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We consider the problem of estimating the fading coefficients of a frequency-selective, spatially correlated channel via Downlink (DL) training and Uplink (UL) feedback in frequency division duplexing (FDD) massive MIMO systems. Using ratedistortion theory, we derive optimal bounds on the achievable channel state estimation error in terms of the number of training pilots in DL (&#x03B2;<inf>tr</inf>) and feedback dimension in UL (&#x03B2;<inf>fb</inf>), 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 &#x0398;pSNR<sup>&#x2212;&#x03B1;</sup>q in estimating the channel state, where &#x03B1; = minp&#x03B2;<inf>fb</inf>{r,1q is the so-called quality scaling exponent (QSE). We then discuss an "analog" feedback strategy, showing that it achieves the optimal QSE 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 these strategies in terms of channel state mean squared error and achievable ergodic sum-rate in DL with zero-forcing precoding.

Channel State Acquisition in FDD Massive MIMO: Rate-Distortion Bound and Effectiveness of "Analog" Feedback