing the dynamic clutter and multitarget detection in a digital video broadcasting-terrestrial (DVB-T)-based passive bistatic radar (PBR). A two-step low-complexity clutter suppression method is presented to attenuate the nonstationary multipath/clutter in a multiple-frequency network. In the first step, we estimate the multipath signals, as orthogonal frequency-division multiplexing channel coefficients, in a symbolwise approach. The variation of the clutter signal is tracked, using the complex exponential basis expansion model, in the second step. Then, the estimated multipath/clutter signals are subtracted from the received signals. An iterative algorithm is also proposed for detecting targets sequentially in a multitarget scenario. The performance of the proposed method is derived analytically, and a criterion is suggested for comparing different clutter cancellation schemes. The resulting solution is shown to be more efficient than other methods in terms of time and memory complexities.

Structured Distributed Compressive Channel Estimation Over Doubly Selective Channels

For an orthogonal frequency-division multiplexing (OFDM) system over a doubly selective (DS) channel, a large number of pilot subcarriers are needed to estimate the numerous channel parameters, resulting in low spectral efficiency. In this paper, by exploiting temporal correlation of practical wireless channels, we propose a highly efficient structured distributed compressive sensing (SDCS) based joint multi-symbol channel estimation scheme. Specifically, by using the complex exponential basis expansion model (CE-BEM) and exploiting the sparsity in the delay domain within multiple OFDM symbols, we turn to estimate jointly sparse CE-BEM coefficient vectors rather than numerous channel taps. Then a sparse pilot pattern within multiple OFDM symbols is designed to obtain an ICI-free structure and transform the channel estimation problem into a joint-block-sparse model. Next, a novel block-based simultaneous orthogonal matching pursuit (BSOMP) algorithm is proposed to jointly recover coefficient vectors accurately. Finally, to reduce the CE-BEM modeling error, we carry out smoothing treatments of already estimated channel taps via piecewise linear approximation.Simulation results demonstrate that the proposed channel estimation scheme can achieve higher estimation accuracy than conventional schemes, although with a smaller number of pilot subcarriers.

A Channel Estimation Method for OFDM Based Wireless Communication System in High Speed Environment

This paper investigates the channel estimation in an Orthogonal Frequency Division Multiplexing system under a fast-varying channel, by exploiting a frequency shifted complex exponential basis expansion models (CE-BEM). The conventional CE-BEM model suffers from power leakage and consequential modelling error floor, especially at the channel boundaries. The proposed BEM model reduces the leakage power efficiently by exploiting a fractional frequency on the coefficients of CE-BEM matrix. Numerical results show that the performance of the proposed channel modeling and coefficients estimation method are robust against various normalized Doppler frequency. The modeling error at the channel boundaries can be reduced substantially.

Compressed Channel Estimation With Position-Based ICI Elimination for High-Mobility SIMO-OFDM Systems

Orthogonal frequency-division multiplexing (OFDM) is widely adopted for providing reliable and high-data-rate communication in high-speed train (HST) systems. However, with increasing train mobility, the resulting large Doppler shift introduces intercarrier interference (ICI) in OFDM systems and greatly degrades channel estimation accuracy. Therefore, it is necessary and important to investigate reliable channel estimation and ICI mitigation methods in high-mobility environments. In this paper, we consider a typical HST communication system and show that the ICI caused by large Doppler shifts can be mitigated by exploiting the train position information and the sparsity of the basis expansion model (BEM)-based channel model. Then, we show that for the complex-exponential BEM (CE-BEM)-based channel model, the ICI can be completely eliminated to get the ICI-free pilots at each receive antenna. After that, we propose a new pilot pattern design algorithm to reduce system coherence to improve the compressed-sensing-based channel estimation accuracy. The proposed optimal pilot pattern is independent of the number of receive antennas, the Doppler shifts, train position, or train speed. Simulation results confirm the effectiveness of the proposed scheme in high-mobility environments. The results also show that the proposed scheme is robust to the speed of the moving train.

Basis expansion model for channel estimation in LTE-R communication system

This paper investigates fast time-varying channel estimation in LTE-R communication systems. The Basis Expansion Model (BEM) is adopted to fit the fast time-varying channel in a high-speed railway communication scenario. The channel impulse response is modeled as the sum of basis functions multiplied by different coefficients. The optimal coefficients are obtained by theoretical analysis. Simulation results show that a Generalized Complex-Exponential BEM (GCE-BEM) outperforms a Complex-Exponential BEM (CE-BEM) and a polynomial BEM in terms of Mean Squared Error (MSE). Besides, the MSE of the CE-BEM decreases gradually as the number of basis functions increases. The GCE-BEM has a satisfactory performance with the serious fading channel.

Channel Estimation for Time-Varying MIMO Relay Systems

In this paper, we investigate the channel estimation problem for multiple-input multiple-output (MIMO) relay communication systems with time-varying channels. The time-varying characteristic of the channels is described by the complex-exponential basis expansion model (CE-BEM). We propose a superimposed channel training algorithm to estimate the individual first-hop and second-hop time-varying channel matrices for MIMO relay systems. In particular, the estimation of the second-hop time-varying channel matrix is performed by exploiting the superimposed training sequence at the relay node, while the first-hop time-varying channel matrix is estimated through the source node training sequence and the estimated second-hop channel. To improve the performance of channel estimation, we derive the optimal structure of the source and relay training sequences that minimize the mean-squared error (MSE) of channel estimation. We also optimize the relay amplification factor that governs the power allocation between the source and relay training sequences. Numerical simulations demonstrate that the proposed superimposed channel training algorithm for MIMO relay systems with time-varying channels outperforms the conventional two-stage channel estimation scheme.

Blind multipath time varying channel estimation using recursive Cholesky update

This paper proposes a simple and high performance least square solver using recursive update of modified Cholesky factors. While most of the methods require inversion of correlation matrix, the proposed method is based on recursive updating of the modified Cholesky factors of correlation matrix and linear prediction error to estimate time varying channel coefficient, without finding the correlation matrix. Blind channel estimation of time varying channel is considered for a SIMO system using only second order statistics (SoS) of the data. The time varying channel is described by complex exponential basis expansion model (CE-BEM). The performance of the proposed method is evaluated by simulation results to demonstrate its effectiveness.

ICI Self-Cancellation With Cosine Windowing in OFDM Transmitters Over Fast Time-Varying Channels

We propose the application of cosine windowing for the orthogonal frequency-division multiplexing (OFDM) systems to self-cancel intercarrier interference (ICI) in fast time-varying channels prior to receptions. With a time-domain cosine window immediately after the inverse discrete Fourier transform (IDFT) unit in OFDM transmitters, the ICI fractions from adjacent subcarriers significantly cancel one another at the expense of the orthogonality violation among subcarriers in the main lobe. As a result, the frequency-domain channel matrix reshaped by the cosine windowing can be closely approximated to a strictly banded matrix. In the complex exponential basis expansion model (CE-BEM), we present the estimation of the channel matrix with the assistance of the pilot clusters. Simulation results show that the receivers implementing the CE-BEM channel estimation and the low-complexity block turbo minimum mean square error (MMSE) equalization perform with considerably lower bit error rates (BER) even in very fast time-varying channels.

Dynamic Individual Channel Estimation for One-Way Relay Networks With Time-Multiplexed-Superimposed Training

In this paper, we design a time-multiplexed superimposed training (TMST) scheme to estimate the individual channels in amplify-and-forward one-way relay networks (OWRNs) under a doubly selective channel scenario, where the two-phase zero-prefixed block transmission scheme is adopted. The complex-exponential basis expansion model (CE-BEM) is utilized to approximate the channel of each individual hop and results in a coefficient vector with much smaller size, called in-BEM-CV. The channel estimation of the individual channel is then converted into the estimation of in-BEM-CVs. We develop an estimation algorithm with three steps: the standard least squares (LS) estimator, the time domain or the fast Fourier transform (FFT)-based decoupler, and the iterative LS-based refiner. We also optimize the training parameters, including the number, the position, and the power allocation of the pilot clusters by minimizing the estimation mean square error (MSE), and derive one performance lower bound for the proposed algorithm. Finally, numerical results are provided to corroborate the proposed studies.

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.

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.