Viterbi Detection for Compressively Sampled FHSS-GFSK Signals

Abstract

This paper proposes a sequence detector designed to retrieve data bits from compressively sampled frequency-hopping spread spectrum (FHSS) Gaussian frequency-shift keying (GFSK) signals. The received signal waveform is not reconstructed from the compressive measurements, nor are received bits detected on a symbol-by-symbol basis. Rather, the entire sequence of transmitted symbols is detected from the entire sequence of compressive measurements. Another novel aspect of the work is that a non-cooperative scenario is assumed. Specifically, the receiver is assumed to have no prior knowledge of the specific spread spectrum hopping sequence used by the transmitter. The most significant contribution of the work is the design of adaptive sampling kernels that exploit the structure of an FHSS-GFSK signal to obtain significant performance improvements over random-kernel sampling. The resulting system can automatically choose an appropriate compression ratio as a function of the signal-to-noise ratio (SNR) without explicit knowledge of the SNR. Additionally, the noise folding problem present in random-kernel sampling is greatly alleviated by use of the adaptive sampling kernels. Compared with Nyquist sampling, adaptive compressive sampling offers compression ratios ranging from 20 to 32, depending on the SNR while suffering less than 1 dB loss in the resulting bit error rate.