OFDM峰均功率比降低技术综述

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OFDM（正交频分复用）是一种广泛应用于无线通信的高效多载波调制技术，其主要优点包括高谱效率、对多径延迟容忍度强、抗频率选择性衰落以及功率效率较高。然而，OFDM信号的一个显著问题是高峰均功率比（Peak-to-Average Power Ratio, PAPR），这可能导致在无线传输过程中功率放大器（High Power Amplifier, HPA）工作在非线性区域，从而降低系统性能并限制了发射功率的提升。本文发表于《IEEE Transactions on Broadcasting》2008年6月第54卷第2期，作者Tao Jiang和Yiyan Wu，两位均为IEEE会员。文章的主旨是对OFDM系统中各种PAPR降低技术进行了全面的回顾与分析。作者根据计算复杂性、带宽扩展、频谱泄漏以及性能指标，对这些技术进行了深入探讨。首先，介绍部分强调了PAPR问题对于OFDM系统的重要性，它直接影响到系统的可靠性和功放效率。为了克服这一挑战，研究者们提出了多种策略，如： 1. **基于计算复杂性的方法**：这些技术可能涉及信号处理算法的优化，以减少峰值出现的频率或降低其幅度，但可能增加系统处理负担，需要权衡复杂度和性能。 2. **带宽扩展技术**：通过在信号的原频带之外添加虚拟子载波，可以分散信号的能量，降低峰值，但可能会占用更多的频谱资源。 3. **频谱泄漏控制**：通过精心设计信号的编码或调制方式，避免能量集中在特定频段，从而减小峰值，但可能影响信号的纯净度。 4. **互补累积分布函数（Complementary Cumulative Distribution Function, CCDF）的应用**：这是一种统计方法，通过调整信号的概率分布来降低峰值出现的概率，但可能牺牲一定的误码率性能。 5. **针对多用户OFDM系统的PAPR降低**：考虑到无线通信中可能存在的多个用户，需要考虑多用户干扰和协作，以实现全局的PAPR降低，这需要更复杂的资源管理和协调策略。 6. **峰值功率管理**：通过对信号进行预处理或后处理，如信号量化、窗口函数应用等，可以在不显著增加系统复杂度的情况下，有效降低PAPR。本文深入分析了OFDM系统中峰均功率比问题的解决方案，为无线通信系统的工程实践提供了有价值的参考，特别是在追求高效、低复杂度和高质量服务的现代无线网络中。通过选择合适的PAPR降低技术，系统设计者能够平衡信号质量、功耗和硬件成本，进一步推动OFDM技术的发展和广泛应用。

JIANG AND WU: OVERVIEW OF PEAK-TO-AVERAGE POWER RATIO REDUCTION TECHNIQUES FOR OFDM SIGNALS 259

B. Passband PAPR

Note that, if

is large, an OFDM system usually does not

employ pulse shaping, since the power spectral density of the

band-limited OFDM signal is approximately rectangular. Thus,

the amplitude of OFDM RF signals can be expressed as

(7)

where

is the carrier frequency and . Therefore, the

peak of RF signals is equivalent to that of the complex baseband

signals.

Moreover, the average power of the passband signal is

(8)

Therefore, the passband PAPR is approximately twice the

baseband PAPR, i.e.

(9)

In this paper, we only consider the PAPR of the baseband

OFDM signals.

IV. M

OTIVATION OF

PAPR R

EDUCTION

A. Nonlinear Characteristics of HPA and ADC

Most radio systems employ the HPA in the transmitter

to obtain sufﬁcient transmission power. For the proposed of

achieving the maximum output power efﬁciency, the HPA is

usually operated at or near the saturation region. Moreover,

the nonlinear characteristic of the HPA is very sensitive to the

variation in signal amplitudes.

However, the variation of OFDM signal amplitudes is

very wide with high PAPR. Therefore, HPA will introduce

inter-modulation between the different subcarriers and in-

troduce additional interference into the systems due to high

PAPR of OFDM signals. This additional interference leads

to an increase in BER. In order to lessen the signal distortion

and keep a low BER, it requires a linear work in its linear

ampliﬁer region with a large dynamic range. However, this

linear ampliﬁer has poor efﬁciency and is so expensive. Power

efﬁciency is very necessary in wireless communication as it

provides adequate area coverage, saves power consumption

and allows small size terminals etc. It is therefore important to

aim at a power efﬁcient operation of the non-linear HPA with

low back-off values and try to provide possible solutions to the

interference problem brought about. Hence, a better solution is

to try to prevent the occurrence of such interference by reducing

the PAPR of the transmitted signal with some manipulations of

the OFDM signal itself.

Large PAPR also demands the DAC with enough dynamic

range to accommodate the large peaks of the OFDM signals.

Although, a high precision DAC supports high PAPR with a

reasonable amount of quantization noise, but it might be very

expensive for a given sampling rate of the system. Whereas,

a low-precision DAC would be cheaper, but its quantization

noise will be signiﬁcant, and as a result it reduces the signal

Signal-to-Noise Ratio (SNR) when the dynamic range of DAC

is increased to support high PAPR. Furthermore, OFDM sig-

nals show Gaussian distribution for large number of subcarriers,

which means the peak signal quite rarely occur and uniform

quantization by the ADCs is not desirable. If clipped, it will in-

troduce in band distortion and out-of-band radiation (adjacent

channel interference) into the communication systems.

Therefore, the best solution is to reduce the PAPR before

OFDM signals are transmitted into nonlinear HPA and DAC.

B. Power Saving

When a HPA have a high dynamic range, it exhibits poor

power efﬁciency. It has been shown that PAPR reduction can

signiﬁcantly save the power, in which the net power saving is

directly proportional to the desired average output power and it

is highly dependent upon the clipping probability level [54].

Suppose that an ideal linear model for HPA, where linear am-

pliﬁcation is achieved up to the saturation point, and thus we

obtain

(10)

where

is the HPA efﬁciency and it is deﬁned as

, where is the average of the output

power and

is the constant amount of power regardless of

the input power.

To illustrate the power inefﬁciency of a HPA in terms of the

PAPR, we give an example of OFDM signals with 256 subcar-

riers and its CCDF has been shown in Fig. 1. In order to guar-

antee that probability of the clipped OFDM frames is less than

0.01%, we need to apply an input backoff (IBO) equivalent to

the PAPR at the

probability level, i.e.

( 25.235), referring to Fig. 1, and thus the efﬁciency of HPA be-

comes

. Therefore, so low efﬁciency

is a strong motivation to reduce the PAPR in OFDM systems.

V. D

ISTRIBUTION OF THE

PAPR IN OFDM SYSTEMS

It is known that the CCDF of PAPR can be used to estimate

the bounds for the minimum number of redundancy bits re-

quired to identify the PAPR sequences and evaluate the perfor-

mance of any PAPR reduction schemes. We can also determine

a proper output back-off of HPA to minimize the total degrada-

tion according to CCDF. Moreover, we can directly apply dis-

tribution of PAPR to calculate the BER and estimate achievable

information rates. In practice, we usually adjust these design

parameters jointly according to simulation results. Therefore, if

we can use an analytical expression to accurately calculate the

PAPR distribution for OFDM systems, it can greatly simplify

the system design process. Therefore, it is of great importance

to accurately identify PAPR distribution in OFDM systems.

Recently, some upper and lower bounds of the PAPR, which

is based on the Rayleigh distribution and Nyquist sampling rate,

have been derived. In the OFDM system with M-Phase-Shift-

Keying (MPSK) modulation, signal constellation has the same

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