Analysis of Mean Field Annealing in Substactive Interference Cancellation
In this contribution we derive the cost function corresponding to the linear complexity Subtractive Interference Cancellation with tangent hyperbolic tentative decisions. We use the cost function to analyse the fix-points of solving the Subtractive Interference Cancellation equations. The analysis show that we can control the slope of the tangent hyperbolic functions so that the corresponding cost function is convex. We also show that increasing the slope can make the cost non-convex. Going from the convex regime into the non-convex regime, we prove that the bifurcation of the fix-points, for non-singular signal correlation matrices, consist of the fix-point of interest together with a saddle node bifurcation. This proves that tracking the solution from low slopes, with a convex cost, gradually increasing to higher slopes, with non-convex cost, can bring us to the best solution being very close to the optimal determined by enumeration. This tracking is the idea behind annealing. We show Monte Carlo studies with a substantial signal to noise ratio gain compared to not using annealing. We also show how annealing can be used to increase capacity at a given target bit error rate. In fact this capacity gain is the same obtained by Improved Parallel Interference Cancellation making us believe that the latter includes a mechanism to avoid local minima similar to annealing.