Basis Expansion Model Research Articles

Sparse Channel Estimation for Massive MIMO-OFDM Systems Over Time-Varying Channels

For downlink orthogonal frequency division multiplexing-based massive multiple-input-multiple-output transmission over the time-varying channel, channel estimation is very challenging due to numerous channel coefficients to be estimated. To track this problem, this paper proposes a novel sparse channel estimation scheme, exploiting the sparsity in the delay domain and the high correlation in the spatial domain. By utilizing the basis expansion model (BEM) to model the time variation and the generalized-spatial BEM to model the spatial correlation, we are able to significantly reduce the number of the coefficients to be estimated. Then, the channel estimation is formulated into a compressive sensing problem with a quasi-block-sparse matrix to be recovered. Motivated by the quasi-block sparsity, a novel quasi-block simultaneous orthogonal matching pursuit (QBSO) algorithm is developed to recover the channel, which seeks nonzero channel tap positions at the first stage and calculates the channel coefficients at the second stage. Moreover, an adaptive-QBSO algorithm is further designed to improve the recovery accuracy, where the measurement matrix is adaptively designed based on the estimated virtual angle of departure, and thus, the sparsity representation can be strengthened. We also discuss the design of pilot pattern including pilot values and positions. Simulation results are provided to validate the effectiveness of our proposed channel estimation scheme.

Channel Estimation With Expectation Maximization and Historical Information Based Basis Expansion Model for Wireless Communication Systems on High Speed Railways

This paper proposes a blind channel estimator based on expectation maximization algorithm and historical information-based basis expansion model for uplink wireless communication systems on high speed railways. The information of basis matrices is obtained from the uplink data of the past trains at the base station (BS). With the known basis matrices at the BS, our suggested estimator can estimate the basis coefficients and recover the channel parameters without requiring training symbols. The modified Cramer–Rao bound is derived for the estimated basis coefficients and the computational complexity of the proposed estimator is analyzed. Numerical results are then provided to corroborate our studies. It is shown that the proposed estimator outperforms existing data-aided estimators, including least square and linear minimum mean square error.

Equalization Techniques of Control and Non-Payload Communication Links for Unmanned Aerial Vehicles

In the next years, several new applications involving unmanned aerial vehicles (UAVs) for public and commercial uses are envisaged. In such developments, since UAVs are expected to operate within the public airspace, a key issue is the design of reliable control and non-payload communication (CNPC) links connecting the ground control station to the UAV. At the physical layer, CNPC design must cope with timeand frequency-selectivity (so-called double selectivity) of the wireless channel, due to lowaltitude operation and flight dynamics of the UAV. In this paper, we consider the transmission of continuous phase modulated (CPM) signals for UAV CNPC links operating over doubly-selective channels. Leveraging on the Laurent representation for a CPM signal, we design a two-stage receiver: the first one is a linear time-varying (LTV) equalizer, synthesized under either the zero-forcing (ZF) or minimum mean-square error (MMSE) criterion; the second one recovers the transmitted symbols from the pseudo-symbols of the Laurent representation in a simple recursive manner. In addition to LTV-ZF and LTV-MMSE equalizers, their widely-linear versions are also developed, to take into account the possible noncircular features of the CPM signal. Moreover, relying on a basis expansion model of the doubly-selective channel, we derive frequencyshift versions of the proposed equalizers, by discussing their complexity issues and proposing simplified implementations. Monte Carlo numerical simulations show that the proposed receiving structures are able to satisfactorily equalize the doubly-selective channel in typical UAV scenarios.

Compressed Sensing Based Recursive Estimation of Doubly-Selective Channels for High-Mobility OFDM Systems

For an orthogonal frequency-division multiplexing (OFDM) system in high-mobility applications, channel suffers from both frequency-selective and time-selective fading introduced by Doppler shift. Large pilot overhead is needed to estimate the numerous parameters of doubly-selective channel, resulting in low-spectral efficiency. In this paper, considering the correlation of practical wireless channels in high-dimensional signal spaces, a recursive channel estimation scheme based on compressed sensing (CS) is proposed for high-mobility OFDM systems to reduce the pilot overhead. Specifically, by exploiting the sparsity of OFDM channel in basis expansion model (BEM), the sparse BEM coefficients is estimated instead of numerous channel taps. Then we theoretically verify that the BEM coefficients corresponding successive OFDM symbols also share a common support. To utilize this temporal correlation of BEM coefficients, a recursive channel estimation algorithm derived from the classical modified CS algorithm is proposed to improve the present estimation by prior channel information from previous estimation. Theoretical and simulation results demonstrate that the proposed recursive channel estimation scheme preforms better than conventional schemes in various scenarios, even with less pilot overhead.

BEM Reference Signal Estimation for an Airborne Passive Radar Antenna Array

In this paper, we consider an airborne passive radar using digital video broadcasting—terrestrial OFDM signals. In such an application, the channel composite nature and the mobility of the receiver deeply alter the signal and, therefore, degrade the decoding processing. Classic methods experience difficulties in dealing with such channel impacts. In order to reconstruct a proper reference signal, we propose here a channel estimation method that exploits both antenna diversity and a basis expansion model modeling the channel time variations. The application of this method to experimental in-flight recorded data demonstrates the performance improvement provided by the proposed method over the classic demodulation and other methods developed to cope with intercarrier interferences.

Basis expansion model based spectral efficient channel recovery scheme for spatial‐temporal correlated massive MIMO systems

In this study, a spectral efficient channel recovery scheme is proposed for spatial-temporal correlated sparse massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing systems. By exploiting the spatial-temporal correlations of massive MIMO channels, superimposed time-frequency training sequences (TSs) are jointly utilised for accurate channel state information (CSI) acquisition. Moreover, a novel time-frequency TS pattern design scheme is proposed to improve the recovery performance based on structured compressive sensing theory. Furthermore, the discrete prolate spheroidal basis expansion model of massive MIMO channels in the space-domain is utilised to reduce the frequency-domain pilots overhead and improve the spectral efficiency. Simulation results show that the proposed scheme could achieve accurate CSI with great improvement in spectral efficiency and computational complexity.

Block Distributed Compressive Sensing-Based Doubly Selective Channel Estimation and Pilot Design for Large-Scale MIMO Systems

The doubly selective (DS) channel estimation in the large-scale multiple-input multiple-output (MIMO) systems is a challenging problem due to the large number of the channel coefficients to be estimated, which requires unaffordable and prohibitive pilot overhead. In this paper, first we conduct the analysis about the common sparsity of the basis expansion model (BEM) coefficients among all the BEM orders and all the transmit–receive antenna pairs. Then, a novel pilot pattern is proposed, which inserts the guard pilots to deal with the intercarrier interference under the superimposed pilot pattern. Moreover, by exploiting the common sparsity of the BEM coefficients among different BEM orders and different antennas, we propose a block distributed compressive sensing-based DS channel estimator for the large-scale MIMO systems. Its structured sparsity leads to the reduction of the pilot overhead under the premise of guaranteeing the accuracy of the estimation. Furthermore, taking consideration of the block structure, a pilot design algorithm referred to as block discrete stochastic optimization is proposed. It optimizes the pilot positions by reducing the coherence among different blocks of the measurement matrix. Besides, a linear smoothing method is extended to large-scale MIMO systems to improve the accuracy of the estimation. Simulation results verify the performance gains of our proposed estimator and the pilot design algorithm compared with the existing schemes.

Beam-Domain Full-Duplex Massive MIMO: Realizing Co-time Co-frequency Uplink and Downlink Transmission in the Cellular System

Co-time co-frequency uplink and downlink (CCUD) transmission was considered challenging in the cellular system due to the strong self-interference (SI) between the transmitter and receiver of base station (BS). In this paper, by investigating the beam-domain representation of channels based on the basis expansion model, we propose a beam-domain full-duplex (BDFD) massive multiple-input multiple-output (MIMO) scheme to make the CCUD transmission possible. The key idea of the BDFD scheme lies in intelligently scheduling the uplink and downlink user equipment (UE) based on the beam-domain distributions of their associated channels to mitigate SI and enhance transmission efficiency. We show that the BDFD scheme achieves significant savings in uplink/downlink training resource and achieves uplink and downlink sum capacities simultaneously as the number of BS antennas approaches infinity. The superiority of the BDFD scheme over the traditional time-division duplex (TDD)/frequency-division duplex (FDD) massive MIMO is evaluated through simulation for the macrocell environment. The results show that the spectral efficiency gain can even exceed 2 $\times$ in the specific scenarios, since the BDFD scheme utilizes the time-frequency resource more efficiently in both the training and data transmission phases.

Joint Estimation of MCFOs and Channel Gains for Two-Way Multi-Relay Systems With High Mobility

This letter proposes space-alternating generalized expectation maximization and expectation conditional maximization-based joint estimation of multiple carrier frequency offsets and channel gains for two-way relay network with multiple relays. The method iteratively updates least square estimates with less time and stable convergence. We adopt discrete prolate spheroidal and Karhunen-Loeve basis expansion models to capture rapid time variations of channel. Proposed estimators result in acceptable performance for very high user mobility (corresponds to long term evolution for railway). The derived Cramer-Rao lower bound is shown to be comparable with MSE performances.

Position-Based Interference Elimination for High-Mobility OFDM Channel Estimation in Multicell Systems

Orthogonal frequency-division multiplexing (OFDM) and multicell architecture are widely adopted in current high-speed train (HST) systems for providing high-data-rate wireless communications. In this paper, a typical multiantenna OFDM HST communication system with multicell architecture is considered, where the intercarrier interference (ICI) caused by high mobility and the multicell interference (MCI) are both taken into consideration. By exploiting the train position information, a new position-based interference elimination method is proposed to eliminate both the MCI and the ICI for a general basis expansion model. We show that the MCI and the ICI can be completely eliminated by the proposed method to get the ICI-free pilots at each receive antenna. In addition, for the considered multicell HST system, we develop a low-complexity compressed channel estimation method and consider the optimal pilot pattern design. Both the proposed interference elimination method and the optimal pilot pattern are robust to the train speed and position, as well as the multicell multiantenna system. Simulation results demonstrate the benefits and robustness of the proposed method in the multicell HST system.

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.

Time-Varying Channel Tracking for Amplify-and-Forward Relay Network in High Doppler Spread

Next generation wireless communication technologies such as wireless metropolitan area network, long-term evolution (LTE), and LTE advanced are designed to deploy cooperative relaying incorporated with orthogonal frequency division multiplexing system. In addition to the higher data rate, these technologies allow users to have a faster mobility than the previous standards. However, due to the fast movement, Doppler frequency causes the carrier frequency offset resulting in intercarrier interference. Modeling and estimating this type of channel play a vital role to fulfill the data rate requirement of the network. In this paper, we develop a high mobility channel estimation method for amplify-and-forward relay-based network. Specifically, we use basis expansion modeling (BEM) to capture the time variation of the channel. Using pilot symbols, the BEM coefficients are estimated by least square and linear minimum mean square error estimators to reconstruct the channel in both time and frequency domains. In addition to the estimators, Cramer–Rao lower bound has been derived as a benchmark of the estimation performance of the channel estimators. It has been shown that the time-domain channel estimation method is simpler and can approximate the channel more efficiently than frequency-domain estimation in very high Doppler spread scenario.

A Unified Transmission Strategy for TDD/FDD Massive MIMO Systems With Spatial Basis Expansion Model

This paper proposes a unified transmission strategy for multiuser time division duplex (TDD)/frequency division duplex (FDD) massive multiple-input–multiple-output (MIMO) systems, including uplink (UL)/downlink (DL) channel estimation and user scheduling for data transmission. With the aid of antenna array theory and array signal processing, we build a spatial basis expansion model (SBEM) to represent the UL/DL channels with far fewer parameter dimensions. Hence, both the UL and DL channel estimations of multiusers can be carried out with a small amount of training resource, which significantly reduces the training overhead and feedback cost. Meanwhile, the pilot contamination problem in the UL training is immediately relieved by exploiting the spatial information of users. To enhance the spectral efficiency, we also design a greedy user scheduling scheme during the data transmission period. Compared with existing low-rank models, the newly proposed SBEM offers an alternative for channel acquisition without the need for channel statistics and can be applied to both TDD and FDD systems. Various numerical results are provided to corroborate the proposed studies.

Orthogonal superimposed training design for doubly selective channel estimation using basis expansion models

AbstractIn this paper, we consider channel estimation for single‐carrier block transmission over doubly selective fading channel, where basis expansion models are used to describe the time‐varying channel. The affine precoding model is used as the transmission strategy, wherein the training sequence is added on the top of the precoded data prior to transmission. By enforcing a special form of orthogonality between training sequence and precoded matrix, we propose orthogonal superimposed training design for doubly selective channel that makes channel estimation decouple from symbol detection, and then the affine precoding model based on orthogonal polyphase sequence set is designed under the orthogonal conditions. To further improve the estimation performance, we exploited a joint iterative approach is used, where the detected symbols, to enhance the estimation performance. Simulations results show that the proposed scheme can yield better detection performance than the data‐dependent superimposed training and can be competitive with time‐multiplexed training scheme with higher bandwidth efficiency.

一种带有ICI自消除的多OFDM符号时变信道估计方法

高速移动环境下，由于多普勒频移增大，信道的时变性破坏了正交频分复用(Orthogonal Frequency Division Multiplexing, OFDM)系统子载波之间的正交性，从而产生子载波间干扰(Inter Carrier Interference, ICI)，导致系统性能严重下降。为了减少待估计量，通常采用基扩展模型(BEM)来近似模拟时变信道。为了提升性能，当信道的相干时间与发送码元的周期可相比拟的时候，本文采用多块(多个OFDM符号)。同时在使用导频符号对参数估计时，忽略了相邻非导频符号的ICI干扰，降低了整个时变信道下的估计准确性。因此我们通过分析子载波所产生的ICI系数变化特点，提出了一种带有ICI自消除的多OFDM符号时变信道估计方法，提高估计的准确性。但是由于基于多OFDM符号的信道估计性能在归一化多普勒频移较大时该方法成立条件不再满足，因此性能呈现明显的衰减，为了解决此问题，我们提出一种带有ICI自消除的自适应OFDM符号个数时变信道估计方法。仿真实验从误码率，归一化均方误差两方面分别验证了该方法的有效性。 In high-speed mobile environment, time-varying channel destroys the orthogonality between subcarriers of orthogonal frequency-division multiplexing (OFDM) systems, giving rise to in-ter-carrier interference (ICI), and degrading the performance of the systems. Basis expansion model (BEM) is usually used to approximate the time-varying channels to reduce the estimators. In order to improve performance, this paper adopts multi block (multiple OFDM symbols) when the coherent time of the channel variations and the symbols can be compared. However, when using pilot-symbol to parameter estimation, the ICI interference from near non-pilot-symbol is ignored, reducing its estimated accuracy of time-varying channel. And in this work the paper proposes a multiple OFDM symbols time-varying channel estimation method with ICI self-cancellation after analyzing the high correlation between subcarriers, improving the accuracy of estimation. But due to the condition of utilizing the multiple OFDM symbols channel estimation method is no longer met in large Doppler frequency shift, the performance of resulting channel estimation attenuates obviously. In order to solve this problem, we put forward a kind of adaptive OFDM symbol time-varying channel estimation method with the ICI self-cancellation. The simulation results show that the proposed method is effective from two aspects of error rate and normalized mean square error.

OFDM Receiver for Fast Time-Varying Channels Using Block-Sparse Bayesian Learning

We propose an iterative algorithm for orthogonal frequency-division multiplexing (OFDM) receivers operating over fast time-varying channels. The design relies on the assumptions that the channel response can be characterized by a few nonnegligible separable multipath components and that the temporal variation of each component gain can be well characterized with a basis expansion model (BEM) using a small number of terms. As a result, the channel estimation problem is posed as that of estimating a vector of complex coefficients that exhibits a block-sparse structure, which we solve with tools from block-sparse Bayesian learning (BSBL). Using variational Bayesian inference, we embed the channel estimator in a receiver structure that performs iterative channel and noise precision estimation, intercarrier interference (ICI) cancelation, detection, and decoding. Simulation results illustrate the superior performance of the proposed receiver over state-of-the-art receivers.

A Full-Space Spectrum-Sharing Strategy for Massive MIMO Cognitive Radio Systems

In this paper, we introduce a new spatial spectrum-sharing strategy for massive multiple-input multiple-output (MIMO) cognitive radio (CR) systems. Different from the conventional MIMO CR system, CR terminals can be discriminated by their angular information with the help of high spatial resolution of massive antennas at CR base station (CBS). Moreover, the discrete Fourier transform can be applied to efficiently obtain such angular information thanks to the massive antennas, again. We then formulate a 2-D spatial basis expansion model to represent the uplink/downlink channels of CRs with reduced parameter dimensions, which immediately alleviates the general headaches of massive MIMO systems, such as uplink pilot contamination and downlink training overhead. Moreover, we present a full-space coverage concept by employing two CBSs at the adjacent sides of each cell, which diminishes the sheltering effect from the primary radio. We also design two greedy CR scheduling algorithms for the dual CBSs to improve the spectral efficiency and enhance the scheduling probability of CRs. Since the proposed strategy exploits angular information and since the angle reciprocity holds for two frequency carriers with moderate distance, the proposed strategy is applied for both time division duplex and frequency division duplex systems.

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.