Computational complexity of narrow band and wide band channel simulators

Some questions such as: is it convenient to simulate channel realizations with the sum of sinusoids or with the filtering approach, are addressed in this work in order to provide a guide on which algorithms and in what situations should be used in the development of channel simulators. The conclusions presented are gathered from the comparison of the methods proposed in the literature to simulate narrowband and wideband separable channels. The comparisons are performed from the point of view of computational complexity and two metrics of approximation error. We also discuss the properties inherent to the algorithms that could determine if the proposals are suitable for channel simulation, such as synthesis complexity and their capability to approximate the conditions encountered in real channels.