On the Optimal Performance in Asymmetric Gaussian Wireless Sensor Networks With Fading

Abstract

Abstract-We study the estimation of a Gaussian source by a Gaussian wireless sensor network (WSN) where distributed sensors transmit noisy observations of the source through a fading Gaussian multiple access channel to a fusion center. In a recent work Gastpar, ["Uncoded transmission is exactly optimal for a Simple Gaussian Sensor Network," IEEE Trans. Inf. Theory, vol. 54, no. 11, pp. 5247-5251, Nov. 2008] showed that for a symmetric Gaussian WSN with no fading, uncoded (analog) transmission achieves the optimal performance theoretically attainable (OPTA). In this correspondence, we consider an asymmetric fading WSN in which the sensors have differing noise and transmission powers. We first present lower and upper bounds on the system's OPTA under random fading. We next focus on asymmetric networks with deterministic fading. By comparing the obtained lower and upper OPTA bounds under deterministic fading, we provide a sufficient condition for the optimality of the uncoded transmission scheme for a given power tuple = ( . . . ).Then, allowing the sensor powers to vary under a weighted sum constraint (this includes the sum-power constraint as a special case), we obtain a sufficient condition for the optimality of uncoded transmission and provide the system's corresponding OPTA.Index Terms-Gaussian multiple access channel with fading, joint source-channel coding, power-distortion tradeoff, remote source coding, sensor networks, uncoded transmission.

Non-linear coding and decoding strategies exploiting spatial correlation in wireless sensor networks

“…to be transmitted over a Gaussian channel, where uncoded and 'instantaneous' (also known as 'single-letter' or 'real-time') transmission is optimal (in the sense of achieving minimum quadratic distortion under a power constraint) [4], there are recent interesting results that prove the optimality of such uncoded schemes for a class of Gaussian sensor networks in general [5] (after a scaling-law optimality of uncoded transmission had been shown previously to hold for the same class of networks [6,7]). The result of [5] has been generalised to the asymmetric case of different power constraints and noise, and by considering also the sum power constraint [8].…”

“…We will refer to (8) and 9here as linear strategies. We must note that, even if (8) and 9result in non-exactly optimal strategies, they represent a reasonable choice for a distributed environment with possibly unknown sensor locations and a useful tool to derive insights into the performance sensitivity of Problem 1.…”

“…We must note that, even if (8) and 9result in non-exactly optimal strategies, they represent a reasonable choice for a distributed environment with possibly unknown sensor locations and a useful tool to derive insights into the performance sensitivity of Problem 1. Actually, a nonuniform power distribution among the sensors under the global constraint (6), instead of the uniform distribution implied by (8), is impractical when the position of the sensors is not under control and the price to pay for some signalling scheme (reporting the state of each sensor to a centralised unit) results in excessive computational and bandwidth overhead. We also must note that no information about the spatial correlation is exploited by the linear strategies.…”

“…We take a different approach here, by trying to determine the optimal strategies (2) and 4, and by then looking at the 'power distribution' that they entail, which is not uniform among the sensors (differently from the linear strategies, which uniformly allocate the available power, see (8)). Since the strategic optimisation of Problem 1 is a dynamic team optimisation problem with non-nested information structure, for which no analytical solution is available, we attempt to approximate the optimal strategies by means of non-linear parametric approximating functions based on neural networks, in order to get some insight into their structure.…”

Power-Distortion Metrics for Path Planning Over Gaussian Sensor Networks

“…For a particular symmetric setting, Gastpar showed that indeed the AF scheme is optimal over all arXiv:1602.06375v1 [cs.IT] 20 Feb 2016 encoding/decoding methods that allow arbitrarily high delay [20]. However, it was also shown that, in more realistic asymmetric settings, the AF scheme may be suboptimal [21]. In [22], optimal communication strategies were studied for transmitting jointly Gaussian sources over a Gaussian MAC.…”