Search

This paper presents the use of nonlinear distributed estimation in a wireless system transmitting over channels with random gains. Specifically, we discuss the development of estimators and analytically determine their attainable variance for two conditions: 1) when full channel state information (CSI) is available at the transmitter and receiver; and 2) when only channel gain statistics and phase information are available. For the case where full CSI is available, we formulate an optimization problem to allocate power among each of the transmitting sensors while minimizing the estimate variance. We show that minimizing the estimate variance when the transmitter is operating in its most nonlinear region can be formulated in a manner very similar to optimizing sensor gains with full CSI and linear transmitters. Furthermore, we show that the solution to this optimization problem in most scenarios is approximately equivalent to one of two low-complexity power allocation systems. [ABSTRACT FROM AUTHOR]

A sensor network is used for distributed signal-to-noise ratio (SNR) estimation in a single-time snapshot. Sensors observe a signal embedded in noise, and each observation is phase modulated using a constant-modulus scheme and transmitted over a Gaussian multiple-access channel to a fusion center. At the fusion center, the mean and variance are estimated jointly, using an asymptotically minimum-variance estimator. It is shown that this joint estimator decouples into simple individual estimators of the mean and the variance. The constant-modulus phase modulation scheme ensures a fixed transmit power, robust estimation across several sensing noise distributions, as well as an SNR estimate that requires a single set of transmissions from the sensors to the fusion center. The estimators are evaluated in terms of asymptotic variance, which are then used to evaluate the performance of the SNR estimator with Gaussian and Cauchy sensing noise distributions in the cases of total transmit power constraint as well as a per-sensor power constraint. For each sensing noise distribution, the optimal phase transmission parameters are also determined. The asymptotic relative efficiency of the estimators is evaluated. It is shown that among the noise distributions considered, the estimators are asymptotically efficient only when the noise distribution is Gaussian. Simulation results corroborate analytical results. [ABSTRACT FROM AUTHOR]

A distributed estimation problem is considered with multiple-access channels between sensors and a fusion center. The sensors phase-modulate their noisy observations before transmitting them to the fusion center, where a signal parameter is estimated. The asymptotic efficiency of this estimator is then determined by using two inequalities that relate the Fisher information and the characteristic function. A necessary and sufficient condition for equality is found for the first time in the literature. The loss in efficiency of the distributed estimation scheme relative to the centralized approach is quantified for different sensing noise distributions. It is shown that this distributed estimation system does not incur an efficiency loss if and only if the sensing noise distribution is Gaussian. [ABSTRACT FROM AUTHOR]

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 4/π 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. [ABSTRACT FROM AUTHOR]