  This work considers distributed sensing and transmission of sporadic random
samples. 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. A retransmission protocol inspired by the
classical scheme in [1] applied to the transmission of single and bi-variate
analog samples analyzed in [2] and [3] is extended to the 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. The latter includes
a minor modification of the protocol to improve reconstruction fidelity.
Numerical results show 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.
