Effect of error in channel state information on the channel capacity with QAM signalling and the design of robust signal constellations

The effects of channel estimation errors on the channel capacity of a discrete time, discrete input, infinite output Rayleigh fading channel are investigated. The case of conventional modulation methods such as phase shift keying (PSK) and quatrature amplitude modulation (QAM) is investigated at first where it was observed that the capacity degrades rapidly with increasing channel estimation errors. The effect of error in the channel estimation is similar to the effect of higher noise in the channel that depends on the transmitted signal. A genetic algorithm is used to optimise the signal constellation in order to maximise the capacity for a given finite number of signal points. The aim of trying to maximise the capacity is to estimate the remaining gap in performance between a traditional modulation scheme such as QAM and the best possible constellation that is optimised for the channel. The constellations obtained from the genetic algorithm are, in general, not directly implementable. A method to design practical robust signal constellations that overcome the effect of channel state information (CSI) error is presented. The robust signal constellations obtained show a performance that is very close to the optimal constellations. In this work, the probability distribution of the error in CSI is assumed to be known.