Abstract—Reliable wireless communications often requires accurate knowledge of the underlying multipath channel. This typically involves probing of the channel with a known training waveform and linear processing of the input probe and channel output to estimate the impulse response. Many real-world channels of practical interest tend to exhibit impulse responses characterized by a relatively small number of nonzero channel coefficients. Conventional linear channel estimation strategies, such as the least squares, are ill-suited to fully exploiting the inherent low-dimensionality of these sparse channels. In contrast, this paper proposes sparse channel estimation methods based on convex/linear programming. Quantitative error bounds for the proposed schemes are derived by adapting recent advances from the theory of compressed sensing. The bounds come within a logarithmic factor of the performance of an ideal channel

Abstract — This paper studies the ergodic capacity of timeand frequency-selective multipath fading channels in the ultrawideband (UWB) regime when training signals are used for channel estimation at the receiver. Motivated by recent measurement results on UWB channels, we propose a model for sparse multipath channels. A key implication of sparsity is that the independent degrees of freedom (DoF) in the channel scale sub-linearly with the signal space dimension (product of signaling duration and bandwidth). Sparsity is captured by the number of resolvable paths in delay and Doppler. Our analysis is based on a training and communication scheme that employs signaling over orthogonal short-time Fourier (STF) basis functions. STF signaling naturally relates sparsity in delay-Doppler to coherence in time-frequency. We study the impact of multipath sparsity on two fundamental metrics of spectral efficiency in the wideband/low-SNR limit introduced by Verdu: first- and second-order optimality conditions. Recent results by Zheng et. al. have underscored the large gap in spectral efficiency between coherent and non-coherent extremes and the importance of channel learning in bridging the gap. Building on these results, our results lead to the following implications of multipath sparsity: 1) The coherence requirements are shared in both time and frequency, thereby significantly relaxing the required scaling in coherence time with SNR; 2) Sparse multipath channels are asymptotically coherent — for a given but large bandwidth, the channel can be learned perfectly and the coherence requirements for first- and second-order optimality met through sufficiently large signaling duration; and 3) The requirement of peaky signals in attaining capacity is eliminated or relaxed in sparse environments. I.

Abstract—In this paper, we present various channel estimators that exploit the channel sparsity in a multicarrier underwater acoustic system, including subspace algorithms from the array precessing literature, namely root-MUSIC and ESPRIT, and recent compressed sensing algorithms in form of Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP). Numerical simulation and experimental data of an OFDM block-by-block receiver are used to evaluate the proposed algorithms in comparison to the conventional least-squares (LS) channel estimator. We observe that subspace methods can tolerate small to moderate Doppler effects, and outperform the LS approach when the channel is indeed sparse. On the other hand, compressed sensing algorithms uniformly outperform the LS and subspace methods. Coupled with a channel equalizer mitigating intercarrier interference, the compressed sensing algorithms can handle channels with significant Doppler spread.

Abstract—Multipath interference is an ubiquitous phenomenon in modern communication systems. The conventional way to compensate for this effect is to equalize the channel by estimating its impulse response by transmitting a set of training symbols. The primary drawback to this type of approach is that it can be unreliable if the channel is changing rapidly. In this paper, we show that randomly encoding the signal can protect it against channel uncertainty when the channel is sparse. Before transmission, the signal is mapped into a slightly longer codeword using a random matrix. From the received signal, we are able to simultaneously estimate the channel and recover the transmitted signal. We discuss two schemes for the recovery. Both of them exploit the sparsity of the underlying channel. We show that if the channel impulse response is sufficiently sparse, the transmitted signal can be recovered reliably. I.

This paper suggests to use a Block MAP-LMS (BMAP-LMS) adaptive filter instead of an Adaptive Filter called MAP-LMS for estimating the sparse channels. Moreover to faster convergence than MAP-LMS, this block-based adaptive filter enables us to use a compressed sensing version of it which exploits the sparsity of the channel outputs to reduce the sampling rate of the received signal and to alleviate the complexity of the BMAP-LMS. Our simulations show that our proposed algorithm has faster convergence and less final MSE than MAP-LMS, while it is more complex than MAP-LMS. Moreover, some lower bounds for sparse channel estimation is discussed. Specially, a Cramer-Rao bound and a Bayesian Cramer-Rao bound is also calculated. 1.

Channel Estimation is an essential component in applications such as radar and data communication. In multi path time varying environments, it is necessary to estimate time-shifts, scale-shifts (the wideband equivalent of Doppler-shifts), and the gains/phases of each of the multiple paths. With recent advances in sparse estimation (or “compressive sensing”), new estimation techniques have emerged which yield more accurate estimates of these channel parameters than traditional strategies. These estimation strategies, however, restrict potential estimates of time-shifts and scale-shifts to a finite set of values separated by a choice of grid spacing. A small grid spacing increases the number of potential estimates, thus lowering the quantization error, but also increases complexity and estimation time. Conversely, a large grid spacing lowers the number of potential estimates, thus lowering the complexity and estimation time, but increases the quantization error. In this thesis, we derive

Abstract—The estimation of doubly-selective channels is challenging since long channel impulse response should be estimated with a fast tracking speed. Provided that a structure of the channel response is sparse, i.e., only a few of channel gains are nonzero, a tracking performance of the channel estimator can be improved significantly by avoiding estimation of zero taps. In this paper, we study estimation of fast time-varying and long reverberant channels that have a sparse structure in multi-input multi-output (MIMO) systems. In order to exploit the sparse structure, we parameterize the locations of nonzero taps using a binary vector and incorporate it into the state-space system built upon auto-regressive (AR) modeling of the time-varying channel gains. Then, we derive a joint estimate of the binary vector and channel gains based on maximum likelihood (ML) criterion. Expectation maximization (EM) algorithm is derived to find a sparse structure and channel gains iteratively. According to the simulation study performed over MIMO Rician fading channels, the proposed sparse channel estimation technique outperforms the previous estimation schemes, especially when Doppler rate is high. I.

Abstract—In this paper, we investigate various channel estimators that exploit channel sparsity in the time and/or Doppler domain for a multicarrier underwater acoustic system. We use a path-based channel model, where the channel is described by a limited number of paths, each characterized by a delay, Doppler scale, and attenuation factor, and derive the exact inter-carrierinterference (ICI) pattern. For channels that have limited Doppler spread we show that subspace algorithms from the array processing literature, namely Root-MUSIC and ESPRIT, can be applied for channel estimation. For channels with Doppler spread, we adopt a compressed sensing approach, in form of Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) algorithms, and utilize overcomplete dictionaries with an increased path delay resolution. Numerical simulation and experimental data of an OFDM block-by-block receiver are used to evaluate the proposed algorithms in comparison to the conventional least-squares (LS) channel estimator. We observe that subspace methods can tolerate small to moderate Doppler effects, and outperform the LS approach when the channel is indeed sparse. On the other hand, compressed sensing algorithms uniformly outperform the LS and subspace methods. Coupled with a channel equalizer mitigating ICI, the compressed sensing algorithms can effectively handle channels with significant Doppler spread.

Abstract — This paper studies the ergodic capacity of timeand frequency-selective multipath fading channels in the ultrawideband (UWB) regime when training signals are used for channel estimation at the receiver. Motivated by recent measurement results on UWB channels, we propose a model for sparse multipath channels. A key implication of sparsity is that the independent degrees of freedom (DoF) in the channel scale sub-linearly with the signal space dimension (product of signaling duration and bandwidth). Sparsity is captured by the number of resolvable paths in delay and Doppler. Our analysis is based on a training and communication scheme that employs signaling over orthogonal short-time Fourier (STF) basis functions. STF signaling naturally relates sparsity in delay-Doppler to coherence in time-frequency. We study the impact of multipath sparsity on two fundamental metrics of spectral efficiency in the wideband/low-SNR limit introduced by Verdu: first- and second-order optimality conditions. Recent results by Zheng et. al. have underscored the large gap in spectral efficiency between coherent and non-coherent extremes and the importance of channel learning in bridging the gap. Building on these results, our results lead to the following implications of multipath sparsity: 1) The coherence requirements are shared in both time and frequency, thereby significantly relaxing the required scaling in coherence time with SNR; 2) Sparse multipath channels are asymptotically coherent — for a given but large bandwidth, the channel can be learned perfectly and the coherence requirements for first- and second-order optimality met through sufficiently large signaling duration; and 3) The requirement of peaky signals in attaining capacity is eliminated or relaxed in sparse environments. I.