WITH: Weighted Truncated Hadamard-Matrix-Based Deterministic Compressive Sampling for Sparse Multiband Signals

This paper considers the orthogonal observation matrix design of deterministic compressive sampling (CS). An observation matrix called the weighted truncated Hadamard-modulated wideband converter (WITH-MWC) is deterministically designed based on the truncated Hadamard matrix. This matrix can meet th...

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Bibliographic Details
Published inCircuits, systems, and signal processing Vol. 42; no. 3; pp. 1723 - 1741
Main Authors Su, Yinuo, Zhang, Jingchao, Qiao, Liyan
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2023
Springer Nature B.V
Subjects
Bandwidths
Circuits and Systems
Electrical Engineering
Electronics and Microelectronics
Engineering
Instrumentation
Noise sensitivity
Sampling
Signal processing
Signal to noise ratio
Signal,Image and Speech Processing
Sparsity
Spectrum allocation
Spectrum analysis
Hadamard matrix
Deterministic sampling
Wideband spectrum sensing
Analog-to-information conversion
Modulated wideband converter
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Summary:This paper considers the orthogonal observation matrix design of deterministic compressive sampling (CS). An observation matrix called the weighted truncated Hadamard-modulated wideband converter (WITH-MWC) is deterministically designed based on the truncated Hadamard matrix. This matrix can meet the restricted isometry property (RIP) condition with overwhelming probability by randomly or strategically extracting from a standard Hadamard matrix. Most compressed sampling systems are highly sensitive to noise. To reduce the adverse effects of noise interference, partial specific matrix elements are weighted according to the sparse characteristics of multiband signals, and the recovery probability is provably better than that of the original system and other deterministic observation matrices, especially in the low signal-to-noise ratio scenario. Compared to the random Gaussian and random Bernoulli matrices, WITH-MWC is much easier to implement in hardware. The simulations verify the above analysis.
ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-022-02191-4