How much training is needed in fading multiple access channels?

We optimize the tradeoff between multiuser diversity and training overhead in a single antenna narrowband multiple access channel with a large number of users. A block fading model with independent Rayleigh gains is considered, in which training sequences are sent to the base station one at a time and the user estimated to be the strongest is scheduled to transmit. Considering a lower bound on the ergodic sum capacity with channel uncertainty under an average total power constraint, we optimize the proportion of time and power spent on training in each block. By analyzing the asymptotic behavior of the system as the block length grows large, we optimize the number of users considered for transmission in each block with respect to an approximate expression for the achievable rate, and find first order expressions for the resulting parameters.