Technological advances have made wireless sensors cheap and reliable enough to be brought into industrial use. A major challenge arises from the fact that wireless channels introduce random packet dropouts. Power control and coding are key enabling t
echnologies in wireless communications to ensure efficient communications. In the present work, we examine the role of power control and coding for Kalman filtering over wireless correlated channels. Two estimation architectures are considered: In the first, the sensors send their measurements directly to a single gateway. In the second scheme, wireless relay nodes provide additional links. The gateway decides on the coding scheme and the transmitter power levels of the wireless nodes. The decision process is carried out on-line and adapts to varying channel conditions in order to improve the trade-off between state estimation accuracy and energy expenditure. In combination with predictive power control, we investigate the use of multiple-description coding, zero-error coding and network coding and provide sufficient conditions for the expectation of the estimation error covariance matrix to be bounded. Numerical results suggest that the proposed method may lead to energy savings of around 50 %, when compared to an alternative scheme, wherein transmission power levels and bit-rates are governed by simple logic. In particular, zero-error coding is preferable at time instances with high channel gains, whereas multiple-description coding is superior for time instances with low gains. When channels between the sensors and the gateway are in deep fades, network coding improves estimation accuracy significantly without sacrificing energy efficiency.
We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice
quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.
