Capacity of Coherent Frequency-Hop Spread-Spectrum Communications
Giovanni Cherubini, W.E. Stark · 2005
The capacity of a coherent frequency-hopped (C-FH) spread-spectrum system is investigated, The channel comprises an M-ary phase-shift keying (M-PSK) modulator, a frequency hopper with phase-continuous carrier, the transmission medium, a nonideal phase-coherent frequency dehopper, an M-PSK demodulator, and a carrier tracking system. Additive white Gaussian noise is considered. The analysis focuses on the effect of imperfect recovery of the carrier phase on the demodulation process. The carrier tracking system includes a maximum likelihood estimator of the phase error and a first-order digital phase-lock loop. The phase error is modeled as a Markov process. An expression for the state transition probabilities of the phase error process is given. Using bounds on the entropy of a function of a Markov process, lower bounds to the capacity of C-FH channels are derived. The input symbols are assumed uniformly distributed and the encoding process independent of the frequency slot selected to send each symbol. Numerical results obtained for various values of M and of the number of frequency slots are presented.