Dispersed spectrum cognitive radio systems represent a promising approach to exploit the utilization of spectral resources to full extent. Therefore, the performance analysis of such systems is conducted in this research. The Average symbol error probability of dispersed spectrum cognitive radio systems is derived for two cases: where each channel realization experiences independent and dependent Nakagami-m fading, respectively. In addition, the derivation is extended to include the effects of modulation type and order by considering M-PSK and M-QAM modulation schemes. We then study the impacts of topology on the effective transport capacity performance of ad hoc dispersed spectrum cognitive radio systems where the nodes assume 3- dimensional (3D) configurations. We derive the effective transport capacity considering a cubic grid distribution. In addition, numerical results are presented to demonstrate the effects of topology on the effective transport capacity of ad hoc dispersed cognitive radio systems.