Estimation in the Gaussian Multiplex Channel

An abstraction for multisensor communication termed the Gaussian Multiplex Channel is presented and analyzed. In this model, the sensor outputs can be added together in any combination through a network of switches, and the combinations can be changed arbitrarily during the observation interval. The sensor output sums are observed in additive Gaussian noise. Using a mean square error cost function and a constraint on the total observation time, an optimal set of combinations (switch positions) and observation times is determined. The solution exhibits high complexity (number of different combinations) even for moderate numbers of sensors. It is then shown that there exists an alternative solution based on Hadamard designs, which achieves the same minimizing MSE cost function and only requires a number of combinations equal to the number of sensors.