TY - JOUR

T1 - Compressive periodogram reconstruction using uniform binning

AU - Ariananda, Dyonisius Dony

AU - Romero, Daniel

AU - Leus, Geert

PY - 2015/8/15

Y1 - 2015/8/15

N2 - 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.

AB - 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.

KW - Averaged periodogram

KW - circulant matrix

KW - circular sparse ruler

KW - compression

KW - coset correlation matrix

KW - multi-coset sampling

KW - non-uniform linear array

KW - periodogram

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U2 - 10.1109/TSP.2015.2430838

DO - 10.1109/TSP.2015.2430838

M3 - Article

AN - SCOPUS:84936805183

VL - 63

SP - 4149

EP - 4164

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 16

M1 - 7103365

ER -