Optimal bit error rate linear rake receiver for signal detection in highly impulsive symmetric alpha-stable noise

Alpha-stable noise arises in many areas of electrical engineering including communications. However, no closed-form solution is known for its probability density function in general. Therefore, the maximum likelihood detector for alpha-stable noise is not known in general. A number of suboptimal detectors have been proposed based on various approximations for the alpha-stable distribution. However, these non-linear structures are not easy to realize. A linear combiner is an easy to implement form of receiver when multiple samples are available. However, the well known maximal ratio combiner and the equal gain combiner are not necessarily the optimal linear combiners for alpha-stable noise. The optimal linear combiner for alpha-stable noise has been derived in the literature for 1 < alpha les 2. However, no solution is known for the case 0 < alpha les 1. In this paper we present and prove the optimal linear Rake combiner for this range of alpha.