At a receiving antenna system we generally find a series of signal vectors that arrive and aggregate in positive and negative ways. Often we have a significant wanted signal and multiple unwanted ones from other co-channel users that lead to the planned service being limited by interference rather than noise. The question arises, how to aggregate these signals so that we can compute a wanted to unwanted ratio such that we can ultimately determine the availability of the desired service as we vary location? This post examines some of the approaches and gives a practical spreadsheet example.
Simple summing of the means of these signals does not suffice, because generally they will fade independently due to the diversity of the interference paths, so a meaningful prediction will require a method that takes account of their stochastic nature. To simplify matters these signal are generally characterised by a mean and variance assuming a log-normal distribution, and they will also have that distribution in aggregate. A straight-forward approach is to use Monte-Carlo method to sum many random samples to compute the aggregate mean and variance. With modern computing power this can be done with a high degree of confidence, however, this may require a significant number of samples. If pixel plotting techniques are used to predict the service at a huge number of locations, then the simulation times can be significantly long, this can be limiting when network plans are being evaluated.
However, there are many alternative techniques using numerical approximations to help estimate the sum of log-normal variates that require substantially less computing power. This includes the seminal method by L F Fenton which is often known as Fenton-Wilkinson method. Fenton’s approach has the benefit of being simple, but suffers from significant accuracy issues which are quite limiting when dealing with a large number of different vectors. The Schwartz-Yeh method is an improvement under most circumstances and is especially useful for summing uncorrelated sources, but it is more complex. Other techniques improve upon these methods and may offer better fidelity in dealing with correlation and larger numbers of signals, but there is no perfect method, and Schwartz-Yeh stands as a good general purpose method for a small number of uncorrelated signals.
The interference summing methods compared spreadsheet implements a number of functions that can be called to compare Monte-Carlo, Fenton-Wilkinson and Schwartz-Yeh methods. The spreadsheet contains an example with 20 components that are assumed to be uncorrelated. These components are simply passed as arrays to user defined VBA functions making the worksheet compact and easy to experiment with. Aside from the helper functions, there are only a few core functions whose code is easily modified for re-use in other programming environments.