BER optimal linear combiner for signal detection in symmetric alpha-stable noise: small values of alpha

The maximum likelihood optimal combiner for signal detection in alpha-stable noise is not known in general, except for some special values of the characteristic exponent ¿. A linear Rake combiner receiver is simple and easy to realize. The optimal linear Rake receiver, in the sense of minimizing the bit error rate, for the detection of signals contaminated by symmetric alpha stable noise is derived for values of ¿, 0 < ¿ ¿ 1. Interestingly, for this range of ¿, the optimal combiner is found to be a selection combiner which selects the channel (finger) with the largest signal amplitude and suppresses all other channels (fingers). This interesting result is valid over the range 0 < ¿ ¿ 1 and allows one to implement effective signal detection without having to know the actual value of the parameter ¿. Therefore, the result yields a very simple form of diversity combiner for signal detection in symmetric alpha-stable noise for 0 < ¿ ¿ 1. Comparisons with the widely used maximal ratio combining and equal gain combining schemes are made in terms of signal-to-noise ratio advantage defined in the bit error rate sense.