FDD Massive MIMO via UL/DL Channel Covariance Extrapolation and Active Channel Sparsification
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We propose a novel method for massive Multiple-Input Multiple-Output (massive MIMO) in Frequency Division Duplexing (FDD) systems. Due to the large frequency separation between Uplink (UL) and Downlink (DL), in FDD systems channel reciprocity does not hold. Hence, in order to provide DL channel state information to the Base Station (BS), closed-loop DL channel probing and feedback is needed. In massive MIMO this incurs typically a large training overhead. For example, in a typical configuration with M ≃ 200 BS antennas and fading coherence block of T ≃ 200 symbols, the resulting rate penalty factor due to the DL training overhead, given by {0, 1 - M/T}, is close to 0. To reduce this overhead, we build upon the observation that the Angular Scattering Function (ASF) of the user channels is invariant over the frequency domain. We develop a robust and stable method to estimate the users' DL channel covariance matrices from pilots sent by the users in the UL. The resulting DL covariance information is used to optimize a sparsifying precoder, in order to limit the effective channel dimension of each user channel to be not larger than some desired DL pilot dimension T_ dl. In this way, we can maximize the rank of the effective sparsified channel matrix subject to a desired training overhead penalty factor {0, 1 - T_ dl / T}. We pose this problem as a Mixed Integer Linear Program, that can be efficiently solved. Furthermore, each user can simply feed back its T_ dl pilot measurements. Thus, the proposed approach yields also a small feedback overhead and delay. We provide simulation results demonstrating the superiority of the proposed approach with respect to state-of-the-art "compressed DL pilot" schemes based on compressed sensing.
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