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Communications receivers are commonly optimized with respect to a stationary interference source. When the interference originates in a composite source, the optimal receiver may be represented as a collection of generically similar subreceivers each one of which is optimized with respect to one of the interference subsources. Selection of the correct subreceiver is conditioned on identifying the subsource that is interfering at a given time. This selection process is controlled by a statistical demultiplexer, In the absence of real communications, when the statistical demultiplexer operates on uncorrelated noise, its function is to estimate the present state of a spectrally white, non-Gaussian, nonstationary random process. To evaluate the performance of the statistical demultiplexer, it is necessary to assert that the state of the observed process is itself a stationary (unobservable) process. Consideration is given to the case in which the unobservable is Markov. When the receiver is an isolated system that draws power from a limited reservior of energy, and messages arrive only sporadically, the statistical demultiplexer in its simplest form detects the mere presence of the message and control a switch in the power line to the main receiver subsystem. The alertness strategy embodied in this scheme can greatly extend the life-time of the system under conditions that are considered in some detail.