Using time-limited pulses in a combined PAM-OMM system over band-limited channels

Practicalcommunication systems use finite duration pulses. As the time-limited pulses have infinite bandwidth, they lose some of their energy when passed through a band-limited channel and their support in time becomes infinite. We derive the achievable rates when using T -seconds time-limited pulses in a combined PAM-OMM system over a W -Hz band-limited Gaussian channel, and we numerically evaluate them. We show that these rates depend on the time-frequency factor c=2WT. When c ≥ 1 the loss of energy has no significant effect and the achievable rates are arbitrarily close to the channel capacity. Furthermore, we establish that there are at most 2WT independent data symbols.