Abstract—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. Index Terms—Channel estimation, optimal training design, time-varying channel, two-way relay network, basis expansion model. I.

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.

We consider the estimation of doubly selective wireless channels within pulseshaping multicarrier systems (which include OFDM systems as a special case). A pilot-assisted channel estimation technique using the methodology of compressed sensing (CS) is proposed. By exploiting a channel’s delay-Doppler sparsity, CS-based channel estimation allows an increase in spectral efficiency through a reduction of the number of pilot symbols that have to be transmitted. We also present an extension of our basic channel estimator that employs a sparsity-improving basis expansion. We propose a framework for optimizing the basis and an iterative approximate basis optimization algorithm. Simulation results using three different CS recovery algorithms demonstrate significant performance gains (in terms of improved estimation accuracy or reduction of the number of pilots) relative to conventional least-squares estimation, as well as substantial advantages of using an optimized basis.

Joint time-variant channel estimation and multiuser detection are key building-blocks for wireless broadband communication for mobile users at vehicular speed. We propose an iterative receiver for a multi-carrier (MC) code division multiple access (CDMA) system in the uplink. Multi-user detection is implemented through iterative parallel interference cancelation and conditional linear minimum mean square error (MMSE) filtering. MC-CDMA is based on orthogonal frequency division multiplexing (OFDM), thus time-variant channel estimation can be performed for every subcarrier individually. The variation of a subcarrier over the duration of a data block is upper bounded by the maximum Doppler bandwidth which is determined by the maximum velocity of the users. We exploit results from the theory of time-concentrated and bandlimited sequences and apply a Slepian basis expansion for time-variant subcarrier estimation. This approach enables time-variant channel estimation without complete knowledge of the second-order statistics of the fading process. The square bias of the Slepian basis expansion is one order of magnitude smaller compared to the Fourier basis expansion. The square bias of the basis expansion is the determining factor for the performance of the iterative joint channel estimation and data detection. We present an iterative linear MMSE estimation algorithm for the basis expansion coefficients in a multi-user system. The consistent performance of the iterative receiver using the Slepian basis expansion is validated by simulations for a wide range of velocities.

This paper considers affine cyclic-prefixed blockbased pilot-aided transmission (PAT) over the single-antenna doubly selective channel, where the channel is assumed to obey a complex-exponential basis expansion model. First, a tight lower bound on the mean-squared error (MSE) of pilot-aided channel estimates is derived, along with necessary and sufficient conditions on the pilot/data pattern that achieves this bound. From these conditions, novel minimum-MSE (MMSE) PAT schemes are proposed and upper/lower bounds on their ergodic achievable rates are derived. A pilot/data power allocation technique is also developed. A high-SNR asymptotic analysis of the ergodic achievable rate of affine MMSE-PAT is then performed which suggests that the channel’s spreading parameters should be taken into account when choosing among affine MMSE-PAT schemes. Specifically, we establish that multicarrier MMSE-PAT achieves higher rates than single-carrier MMSE-PAT when the channel’s delay-spread dominates its Doppler-spread, and vice versa.

We derive bounds on the noncoherent capacity of wide-sense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel’s delay spread and Doppler spread is small. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channel’s scattering function, are accurate for a large range of bandwidth and allow to coarsely identify the capacity-optimal bandwidth as a function of the peak power and the channel’s scattering function. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of large bandwidth, and show that our bounds are tight in the wideband regime. For input signals that are peak constrained in time only (and, hence, allowed to be peaky in frequency), we provide upper and lower bounds on the infinite-bandwidth capacity and find cases when the bounds coincide and the infinite-bandwidth capacity is characterized exactly. Our lower bound is closely related to a result by Viterbi (1967). The analysis in this paper is based on a discrete-time discrete-frequency approximation of WSSUS time- and frequency-selective channels. This discretization explicitly takes into account the underspread

In this paper, we develop and analyze the basic methodology for minimum-energy (ME) band-limited prediction of sampled time-variant flat-fading channels. This predictor is based on a subspace spanned by time-concentrated and bandlimited sequences. The time-concentration of these sequences is matched to the length of the observation interval and the bandlimitation is determined by the support of the Doppler power spectral density of the fading process. Slepian showed that discrete prolate spheroidal (DPS) sequences can be used to calculate the ME band-limited continuation of a finite sequence. We utilize this property to perform channel prediction. We generalize the concept of time-concentrated and band-limited sequences to a band-limiting region consisting of disjoint intervals. For a fading process with constant spectrum over its possibly discontiguous support we prove that the ME band-limited predictor is identical to a reduced-rank maximum-likelihood predictor which is a close approximation of a Wiener predictor. In current cellular communication systems the time-selective fading process is highly oversampled. The essential dimension of the subspace spanned by time-concentrated and band-limited sequences is in the order of two to five only. The prediction error mainly depends on the support of the Doppler spectrum. We exploit this fact to propose low-complexity time-variant flat-fading channel predictors using dynamically selected predefined subspaces. The subspace selection is based on a probabilistic bound on the reconstruction error. We compare the performance of the ME band-limited predictor with a predictor based on complex exponentials. For a prediction horizon of one eights of a wavelength the numerical simulation

In this paper, we propose several methods for the pilot-aided estimation of significant ICI coefficients resulting from pulse-shaped multicarrier modulation (PS-MCM) over DD channels. Specifically, we outline Wiener and reduced-rank (RR) Wiener estimation schemes that leverage statistical channel structure, as well as deterministic least-squares (LS) schemes based on basis expansion modeling (BEM). We then report the results of a numerical study which suggests that RR Wiener estimation outperforms LS estimation based on polynomial and oversampled complex exponential BEM, even under significant statistical mismatch. In addition, the RR Wiener estimator is computationally cheaper than the LS-BEM techniques. These findings have implications on the practical design of PS-MCM channel estimation schemes.

We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of such computationally hard problems to the classical spin glass problems. The quantum spin glass problems arise with the introduction of quantum

This paper presents an iterative receiver for