Compressive Periodogram Reconstruction Using Uniform Binning

D.D. Ariananda, Daniel Romero, G Leus

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

In this paper, two problems that show great similarities are examined. The first problem is the reconstruction of the angular-domain periodogram from spatial-domain signals received at different time indices. The second one is the reconstruction of the frequency-domain periodogram from time-domain signals received at different wireless sensors. We split the entire angular or frequency band into uniform bins. The bin size is set such that the received spectra at two frequencies or angles, whose distance is equal to or larger than the size of a bin, are uncorrelated. These problems in the two different domains lead to a similar circulant structure in the so-called coset correlation matrix. This circulant structure allows for a strong compression and a simple least-squares reconstruction method. The latter is possible under the full column rank condition of the system matrix, which can be achieved by designing the spatial or temporal sampling patterns based on a circular sparse ruler. We analyze the statistical performance of the compressively reconstructed periodogram, including bias and variance. We further consider the case when the bins are so small that the received spectra at two frequencies or angles, with a spacing between them larger than the size of the bin, can still be correlated. In this case, the resulting coset correlation matrix is generally not circulant and thus a special approach is required.
Original languageEnglish
Pages (from-to)4149-4164
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume63
Issue number16
DOIs
Publication statusPublished - 2015

Keywords

  • periodogram
  • Averaged periodogram
  • circulant matrix
  • circular sparse ruler
  • compression
  • closet correlation matrix
  • multi-coset sampling
  • non-uniform linear array

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