Multicoset-based deterministic measurement matrices for compressed sensing of sparse multiband signals

• Published in: Signal processing 2023-12, Vol.213, p.109154, Article 109154
• Main Authors: Domínguez–Jiménez, M. Elena, González–Prelcic, Nuria, Rusu, Cristian
• Format: Article
• Language: English
• Subjects: Compressed sensing; Deterministic measurement; Multiband signals; Mutual coherence analysis; Non-uniform sampling
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2023.109154

•It is possible to design deterministic universal multicoset sampling strategies implemented with both asynchronous TI-ADC structures and synchronous multirate TI-ADC schemes for the reconstruction of sparse multiband signals.•For a signal block length L, if the indices of the selected samples are in arithmetic progression of difference D coprime with the block length L, then the sampling pattern is universal.•Most 2M-1 bands of the multiband signal can be reconstructed for M ADCs working at different sampling rates and a block length that is the lcm of the M subsampling factors. Signal acquisition is a basic function in signal processing systems. In the context of digital communications, the analog-to-digital (ADC) converters have to be carefully designed as part of the radio frequency front end, to reduce power consumption while avoiding aliasing. When operating with sparse multiband signals, compressive sampling becomes an attractive alternative to enable low sampling rates at the front end. Starting from previous results on multicoset sampling and compressed sensing, we analyze sampling strategies for sparse multiband signals based on the operation of a set of ADC converters working in parallel. Different architectures are considered, with equal and different sampling rates in the ADCs, and their associated deterministic measurement matrices and sampling patterns are studied. The matrices involved in the corresponding reconstruction equations for the different architectures are also analyzed in terms of their mutual coherence. As a result, we are able to design different universal multicoset sampling patterns. We obtain the parameters for the different sampling architectures that guarantee reconstruction of the multiband sparse signal, even at high compression rates. Simulation results show the effectiveness of the theoretical designs for sparse reconstruction of this type of signals.