Wireless Communications
Fundamentals of wireless communication
Fundamentals of wireless communication
Compressive Sensing by Random Convolution
SIAM Journal on Imaging Sciences
Optimal training design for MIMO OFDM systems in mobile wireless channels
IEEE Transactions on Signal Processing
Optimal training signals for MIMO OFDM channel estimation
IEEE Transactions on Wireless Communications
Cluster Characteristics in a MIMO Indoor Propagation Environment
IEEE Transactions on Wireless Communications
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
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Subsampled (or partial) Fourier matrices were originally introduced in the compressive sensing literature by Candès et al. Later, in papers by Candès and Tao and Rudelson and Vershynin, it was shown that (random) subsampling of the rows of many other classes of unitary matrices also yield effective sensing matrices. The key requirement is that the rows of U, the unitary matrix, must be highly incoherent with the basis in which the signal is sparse. In this paper, we consider acquisition systems that--despite sensing sparse signals in an incoherent domain-- cannot randomly subsample rows from U. We consider a general class of systems in which the sensing matrix corresponds to subsampling of the rows of matrices of the form φ = RU (instead of U), where R is typically a low-rank matrix whose structure reflects the physical/technological constraints of the acquisition system. We use the term "structurally-subsampled unitary matrices" to describe such sensing matrices. We investigate the restricted isometry property of a particular class of structurally-subsampled unitary matrices that arise naturally in application areas such as multiple-antenna channel estimation and sub-nyquist sampling. In addition, we discuss an immediate application of this work in the area of wireless channel estimation, where the main results of this paper can be applied to the estimation of multiple-antenna orthogonal frequency division multiplexing channels that have sparse impulse responses.