Adaptive Training for Correlated Fading Channels with Feedback

We consider data transmission through a time selective(correlated) flat Rayleigh fading channel under an average power constraint. The channel is estimated at the receiver with a pilot signal, and the estimate is fed back to the transmitter. The estimate is used for coherent demodulation, and to adapt the data and pilot powers. We start with a block fading channel in which the channel gain changes according to a Gauss-Markov process. The channel estimate is updated during each coherence block with a Kalman filter, and optimizing the data and pilot powers is formulated as a dynamic program. We then study a continuous limit in which the coherence time tends to zero, and the correlation between successive channel gains tends to one, so that the channel process becomes a diffusion process. In this limit it is shown that the optimal pilot power control policy is