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Register a new userMessage Passing Based Structured Sparse Signal Recovery for Estimation of OTFS Channels with Fractional Doppler Shifts
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Added by
Zhengdao Yuan
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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.
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The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows advantage in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a much lower complexity and is computationally tractable. In the GAMP framework, the sparse signal and the observation are viewed to be generated according to some pre-specified probability distributions in the input and output channels. However, the parameters of the distributions are usually unknown in practice. In this paper, we propose an extended GAMP algorithm with built-in parameter estimation (PE-GAMP) and present its empirical convergence analysis. PE-GAMP treats the parameters as unknown random variables with simple priors and jointly estimates them with the sparse signals. Compared with Expectation Maximization (EM) based parameter estimation methods, the proposed PE-GAMP could draw information from the prior distributions of the parameters to perform parameter estimation. It is also more robust and much simpler, which enables us to consider more complex signal distributions apart from the usual Bernoulli-Gaussian (BGm) mixture distribution. Specifically, the formulations of Bernoulli-Exponential mixture (BEm) distribution and Laplace distribution are given in this paper. Simulated noiseless sparse signal recovery experiments demonstrate that the performance of the proposed PE-GAMP matches the oracle GAMP algorithm. When noise is present, both the simulated experiments and the real image recovery experiments show that PE-GAMP is still able to maintain its robustness and outperform EM based parameter estimation method when the sampling ratio is small. Additionally, using the BEm formulation of the PE-GAMP, we can successfully perform non-negative sparse coding of local image patches and provide useful features for the image classification task.
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This paper investigates the problem of estimating sparse channels in massive MIMO systems. Most wireless channels are sparse with large delay spread, while some channels can be observed having sparse common support (SCS) within a certain area of the antenna array, i.e., the antenna array can be grouped into several clusters according to the sparse supports of channels. The SCS property is attractive when it comes to the estimation of large number of channels in massive MIMO systems. Using the SCS of channels, one expects better performance, but the number of clusters and the elements for each cluster are always unknown in the receiver. In this paper, {the Dirichlet process} is exploited to model such sparse channels where those in each cluster have SCS. We proposed a low complexity message passing based sparse Bayesian learning to perform channel estimation in massive MIMO systems by using combined BP with MF on a factor graph. Simulation results demonstrate that the proposed massive MIMO sparse channel estimation outperforms the state-of-the-art algorithms. Especially, it even shows better performance than the variational Bayesian method applied for massive MIMO channel estimation.
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.
Although the combination of the orthogonal time frequency space (OTFS) modulation and the massive multiple-input multiple-output (MIMO) technology can make communication systems perform better in high-mobility scenarios, there are still many challenges in downlink channel estimation owing to inaccurate modeling and high pilot overhead in practical systems. In this paper, we propose a channel state information (CSI) acquisition scheme for downlink massive MIMO-OTFS in presence of the fractional Doppler, including deterministic pilot design and channel estimation algorithm. First, we analyze the input-output relationship of the single-input single-output (SISO) OTFS based on the orthogonal frequency division multiplexing (OFDM) modem and extend it to massive MIMO-OTFS. Moreover, we formulate an accurate model for the practical system in which the fractional Doppler is considered and the influence of subpaths is revealed. A deterministic pilot design is then proposed based on the model and the structure of the pilot matrix to reduce pilot overhead and save memory consumption. Since channel geometry changes very slowly relative to the communication timescale, we put forward a modified sensing matrix based channel estimation (MSMCE) algorithm to acquire the downlink CSI. Simulation results demonstrate that the proposed downlink CSI acquisition scheme has significant advantages over traditional algorithms.
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