  We consider the problem of estimating the states of weakly coupled linear
systems from sampled measurements. We assume that the total capacity available
to the sensors to transmit their samples to a network manager in charge of the
estimation is bounded above, and that each sample requires the same amount of
communication. Our goal is then to find an optimal allocation of the capacity
to the sensors so that the average estimation error is minimized. We show that
when the total available channel capacity is large, this resource allocation
problem can be recast as a strictly convex optimization problem, and hence
there exists a unique optimal allocation of the capacity. We further
investigate how this optimal allocation varies as the available capacity
increases. In particular, we show that if the coupling among the subsystems is
weak, then the sampling rate allocated to each sensor is nondecreasing in the
total sampling rate, and is strictly increasing if and only if the total
sampling rate exceeds a certain threshold.
