Capacity Bounds for Frequency-Hopped BPSK

In some channels, such as the frequency-hop channel, the transmission may undergo abrupt transitions in phase. This can require the receiver to re-estimate the phase on each hop, or for the system to utilize modulation techniques that lend themselves to noncoherent detection. How well the receiver can estimate the phase depends on the channel signal-to-noise ratio and how long phase coherence can be assumed. Although prior work has shown that using any reference symbols to aid the phase estimation process is suboptimal with respect to capacity, their presence may be useful in practice as they can simplify the receiver processing. In this paper, the effects of per-pulse phase uncertainty are examined for systems using binary modulation. Both the fraction of the transmission that may be devoted to reference symbols without substantially reducing the overall channel capacity and the point at which it is better to forego coherent processing in favor of noncoherent demodulation are examined.