Lower bound on mean squared channel estimation error for multiuser receiver

We investigate pilot-based multiuser channel estimation systems for a multipath radio environment, in which each user sends an individual N-periodic pilot sequence to the common receiver so as to estimate its N uncorrelated multipath components. For the case that all paths having the same average power output, we derive the optimal linear estimator in the absence of any prior knowledge about any distribution and give a lower bound on the maximum mean squared estimation error that grows linearly with the number of users. We also specify necessary and sufficient condition to attain this bound.