[Paper Review] Structured Distributed Compressive Channel Estimation over Doubly Selective Channels

Qibo Qin, Lin Gui+3 more|arXiv (Cornell University)|Apr 23, 2020

Sparse and Compressive Sensing Techniques30 references20 citations

TL;DR

This paper proposes a structured distributed compressive sensing (SDCS) scheme for joint multi-symbol channel estimation in doubly selective OFDM systems. By exploiting temporal correlation and delay-domain sparsity via complex exponential basis expansion modeling and a tailored pilot pattern, it enables accurate recovery of channel coefficients with fewer pilots, achieving superior estimation accuracy and spectral efficiency compared to conventional methods.

ABSTRACT

For an orthogonal frequency-division multiplexing (OFDM) system over a doubly selective (DS) channel, a large number of pilot subcarriers are needed to estimate the numerous channel parameters, resulting in low spectral efficiency. In this paper, by exploiting temporal correlation of practical wireless channels, we propose a highly efficient structured distributed compressive sensing (SDCS) based joint multi-symbol channel estimation scheme. Specifically, by using the complex exponential basis expansion model (CE-BEM) and exploiting the sparsity in the delay domain within multiple OFDM symbols, we turn to estimate jointly sparse CE-BEM coefficient vectors rather than numerous channel taps. Then a sparse pilot pattern within multiple OFDM symbols is designed to obtain an ICI-free structure and transform the channel estimation problem into a joint-block-sparse model. Next, a novel block-based simultaneous orthogonal matching pursuit (BSOMP) algorithm is proposed to jointly recover coefficient vectors accurately. Finally, to reduce the CE-BEM modeling error, we carry out smoothing treatments of already estimated channel taps via piecewise linear approximation.Simulation results demonstrate that the proposed channel estimation scheme can achieve higher estimation accuracy than conventional schemes, although with a smaller number of pilot subcarriers.

Motivation & Objective

• To address the low spectral efficiency caused by excessive pilot subcarriers in OFDM systems over doubly selective (DS) channels.
• To exploit temporal correlation and delay-domain sparsity across multiple OFDM symbols to enhance channel estimation accuracy.
• To develop a structured distributed compressive sensing (SDCS) framework that jointly recovers sparse channel coefficients across multiple symbols.
• To reduce modeling error from basis expansion models through piecewise linear smoothing of estimated taps.
• To achieve higher estimation accuracy and spectral efficiency than conventional single-symbol or non-structured compressive sensing schemes.

Proposed method

• Models time-varying doubly selective channels using the complex exponential basis expansion model (CE-BEM) to represent time variations across multiple OFDM symbols.
• Designs a sparse pilot pattern across multiple symbols to create an ICI-free structure and enable joint-block-sparse representation of channel coefficients.
• Transforms the channel estimation problem into a joint-block-sparse model by exploiting sparsity in the delay domain and temporal correlation.
• Proposes a block-based simultaneous orthogonal matching pursuit (BSOMP) algorithm to jointly recover coefficient vectors from the structured model.
• Applies piecewise linear approximation to smooth estimated channel taps and reduce CE-BEM modeling error.
• Derives a mathematical formulation that decouples the joint estimation problem into a structured system model using pilot subcarrier selection matrices and block-wise signal reconstruction.

Experimental results

Research questions

• RQ1 Can joint multi-symbol channel estimation using structured distributed compressive sensing improve spectral efficiency in doubly selective OFDM systems?
• RQ2 How does exploiting temporal correlation and delay-domain sparsity across multiple OFDM symbols enhance estimation accuracy compared to single-symbol approaches?
• RQ3 What pilot pattern design enables an ICI-free, joint-block-sparse structure for efficient channel estimation in DS channels?
• RQ4 To what extent does the proposed BSOMP algorithm outperform conventional CS and DCS methods in terms of estimation accuracy and pilot overhead?
• RQ5 How effective is piecewise linear smoothing in reducing modeling error from the CE-BEM approximation?

Key findings

• The proposed SDCS-based scheme achieves higher estimation accuracy than conventional CS- and DCS-based methods when tracking joint multi-symbol channel models.
• With only 10% of the pilot subcarriers used in traditional LS or MMSE schemes, the proposed method achieves comparable or better performance in terms of NMSE.
• At an SNR of 20 dB, the joint multi-symbol scheme achieves an SNR gain of approximately 1 dB over the single-symbol scheme at BER = 10^-2.
• The proposed scheme is only about 0.2 dB away from the ideal case with perfect channel knowledge in coded BER performance.
• The scheme maintains high accuracy even at high Doppler shifts, such as 500 km/h, demonstrating robustness in practical vehicular environments.
• Simulation results confirm that the combination of structured pilot design, BSOMP recovery, and piecewise linear smoothing significantly reduces estimation error and modeling distortion.