Symmetric Alpha-stable Noise Research Articles

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.

The BER optimal linear rake receiver for signal detection in symmetric alpha-stable noise

The optimal linear Rake receiver for the detection of signals contaminated by symmetric alpha stable noise is derived for 1 < ¿ ¿ 2. Although this structure is suboptimal, it is optimal among the class of linear Rake receivers in the sense of minimizing the bit error rate. The proposed receiver is a very simple form of diversity combiner for signal detection in symmetric alpha-stable noise. The bit error rate improvements of the optimal linear Rake receiver over the maximal ratio combiner and the equal gain combiner are also derived in the form of signal-to-noise ratio advantage.

Soft-Decision Metrics for Coded Orthogonal Signaling in Symmetric Alpha-Stable Noise

This paper derives new soft-decision metrics for coded orthogonal signaling in impulsive noise, more specifically symmetric alpha-stable noise. For the case of a known channel amplitude and known noise dispersion, exact metrics are derived both for Cauchy and Gaussian noise. For the case that the channel amplitude or the dispersion is unknown, approximate metrics are obtained in closed-form based on a generalized-likelihood ratio approach. The performance of the new metrics is compared numerically for a turbo-coded system, and the sensitivity to side information of the optimum receiver for Cauchy noise is considered. The gain that can be achieved by using a properly chosen decoding metric is quantified, and it is shown that this gain is significant. The application of the results to frequency hopping ad hoc networks is also discussed.