Outage Behavior of Discrete Memoryless Channels (DMCs) Under Channel Estimation Errors

Communication systems are usually designed by assuming perfect channel state information (CSI). However, in many practical scenarios, only a noisy estimate of the channel is available, which may strongly differ from the true channel. This imperfect CSI scenario is addressed by introducing the notion of estimation-induced outage (EIO) capacity. We derive a single-letter characterization of the maximal EIO rate and prove an associated coding theorem and its strong converse for discrete memoryless channels (DMCs). The transmitter and the receiver rely on the channel estimate and the statistics of the estimate to construct codes that guarantee reliable communication with a certain outage probability. This ensures that in the non-outage case the transmission meets the target rate with small error probability, irrespective of the quality of the channel estimate. Applications of the EIO capacity to a single-antenna (non-ergodic) Ricean fading channel are considered. The EIO capacity for this case is compared to the EIO rates of a communication system in which the receiver decodes by using a mismatched ML This research is supported in part by the FP7 Network of Excellence in Wireless COMmunications NEWCOM. P. Piantanida is with the Department of Telecommunications, SUPELEC, 91192 Gif-sur-Yvette, France, Email: [email protected]. G. Matz is with the Institute of Communications and Radio-Frequency Engineering, Vienna University of Technology, A-1040 Wien, Austria, Email: [email protected]. P. Duhamel is with the Laboratoire des Signaux et Systemes, CNRS-SUPELEC, 91192 Gif-sur-Yvette, France, Email: [email protected].