caa a22 4500 606206388 CHVBK 20210128101011.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s00034-014-9912-4 doi (NATIONALLICENCE)springer-10.1007/s00034-014-9912-4 Compressive Sampling and Rapid Reconstruction of Broadband Frequency Hopping Signals with Interference [Elektronische Daten] [Li-xin Wang, Bin-ze Zhang, Yi-zhi Zhao] In differential frequency hopping (FH) wireless systems, data are expressed by frequency hopping pattern, and frequency detection involving the Fourier transform and widebands requires large numbers of Nyquist samples, which makes them difficult to implement. Due to the sparseness of FH signals in the frequency domain, compressive sampling (CS) techniques have been explored for the sampling and reconstruction of such signals. In CS, the number of measurements must satisfy $$M\ge {C}\cdot {\mu }^2(\varvec{\varPhi },\varvec{\varPsi })\cdot {K}\cdot {}log(N)$$ M ≥ C · μ 2 ( Φ , Ψ ) · K · l o g ( N ) , where $$C$$ C and $$\mu (\varvec{\varPhi },\varvec{\varPsi })$$ μ ( Φ , Ψ ) are the constants, $$K$$ K is the sparsity level, and $$N$$ N is the dimension of the original signal. Because of the large number of channels in the operation band, many of these channels are often occupied by diverse frequency-fixed (FF) signals. For this reason, the band compression rate (BCR $$=N/M$$ = N / M ) may be greatly reduced. However, the FH signals only occupy a single frequency at a time. This means that $$K=1$$ K = 1 , and the number of measurements can be far smaller than the number to restore the mixture of FH and FF signals. In this paper, a CS method that is not subject to the influence is presented, and the BCR can reach 1,000:6 when the FH signal is mixed with 50 interferences. The proposed algorithm covers the generation of the sampling matrix and signal reconstruction. Specifically, it maximizes the signal-to-noise ratio of the compressed signal with a white noise background. The new reconstruction algorithm was found to be 5 times faster than the OMP algorithm in the case of that $$K=4$$ K = 4 , and it is not limited by the inequality given above. Springer Science+Business Media New York, 2014 Frequency hopping nationallicence Compressive sampling nationallicence Interference nationallicence Equiangular tight frame nationallicence Reconstruction nationallicence Wang Li-xin College of Communication Engineering, Hangzhou Dianzi University, Hangzhou, China aut Zhang Bin-ze College of Communication Engineering, Hangzhou Dianzi University, Hangzhou, China aut Zhao Yi-zhi College of Communication Engineering, Hangzhou Dianzi University, Hangzhou, China aut Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/5(2015-05-01), 1535-1547 0278-081X 34:5<1535 2015 34 34 https://doi.org/10.1007/s00034-014-9912-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-014-9912-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Li-xin College of Communication Engineering, Hangzhou Dianzi University, Hangzhou, China aut NATIONALLICENCE 700 1- Zhang Bin-ze College of Communication Engineering, Hangzhou Dianzi University, Hangzhou, China aut NATIONALLICENCE 700 1- Zhao Yi-zhi College of Communication Engineering, Hangzhou Dianzi University, Hangzhou, China aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/5(2015-05-01), 1535-1547 0278-081X 34:5<1535 2015 34 34