Compressive Covariance Sensing: Structure-Based Compressive Sensing Beyond Sparsity - Daniel Romero; Dyonisius D Ariananda; Zhi Tian; Geert Leus (IEEE Signal Processing Magazine, 2016)
Compressed sensing deals with the reconstruction of signals from sub-Nyquist samples by exploiting the sparsity of their projections onto known subspaces. In contrast, the present article is concerned with the reconstruction of second-order statistics, such as covariance and power spectrum, even in the absence of sparsity priors. The framework described here leverages the statistical structure of random processes to enable signal compression and offers an alternative perspective at sparsity-agnostic inference. Capitalizing on parsimonious representations, we illustrate how compression and reconstruction tasks can be addressed in popular applications such as power spectrum estimation, incoherent imaging, direction of arrival estimation, frequency estimation, and wideband spectrum sensing.
Keywords: compass; compressed sensing

Compression Limits for Random Vectors with Linearly Parameterized Second-Order Statistics - Daniel Romero; R. López-Valcarce; Geert Leus (IEEE Trans. Information Theory, 2015)
The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all second-order information are derived — the statistics of the uncompressed vector must be recoverable from a set of linearly compressed observations. This kind of vectors arises naturally when sampling widesense stationary random processes and features a number of applications in signal and array processing. Explicit guidelines to design optimal and nearly optimal schemes operating both in a periodic and non-periodic fashion are provided by considering two of the most common linear compression schemes, which we classify as dense or sparse. It is seen that the maximum compression ratios depend on the structure of the HT subspace containing the covariance matrix of the uncompressed observations. Compression patterns attaining these maximum ratios are found for the case without structure as well as for the cases with circulant or banded structure. Universal samplers are also proposed to compress unknown HT subspaces.
Keywords: compass; compressed sensing

Cooperative compressive power spectrum estimation - Dyonisius D Ariananda; Daniel Romero; Geert Leus (IEEE Sensor Array Multichannel Signal Process. Workshop (SAM), 2014)
Keywords: cognitive radio; wsn

Compressive Angular and Frequency Periodogram Reconstruction for Multiband Signals - Ariananda, D. D.; Daniel Romero; Geert Leus (IEEE Int. Workshop Comput. Advances Multi-Sensor Adaptive Process (CAMSAP), 2013)
Keywords: cognitive radio; dynacs

Compressive Covariance Sampling - Daniel Romero; Geert Leus (Inform. Theory Appl. Workshop, 2013)
Keywords: cognitive radio; dynacs

Compressive wideband spectrum sensing with spectral prior information - Daniel Romero; R. López-Valcarce; Geert Leus (Int. Conf. Acoust., Speech, Signal Process. (ICASSP), 2013)
Wideband spectrum sensing provides a means to determine the occupancy of channels spanning a broad range of frequencies. Practical limitations impose that the acquisition should be accomplished at a low rate, much below the Nyquist lower bound. Dramatic rate reductions can be obtained by the observation that only a few parameters need to be estimated in typical spectrum sensing applications. This paper discusses the joint estimation of the power of a number of channels, whose power spectral density (PSD) is known up to a scale factor, using compressive measurements. First, relying on a Gaussian assumption, an efficient approximate maximum likelihood (ML) technique is presented. Next, a least-squares estimator is applied for the general non-Gaussian case.
Keywords: cognitive radio; dynacs; spectrum sensing

Wideband Spectrum Sensing From Compressed Measurements Using Spectral Prior Information - Daniel Romero; Geert Leus (IEEE Trans. Signal Process., 2013)
Keywords: cognitive radio; compressed sensing; dynacs; spectrum sensing

Generalized matched filter detector for fast fading channels - Daniel Romero; R. López-Valcarce; Geert Leus (IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 2012), 2012)
We consider the problem of detecting a known signal with constant magnitude immersed in noise of unknown variance, when the propagation channel is frequency-flat and randomly time-varying within the observation window. A Basis Expansion Model with random coefficients is used for the channel, and a Generalized Likelihood Ratio approach is adopted in order to cope with deterministic nuisance parameters. The resulting scheme can be seen as a generalization of the well-known Matched Filter detector, to which it reduces for timeinvariant channels. Closed-form analytical expressions are provided for the distribution of the test statistic under both hypotheses, which allow to assess the detection performance.
Keywords: cognitive radio; dynacs; spectrum sensing