No Arabic abstract
This paper proposes an off-grid channel estimation scheme for orthogonal time-frequency space (OTFS) systems adopting the sparse Bayesian learning (SBL) framework. To avoid channel spreading caused by the fractional delay and Doppler shifts and to fully exploit the channel sparsity in the delay-Doppler (DD) domain, we estimate the original DD domain channel response rather than the effective DD domain channel response as commonly adopted in the literature. OTFS channel estimation is first formulated as a one-dimensional (1D) off-grid sparse signal recovery (SSR) problem based on a virtual sampling grid defined in the DD space, where the on-grid and off-grid components of the delay and Doppler shifts are separated for estimation. In particular, the on-grid components of the delay and Doppler shifts are jointly determined by the entry indices with significant values in the recovered sparse vector. Then, the corresponding off-grid components are modeled as hyper-parameters in the proposed SBL framework, which can be estimated via the expectation-maximization method. To strike a balance between channel estimation performance and computational complexity, we further propose a two-dimensional (2D) off-grid SSR problem via decoupling the delay and Doppler shift estimations. In our developed 1D and 2D off-grid SBL-based channel estimation algorithms, the hyper-parameters are updated alternatively for computing the conditional posterior distribution of channels, which can be exploited to reconstruct the effective DD domain channel. Compared with the 1D method, the proposed 2D method enjoys a much lower computational complexity while only suffers slight performance degradation. Simulation results verify the superior performance of the proposed channel estimation schemes over state-of-the-art schemes.
The performance of the existing sparse Bayesian learning (SBL) methods for off-gird DOA estimation is dependent on the trade off between the accuracy and the computational workload. To speed up the off-grid SBL method while remain a reasonable accuracy, this letter describes a computationally efficient root SBL method for off-grid DOA estimation, where a coarse refinable grid, whose sampled locations are viewed as the adjustable parameters, is adopted. We utilize an expectation-maximization (EM) algorithm to iteratively refine this coarse grid, and illustrate that each updated grid point can be simply achieved by the root of a certain polynomial. Simulation results demonstrate that the computational complexity is significantly reduced and the modeling error can be almost eliminated.
In this paper, we investigate the impacts of transmitter and receiver windows on orthogonal time-frequency space (OTFS) modulation and propose a window design to improve the OTFS channel estimation performance. Assuming ideal pulse shaping filters at the transceiver, we first identify the role of window in effective channel and the reduced channel sparsity with conventional rectangular window. Then, we characterize the impacts of windowing on the effective channel estimation performance for OTFS modulation. Based on the revealed insights, we propose to apply a Dolph-Chebyshev (DC) window at either the transmitter or the receiver to effectively enhance the sparsity of the effective channel. As such, the channel spread due to the fractional Doppler is significantly reduced, which leads to a lower error floor in channel estimation compared with that of the rectangular window. Simulation results verify the accuracy of the obtained analytical results and confirm the superiority of the proposed window designs in improving the channel estimation performance over the conventional rectangular or Sine windows.
In communication systems, efficient use of the spectrum is an indispensable concern. Recently the use of compressed sensing for the purpose of estimating Orthogonal Frequency Division Multiplexing (OFDM) sparse multipath channels has been proposed to decrease the transmitted overhead in form of the pilot subcarriers which are essential for channel estimation. In this paper, we investigate the problem of deterministic pilot allocation in OFDM systems. The method is based on minimizing the coherence of the submatrix of the unitary Discrete Fourier Transform (DFT) matrix associated with the pilot subcarriers. Unlike the usual case of equidistant pilot subcarriers, we show that non-uniform patterns based on cyclic difference sets are optimal. In cases where there are no difference sets, we perform a greedy search method for finding a suboptimal solution. We also investigate the performance of the recovery methods such as Orthogonal Matching Pursuit (OMP) and Iterative Method with Adaptive Thresholding (IMAT) for estimation of the channel taps.
The problem of wideband massive MIMO channel estimation is considered. Targeting for low complexity algorithms as well as small training overhead, a compressive sensing (CS) approach is pursued. Unfortunately, due to the Kronecker-type sensing (measurement) matrix corresponding to this setup, application of standard CS algorithms and analysis methodology does not apply. By recognizing that the channel possesses a special structure, termed hierarchical sparsity, we propose an efficient algorithm that explicitly takes into account this property. In addition, by extending the standard CS analysis methodology to hierarchical sparse vectors, we provide a rigorous analysis of the algorithm performance in terms of estimation error as well as number of pilot subcarriers required to achieve it. Small training overhead, in turn, means higher number of supported users in a cell and potentially improved pilot decontamination. We believe, that this is the first paper that draws a rigorous connection between the hierarchical framework and Kronecker measurements. Numerical results verify the advantage of employing the proposed approach in this setting instead of standard CS algorithms.
The orthogonal time frequency space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To enable efficient OTFS detection in the delay-Doppler (DD) domain, the DD domain channels need to be acquired accurately. To achieve the low latency requirement in future wireless communications, the time duration of the OTFS block should be small, therefore fractional Doppler shifts have to be considered to avoid significant modelling errors due to the assumption of integer Doppler shifts. However, there lack investigations on the estimation of OTFS channels with fractional Doppler shifts in the literature. In this work, we develop a high performing channel estimator for OTFS with the bi-orthogonal waveform or the rectangular waveform. Instead of estimating the DD domain channel directly, we estimate the channel gains and (fractional) Doppler shifts that parameterize the DD domain channel. The estimation is formulated as a structured signal recovery problem with a Bayesian treatment. Based on a factor graph representation of the problem, an efficient message passing algorithm is developed to recover the structured sparse signal (thereby the OTFS channel). The Cramer-Rao Lower Bound (CRLB) for the estimation is developed and the effectiveness of the algorithm is demonstrated through simulations.