Compressive Sampling and Rapid Reconstruction of Broadband Frequency Hopping Signals with Interference

Abstract

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 $M\ge {C}\cdot {\mu }^2(\varvec{\varPhi },\varvec{\varPsi })\cdot {K}\cdot {}log(N)$, where $C$ and $\mu (\varvec{\varPhi },\varvec{\varPsi })$ are the constants, $K$ is the sparsity level, and $N$ 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 $=N/M$) may be greatly reduced. However, the FH signals only occupy a single frequency at a time. This means that $K=1$, 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 $K=4$, and it is not limited by the inequality given above.