# Low-Complexity OFDM Spectral Precoding

## TL;DR

This paper introduces a low-complexity spectral precoding method for OFDM systems that efficiently enforces spectrum masks using divide-and-conquer and specialized algorithms, significantly reducing computational load.

## Contribution

It proposes a novel divide-and-conquer approach with closed-form solutions and three low-complexity algorithms for spectral precoding in large-scale OFDM systems.

## Key findings

- Outperforms previous methods in computational efficiency.
- Achieves spectrum mask compliance with reduced complexity.
- Semi-analytical method converges in about 3 iterations.

## Abstract

This paper proposes a new large-scale mask-compliant spectral precoder (LS-MSP) for orthogonal frequency division multiplexing systems. In this paper, we first consider a previously proposed mask-compliant spectral precoding scheme that utilizes a generic convex optimization solver which suffers from high computational complexity, notably in large-scale systems. To mitigate the complexity of computing the LS-MSP, we propose a divide-and-conquer approach that breaks the original problem into smaller rank 1 quadratic-constraint problems and each small problem yields closed-form solution. Based on these solutions, we develop three specialized first-order low-complexity algorithms, based on 1) projection on convex sets and 2) the alternating direction method of multipliers. We also develop an algorithm that capitalizes on the closed-form solutions for the rank 1 quadratic constraints, which is referred to as 3) semi-analytical spectral precoding. Numerical results show that the proposed LS-MSP techniques outperform previously proposed techniques in terms of the computational burden while complying with the spectrum mask. The results also indicate that 3) typically needs 3 iterations to achieve similar results as 1) and 2) at the expense of a slightly increased computational complexity.