# Practical GFDM-based Linear Receivers

## TL;DR

This paper introduces GFDM-based linear receivers that simplify the design of MIMO systems by separating channel equalization and demodulation, providing practical solutions that approach optimal performance.

## Contribution

It defines GFDM-based linear receivers, demonstrating their equivalence to joint LMMSE receivers and proposing practical designs for non-orthogonal modulation.

## Key findings

- Optimal GFDM-based receiver is equivalent to joint LMMSE with CEq and ZF demodulation.
- Proposed practical designs approach joint LMMSE performance.
- GFDM-based receivers achieve equal SNR per subsymbol within the same subcarrier.

## Abstract

The conventional receiver designs of generalized frequency division multiplexing (GFDM) consider a large scale multiple-input multiple-output (MIMO) system with a block circular matrix of combined channel and modulation. Exploiting this structure, several approaches have been proposed for low complexity joint linear minimum mean squared error (LMMSE) receiver. However, the joint design is complicated and inappropriate for hardware implementation. In this paper, we define the concept of GFDM-based linear receivers, which first performs channel equalization (CEq) and afterwards the equalized signal is processed with GFDM demodulator. We show that the optimal joint LMMSE receiver is equivalent to a GFDM-based one, that applies LMMSE-CEq and zero-forcing demodulation. For orthogonal modulation, the optimal LMMSE receiver has an implementation-friendly structure. For the non-orthogonal case, we propose two practical designs that approach the performance of the joint LMMSE. Finally, we analytically prove that GFDM-based receivers achieve equal signal-to-interference-plus-noise ratio per subsymbols within the same subcarrier.