  This paper proposes a new method for optimizing frequency-hopping ad hoc
networks in the presence of Rayleigh fading. It is assumed that the system uses
a capacity-approaching code (e.g., turbo or LDPC) and noncoherent binary
continuous-phase frequency-shift keying (CPFSK) modulation. By using
transmission capacity as the performance metric, the number of hopping
channels, CPFSK modulation index, and code rate are jointly optimized. Mobiles
in the network are assumed to be uniformly located within a finite area.
Closed-form expressions for outage probability are given for a network
characterized by a physical interference channel. The outage probability is
first found conditioned on the locations of the mobiles, and then averaged over
the spatial distribution of the mobiles. The transmission capacity, which is a
measure of the spatial spectral efficiency, is obtained from the outage
probability. The transmission capacity is modified to account for the
constraints of the CPFSK modulation and capacity-approaching coding. Two
optimization methods are proposed for maximizing the transmission capacity. The
first is a brute-force method and the second is a gradient-search algorithm.
The results obtained from the optimization shed new insight into the
fundamental tradeoffs among the number of frequency-hopping channels, the
modulation index, and the rate of the error-correcting code.
