Sparse Representation of FHSS Signals in the Hermite Transform Domain

Abstract

Signal sparsity is exploited in various signal processing approaches. Signal compression, classification, coding, as well as the recently introduced compressed sensing are some examples where the possibility to represent a signal sparsely determines the efficiency of the applied processing technique. However, the possibility of a sparse signal representation in a transform basis is highly dependent on the signal nature. Therefore, finding a suitable basis where the signal exhibits a compact support is a challenging task. In this paper, the Hermite Transform (HT) is considered as a sparsity domain for the FHSS wireless communication signals. The transform coefficients sparsification is done by optimizing the scaling factor and time-shift of basis functions. The optimization is done by minimizing the concentration measure of HT coefficients. The theory is verified by numerical examples with synthetic FHSS signals.

Keywords

• FHSS signals
• signal sparsity
• sparsification
• Hermite transform domain