  We consider the problem of estimating channel fading coefficients (modeled as
a correlated Gaussian vector) via Downlink (DL) training and Uplink (UL)
feedback in wideband FDD massive MIMO systems. Using rate-distortion theory, we
derive optimal bounds on the achievable channel state estimation error in terms
of the number of training pilots in DL ($\beta_{tr}$) and feedback dimension in
UL ($\beta_{fb}$), with random, spatially isotropic pilots. It is shown that
when the number of training pilots exceeds the channel covariance rank ($r$),
the optimal rate-distortion feedback strategy achieves an estimation error
decay of $\Theta (SNR^{-\alpha})$ in estimating the channel state, where
$\alpha = min (\beta_{fb}/r , 1)$ is the so-called quality scaling exponent. We
also discuss an "analog" feedback strategy, showing that it can achieve the
optimal quality scaling exponent for a wide range of training and feedback
dimensions with no channel covariance knowledge and simple signal processing at
the user side. Our findings are supported by numerical simulations comparing
various strategies in terms of channel state mean squared error and achievable
ergodic sum-rate in DL with zero-forcing precoding.
