Estimation Over Fading Channels With Limited Feedback Using Distributed Sensing

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We consider a wireless sensor network for distributed estimation over fading channels. The sensors transmit their observations over a multiple access fading channel to a fusion center (FC), where a source parameter is estimated. The sensor transmissions add incoherently over a multiple access channel, which motivates the need for channel knowledge at the sensors to improve performance. We consider the effects of different fading channel models on the performance of the system, and characterize the effect of different amounts of channel information at the sensors. We calculate the variance of the estimate for cases when both perfect, and differing amounts of partial channel information are available at the sensors. Asymptotic variance expressions for large number of sensors are derived for different channel statistics and feedback scenarios. We show that the degradation in variance due to using only channel phase information is at most a factor of <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$4/\pi$</tex></formula></emphasis> over Rayleigh fading channels. We consider continuous feedback error and evaluate the degradation in performance due to differing degrees of error. The loss in performance due to feedback quantization, and effect of error in feedback are also quantified. We also consider speed of convergence, and compare the rate of convergence under different conditions. Further, we characterize the effect of correlated channels between sensors and the FC, and provide the different values for the speed of convergence for this case. Simulation results are provided to show that only a few tens of sensors are required for the asymptotic results to hold. Numerical results corroborate our analytical results. </para>