[Paper Review] The Problem of Peak-to-Average Power Ratio in OFDM Systems

Martha Cecilia Paredes Paredes, M. Julia Fernández‐Getino García|arXiv (Cornell University)|Mar 28, 2015

PAPR reduction in OFDM25 references22 citations

TL;DR

This paper provides a comprehensive survey and mathematical analysis of Peak-to-Average Power Ratio (PAPR) reduction techniques in Orthogonal Frequency Division Multiplexing (OFDM) systems. It evaluates clipping, coding, Selected Mapping (SLM), Orthogonal Pilot Sequences (OPS), and amplitude predistortion methods, demonstrating that SLM and OPS achieve up to 1.5 dB PAPR reduction at 10⁻³ CCDF, while amplitude predistortion achieves up to 2.5 dB reduction for N=256 subcarriers.

ABSTRACT

Orthogonal Frequency Division Multiplexing (OFDM) is widely used in many digital communication systems due to its advantages such us high bit rate, strong immunity to multipath and high spectral efficiency but it suffers a high Peak-to-Average Power Ratio (PAPR) at the transmitted signal. It is very important to deal with PAPR reduction in OFDM systems to avoid signal degradation. Currently, the PAPR problem is an active area of research and in this paper we present several techniques and that mathematically analyzed. Moreover their advantages and disadvantages have been enumerated in order to provide the readers the actual situation of the PAPR problem.

Motivation & Objective

• To analyze the root cause and impact of high PAPR in OFDM systems, particularly its degradation of performance due to nonlinear high-power amplifiers (HPAs).
• To evaluate and compare the effectiveness of major PAPR reduction techniques, including clipping, coding, SLM, OPS, and amplitude predistortion.
• To provide a mathematical foundation and comparative assessment of advantages and disadvantages of each technique, especially regarding in-band distortion, out-of-band radiation, and need for side information.
• To present simulation results quantifying PAPR reduction performance across different techniques and system parameters (e.g., subcarrier count N).

Proposed method

• Models the OFDM signal using an Inverse Discrete Fourier Transform (IDFT), with time-domain signal s[n] derived from frequency-domain symbols S(k) via IDFT operation.
• Defines PAPR as the ratio of maximum instantaneous power to average power: χ = max(|s|²) / E[|s|²], with performance evaluated using the Complementary Cumulative Distribution Function (CCDF).
• Applies clipping by limiting signal amplitude to a threshold A, with phase preservation for clipped values, but acknowledges resulting in-band distortion and out-of-band radiation.
• Evaluates coding techniques that select codewords with inherently low PAPR to reduce peak power without signal distortion.
• Analyzes distortionless techniques: SLM (uses multiple phase sequences), OPS (uses orthogonal pilot sequences), and Tone Reservation (TR), distinguishing those requiring side information (e.g., PTS) from those that do not (e.g., SLM, OPS).
• Introduces amplitude predistortion (SAP) as a linear pre-processing technique that modifies signal envelope before transmission to reduce PAPR without introducing distortion.

Experimental results

Research questions

• RQ1 What are the primary causes and consequences of high PAPR in OFDM systems, particularly in relation to HPA nonlinearity?
• RQ2 How do clipping-based techniques affect system performance in terms of BER and adjacent channel interference?
• RQ3 What are the trade-offs between PAPR reduction gain, computational complexity, and the need for side information across different distortionless techniques?
• RQ4 To what extent can amplitude predistortion reduce PAPR without introducing distortion or out-of-band radiation?
• RQ5 How does the number of subcarriers (N) and the number of sequences (U or M) influence the PAPR reduction performance of SLM and OPS techniques?

Key findings

• For N=256 subcarriers, conventional OFDM signals exceed a PAPR of 10.5 dB with a probability of 10⁻³, highlighting the severity of the PAPR problem.
• Selected Mapping (SLM) with U=2 sequences achieves approximately 1.5 dB PAPR reduction at a CCDF of 10⁻³, with further gains observed as U increases.
• Orthogonal Pilot Sequences (OPS) with M=16 sequences also achieves around 1.5 dB PAPR reduction at 10⁻³ CCDF for N=256 subcarriers.
• Simple Amplitude Predistortion (SAP) with α=1.55 and L≥4 oversampling achieves up to 2.5 dB PAPR reduction at 10⁻³ CCDF, outperforming SLM and OPS.
• Oversampling (L≥4) significantly reduces peak power regrowth in clipping-based methods, improving effectiveness when combined with filtering.
• Techniques like SLM and OPS do not require side information transmission, while PTS and TR do, which affects system complexity and spectral efficiency.