This paper considers the implementation of a frequency hopping modem utilising a highly bandwidth efficient linear modulation scheme. The bandwidth of the narrowband message is minimised, and differential operation provides resilience to fading and the nonlinearity of the FH channel. The performance of a single user system has been derived through simulation, with a novel approach for modelling of the FH channel. Instead of simulating a frequency hopper, transmitting through a wideband channel and de-hopping the FH signal at the receiver, the system uses a narrowband `hopping' channel model, which alters its characteristics to reflect those of the FH propagation environment. To validate this model, measurements have been undertaken into the nature of propagation through the channel. The results are presented in terms of the fading undergone by a hopped signal, and the statistics of that signal at the receiver