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Wireless Information Transmission System Lab PAPR Reduction Methods
1. Wireless Information Transmission System Lab.
Institute of Communications Engineering
National Sun Yat-sen University
Peak-to-Average Power Ratio
(PAPR)
2012/07/30
邱營棋
2. 2
Multi-carrier systems
◊ The complex baseband representation of a multicarrier signal
consisting of N subcarriers is given by
where is the subcarrier spacing.
◊ In OFDM systems, the subcarriers are chosen to be orthogonal.
(i.e., )
1
2
0
1
,0
N
j n ft
n
n
x t X e t T
N
f
1
f T
3. 3
An example of the time-domain signals with 64
subcarriers
0 10 20 30 40 50 60 70
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Amplitude
Sample Index
4. ◊ Due to the large number of sub-carriers in typical OFDM systems,
the amplitude of the transmitted signal has a large dynamic range,
leading to in-band distortion and out-of-band radiation when the
signal is passed through the nonlinear region of power amplifier.
◊ Although the above-mentioned problem can be avoided by operating
the amplifier in its linear region, this inevitably results in a reduced
power efficiency.
◊ The PAPR of the transmit signal is defined as
4
The effect of high PAPR
2
0
2
0
max
1/
t T
T
x t
PAPR
T x t dt
7. ◊ If we sample x(t) by a sampling rate of 1/Ts (the sampling period Ts
= T/N ), we may miss some signal peaks and get optimistic results
for the PAPR.
◊ For better approximating the true PAPR in the discrete-time case,
we usually oversample x(t) by a factor of L , i.e., the sampling rate is
L/Ts .
◊ It was shown in [15] that an oversampling factor L=4 is sufficient to
approximate the true PAPR.
7
PAPR in discrete-time case
8. ◊ For an OFDM system with N sub-carriers, an oversampling rate of L
can be achieved by inserting (L－1)·N zeros in the middle of the
modulated symbol vector to form a 1×LN data vector X, i.e.
◊ The PAPR computed from the L-times oversampled time-domain
signal samples is given by
8
PAPR in discrete-time case
2
0 1
2
max k
k LN
k
x
PAPR
E x
1
0 , 1 , , / 2 1 , 0, , 0, / 2 , , 1
L N
X X X N X N X N
X
10. ◊ The simplest way to reduce the PAPR.
◊ The peak amplitude becomes limited to a desired level.
◊ Clipping
◊ Clipping Ratio
10
Clipping
,
exp{ arg( )} ,
n n
n
n n
x x A
y
A j x x A
20log
X
A
CR dB
: RMS value of
X n
x
11. ◊ By distorting the OFDM signal amplitude, a kind of self-
interference introduced that degrades the BER.
◊ Nonlinear distortion increases out-of-band radiation.
11
Clipping
14. 14
Selected mapping (SLM)
Serial-to-
parallel
conversion of
user bit stream
Coding &
Interleaving
Mapping
Bit
source
Optionally:
Differential
encoding
Optionally:
Differential
encoding
Optionally:
Differential
encoding
IDFT
IDFT
IDFT
Selection
of a
desirable
symbol
If necessary:
Side information
A
(1)
A
(2)
A
( )
U
A ( )
U
a
(2)
a
(1)
a
a
.
.
.
.
.
.
.
.
.
(1)
P
(2)
P
( )
U
P
15. 1. A set of U markedly different, distinct, pseudo-random but fixed
vectors P(u) = [P0
(u) ,…, PN-1
(u) ], with
must be defined.
2. The subcarrier vector A is multiplied subcarrier-wise with each one
of the U vectors P(u), then resulting to component
3. Then all U alternative subcarrier vectors are transformed into time
domain to get and finally that transmit
sequence
with the lowest PAPR is chosen.
◊ For implementation, the SLM technique needs U IDFT operations,
and the number of required side information bits is ,
denotes the smallest integer that exceed y.
15
Selected mapping (SLM)
( )
( ) ( )
, [0,2 ),
u
n
j
u u
n n
P e
0 , 1
n N u U
0 ,
n N
( ) ( )
{ }
u u
IDFT
a A
( )
u
a a
( ) ( )
,
u u
n n n
A A P
1 .
u U
2
log U
y
17. 17
Partial transmit sequence (PTS)
Serial-to-parallel
conversion of
user bit stream
Coding &
Interleaving
Mapping
Subblock
partationing
Optionally:
Differential
encoding
Bit source
IDFT
IDFT
IDFT
Pack value optimization
+
(2)
A
( )
M
A
(1)
A
(1)
a
(2)
a
( )
M
a
(1)
b
(2)
b
.
.
.
.
.
.
.
.
.
If necessary :
side information
a
( )
M
b
18. 1. In this scheme, the subcarrier vector A is partitioned into M pairwise
disjoint subblocks All subcarrier positions in
which are already represented in another subblock are set to zero, so
that
2. We introduce complex-valued rotation factors
, and μ is index of all phase rotation of “Peak
value optimization”. Enabling a modified subcarrier vector
which represents the same information as A, if the set
(as side information) is known for each μ.
18
Partial transmit sequence (PTS)
( )
, 1 .
m
m M
A ( )
m
A
( )
1
.
M
m
m
A A
( )
( )
,
m
j
m
b e
( )
[0,2 ), 1
m
m M
( ) ( )
1
M
m m
m
b
A A
( )
,1
m
b m M
19. 3. To calculate , the linearity of the IDFT is exploited.
Accordingly, the subblocks are transformed by M separate and
parallel N-point IDFTs, yielding
4. Based on them a peak value optimization is performed by suitably
choosing the free parameters such that the PAPR is minimized
for .
◊ It should be noted, that PTS can be interpreted as a structurally
modified special case of SLM.
19
Partial transmit sequence (PTS)
{ }
IDFT
a A
( ) ( ) ( ) ( )
1 1
{ } .
M M
m m m m
m m
b IDFT b
a A a
( )
m
b
( )
m
b
20. 20
Partial transmit sequence (PTS)
◊ In general, the selection of the phase factors is limited to a set with a
finite number of elements to reduce the search complexity.
◊ The set of allowed phase factors is written as
, where W is the number of allowed phase factors.
◊ In addition, we can set without any loss of performance.
◊ Hence, sets of phase factors are searched to find the optimum
set of phase factors.
◊ PTS needs M IDFT operations for each data block, and the number
of required side information bits is .
2 /
| 0,1, ,
j n W
P e n
1
W
(1)
1
b
1
M
W
1
2
log M
W
21. 21
PAPR reduction performance of PTS
◊ N = 256, L = 4, 16-QAM, exhausted research for .
W=2 means [+1,-1], W=4 means [+1, -1, +1j, -1j].
1
M
W
22. ◊ In this technique, some of the outer signal constellation points in the
data block are dynamically extended toward the outside of the
original constellation such that the PAPR of the data block is
reduced.
22
Active Constellation Extension (ACE)
Re
Im
Re
Im
a1
QPSK 16-QAM
23. Active Constellation Extension (ACE)
PAPR
23
X IFFT x x FFT X
Iteration?
clipping
, | |
, | |
j n
x n x n A
x n
Ae x n A
24. ◊ N = 256, L = 4, QPSK, A = 4.86 dB.
PAPR reduction performance of ACE
PAPR
24
25. 25
Tone Reservation (TR)
◊ The transmitter reserves a small number of unused subcarriers. These
subcarriers are referred to as peak reduction carriers (PRCs).
◊ Since PRCs do not carry data, this increment induces a severe
degradation of system’s power efficiency.
◊ In general, there are two approaches to reduce the PAPR in the TR
technique.
◊ The first is to select the PRC indices for the TR technique to be used in
reducing the PAPR.
◊ The second is to design the proper values on these PRCs to generate an
optimal peak-canceling signal that minimizes the PAPR of a transmitted
OFDM signal.
