A composite impulse radio ultra-wideband (IR-UWB) communication system is presented. The proposed system model aims to transmit UWB pulses over several kilometers through free-space optical (FSO) links and depending on the link design, the electrical estimates of the FSO system can be directly used or distributed to end-user through radio-frequency (RF) links over short ranges. However, inhomogeneities on the FSO transmission path cause random fluctuations in the received signal intensity and these effects induced by atmospheric turbulence closely effect the system performance. Several distinct probability distributions based on experimental measurements are used to characterize FSO channels and using these probabilistic models, detection error probability analysis of the proposed system for different link designs are carried out under weak, moderate and strong turbulence conditions. The results of the analysis show that depending on the atmospheric conditions, system performance of the composite link can have high error floors due to the false estimates of FSO link. The system performance can be improved by employing error control coding techniques. One simple solution employing a convolutional encoder and Viterbi decoder pair is also analyzed in this thesis. Another important system parameter that is the average channel capacity of the FSO system is analyzed under weak and moderate turbulence conditions. Theoretical derivations that are verified via simulation results indicate a reliable high data rate communication system that is effective in long distances.