@phdthesis {606,
	title = {Subspace-based Order Estimation Techniques in Massive MIMO},
	year = {2021},
	school = {University of Cantabria},
	address = {Santander},
	author = {Garg, Vaibhav}
}
@article {549,
	title = {Subspace Averaging and Order Determination for Source Enumeration},
	journal = {IEEE Transactions on Signal Processing},
	volume = {67},
	year = {2019},
	month = {June},
	pages = {3028-3041},
	abstract = {In this paper we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization-minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally-determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support.},
	doi = {10.1109/TSP.2019.2912151},
	author = {Garg, Vaibhav and Santamar{\'\i}a, Ignacio and Ram{\'\i}rez, David and Louis L. Scharf}
}
@article {611,
	title = {Order Estimation via Matrix Completion for Multi-Switch Antenna Selection},
	journal = {IEEE Signal Processing Letters},
	volume = {28},
	year = {2021},
	pages = {2063-2067},
	abstract = {This letter addresses the problem of order estimation for uniform linear arrays (ULAs) with multi-switch antenna
selection in the small-sample regime. Multi-switch antenna selection results in a data matrix with missing entries, a scenario for which existing order estimation methods that build on the eigenvalues of the sample covariance matrix do not perform well. A direct application of the Davis-Kahan theorem allows us to
show that the signal subspace is quite robust in the presence of missing entries. Based on this finding, this letter proposes a matrix completion (MC) subspace-based order estimation criterion that exploits the shift-invariance property of ULAs. A recently proposed shift-invariant matrix completion (SIMC) method is used for reconstructing the data matrix, and the proposed order estimation criterion is based on the chordal subspace distance between two submatrices extracted from the reconstructed matrix for increasing values of the dimension of
the signal subspace. Our simulation results show that the method provides accurate order estimates with percentages of missing entries higher than 50\%.},
	doi = {10.1109/LSP.2021.3116525},
	author = {Garg, Vaibhav and Pages-Zamora, Alba and Santamar{\'\i}a, Ignacio}
}
@article {601,
	title = {DOA Estimation via Shift-Invariant Matrix Completion},
	journal = {Signal Processing},
	volume = {183},
	year = {2021},
	abstract = {This paper presents a method to estimate the direction of arrival (DOA) of multiple sources received by a uniform linear array (ULA) with a reduced number of radio-frequency (RF) chains. The receiving array relies on antenna switching so that at every time instant only the signals received by a randomly selected subset of antennas are downconverted to baseband and sampled. Low-rank matrix completion (MC) techniques are then used to reconstruct the missing entries of the signal data matrix to keep the angular resolution of the original large-scale array. The proposed MC algorithm exploits not only the low- rank structure of the signal subspace, but also the shift-invariance property of ULAs, which results in a better estimation of the signal subspace. Further, the effect of MC on DOA estimation is discussed under the perturbation theory framework. The simulation results suggest that the proposed method provides accurate DOA estimates even in the small-sample regime with a significant reduction in the number of RF chains required for a given spatial resolution.},
	doi = {https://doi.org/10.1016/j.sigpro.2021.107993},
	author = {Garg, Vaibhav and Gimenez-Febrer, Pere and Pages-Zamora, Alba and Santamar{\'\i}a, Ignacio}
}
@conference {560,
	title = {Subspace Averaging in Multi-Sensor Array Processing},
	booktitle = {SIAM Conference on Applied Algebraic Geometry},
	year = {2019},
	month = {July},
	address = {Bern, Switzerland},
	author = {Santamar{\'\i}a, Ignacio and Louis L. Scharf and Garg, Vaibhav and Ram{\'\i}rez, David}
}
@conference {605,
	title = {Sparse subspace averaging for order estimation},
	booktitle = {IEEE Statistical Signal Processing Workshop},
	year = {2021},
	month = {July},
	abstract = {This paper addresses the problem of source enumeration for arbitrary geometry arrays in the presence of spatially correlated noise. The method combines a sparse reconstruction (SR) step with a subspace averaging (SA) approach, and hence it is named sparse subspace averaging (SSA). In the first step, each received snapshot is
approximated by a sparse linear combination of the rest of snapshots. The SR problem is regularized by the logarithm-based surrogate of the l0-norm and solved using a majorization-minimization approach. Based on the SR solution, a sampling mechanism is proposed in the second step to generate a collection of subspaces, all of which approximately span the same signal subspace. Finally, the dimension of the average of this collection of subspaces provides a robust estimate for the number of sources. Our simulation results show that SSA provides robust order estimates under a variety of noise models.},
	author = {Garg, Vaibhav and Ram{\'\i}rez, David and Santamar{\'\i}a, Ignacio}
}
@conference {570,
	title = {Source Enumeration via Toeplitz Matrix Completion},
	booktitle = {Int. Conf. Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2020},
	month = {May},
	pages = {6004-6008},
	address = {Barcelona, Spain},
	abstract = {This paper addresses the problem of source enumeration by an array of sensors in the presence of noise whose spatial covariance structure is a diagonal matrix with possibly different variances, referred to non-iid noise hereafter, when the sources are uncorrelated. The diagonal terms of the sample covariance matrix are removed and, after applying Toeplitz rectification as a denoising step, the signal covariance matrix is reconstructed by using a low-rank matrix completion method adapted to enforce the Toeplitz structure of the sought solution. The proposed source enumeration criterion is based on the Frobenius norm of the reconstructed signal covariance matrix obtained for increasing rank values. As illustrated by simulation examples, the proposed method performs robustly for both small and large-scale arrays with few snapshots, i.e. small-sample regime.},
	author = {Garg, Vaibhav and Gimenez-Febrer, Pere and Pages-Zamora, Alba and Santamar{\'\i}a, Ignacio}
}
@conference {553,
	title = {Source Enumeration in Non-White Noise and Small Sample Size via Subspace Averaging},
	booktitle = {European Signal Processing Conference (EUSIPCO)},
	year = {2019},
	month = {September},
	address = {La Coru{\~n}a, Spain},
	abstract = {This paper addresses the problem of source enumeration by an array of sensors in the challenging conditions of: i) large uniform arrays with few snapshots, and ii) non-white or spatially correlated noises with arbitrary correlation. To solve this problem, we combine a subspace averaging (SA) technique, recently proposed for the case of independent and identically distributed (i.i.d.) noises, with a majority vote approach. The number of sources is detected for increasing dimensions of the SA technique and then a majority vote is applied to determine the final estimate. As illustrated by some simulation examples, this simple modification, makes SA a very robust method of enumerating sources in these challenging scenarios.},
	author = {Garg, Vaibhav and Santamar{\'\i}a, Ignacio}
}
