# The Method of Conditional Expectations for Cubic Metric Reduction in OFDM

## TL;DR

This paper introduces a low-complexity algorithm based on the Method of Conditional Expectations for reducing Cubic Metric in OFDM signals, significantly improving signal quality with guaranteed reduction.

## Contribution

It develops a novel CM reduction algorithm using CE Method and Sign Selection, providing analytical guarantees and nearly 3 dB gain with reduced rate loss.

## Key findings

- Achieves nearly 3 dB reduction in Cubic Metric.
- Provides analytical proof of guaranteed reduction for all data symbol combinations.
- Uses half the rate loss compared to traditional Sign Selection methods.

## Abstract

High variations in the OFDM signal envelope cause nonlinear distortion in the power amplifier of the transmitter, which is a major drawback. Peak-to-Average Power Ratio (PAPR) and Cubic Metric (CM) are commonly used for quantifying this characteristic of the signal. Despite the reportedly higher accuracy compared to PAPR, limited research has been done on reduction algorithms for CM. In this paper, the Method of Conditional Expectations (CE Method) is used to achieve CM reduction by the Sign Selection approach. Using the CE Method, the amenable mathematical structure of CM is exploited to develop a low complexity algorithm. In addition, guaranteed reduction is analytically proved for every combination of the data symbols. Simulations show a reduction gain of almost 3 dB in Raw Cubic Metric (RCM) for practically all subcarrier numbers, which is achieved using only half the full rate loss of the Sign Selection approach.