Sparse Representation of FHSS Signals in the Hermite Transform Domain

• Main Authors: M. Brajović, A. Draganić, I. Orović, S. Stanković
• Format: Article
• Language: English
• Published: Telecommunications Society, Academic Mind 2017-11-01
• Series: Telfor Journal
• Subjects: FHSS signals; signal sparsity; sparsification; Hermite transform domain
• Online Access: http://journal.telfor.rs/Published/Vol9No2/Vol9No2_A4.pdf

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.