On Adaptive Sensing of Complex Communication Channels

We consider the application of an optimal measurement selection technique to a discrete-time extended Kalman filter for tracking a complex vector communication channel. The optimal linear measurement is selected prior to taking the observation at each step of the filter. The measurement is described through a measurement matrix B that depends on the prior state covariance, the available energy, and the observation noise variance. The rows of this measurement matrix represent the complex vector excitations to the communication channel, i.e. the transmitted signals, and outputs are used for channel estimation. Two aspects of the problem are discussed: 1) inherent difficulties with complex state vectors, and 2) a dynamical system model for the time-varying channel.