Compressive Sampling for Detection of Frequency-Hopping Spread Spectrum Signals

In this paper, methods for detection of frequency-hopping spread spectrum (FHSS) signals from compressive measurements are proposed. Rapid switching of the carrier frequency in a pseudorandom manner makes detection of FHSS signals challenging. Conventionally, FHSS detection is performed by scanning small segments of the spectrum in a sequential manner using a sweeping spectrum analyzer (SSA). However, SSAs have the inherent risk of missing the transmitted signal depending on factors such as the rate of hopping and scanning. In this paper, we propose compressive detection strategies that sample the full FHSS spectrum in a compressive manner. We discuss the use of random measurement kernels as well as designed measurement kernels in the proposed architecture. The measurement kernels are designed to maximize the mutual information between the FHSS signal and the compressive measurements. Using a mixture-of-Gaussian model to represent the FHSS signal, we derive a closed-form gradient of the mutual information with respect to the measurement kernel. Theoretical analysis and simulation results are provided to compare different systems. These results demonstrate that the proposed compressive system with random measurement kernels is not subject to the performance limitations suffered by SSAs when their scanning rates are low and designed adaptive measurement kernels provide enhanced detection performance compared to random ones.