Performance of Distributed Estimation Over Unknown Parallel Fading Channels

Abstract

Print\ud Request Permissions\ud We consider distributed estimation of a source in additive Gaussian noise, observed by sensors that are connected to a fusion center with unknown orthogonal (parallel) flat Rayleigh fading channels. We adopt a two-phase approach of i) channel estimation with training and ii) source estimation given the channel estimates and transmitted sensor observations, where the total power is fixed. In the second phase we consider both an equal power scheduling among sensors and an optimized choice of powers. We also optimize the percentage of total power that should be allotted for training. We prove that 50% training is optimal for equal power scheduling and at least 50% is needed for optimized power scheduling. For both equal and optimized cases, a power penalty of at least 6 dB is incurred compared to the perfect channel case to get the same mean squared error performance for the source estimator. However, the diversity order is shown to be unchanged in the presence of channel estimation error. In addition, we show that, unlike the perfect channel case, increasing the number of sensors will lead to an eventual degradation in performance. We approximate the optimum number of sensors as a function of the total power and noise statistics. Simulations corroborate our analytical findings

Water-Filling Solution for Distributed Estimation of Correlated Data in WSN MIMO System

“…The simulation with ideal sensor condition is taken by assuming that the sensor observations have no distortion. To accommodate the assumption, we set the distortion due to observation noise, = 0, in (8). Then, the simulation with ideal channel condition is taken by assuming that the fusion center has a perfect channel knowledge between the sensors and the fusion center.…”

“…They revealed that extra transmissions beyond the dimension of the target do not improve the estimation performance. An orthogonal multiple access channel (MAC) model for distributed estimation was studied in [6,8]. To save energy, multiple-input and multipleoutput (MIMO) system has been analyzed by involving signaling overhead [9], in which the MIMO system can offer substantial energy savings in WSN.…”

“…Because the sensors deployed in a certain region are difficult to change the batteries, the low power consumption is important to guarantee a lifetime of the sensors. The distributed estimation is also applied on the orthogonal multiple access channel (MAC) model [4,6,8] and the coherent MAC model [2,5] that considers single-input single-output (SISO). To save energy, multiple-input and multiple-output (MIMO) system has been analyzed by involving signaling overhead [9], in which the MIMO system can offer substantial energy savings in WSN.…”

Decentralized estimation over orthogonal multiple-access fading channels in wireless sensor networks--optimal and suboptimal estimators

“…In orthogonal MACs, most of the existing works assume that perfect CSI is available at the FC. Recently, the impact of channel estimation errors on the decentralized detection in WSNs is studied in [22], and its impact on the decentralized estimation when using AF transmission is investigated in [23]. However, the decentralized estimation with unknown CSI for digital communications has still not been well understood.…”

Distributed Estimation over Unknown Fading Channels

“…In most works on distributed estimation, fading is in general ignored or assumed to be known. In a recent work, a distributed estimation scheme including a channel estimation using pilot signals has been suggested, Senol and Tepedelenlioglu (2008). The derivations were made for parallel channels in a fusion center based WSN.…”