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Aiming at the problem that existing channel estimation methods are unable to track the channel parameter variations within a single frame under continuous Doppler spread channel (CoDSC) which leads to serious estimation errors, this paper proposes a basis expansion model (BEM) orthogonal time frequency space (OTFS) channel estimation method based on Cluster-Pruning Stagewise Weak Orthogonal Matching Pursuit (CP-SWOMP). This method first uses a discrete prolate spheroidal sequences (DPSS) as a basis function to model the channel response, converting the underdetermined channel estimation into a sparse reconstruction problem with basis coefficients. Then the basis coefficients are solved for using compressed sensing methods, the nearest neighbor clustering criterion is introduced into the Stagewise Weak Orthogonal Matching Pursuit (SWOMP) algorithm, and the atoms of the iterative intermediate process are subjected to a quadratic pruning operation, which solves the redundancy problem of the support set and improves the reconstruction accuracy. In this paper, multiple methods are simulated and validated at different normalized Doppler frequency, and the results demonstrate that the proposed method can achieve better normalized mean square error (NMSE) and bit error rate (BER) performance with less pilot overhead. [ABSTRACT FROM AUTHOR]

Summary: This paper introduces the concept of spatial and media‐based modulated (SMBM) orthogonal frequency division multiplexing (OFDM) as a potential candidate for highly mobile next generation beyond 5G (B5G) wireless communications. The proposed SMBM‐OFDM technique utilizes not only the transmit antenna and channel state indices but also OFDM subcarriers to improve the system performance under high mobility. In addition, this study sheds light on challenging fast time‐varying channel estimation problem of MBM‐based systems by using the linear minimum mean square error (LMMSE) approach due to its optimality to investigate the achievable system performance with the aid of basis expansion modeling. The minimum lower bound on the channel estimation error (Bayesian Cramer–Rao bound) is derived theoretically and shown to be attainable by the considered LMMSE estimator. Moreover, symbol detection performance is provided for different modulation types and higher mobile velocities. Simulation results demonstrate that SMBM‐OFDM system under high mobility is able to provide around 12‐dB performance gains in terms of both channel estimation and symbol detection error compared to conventional spatial modulation (SM)‐OFDM systems without MBM. The presented framework is important due to addressing the high mobility support of SMBM‐OFDM systems for B5G wireless communications in terms of achievable channel estimation and data detection performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose three new compressive sensing-based algorithms for channel estimation in millimeter wave hybrid MIMO systems over doubly (time and frequency) selective channels. Utilizing the basis expansion model (BEM) for effectively representing doubly selective channels, we first propose a BEM-based block orthogonal matching pursuit (BBOMP) algorithm, which can work with any training sequence structure. Next, we present the second algorithm to reduce the complexity of the BBOMP method by employing a special training sequence which results in a computationally efficient block sparse sensing matrix. Finally, in order to further decrease the computational complexity, we propose the third algorithm, where the channel estimation is split into two separate steps of tap detection and gain estimation. The proposed algorithms exploit the entire available training sequence to estimate all channel parameters, and can capture channel variations across the entire training frames without requiring a feedback channel. The Cramer-Rao lower bound and the computational complexity of the proposed algorithms are also addressed. Intensive computer simulations are conducted to evaluate the accuracy of the proposed approaches, showing that they can significantly improve the mean squared error performance compared with the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

The channel estimation and data detection of orthogonal frequency-division multiplexing with index modulation in doubly selective channels is a challenging problem due to the large number of channel parameters and the severe inter-carrier interference. In this paper, an iterative channel estimation and data detection scheme is proposed with the aid of the recent compressed sensing algorithm of approximate message passing (AMP). The time-varying channel is first approximated by basis expansion model (BEM) to reduce the number of channel parameters to be estimated, and AMP is utilized to estimate the BEM coefficients based on the pilot signals and soft information of data from the decoder. The channel is then reconstructed from the estimated BEM coefficients, and AMP is also employed to recover the transmit data based on the estimated channel and soft information of data from the decoder. The soft information of AMP detector is further sent to the decoder, which feeds soft information to both AMP estimator and AMP detector. To address the undesired measurement matrix in both channel estimation and data detection, two variants of AMP, i.e., damped AMP and vector AMP (VAMP), are utilized as practical estimator and/or detector here. Moreover, in both damped AMP/VAMP estimator and detector, the efficient utilization of soft data information is presented. Finally, simulation results are given to verify the performance of the proposed receiver.

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.

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.

In interference channels, channel state information (CSI) can be exploited to reduce the interference signal dimensions, and thus, achieve the optimal capacity scaling, i.e., degrees of freedom, promised by the interference alignment technique. However, imperfect CSI, due to channel estimation error, imperfect CSI feedback and time selectivity of the channel, lead to a performance loss. In this paper, we propose a novel limited feedback algorithm for single-input single-output interference alignment in time-variant channels. The feedback algorithm encodes the channel evolution in a small number of subspace coefficients, which allow for reduced-rank channel prediction to compensate for the channel estimation error due to time selectivity of the fading process and feedback delay. An upper bound for the rate loss caused by feedback quantization and channel prediction is derived. Based on this bound, we develop a dimension switching algorithm for the reduced-rank predictor to find the best tradeoff between quantization and prediction error. Besides, we characterize the scaling of the required number of feedback bits in order to decouple the rate loss due to channel quantization from the transmit power. Simulation results show that a rate gain over the traditional nonpredictive feedback strategy can be secured and a $60\%$ higher rate is achieved at 20-dB signal-to-noise ratio with moderatesxst mobility. [ABSTRACT FROM PUBLISHER]

Reliable underwater acoustic (UWA) communications are challenging since the channels are well known to be doubly selective in both time and frequency domains. The doubly-selective fading UWA channels, however, also provide double diversity gains. In addition, multiple transducers and/or hydrophones are often deployed, providing space diversity to combat channel fading. To exploit all these diversities, a differential multiple-input–multiple-output (MIMO) scheme for doubly-selective fading channels is presented in this paper. The proposed differential orthogonal space-time block coding (DOSTBC) approach adopts the basis expansion model (BEM) to capture the channel variation in time domain. Both analytical and simulated results show that the proposed BEM–DOSTBC approach is reliable by collecting 3-D diversity: space, multipath, and Doppler. The proposed approach was tested during the RACE08 sea experiment and its reliability was confirmed by the experiment results. [ABSTRACT FROM AUTHOR]

Current communication standards are designed to operate under either frequency or time selectivity. However, the rising demand of higher data rates combined with the mobility of the transceivers has led to the necessity of transmitting under doubly selective channels. In these channels, both single-carrier and multi-carrier approaches find high interference conditions, where the performance in terms of spectral efficiency and bit error rate is low. The state-of-the-art solutions involve high complexity and/or low compatibility making them infeasible. In this paper, a modified orthogonal frequency-division multiplexing (OFDM) communication system based on the virtual decomposition of the channel is proposed. The system is fully compatible with the standard OFDM transmitters and maintains several blocks of the standard OFDM receivers. This novel system substantially surpasses the performance of current approaches while requiring low computational complexity. [ABSTRACT FROM PUBLISHER]

This correspondence presents an alternate approach for the simulation of basis expansion model (BEM) for channel fading, in which each time-varying BEM coefficient is considered to be governed by the first-order autoregressive (AR1) process. To introduce a high degree of uncorrelation among the BEM coefficients, the Markov parameter of each AR1 process is also assumed to be time-varying according to another independent stationary ergodic AR1 process, which forms the base of BEM-AR1-AR1 paradigm. The simulation results manifest that the proposed BEM-AR1-AR1 scheme is in close agreement with the ideal BEM for slow as well as fast channel fading, which may find applications in the time-varying channel estimation due to its compatibility with model based adaptive algorithms. [ABSTRACT FROM AUTHOR]

A BEM-based low-complexity channel estimation algorithm with analytical solution is proposed over rapidly time-varying channels for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The time-varying channel taps are estimated with the aid of the designed clustered frequency-multiplexed pilots across different antennas along with basis expansion model (BEM). The proposed approach is specifically designed for MIMO OFDM systems over doubly selective channels. For each subchannel, the derived BEM coefficients can be expressed by explicit analytical solution, whose calculations are partitioned into two steps. During the two steps, two different basis functions such as the critically sampled complex exponential (CCE)-BEM and P-BEM are adopted, respectively. For a MIMO system with $$N_T$$ transmit antennas, $$N_R$$ receive antennas and $$L$$ channel taps, the complexity order of the proposed channel estimation is $$O(N_T N_R L\log L)$$ , whereas the complexity order of least squares (LS) estimation is $$O((N_T N_R L)^3)$$ . Additionally, the proposed channel estimation can be iteratively improved in conjunction with hybrid interference cancelation, with only requiring one iteration. Simulation results corroborate the performance advantages of the proposed solution over CCE-BEM based LS scheme under different normalized Doppler spreads. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Modern communication systems are based on orthogonal frequency division multiplexing (OFDM). They are designed for dealing with frequency selective channels considering invariance within the time-span of an OFDM symbol. However, this assumption is no longer valid when the transceivers operate in higher mobility scenarios or higher carrier frequencies. This condition provokes inter-carrier interference (ICI) that greatly degrades system performance. State-of-the-art approaches that satisfactorily mitigate this problem have a complexity of O(N^3), which makes them infeasible with current technology. In this paper, a novel channel estimation algorithm to cope with this problem is presented. It is based on a subspace approach using two-dimensional Prolate functions, achieving a complexity of only O(N^2). It depends only on the maximum delay spread and maximum Doppler spread while being robust in the sense that it is independent of the particular channel scattering function. Performance analysis of the proposed algorithm is presented. Simulation results under the WiMAX standard show that this algorithm improves previous results, achieving a bit error rate (BER) close to the one obtained with perfect channel state information (CSI) in very-fast transceiver mobility, as high as 874 Km/h over a 2.4 Ghz carrier frequency. [ABSTRACT FROM PUBLISHER]

This letter considers the channel estimation for subband orthogonal frequency division multiple access (OFDMA) operating over highly time-frequency selective (i.e., doubly selective) channels. Based on general basis expansion model, two expectation maximization-type channel estimation methods are proposed for subband OFDMA in order to overcome channel time-frequency selectivity. The proposed method is compared with conventional approach and is shown to be superior to the conventional one. [ABSTRACT FROM AUTHOR]

In orthogonal frequency division multiplexing systems, significant inter-carrier interference (ICI) caused by doubly selective channels make challenge for reliable reception. In this paper, channel estimation and ICI cancellation are considered jointly. Relying on the basis expansion model (BEM) of time-varying channel, the linear system model of transceiver is established, and the corresponding joint optimization of the transmitted data and BEM coefficients is formulated. Due to the separability of the data and BEM coefficients, we use cyclic minimizing technique to perform channel estimation and equalization alternately. This yields a linear minimum mean square-error (LMMSE) channel estimator and a block MMSE equalizer respectively. The block MMSE equalizer has complexity O( N), where N is the number of data subcarriers. To reduce the complexity, instead of equalizing all the data simultaneously, we consider estimating each data symbol successively. This idea results in the per subcarrier interference canceller with lower complexity O( N). Finally, an iterative receiver consisting of the data-aided LMMSE channel estimator and the successive interference canceller is developed. Simulation results show the scheme is effective over the channel with relatively large Doppler spread. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new joint carrier frequency offset (CFO) and channel estimation algorithm for Amplify-and-Forward (AF) cooperative (CO)-OFDM systems. An expanded Basis Expansion Model (E-BEM) is proposed for time variant multipath channels. Based on the E-BEM, a joint OFDM channel estimation and synchronization method is derived. We also apply the space-frequency-block-code (SFBC) to AF CO-OFDM systems. Simulation results reveal that the proposed joint algorithm works well, leading to considerable gains of overall performance. [ABSTRACT FROM AUTHOR]

We propose a novel equalization method for doubly selective wireless channels, whose taps are represented by an arbitrary Basis Expansion Model (BEM). We view such a channel in the time domain as a sum of product-convolution operators created from the basis functions and the BEM coefficients. Equivalently, a frequency-domain channel can be represented as a sum of convolution-products. The product-convolution representation provides a low-complexity, memory efficient way to apply the channel matrix to a vector. We compute a regularized solution of a linear system involving the channel matrix by means of the GMRES and the LSQR algorithms, which utilize the product-convolution structure without ever explicitly creating the channel matrix. Our method applies to all cyclic-prefix transmissions. In an OFDM transmission with K subcarriers, each iteration of GMRES or LSQR requires only \cal O(K\log K) flops and \cal O(K) memory. Additionally, we further accelerate convergence of both GMRES and LSQR by using the single-tap equalizer as a preconditioner. We validate our method with numerical simulations of a WiMAX-like system (IEEE 802.16e) in channels with significant delay and Doppler spreads. The proposed equalizer achieves BERs comparable to those of MMSE equalization, and noticeably outperforms low-complexity equalizers using an approximation by a banded matrix in the frequency domain. With preconditioning, the lowest BERs are obtained within 3–16 iterations. Our approach does not use any statistical information about the wireless channel. [ABSTRACT FROM PUBLISHER]

This paper introduces a novel method to estimate fractional carrier frequency offset (CFO) under time-varying multipath channels in OFDM systems based on the approximation of Basis Expansion Model (BEM). Due to the symmetrical character of the BEM basis, we propose a new design of training sequence with trailing zeros. This training sequence can be used at the receiver to estimate the frequency offset without channel estimation only in one OFDM symbol. We also compare our method with Beek’s ML estimator and Lv’s fine synchronization estimator. The numerical results demonstrate that the proposed method provides an improved performance when the training sequence has a short length. [ABSTRACT FROM AUTHOR]

In this paper, we present a single-carrier transceiver for rapidly time-varying channels, where the equalization step is implemented in the frequency domain. When the channel abides with both fast fading and severe inter-block interference, our equalizer relies on a band approximation of the frequency-domain channel matrix to maintain low complexity. We will show that the band approximation error can be associated in the time domain to a critically-sampled complex exponential basis expansion modeling error. Based on this property, we propose a novel receiver architecture that extends the original data model by inserting zeros at the receiver. The resulting effective channel can be characterized by an oversampled complex exponential basis expansion model, which has a considerably reduced modeling error compared to the critically-sampled one. In other words, the band assumption that is essential to the equalizer will be made more accurate and thus the equalization performance can be improved. [ABSTRACT FROM AUTHOR]

In this paper, we deal with channel estimation for orthogonal frequency-division multiplexing (OFDM) systems. The channels are assumed to be time-varying (TV) and approximated by a basis expansion model (BEM). Due to the time-variation, the resulting channel matrix in the frequency domain is no longer diagonal, but approximately banded. Based on this observation, we propose novel channel estimators to combat both the noise and the out-of-band interference. In addition, the effect of a receiver window on channel estimation is also studied. Our claims are supported by simulation results, which are obtained considering Jakes' channels with fairly high Doppler spreads [ABSTRACT FROM PUBLISHER]

We propose a time-varying (TV) finite impulse response (FIR) equalizer for doubly selective (time- and frequency-selective) channels. We use a basis expansion model (BEM) to approximate the doubly selective channel and to design the TV FIR equalizer. This allows us to turn a complicated equalization problem into an equivalent simpler equalization problem, containing only the BEM coefficients of both the doubly selective channel and the TV FIR equalizer. The minimum mean-square error (MMSE) as well as the zero-forcing (ZF) solutions are considered. Comparisons with the block linear equalizer (BLE) are made. The TV FIR equalization we propose here unifies and extends many previously proposed serial equalization approaches. In contrast to the BLE, the proposed TV FIR equalizer allows a flexible tradeoff between complexity and performance. Moreover, through computer simulations, we show that the performance of the proposed MMSE TV FIR equalizer comes close to the performance of the ZF and MMSE BLE, at a point where the design as well as the implementation complexity are much lower. [ABSTRACT FROM PUBLISHER]

In this letter, a jamming resilient communication technique for unmanned aircraft vehicle (UAV) is proposed. Multiple-input multiple-output (MIMO) interference cancellation is exploited to combat reactive jamming. An improved channel estimation algorithm based on Kalman filter and basis expansion model (BEM) is used to track the quick changes of the combined channel components. Simulation results show that the performance of the proposed technique is significantly better than the existing jamming resilient communication technique. [ABSTRACT FROM PUBLISHER]

In wireless communications, knowledge of the radio channel is essential for channel equalization at the receiver side. Time-variant frequency-selective (doubly-selective) radio channels are typically tracked over time by using basis expansion model (BEM). The BEM models time variations by using the Doppler bandwidth, caused by the relative movement of receiver and transmitter/scatterers in a multipath environment. Tracking accuracy of the BEM relies on the use of the basis functions and the information of the Doppler bandwidth, e.g. use of discrete prolate spheroidal (DPS) sequences provides good accuracy but require high computational effort to generate DPS sequences. We present optimum BEM based on complex exponentials (CEs), computationally simple basis functions, which is able to track doubly-selective radio channels with accuracy better than other BEM variants. The analytical approach is confirmed by the simulation results for mobility up to 700 km/h in LTE-downlink. A novel method is also presented which does not require prior knowledge of the Doppler bandwidth for tracking doubly-selective radio channels yet providing results close to the proposed optimum BEM. [ABSTRACT FROM AUTHOR]

Combating time and frequency selectivity in wireless channels is one of the most challenging tasks in next generation wireless networks. In this paper, we propose an adaptive estimation algorithm to estimate Doppler shifts in a direct sequence code division multiple access (DS-CDMA) radio system with multiple Doppler subpaths. By modeling doubly selective channels using a basis expansion model (BEM), an expectation-maximization (EM) algorithm based adaptive estimation method is developed to extract accurate Doppler shift information. The Cramer-Rao lower bound (CRLB) analysis is conducted to study the performance bound of the proposed estimation algorithm. Based on the estimated Doppler shift results, a frequency domain equalizer (FDE) based receiver architecture is developed to exploit Doppler diversity in the frequency domain. Our analysis and simulation results demonstrate that this receiver architecture features a low complexity while still achieving a good performance compared with traditional CDMA receivers. [ABSTRACT FROM AUTHOR]

We propose a novel pilot-aided algorithm for estimation of rapidly varying wireless channels in OFDM systems. Our approach is specifically designed for channels varying on the scale of a single OFDM symbol duration, which occur, for example, in mobile WiMAX, WAVE, and DVB-T. From the pilot information, we recover information about the channel taps in the framework of the Basis Expansion Model (BEM). We derive explicit formulas for the BEM coefficients in terms of the receive signal. Algebraically, the algorithm is FFT-based, and can be easily implemented in hardware. For a system with L channels taps, our method uses \cal O(L log L) operations and \cal O(L) memory per OFDM symbol. This complexity is the best possible up to the order of magnitude. Previously published methods require \cal O(L^2) operations and \cal O(L^2) memory. Numerical simulations illustrate performance gains achieved by our estimator at sufficiently high Doppler frequencies. Our approach does not assume any prior statistical information. [ABSTRACT FROM AUTHOR]

In this paper, channel estimation and training sequence design are considered for amplify-and-forward (AF)-based two-way relay networks (TWRNs) in a time-selective fading environment. A new complex-exponential basis expansion model (CE-BEM) is proposed to represent the mobile-to-mobile time-varying channels. To estimate such channels, a novel pilot symbol-aided transmission scheme is developed such that a low complex linear approach can estimate the BEM coefficients of the convoluted channels. More essentially, two algorithms are designed to extract the BEM coefficients of the individual channels. The optimal training parameters, including the number of the pilot symbols, the placement of the pilot symbols, and the power allocation to the pilot symbols, are derived by minimizing the channel mean-square error (MSE). The selections of the system parameters are thoroughly discussed in order to guide practical system design. Finally, extensive numerical results are provided to corroborate the proposed studies. [ABSTRACT FROM PUBLISHER]