Linear Encoder-Decoder-Controller Design over Channels with Packet Loss and Quantization Noise

Abstract — In this paper we consider the problem of designing coding and decoding schemes for linear control design of a scalar unstable stochastic linear system in the presence of a wireless communication channel between the sensor and the estimator. In particular, we consider a communication channel which is prone to packet loss and includes quantization noise due to its limited capacity. We first study the case of perfect channel feedback, where the transmitter is aware of the quantization noise and the packet loss history of the channel. We show that in this case, the optimal strategy among all possible linear encoders corresponds to the transmission of the Kalman filter innovation (the difference between the filtered state estimate at the transmitter and the predicted state estimate at the receiver) similarly to the differential pulse-code modulation (DPCM). Although the critical Signal-to-Quantization Noise Ratio (SQNR) required for stabilizing the system is the same for innovation forwarding as well as measurement forwarding at the transmitter, the latter is strictly suboptimal in terms of control performance. For the case of imperfect feedback, we assume that the channel feedback or acknowledgement is randomly lost with a certain erasure probability, rendering the transmitter ignorant of the control action taken by the receiver and subsequently applied to the plant. We propose several heuristic strategies for a suboptimal Kalman filter design at the transmitter based on estimation of the channel feedback status and compare their performances via numerical simulation studies. I