Structured Tensor Decomposition for FDD Massive MIMO Downlink Channel Reconstruction

The downlink channel reconstruction at the base station holds paramount significance across a multitude of applications in FDD massive MIMO systems. Conventional approaches rely on downlink training and feedback with a considerable overhead. In order to mitigate this issue, we propose a tensor-based framework for downlink channel reconstruction that leverages the partial reciprocity between the uplink and downlink channels. By modeling the uplink channel as a multi-dimensional tensor, we estimate the reciprocal channel parameters via a low-rank tensor decomposition. This approach effectively captures the correlation between arrays, subcarriers, and polarizations of the channel. In addition to the classical tensor decomposition, we exploit the exponential structure of the decomposed antenna and delay steering matrices, and propose a structured tensor decomposition algorithm. The proposed algorithm enhances the exponential structure via a tensor rank-1 constraint by incorporating the Hankel transform. The resulting optimization problem is rendered tractable by introducing a domain conversion matrix to facilitate the mapping of variables between the Hankel transform domain and the original domain. The proposed method exhibits superior noise robustness compared to conventional algebraic closed-form methods based on the Vandermonde constrained tensor decomposition. Experimental results with both simulated data and a Ray-tracing dataset demonstrate the effectiveness and superior downlink reconstruction accuracy of our proposed methods compared with several alternative approaches.