This document discusses peak-to-average power ratio (PAPR) reduction techniques for orthogonal frequency-division multiplexing (OFDM) signals. It begins with an introduction to PAPR and its causes for OFDM signals. It then outlines various PAPR reduction techniques including clipping, coding, probabilistic/scrambling, predistortion, and DFT-spreading. Each technique has benefits but also cons such as distortion, reduced efficiency, or increased complexity. The document provides analysis of PAPR characteristics for different OFDM parameters and modulation schemes.

1. PAPR Reduction
Jay Chang
1

2. 2
Introduction to PAPR
PAPR Reduction Techniques
Agenda

3. 3
OFDM have high PAPR → many subcarrier components are added via an IFFT operation.
Cons:
• Peak signal fall in the nonlinear region of power amplifier (PA) cause distortion.
• Degrading the efficiency of the PA in the transmitter.
• Decreases the SQNR (Signal-to-Quantization Noise Ratio) of ADC and DAC.
• Destroy the orthogonality of the different subcarriers and generate power leakage among the
subcarriers → ICI.
The PAPR problem is more important in the uplink since the efficiency of PA is critical due to the
limited battery power in a mobile terminal.
Root Cause Analysis

4. 4
Introduction to PAPR
PAPR Reduction Techniques
Agenda

5. 5
Introduction to PAPR
nonlinear region can be described by IBO (Input Back-Off) or OBO (Output Back-Off).
nonlinear characteristic of HPA (High Power Amplifier), excited by a large input, causes the
out-of-band radiation that affects signals in adjacent bands, and in-band distortions that
result in rotation, attenuation, and offset on the received signal.
Input-output characteristic of an HPA.

6. 放大器的工作狀態和偏置網路放大器的工作狀態和偏置網路放大器的工作狀態和偏置網路放大器的工作狀態和偏置網路
放大器的工作狀態和效率放大器的工作狀態和效率放大器的工作狀態和效率放大器的工作狀態和效率
偏置的作用是在特定的工作條件下為有源器件提供適當的靜態工作點靜態工作點靜態工作點靜態工作點，並
抑制電晶體參數的離散性抑制電晶體參數的離散性抑制電晶體參數的離散性抑制電晶體參數的離散性以及溫度變化的影響溫度變化的影響溫度變化的影響溫度變化的影響從而保持恒定的工作特性保持恒定的工作特性保持恒定的工作特性保持恒定的工作特性。
信號失真較大
要push-pull工作
信號失真最大
效率最高
信號失真大
要push-pull工作
信號失真最小
功率小, 效率低
不同的工作狀態對應不同的偏置條件, 是根據導通角來劃分的。
導通角導通角導通角導通角: 對應於一個信號週期內有電流流過負載的時間對應於一個信號週期內有電流流過負載的時間對應於一個信號週期內有電流流過負載的時間對應於一個信號週期內有電流流過負載的時間。
Class A: 360A
°
Θ = Class B: 180B
°
Θ = Class AB: 180 360AB
° °
< Θ < Class C: 0 180C
° °
< Θ <
100%RF
s
P
P
η = × =
0 0
0 0
0
sin
2 2sin cos
2 2
η
Θ − Θ
=
 Θ Θ    
− Θ    
    
Q point: AC input = 0, DC工作狀態下, output的特性曲線
6

7. 7

8. 0 50 100 150 200 250 300 350
0
20
40
60
80
100
50
Class C
Class B
Class AB
Conduction angle (degree)
PADrainefficiency(%)
180
78.5
Class A
0Θ
0 0
0 0
0
sin
2 2sin cos
2 2
η
Θ − Θ
=
 Θ Θ    
− Θ    
    
8

9. 假設, 傳遞到PA的總功率, Pdc+Pin 中的一部分被
消耗了, 產生了熱耗散+諧波(harmonic distortion)
或互調失真(IMD)形式所表現出來的Pdis.
( )
1
1
in dc out dis
out dc dis
in in
out in in
dc dc
P P P P
P P P
G
P P
P P P
PAE G
P P
+ = +
−
≡ = +
−
≡ = −
www.STADTAUS.com_C55_Lavrador_Efficiency_Linearity
9
如果要依賴於有限的電源, 沒有任何電子器件可以保持恒定的增益, 因而無法保持恒定的線
性度.
為了使PAE更高, 在同樣的輸出功率條件下, 系統需要從電源吸收較少的功率. 這便不可避免
地導致了更高的增益壓縮, 而這又會使得系統的頻譜效益降低.
這便是線性度-效率之間矛盾關係的基本原理, 同樣也可稱作為功率-頻譜效率的折衷.

10. Linearity technology - feedforward
1τ∆
2τ∆
/ /
A in err
B A in err
C B err
out A C in
V V G V
V V G V V G
V V G V
V V V V G
= +
= − =
= =
= − =
10
Pros: good stability.
Cons: Amplitude and phase should be exacted
matching so need delay line not easy to integrate.

11. Linearity technology - feedback
cos
cos( )
LO
LO
t
t
ω
ω θ+
1
1
out
f
in
V A
A
V AF F
= = ≈
+
if 1AF >>
Cons: Phase shift control
Stability
11

12. 12
Linearity technology - predistortion

13. Linear amplification with Nonlinear Components (LINC)
1 2
1 0
2 0
1
0
( ) ( )cos[ ( )] ( ) ( )
1
( ) sin[ ( ) ( )]
2
1
( ) sin[ ( ) ( )]
2
( )
( ) sin
in c
c
c
v t a t t t v t v t
v t V t t t
v t V t t t
a t
t
V
ω ϕ
ω ϕ θ
ω ϕ θ
θ −
= + = +
= + +
= − + −
 
=  
 
1 2
1
2
2 2
0
( ) ( )cos[ ( )] ( ) ( )
( ) ( )cos( ) ( )sin( )
( ) ( )cos( ) ( )sin( )
( ) ( ) / 2
( ) ( ) / 2
in c
I c Q c
I c Q c
I
Q
v t a t t t v t v t
v t v t t v t t
v t v t t v t t
v t a t
v t V a t
ω ϕ
ω ϕ ω ϕ
ω ϕ ω ϕ
= + = +
= + + +
= − + + +
=
= −
13

14. Envelope Elimination and Restoration (EE&R)
( ) ( )cos[ ( )]
envelope : ( )
phase : ( )
in cv t a t t t
a t
t
ω ϕ
ϕ
= + non-linear PA
a(t)
linear
PA
b(t)
0( ) cos[ ( )]
phase modulation
cb t b t tω ϕ= +
http://ww.radioliberty.org/document23.pdf14

15. 15

16. 16
Definition of PAPR
Passband PAM transmitter.
output of the passband quadrature modulator is represented as
( )s tɶ

17. 17
Peak-to-Mean Envelope Power Ratio (PMEPR)
PMEPR is the ratio between the maximum power and the average power for
the envelope of a baseband complex signal ( )s tɶ
Peak Envelope Power (PEP)
PEP represents the maximum power of a complex baseband signal ( )s tɶ
Peak-to-Average Power Ratio (PAPR)
PAPR is the ratio between the maximum power and the average power of the complex passband signal ( )s t
The above power characteristics can also be described in terms of their
magnitudes (not power) by defining the crest factor (CF) as
We are interested in finding
the probability that the signal
power is out of the linear
range of the HPA!!

18. OFDM PAPR ?
2
Crest factor peak
rms
x
C
x
PAPR C
= =
=
( )
/2 2
0
/2
0
1 1
sin 0.707
/ 2 2
1 2
sin 0.636
/ 2
rms peak peak peak
avg peak peak peak
V V d V V
V V d V V
π
π
θ θ
π
θ θ
π π
= = =
= = =
∫
∫
For sin wave:
18

19. 19
Fig. Block diagram of transmitter and receiver in an OFDM system.
(S/P)
Pulse
shaping
(S/P)

20. 20
Central limit theorem:
Input signals of N-point IFFT have the independent and finite magnitudes which are uniformly distributed for QPSK
and QAM, we can assume that the real and imaginary parts of the time-domain complex OFDM signal s(t) (after IFFT
at the transmitter) have asymptotically Gaussian distributions for a sufficiently large number of subcarriers.
→ amplitude of the OFDM signal s(t) follows a Rayleigh distribution.
we consider the following complementary CDF (CCDF):
• assumption that N samples are independent
and N is sufficiently large.
• assumption that N samples are independent
and N is sufficiently large.
Real, Imag follow (0, 1/2) Gaussian distributions
(均值均值均值均值, 方差方差方差方差σ2 )

21. 21
Sampled signal does not necessarily contain the maximum point of the original continuous-time signal.
It is difficult to derive the exact CDF for the oversampled signals and therefore, the following simplified CDF will
be used:
CCDFs of OFDM signals with N = 64, 128, 256, 512, and 1024.
N = 1024
N = 64
https://github.com/oklachumi/octave-in-communications/blob/master/plot_OFDM_CCDF.m

22. 22
Baseband/passband signals for QPSK-modulated symbols.
Baseband Passband
QPSK, 4 symbols, Ts = 1 s, Fs = 8 Hz, oversampling factor L = 8
https://github.com/oklachumi/octave-in-communications/blob/master/single_carrier_PAPR.m

23. 23
Distribution of OFDM Signal
Characteristics of time-domain QPSK/OFDM signals: N = 8 and 16.

24. 24
Characteristics of time-domain QPSK/OFDM signals: N = 8 and 16.
Time-domain OFDM signals Magnitude distribution of OFDM signal
Probabilistic Analysis of Time-Domain OFDM Signals
https://github.com/oklachumi/octave-in-communications/blob/master/OFDM_signal_distribution.m

25. 25
PAPR and Oversampling
PAPR for x[n] is lower than that for x(t), because x[n] may not have all the peaks of x(t).
In practice, the PAPR for the continuous-time baseband signal can be measured only after implementing the
actual hardware, including digital-to-analog convertor (DAC).
Measurement of the PAPR for the continuous-time baseband signal is not straightforward.
x[n] can show almost the same PAPR as x(t) if it is L-times interpolated (oversampled) where L ≥ 4.
Block diagram of L-times interpolator.
Interpolation with L = 4 in the time domain. Interpolation with L = 4 in the frequency domain.

26. 26

27. 27
PAPRs of Chu Sequence and IEEE 802.16e Preambles
PAPR characteristics of Chu sequence in the time domain.
https://github.com/oklachumi/octave-in-communications/blob/master/PAPR_of_Chu.m

28. 28
PAPRs of Chu Sequence and IEEE 802.16e Preambles
The values of PAPR with oversampling are just about 0.4 dB greater than those without oversampling.
These preambles are originally designed to have the low PAPR, since they are subject to power boosting in
practice.
PAPR characteristics of IEEE 802.11e preamble in the time domain.
https://github.com/oklachumi/octave-in-communications/blob/master/PAPR_of_preamble.m

29. 29
PAPR of the passband signal in front of HPA is generally larger than that of the
baseband signal after the RF filtering and other processing.

30. 30
Clipping and SQNR
Probabilistic distribution of the real part of a time-domain OFDM signal.
One simplest approach of reducing the PAPR is to
clip the amplitude of the signal to a fixed level.
The pseudo-maximum amplitude in this approach is
referred to as the clipping level and denoted by μ.
Reducing PAPR, the clipping approach helps improve
the signal-to-quantization noise ratio (SQNR) in
analog-to-digital conversion (ADC).
If the clipping level is low, the signal will suffer from
a clipping distortion while the PAPR and
quantization noise will decrease.
If the clipping level is high, a clipping distortion
decreases while it suffers from the PAPR and
quantization noise.
• This trade-off relationship between the clipping distortion and quantization noise
should be taken into consideration in selecting the clipping level and the number
of bits for quantization.

31. 31
Introduction to PAPR
PAPR Reduction Techniques
Agenda

32. 32
PAPR Reduction Techniques
Classified into the different approaches: clipping technique, coding technique, probabilistic (scrambling) technique, adaptive
predistortion technique, and DFT-spreading technique.
1. The clipping technique employs clipping or nonlinear saturation around the peaks to reduce the PAPR.
Cons:
• in-band and out-of-band interferences while destroying the orthogonality among the subcarriers.
2. The coding technique is to select such codewords that minimize or reduce the PAPR.
Cons:
• bandwidth efficiency as the code rate is reduced.
• complexity to find the best codes and to store large lookup tables for encoding and decoding.
3. The probabilistic (scrambling) technique is to scramble an input data block of the OFDM symbols and transmit one of them with
the minimum PAPR so that the probability of incurring high PAPR can be reduced.
Cons:
• spectral efficiency decreases and the complexity increases as the number of subcarriers increases.
4. The adaptive predistortion technique can compensate the nonlinear effect of a high power amplifier (HPA) in OFDM systems.
Pons:
• cope with time variations of nonlinear HPA by automatically modifying the input constellation with the least hardware
requirement (RAM and memory lookup encoder).
5. The DFT-spreading technique is to spread the input signal with DFT, which can be subsequently taken into IFFT.
Pons:
• can reduce the PAPR of OFDM signal to the level of single-carrier transmission.
• particularly useful for mobile terminals in uplink transmission, and is known as the Single Carrier-FDMA (SC-FDMA), which
is adopted for uplink transmission in the 3GPP LTE.

33. 33
Review…

34. ET Overview & Principle
• Maximizes the PA efficiency by operating the PA in compression for most envelope amplitudes.
• Envelope amplifier (for example, QET4100/QFE1100) provides a dynamic supply voltage.
Env amp
provides a dynamic
supply voltage
• CW sweeps of PA PAE versus Pout.
• Each colored line represents a different PA Vcc,
from 0.5 V to 3.7 V, in 0.2 V steps.
34
• Vcc track the envelope of RF signal.
Review…

35. PA Compression and PAE
CW PAE and Pout vs. Pin
PA PAE maximum occurs in the
compressed region.
(PAE drops rapidly with back-off)
35
This plot shows the CW PAE and Pout vs. Pin.
The PA PAE maximum occurs in the compressed region.
The PAE drops rapidly with back-off.
The PAE for high PAR waveforms drop.
Review…

36. ET Mode – (1) Digital Predistortion (DPD)
DPD compensates for RF chain nonlinearities.
• RF nonlinearity is dominated by the PA.
• Corrects for AM/AM and AM/PM nonlinear distortion.
Tx baseband signal has wider bandwidth due to DPD.
• Legacy SAW filters limit the systems ability for predistortion due to the sharp roll off at the band edges.
• Wideband SAW filters are being developed to cope with this issue.
Tx BB signal has
wider BW due to DPD
improve the close-in
linearity of a system
36
Review…

37. ET Mode – (2) Detroughing
Most Tx waveforms result in I-Q origin crossings.
• Cause ET envelope signal BW expansion and low PA supply voltages.
The solution is detroughing (envelope shaping).
• Detroughing of the envelope waveform reduces the envelope signal bandwidth, and also eliminates the
issue of low PA supply voltages.
After detroughing
• low PA supply voltages
• Sharp V cause BW expansion
I-Q origin crossings
Envelope signal BW expansion
Modem detroughing LUT:
• Enables flexible control over the detroughing (envelope shaping) function.
• Allows for precise Vcc versus VRF_IN trajectory control.
37
After detroughing
reduces the envelope signal BW
就是用一種detroughing的技術, 讓他PA Vcc電壓限制在某點以上
Review…

38. ET Mode – (3) Time Alignment
The time alignment adjusts the envelope path delay to match the RF Tx path delay.
• The two paths are separated from modem and combined at PA.
• RF Tx path: modem → WTR → (Tx SAW) → PA.
• Envelope (Vcc) path: modem → QET4100 → PA.
modem → QET4100 → PA
modem → WTR → (Tx SAW) → PA
delay
38
Review…

39. ET Mode – (4) Rx-band Noise into PRx LNA
ET system uses DPD to linearize the PA.
• Meet ACLR emissions.
• Predistortion BW limited by Tx system filters (Tx BB BW increased due to DPD).
• Outside predistortion BW, emissions met by inherent linearity of PA in the ET mode.
ET introduces new noise sources that can degrade LNA performance.
• There is potential Rx desense in ET mode due to additional noise sources.
1. Typical desense is ~ 0.25 dB (50 dB isolation duplexers).
2. Improved duplexers, recommendation is 55 dB isolation in the Rx band, Tx port to Rx port.
3. Good layout of buck/boost bypass capacitors placement and routing; isolate the Rx trace from the Tx trace as much as possible;
ground plane below QFE1100; DPx layout/grounding is critical; ground vias, etc can suppress RxBN.
4. Buck inductor selection is critical for the QET4100 ET RxBN performance. 5. ET PA matching, Rx band impedance short circuit.
solutions
delay
ACLR emission
experiments
39
Review…

40. 40
Clipping and Filtering
Limits the maximum of transmit signal to a pre-specified level.
Drawbacks:
• Clipping causes in-band distortion, resulting in BER performance degradation.
• Clipping causes out-of-band radiation, which imposes out-of-band interference
signals to adjacent channels.
• Filtering the clipped signal can reduce out-of-band radiation at the cost of peak
regrowth. The signal after filtering operation may exceed the clipping level
specified for the clipping operation.
Block diagram of a PAPR reduction scheme using clipping and filtering.
Define the clipping ratio (CR) as the clipping level
normalized by the RMS value σ of OFDM signal
or
in-band distorƟon ↓
out-of-band radiation ↓
Better BER
performance

41. 41
The performance of PAPR reduction schemes can be evaluated in the following three aspects:
• In-band ripple and out-of-band radiation that can be observed via the power spectral density (PSD).
• Distribution of the crest factor (CF) or PAPR, which is given by the corresponding CCDF.
• Coded and uncoded BER performance.
Parameters used for simulation of clipping and filtering.

42. 42
[ ]x m′ [ ]p
x m
https://github.com/oklachumi/octave-in-communications/blob/master/PDF_of_clipped_and_filtered_OFDM_signal.m

43. 43
[ ]p
cx m [ ]p
cx mɶ
https://github.com/oklachumi/octave-in-communications/blob/master/PDF_of_clipped_and_filtered_OFDM_signal.m

44. 44
Filter coefficient Filter response
https://github.com/oklachumi/octave-in-communications/blob/master/PDF_of_clipped_and_filtered_OFDM_signal.m