Rayleigh-normalized Gaussian noise in blind signal fusion

This paper builds upon a previously defined fusion process that exploits multichannel receiver diversity to enhance received SNR. This particular diversity combiner aims to enhance SNR under the challenging constraints that channel gains are unknown, there is no direct knowledge of the transmitted signal, and no opportunity to precode the signal into a known waveform. Thus, fusion is blind in the sense that indirect techniques are invoked to intelligently weight each sample during fusion, and to measure the outcome. Having already established a critical threshold that determines whether fusion does or does not enhance SNR, this paper takes the next step by pursuing rigorous analytical development of a statistical noise model for the effects of the combiner. We provide the probability distributions of this noise, termed Rayleigh-normalized Gaussian. With the probability distributions in hand, we apply them to sample sets of various sizes to understand how the combiner behaves with each incremental sample. This allows us to investigate the likelihood that the critical threshold for SNR gain is met, relative to additional samples, as well as the likelihood of meeting arbitrary target SNR gains. We also develop an expression for the average power of the Rayleigh-normalized Gaussian noise variable.