Capacity of Markov Channels with

While feedback does not increase the capacity of memoryless channels, the capacity of time-varying channels with feedback can be increased by exploiting the structure in the channel variations. Feedback information from the receiver is usually available at the transmitter only after some time delay. The capacity increase due to feedback depends on the feedback delay relative to the channel decorrelation time. We model time-varying channels as finite-state Markov channels and determine their capacity as a function of the feedback delay assuming perfect channel state information at the receiver. We apply the result to derive power control strategies to maximize the capacity for finite-state additive Gaussian noise channels and log-normal shadow fading channels. Mobile wireless communication channels are subject not only to additive white Gaussian noise but also to short-term and long- term fluctuations in the received signal strength. The received signal strength undergoes short-term fluctuations (fast fading) due to multi- path, and long-term fluctuations (slow fading) due to shadowing. Fast fading may be handled adequately through coding and interleaving. On the other hand, the interleaving depth required to combat slow fading is prohibitively large. In the absence of other diversity tech- niques such as multiple receive antennas, higher transmit power is required to prevent outage for slowly fading channels. Alternately, if feedback from the receiver to the transmitter is possible, then power control can be used to adjust the transmit power in accordance with the channel variations so that the received signal strength is constant. However, this constant received powercontrol scheme does not maximize throughput. Feedback information can be used more effectively to maximize throughput. Feedback does not increase the capacity of memoryless channels (3). But for time-varying channels, the use of feedback can increase