This paper investigates the design of a wireless broadband data transceiver (WBDT) system. The WBDT system works on hundreds of narrowband discrete channels. Cognitive radio (CR) technology is adopted to detect idle channels. Discrete channels are aggregated into large frequency bands to provide higher transmission capability than traditional wireless data transceivers (WDTs). Guard gaps are used to avoid interference among WBDTs/WDTs working on adjacent channels according to existing WDT standards. To make full use of the idle channels, a new spectrum aggregation (SA) method, maximum space first assignment (MSFA), is proposed after analysing the performance of the WBDT system. MSFA provides a way to reduce the negative effect of the guard gap. The simulation and analysis results show that the novel system architecture and MSFA improve spectral efficiency.