Multidimensional Spectral Super-Resolution with Prior Knowledge with Application to High Mobility Channel Estimation

Yinchuan Li, Xiaodong Wang, Zegang Ding*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

The problem of estimating high-mobility channels is a special case of the general problem of recovering multi-dimensional (MD) complex sinusoids. This paper is concerned with estimation of multiple frequencies with prior knowledge from incomplete and/or noisy samples. Suppose that it is known a priori that the frequencies lie in some given intervals, we develop efficient super-resolution estimators by exploiting such prior knowledge based on frequency-selective (FS) atomic norm minimization. We study the MD Vandermonde decomposition of block Toeplitz matrices in which the frequencies are restricted to lie in given intervals. We then propose to solve the FS atomic norm minimization problems for the low-rank spectral tensor recovery by converting them into semidefinite programs based on the MD Vandermonde decomposition. We also develop fast solvers for solving these semidefinite programs via the alternating direction method of multipliers (ADMM), where each iteration involves a number of refinement steps to utilize the prior knowledge. Extensive simulation results are presented to illustrate the high performance of the proposed methods.

Original languageEnglish
Article number9131691
Pages (from-to)2836-2852
Number of pages17
JournalIEEE Journal on Selected Areas in Communications
Volume38
Issue number12
DOIs
Publication statusPublished - Dec 2020

Keywords

  • ADMM
  • Multi-dimensional super-resolution
  • atomic norm
  • channel estimation
  • frequency-selective Vandermonde decomposition
  • high mobility
  • low-rank tensor
  • prior knowledge

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