To Drop or Not to Drop: Receiver Design Principles for Estimation over Wireless Links

In this paper we consider estimation of a multiple-input multiple-output dynamical system over a wireless fading communication channel using a Kalman filter. We are interested in finding the optimum receiver design in terms of handing noisy samples. We reformulate the estimation problem to include the impact of stochastic communication noise in the noisy packets. We will show how the eigenvalues of the state transition matrix A affect the optimum receiver design. We prove that, in the absence of a cross-layer information path, packet drop should be designed to balance information loss and communication noise in order to optimize the performance. In the presence of a cross-layer path, we show that keeping all the packets will minimize the average estimation error covariance. We also derive the stability condition in the presence of noisy packets and prove that it is independent of the shape of the communication noise variance or availability of a cross-layer information path.