# Moment-Based Bound on Peak-to-Average Power Ratio and Reduction with Unitary Matrix

## TL;DR

This paper derives a modulation-agnostic bound on the CCDF of PAPR in OFDM systems using moment analysis and proposes a unitary matrix-based method to reduce this bound, enhancing PAPR reduction strategies.

## Contribution

It introduces a new bound on PAPR CCDF that does not depend on modulation schemes and links it to fourth moments of codewords, along with a novel reduction method using unitary matrices.

## Key findings

- Derived a modulation-independent CCDF bound for PAPR.
- Established the relation between the bound and fourth moments of codewords.
- Proposed a unitary matrix method to effectively reduce the PAPR bound.

## Abstract

Reducing Peak-to-Average Power Ratio (PAPR) is a significant task in OFDM systems. To evaluate the efficiency of PAPR-reducing methods, the complementary cumulative distribution function (CCDF) of PAPR is often used. In the situation where the central limit theorem can be applied, an approximate form of the CCDF has been obtained. On the other hand, in general situations, the bound of the CCDF has been obtained under some assumptions. In this paper, we derive the bound of the CCDF with no assumption about modulation schemes. Therefore, our bound can be applied with any codewords and that our bound is written with fourth moments of codewords. Further, we propose a method to reduce the bound with unitary matrices. With this method, it is shown that our bound is closely related to the CCDF of PAPR.