Improving control performance across AWGN channels using a relay node†

Consider an unstable linear time-invariant system in which the sensor transmits information to a controller across an additive white Gaussian noise channel. The designer can optionally utilise a relay node to assist the controller; however, the total transmission power consumed by the sensor and the relay node is constant. We consider two topologies: (1) a Gaussian relay channel and (2) a cascade of two Gaussian point-to-point channels. We propose coding schemes and present sufficient conditions for the stabilisability of the plant through such schemes. The analysis suggests that it is useful to utilise a relay node, even if the total transmission power remains the same.

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