Next-generation wireless systems facilitating better utilisation of the scarce radio spectrum have emerged as a response to inefficient and rigid spectrum assignment policies. These are comprised of intelligent radio nodes that opportunistically operate in the radio spectrum of existing primary systems, yet unwanted interference at the primary receivers is unavoidable. In order to design efficient next-generation systems and to minimise the adverse effect of their interference, it is necessary to realise how the resulting interference impacts the performance of the primary systems. In this work, a generalised framework for the interference analysis of such a next-generation system is presented where the next-generation transmitters may transmit randomly with different transmit powers. The analysis is built around a model developed for the statistical representation of the interference at the primary receivers, which is then used to evaluate various performance measures of the primary system. Applications of the derived interference model in designing the next-generation network system parameters are also demonstrated. Such approach provides a unified and generalised framework, the use of which allows a wide range of performance metrics can be evaluated. Findings of the analytical performance analyses are confirmed through extensive computer-based Monte-Carlo simulations. Copyright (c) 2014 John Wiley & Sons, Ltd.