  Massive multi-input multi-output (MIMO) in Frequency Division Duplex (FDD)
mode suffers from heavy feedback overhead for Channel State Information (CSI).
In this paper, a novel manifold learning-based CSI feedback framework (MLCF) is
proposed to reduce the feedback and improve the spectral efficiency of FDD
massive MIMO. Manifold learning (ML) is an effective method for dimensionality
reduction. However, most ML algorithms focus only on data compression, and lack
the corresponding recovery methods. Moreover, the computational complexity is
high when dealing with incremental data. To solve these problems, we propose a
landmark selection algorithm to characterize the topological skeleton of the
manifold where the CSI sample resides. Based on the learned skeleton, the local
patch of the incremental CSI on the manifold can be easily determined by its
nearest landmarks. This motivates us to propose a low-complexity compression
and reconstruction scheme by keeping the local geometric relationships with
landmarks unchanged. We theoretically prove the convergence of the proposed
algorithm. Meanwhile, the upper bound on the error of approximating the CSI
samples using landmarks is derived. Simulation results under an industrial
channel model of 3GPP demonstrate that the proposed MLCF method outperforms
existing algorithms based on compressed sensing and deep learning.
