On Capacity of the Writing onto Fast Fading Dirt Channel

The classic Costa’s “writing on dirty paper” capacity result establishes that full state pre-cancellation can be attained in the Gel’fand-Pinsker channel with additive state and additive Gaussian noise. This result holds under the assumption that perfect channel knowledge is available at both transmitter and receiver: such an assumption is not valid in wireless scenarios affected by fading and with limited feedback rates. For this reason, we investigate the capacity of the “writing on fast fading dirt’ channel, a variation of the “writing on dirty paper” channel in which the state sequence is multiplied by an ergodic fading process unknown at the transmitter. We consider two scenarios: when the fading process in not known at either the transmitter or the receiver and when it is known only at the receiver. For both, cases we derive novel assessments of capacity which clearly indicate the limits of state pre-cancellation in the presence of fast fading. Index Terms Gel’fand-Pinsker Problem; Writing on Fading Dirt; Carbon Copying onto Dirty Paper; Ergodic Fading; Costa pre-coding; INTRODUCTION Costa [1] showed that the capacity of the “writing on dirty paper” channel, the Gaussian version of the Gel’fand-Pinsker [2] channel, is equal to the capacity of the Gaussian point-to-point channel without state, regardless of the power or the distribution of the state sequence. Albeit very promising, this result assumes that perfect channel knowledge is available at the users and the attainable rate quickly degrade with any uncertainty in the channel knowledge. The assumption of perfect channel knowledge does not hold in communication scenarios where channel conditions vary over time and with limited feedback between the receiver and the transmitter. This paper investigates the effects of partial channel knowledge on the performance of state precancellation and the topic of robust pre-coding. More specifically, we study the “dirty paper channel with fast fading dirt”, a variation of Costa’s “writing on dirty paper” channel in which the state sequence is multiplied by an ergodic fading process. We consider both the case in which neither the transmitter nor the receiver have knowledge of the fading values and the case The work of S. Rini was funded by the Ministry Of Science and Technology (MOST) under the grant 103-2218-E-009-014-MY2. The work of S. Shamai was supported by the Israel Science Foundation (ISF) and by the European FP7 NEWCOM#.