Outage scaling laws and diversity for distributed estimation over parallel fading channels

We consider scaling laws of the outage for distributed estimation problems over fading channels with respect to the total power and the number of sensors. Using a definition of diversity which involves a fixed number of sensors, we find tight upper and lower bounds on diversity which are shown to depend on the sensing (measurement) signal-to-noise ratios (SNRs) of the sensors. Our results indicate that the diversity order can be smaller than the number of sensors, and adding new sensors might not add to the diversity order depending on the sensing SNR of the added sensor. We treat a large class of envelope distributions for the wireless channel including those appropriate for line of sight scenarios. Finally, we consider fixed power per sensor with an asymptotically large number of sensors and show that the outage decays faster than exponentially in the number of sensors.