Aggregate Interference Distribution From Large Wireless Networks With Correlated Shadowing: An Analytical–Numerical–Simulation Approach

As the number and variety of wireless devices sharing spectrum increases, it becomes increasingly important to characterize the sum interference that is produced by a large number of interferers. We show that, in the case of several interferers, the assumption of independent shadowing paths is very inaccurate and must be replaced by an appropriate correlation model. We choose one such model, which has desirable mathematical and physical properties, is tunable, and is particularly well suited for simulation, although our approach can also be used with other correlation models. In addition, we allow a very versatile channel and system model. The simulation cost of such systems quickly grows for large numbers of interferers due to the time and memory constraints of the Monte Carlo simulation algorithm using the classic matrix factorization (e.g., Cholesky) approach. We show how an alternative simulation approach using shadowing fields can significantly reduce the order of the computational cost. In addition, we show how judicious random sample reuse and extrapolation based on a numerical analysis of moments can be used to further simplify the simulation. Through the combination of these three approaches, using a mixture of simulation, numerical, and analytical techniques, we can obtain accurate approximations of the distribution of the total interference power while reducing computational time by factors of more than 1000. We can also make some mathematical statements about the problem, which may be useful for further developments. We argue that our model is complex enough to accommodate a good degree of realism and that our approach is a viable alternative to the pure analysis of such a complex and versatile problem.