Polynomial Expansion-Based MMSE Channel Estimation and Precoding for Massive MIMO-GFDM Systems

In this paper, low-complexity channel estimators and precoders are proposed for massive multiple-input multiple-output generalized frequency division multiplexing (MIMO-GFDM) systems. In order to combat the effect of non-orthogonality in GFDM, interference-free pilots are used in frequency-domain minimum mean square error (MMSE) channel estimation. Polynomial expansion is used to approximately compute the matrix inverses in the conventional MMSE estimation and precoding, consequently reducing the cubic computational complexity to square order. The degree of the matrix polynomial can be properly selected to get a required trade-off between complexity and estimation/precoding performance. Different weights can be assigned to the terms in the polynomial expansion and be optimized to achieve a minimal mean square error (MSE). Derived limits on the MSE of the proposed estimators can predict their performance in the high E-s/N-0 region. Then, we derive a Cramer-Rao lower bound (CRLB) and use it as a benchmark for the estimators. In addition, the related computational complexity and the impacts of the polynomial degree are also investigated. Numerical results show the accuracy of the proposed channel estimators and precoders.