# Reconfigurable Fully-Unrolled 2D-FFT Core Generator for Multi-Antenna mmWave Communication

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## Short Description

The millimeter wave (mmWave) spectrum offers vast amounts of unused frequency bands available for high-bandwidth wireless communication and is widely believed to be a key enabler in beyond 5G (B5G) systems. Due to the high propagation loss at these frequencies, mmWave communication is expected to be combined with large antenna arrays in order to compensate for the path loss. On the other hand, the high path loss results in only a few transmission paths with significant energy between transmitter and receiver, which makes the beamspace-domain representation of channel vectors sparse [1]. This beamspace-domain sparsity provides an opportunity for designing low-power baseband processing architectures by reducing the average number of multiplications [2,3].

In order to exploit this beamspace-domain sparsity, one has to first transform the antenna-domain received vectors into the beamspace domain using the discrete Fourier transform (DFT). Almost all existing DFT processors are based on the well-known fast Fourier transform (FFT) algorithm [4]. Most existing implementations focus on iterative or parallel pipelined FFT architectures which process one or multiple complex words of the input vector at a time. However, for beamspace transform applications, we need to convert each received vector into the beamspace domain at the baseband sampling rate, which can be in the order of billions of vectors per second for the future high-bandwidth wireless communication systems. Therefore, the most efficient architectures are the fully-unrolled FFTs, which process all entries of the vector at once and produce one transformed vector per clock cycle. We have designed a MATLAB script that generates Verilog code for fully-unrolled FFTs suitable for uniform linear antenna arrays [5]. Recently, there has been growing interest in utilizing rectangular antenna arrays, which require 2-dimensional DFTs to transform the received data from the antenna array into the beamspace domain [6,7].

The goal of this project is to design an FFT core generator that can support N-point 1-D FFT as well as N_1×N_2 2-D FFTs, for N_1 and N_2 that are powers of 2 and N=N_1×N_2, on the same hardware. This can be achieved by extending our FFT core generator, so that twiddle factors can be programmed to perform the desired 1-D or 2-D FFT operations. We will then implement the resulting 2-D FFT core as an ASIC and explore its area and power consumption using realistic stimuli. The project also includes MATLAB simulations for a mmWave massive MIMO system with channels generated by QuadRiGa [8] or from a commercial raytracing channel simulator for rectangular antenna arrays.

[1] S. H. Mirfarshbafan, A. Gallyas-Sanhueza, R. Ghods and C. Studer, "Beamspace Channel Estimation for Massive MIMO mmWave Systems: Algorithm and VLSI Design," IEEE Transactions on Circuits and Systems I, Dec. 2020

[2] S. H. Mirfarshbafan and C. Studer, "Sparse Beamspace Equalization for Massive MU-MIMO MMWave Systems," IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020

[3] S. H. Mirfarshbafan and C. Studer, "SPADE: Sparsity-Adaptive Equalization for MMwave Massive MU-MIMO," IEEE Statistical Signal Processing Workshop (SSP), 2021

[4] J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Mathematics of computation, vol. 19, no. 90, pp. 297–301, 1965

[5] S. H. Mirfarshbafan, S. Taner and C. Studer, "SMUL-FFT: A Streaming Multiplierless Fast Fourier Transform," in IEEE Transactions on Circuits and Systems II: Express Briefs, May 2021

[6] M. Mahmood, A. Koc and T. Le-Ngoc, "2D Antenna Array Structures for Hybrid Massive MIMO Precoding," IEEE GLOBECOM 2020

[7] A. Koc, A. Masmoudi and T. Le-Ngoc, "3D Angular-Based Hybrid Precoding and User Grouping for Uniform Rectangular Arrays in Massive MU-MIMO Systems," IEEE Access, vol. 8, pp. 84689-84712, 2020, doi: 10.1109/ACCESS.2020.2992713.

[8] S. Jaeckel, L. Raschkowski, K. Börner, L. Thiele, F. Burkhardt, and E. Eberlein, “QuaDRiGa - quasi deterministic radio channel generator user manual and documentation,” Fraunhofer Heinrich Hertz Institute, Tech. Rep. v2.0.0, Aug. 2017

### Status: Available

- Semester or master project for 1-2 students
- Contact: Seyed Hadi Mirfarshbafan

### Prerequisites

- Matlab or Python
- Verilog or VHDL
- VLSI II

### Character

- 50% VLSI implementation
- 30% MATLAB simulation
- 20% Literature search

### Professor