ThesisTransmission of Analog Source Samples for Remote and Distributed Sensing
This thesis considers transmission of sporadic random samples in three scenarios which can be summarized as a single source with remote sensing, dual and multiple source cases with distributed and remote sensing. The protocol and the transmission strategy is reminiscent of reverse ARQ protocols appearing in different contexts in the literature and we show how it can be used for energy-limited sensors making use of future broadband cellular networks. To begin with, a low-latency, two-way parameter modulation-estimation protocol for wide-band channels which is inspired by the classical scheme in  is presented and analyzed in terms of its asymptotic behaviour with non-coherent detection on both pure line-of sight and more general fading channels. The proposed scheme as well as known one-way schemes are compared with classical [2, 3] and very recent lower bounds . Both the bounds and performance evaluation of the two-way protocol are extended to a multi-channel fading model. The improvement of the feedback protocol over one-shot transmission is shown to be very significant on both line-of-sight and fading channels.
We proceed with introducing lower bounds on the reconstruction error for transmission of two continuous correlated random vectors sent over a sum channel using the help of two causal feedback links from the decoder to the encoders connected to each sensor. This construction is considered for both for uniformly and normally distributed and correlated sources. Additionally, the novel single-source protocol from the first part described above is extended to the dual-source case again both for uniformly and normally distributed sources. The asymptotic performance of the protocol is analyzed and an upper bound on the distortion level is derived for two rounds considering the extreme case of high correlation among the sources for each distribution. It is shown by both the upper and lower-bounds that collaboration can be achieved through energy accumulation. Analytical results are supported by numerical analysis to show the improvement in terms of distortion to be gained by retransmission subject to the average energy used by protocol.
Lastly, lower bounds are derived for the reconstruction error of a single normally or uniformly-distributed finite-dimensional vector imperfectly measured by a network of sensors and transmitted with finite energy to a common receiver via an additive white Gaussian noise asynchronous multiple access channel. Transmission makes use of a perfect causal feedback link to the encoder connected to each sensor. The retransmission protocol from the first part is further extended to this more general network scenario, for which asymptotic upper-bounds on the reconstruction error are provided. Both the upper and lower-bounds show that collaboration can
be achieved through energy accumulation under certain circumstances. In order to investigate the practical performance of the proposed retransmission protocol we provide a numerical evaluation of the upper-bounds in the non-asymptotic energy regime using low-order quantization in the sensors. It is shown through numerical evaluation that an increase in the size of the network brings benefit in terms of performance, but that the gain in terms of energy efficiency diminishes quickly at finite energies due to a non-coherent combining loss.