ChapterPDF Available

Peak-to-Average Power Ratio Reduction in Orthogonal Frequency Division Multiplexing Systems

Authors:
11
Peak-to-Average Power Ratio
Reduction in Orthogonal
Frequency Division
Multiplexing Systems
Pooria Varahram and Borhanuddin Mohd Ali
Universiti Putra Malaysia,
Malaysia
1. Introduction
Broadband wireless is a technology that provides connection over the air at high speeds.
Orthogonal frequency division multiplexing (OFDM) system has generally been adopted in
recent mobile communication systems because of its high spectral efficiency and robustness
against intersymbol interference (ISI). However, due to the nature of inverse fast Fourier
transform (IFFT) in which the constructive and destructive behaviour could create high peak
signal in constructive behaviour while the average can become zero at destructive
behaviour, OFDM signals generally become prone to high peak-to-average power ratio
(PAPR) problem. In this chapter, we focus on some of the techniques to overcome the PAPR
problem (Krongold and Jones, 2003; Bauml, et al. 1996).
The other issue in wireless broadband is how to maximize the power efficiency of the power
amplifier. This can be resolved by applying digital predistortion to the power amplifier (PA)
(Varahram, et al. 2009). High PAPR signal when transmitted through a nonlinear PA creates
spectral broadening and increase the dynamic range requirement of the digital to analog
converter (DAC). This results in an increase in the cost of the system and a reduction in
efficiency. To address this problem, many techniques for reducing PAPR have been
proposed. Some of the most important techniques are clipping (Kwon, et al. 2009),
windowing (Van Nee and De Wild, 1998), envelope scaling (Foomooljareon and Fernando,
2002), random phase updating (Nikookar and Lidsheim, 2002), peak reduction carrier (Tan
and Wassell, 2003), companding (Hao and Liaw, 2008), coding (Wilkison and Jones, 1995),
selected mapping (SLM) (Bauml, et al. 1996), partial transmit sequence (PTS) (Muller and
Huber, 1997), DSI-PTS (Varahram et al. 2010), interleaving (Jayalath and Tellambura, 2000),
active constellation extension (ACE) (Krongold, et al. 2003), tone injection and tone
reservation (Tellado, 2000), dummy signal insertion (DSI) (Ryu, et al. 2004), addition of
Guassian signals (Al-Azoo et al. 2008) and etc (Qian, 2005).
Clipping is the simplest technique for PAPR reduction, where the signal at the
transmitter is clipped to a desired level without modifying the phase information. In
windowing a peak of the signal is multiplied with a part of the frame. This frame can be
Advanced Transmission Techniques in WiMAX
218
in Gaussian shape, cosine, Kaiser or Hanning window, respectively. In companding
method the OFDM signal is companded before digital to analog conversion. The OFDM
signal after IFFT is first companded and quantized and then transmitted through the
channel after digital to analog conversion. The receiver first converts the signal into
digital format and then expands it. The companding method has application in speech
processing where high peaks occur infrequently. In PTS, by partitioning the input signal
and applying several IFFT, the optimum phase sequence with lowest PAPR will be
selected before being transmitted. This technique results in high complexity. In SLM, a
copy of input signal is used to choose the minimum PAPR among the multiple signals.
We can conclude that there is always a trade-off in choosing a particular PAPR
technique. The trade-off comes in the form of complexity, power amplifier output
distortion, cost, side information, PAPR reduction, Bit Error Rate (BER) performance,
spectrum efficiency and data rate loss.
2. OFDM signal
In OFDM systems, first a specific number of input data samples are modulated (e.g. PSK or
QAM), and by IFFT technique the input samples become orthogonal and will be converted
to time domain at the transmitter side. The IFFT is applied to produce orthogonal data
subcarriers. In theory, IFFT combines all the input signals (superposition process) to
produce each element (signal) of the output OFDM symbol. The time domain complex
baseband OFDM signal can be represented as (Han and Lee, 2005):
N1 n
j2 k
N
k
n
k0
1
x X e , n 0,1,2,.......,N 1
N

(1)
where n
xis the n-th signal component in OFDM output symbol, k
X is the k-th data
modulated symbol in OFDM frequency domain, and N is the number of subcarrier.
The PAPR of the transmitted OFDM signal can be given by (Cimini and Sollenberger,
2000):
2
max xn
PAPR(dB) 2
Ex
n
(2)
where
E.is the expectation value operator. The theoretical maximum of PAPR for N
number of subcarriers is as follows:
max
PAPR 10 log(N )dB (3)
PAPR is a random variable since it is a function of the input data, while the input data is a
random variable. Therefore PAPR can be analyzed by using level crossing rate theorem
which calculates the mean number of times that the envelope of a stationary signal crosses a
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
219
given level. Knowing the amplitude distribution of the OFDM output signals, it is easy to
compute the probability that the instantaneous amplitude will lie above a given threshold
and the same goes for power. This is performed by calculating the complementary
cumulative distribution function (CCDF) for different PAPR values as follows:
0
CCDF Pr( PAPR PAPR )
(4)
Here the effect of additive white Gaussian noise (AWGN) on OFDM performance is studied.
As OFDM systems use standard digital modulation formats to modulate the subcarriers,
PSK and QAM are usually used due to their excellent error resilient properties. The most
important block in OFDM is IFFT. IFFT changes the distribution of the signal without
altering its average power. The BER or bit error probability Pbe in an AWGN channel is
given by (Han and Lee, 2005):
b
be, MQAM
o
4( M 1) 3k E
PQ.
(M 1) N
kM




(5)
where M is the modulation order, k= log2(M) is the number of bits per symbol, and Q(.) is
the Gaussian Q function defined as:
y
Q( y ) e rfc( )
2
(6)
In this chapter the performance of BER versus energy per bit to noise power spectral density
ratio (Eb/No) is analyzed.
3. PAPR reduction techniques
In this section, some of the most important PAPR reduction techniques such as Selected
Mapping (SLM), Partial Transmit Sequence (PTS) and Enhanced PTS EPTS) are presented.
3.1 Conventional SLM (C-SLM)
In Conventional SLM (C-SLM) method, OFDM signal is first converted from serial to
parallel by means of serial-to-parallel converter. The parallel OFDM signal is then
multiplied by several phase sequences that are created offline and stored in a matrix. A copy
of the OFDM signal is multiplied with a random vector of phase sequence matrix. For each
subblock IFFT is performed and its PAPR is calculated to look for the minimum one. The
OFDM signal having minimum PAPR is then selected and be transmitted. The main
drawbacks of this technique are the high complexity due to the high number of subblocks
and the need to send side information which result in data rate and transmission efficiency
degradation, respectively. In Fig. 1, the number of candidate signal or subblocks is given by
U, hence 2
log U number of bits is required to be sent as side information.
The other drawback of this method is that by increasing U, higher number of IFFT blocks
are required which increase the complexity significantly. Hence, a method with low
complexity and high PAPR performance is required.
Advanced Transmission Techniques in WiMAX
220
Fig. 1. The block diagram of the C-SLM method.
3.2 Conventional PTS (C-PTS)
To analyze C-PTS let X denotes random input signal in frequency domain with length N. X
is partitioned into V disjoint subblocks Xv=[Xv,0,Xv,1,…,Xv,N-1]T, v=1,2,…,V such that
V
v
v1
XX
and then these subblocks are combined to minimize the PAPR in time domain.
The Sbblock partitioning is based on interleaving in which the computational complexity is
less compared to adjacent and pseudo-random, however it gives the worst PAPR
performance among them (Han and Lee, 2005).
By applying the phase rotation factor v
j
v
b e ,v 1,2,...,V
 to the IFFT of the vth subblock Xv,
the time domain signal after combining is obtained as:
V
vv
v1
x(b) b x
(7)
where T
01 NF1
x(b) [x (b),x (b),...x (b)]

. The objective is to find the optimum signal x(b)
with
the lowest PAPR.
Both b and x can be shown in matrix forms as follows:
11 1
VV V
VN
b , b ,...., b
b
b , b ,..., b





 (8)
1,0 1,1 1,NF 1
V,0 V,1 V,NF 1 VNF
x , x ,...,x
x
x , x ,...,x





 (9)
Fig. 2 shows the block diagram of C-PTS. It should be noted that all the elements of each
row of matrix b are of the same values and this is in accordance with the C-PTS method. In
order to obtain exact PAPR calculation, at least four times oversampling is necessary (Han
and Lee, 2005).
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
221
Fig. 2. Block diagram of the C-PTS scheme with Digital predistortion and power amplifier in
series
This process is performed by choosing the optimization parameter b
which satisfies the
following condition:
V
vv
0kNF1
v1
bar
g
min( max b x )

(10)
where V is the number of subblocks partitioning and F is the oversampling factor. After
obtaining the optimum b
, the signal is transmitted.
For finding the optimum b
, we should perform exhaustive search for (V-1) phase factors
since one phase factor can remain fixed, b1=1. Hence to find the optimum phase factor, WV-1
iteration should be performed, where W is the number of allowed phase factors.
3.3 Enhanced PTS (EPTS)
In order to decrease the complexity of C-PTS, a new phase sequence is generated. The
block diagram of the enhanced partial transmit sequence (EPTS) scheme is shown in
Fig. 3.
This new phase sequence is based on the generation of N random values of {1 -1 j –j} if the
allowed phase factors is W=4. The phase sequence matrix can be given by:
Advanced Transmission Techniques in WiMAX
222
[P N]
1,1 1,N
V,1 2,N
V1,1 V1,N
P,1 P,N
b ,..., b
b ,..., b
ˆ
bb ,..., b
b ,..., b












(11)
where P is the number of iterations that should be set in accordance with the number of
iterations of the C-PTS and N is the number of samples (IFFT length) and V is the number of
subblock partitioning. The value of P is given as follows:
V1 N
PDW ,D1,2,...,D

(12)
where D is the coefficient that can be specified based on the PAPR reduction and complexity
requirement and DN is specified by the user. The value of P explicitly depends on the
number of subblocks V, if the number of allowed phase factor remains constant.
There is a tradeoff for choosing the value of D. higher D leads to higher PAPR reduction but at
the expense of higher complexity; while lower D results in smaller PAPR reduction but with less
complexity. For example if W=2 and V=4, then in C-PTS there are 8 iterations and hence P=8D. If
D=2, then P=16 and both methods have the same number of iterations. But when D=1, then
number of iterations to find the optimum phase factor will be reduced to 4 and this will result in
complexity reduction. The main advantage of this method over C-PTS is the reduction of
complexity while at the same time maintaining the same PAPR performance. In the case of C-
PTS, each row of the matrix ˆ
b contains same phase sequence while each column is periodical
with period V, whereas in the proposed method each element of matrix ˆ
b has different random
values. The other formats that matrix in (11) can be expressed are as follows:
[P
P
1,1 1,N / P 1,1 1,N / P
V,1V,N/P V,1V,N/P
V1,1 V1,N/P V1,1 V1,N/P
P,1 P,N/P P,1 P,N/P
b ,...,b ,..., b ,...,b
b ,...,b ,..., b ,...,b
ˆ
b
b ,...,b ,..., b ,...,b
b ,...,b ,..., b ,...,b
 














N]
(13)
PP P
1,1 1,1 1,2 1,2 1,N / P 1,N / P
V,1 V,1 V,2 V,2 V,N /P V,N/ P
V1,1 V1,1 V1,N/P V1,N/P
P,1 P,1 P,N/ P
b ,...,b , b ,...,b ,..., b ,...,b
b ,...,b ,b ,..., b ,..., b ,...,b
ˆ
b
b ,...,b ,..., b ,...,b
b ,...,b ,..., b ,...,b

 


[P N]
P,N/ P











(14)
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
223
where (13) and (14) are the interleaved and adjacent phase sequences matrix, respectively.
As an example take the case of N=256, and the number of allowed phase factor and subblock
partitioning are W=4 and V=4 respectively. With C-PTS there are WM-1=64 possible
iterations, whereas for the proposed method, in the case of D=2, the phase sequence is a
matrix of [128x256] elements according to (11). In this case 64 iterations are required for
finding the optimum phase sequence, because each two rows of the matrix in (11) multiply
point-wise with the time domain input signal xv with length [2x256].
Fig. 3. The block diagram of enhanced PTS
The reduction of subblocks to 2 is because it gives almost the same PAPR reduction as C-
PTS with V=4. It should be noted that if D=1 then the complexity increases while if D>2 then
the PAPR reduction is less.
Therefore the algorithm can be expressed as follows:
Step 1: Generate the input data stream and map it to the M-QAM modulation.
Step 2: Construct a matrix of random phase sequence with dimension of [PxN].
Step 3: Point-wise multiply signal xv with the new phase sequence.
Step 4: Find the optimum phase sequence after P iterations to minimize the PAPR.
Advanced Transmission Techniques in WiMAX
224
3.3.1 Numerical analysis
In order to evaluate and compare the performance of the PAPR methods with C-PTS,
simulations have been performed. In all the simulations, we employed QPSK modulation
with IFFT length of N=512, and oversampling factor F=4. To obtain the complementary
cumulative distribution function (CCDF), 40000 random OFDM symbols are generated.
Fig. 4 shows the CCDF of three different types of phase sequences interleaved, adjacent and
random for D=2. From this figure, PAPR reduction with random phase sequence
outperforms the other types and hence this type of phase sequence is applied in the
following simulations.
Fig. 4. CCDF of PAPR of the proposed method for different phase sequence when D=2
Fig. 5 shows the CCDF comparison of the PAPR of the C-PTS and EPTS for V=2 and 4. It is
clear that the proposed EPTS shows better PAPR performance compared to C-PTS where
almost 0.3 dB reduction is achieved with EPTS.
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
225
Fig. 5. CCDF comparison of PAPR of the proposed EPTS and C-PTS
3.4 Dummy Sequence Insertion (DSI)
The DSI method reduces PAPR by increasing the average power of the signal. Here, after
converting the input data stream into parallel through the serial to parallel converter a,
dummy sequence is inserted in the input signal. Therefore, the average value in Equation (2)
is increased and the PAPR is subsequently reduced (Ryu, et al. 2004). IEEE 802.16d standard,
specifies that the data frame of OFDM signal is allocated with 256 subcarriers which is
composed of 192 data subcarriers, 1 zero DC subcarrier, 8 pilot subcarriers, and 55 guard
subcarriers. Therefore, the dummy sequence can be inserted within the slot of 55 guard
subcarriers without degradation of user data. However, if added dummies are more than 55,
the length of the data and the bandwidth required, will be increased. This will degrade the
Transmission Efficiency (TE) which is defined as:
= K
TE ×100%
K+L (15)
where K is the number of the subcarriers and L is the number of dummy sequence. In this
chapter we apply a different DSI method from the one in (Ryu, et al. 2004), where the TE is
always 100%.
Advanced Transmission Techniques in WiMAX
226
3.5 Dummy Sequence Insertion with Partial Transmit Sequence (DSI-PTS)
The block diagram of this technique is shown in Fig. 6. A complex valued dummy signals
are first generated and then added to the vector of data subcarriers. The new vector in
frequency domain is then constructed from K-data and L-dummy subcarriers, respectively.
L can be any number less than K. The new vector S is given by:
kl
SX,W
(16)
where kk,0k,1k,NL1
X [ X ,X ,..., X ],k 1,2,...,K

is the data subcarrier vector and
ll,0l,1l,L1
W [ W ,W ,...,W ],l 1,2,...,L
is the dummy signals vector.
After generation of the optimum OFDM signal then the PAPR is checked with the
acceptable threshold that was pre-defined before. If the PAPR value is less than the
threshold then the OFDM signal will be transmitted otherwise the dummy sequence is
generated again as depicted with the feedback in Fig. 6. This process is one iteration. The
number of iterations can be increased to achieve the desired PAPR ( th
PAPR ) reduction
but the processing time will also increase likewise and causes the system performance to
drop.
Fig. 6. Block diagram of DSI-PTS technique
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
227
As for the DSI-PTS method, consider L as the number of dummy sequence which later will
be shown to be L55
and N is the IFFT length which is 256 in the case of fixed WiMAX that
includes 192 data carriers, 8 pilots and 55 zero padding and 1 dc subcarrier. Here
complementary sequence is applied for the DSI (Ryu, et al. 2004).
From the block diagram in Fig. 6, X is the input signal stream with length N after which the
dummy sequence is added. The dummy sequence can be replaced with zeros in data
sample. This makes the IFFT length remain unchanged and decoding of the samples in
receiver becomes simpler. Then the signal is partitioned into V disjoint blocks
v12V
S=[S,S,...,S]
such that
V
v
v1
SS
and then these subblocks are combined to minimize the PAPR in time domain. In time
domain the signal v
sis oversampled Ftimes which is obtained by taking an IFFT of length
FN on signal v
Xconcatenated with (F 1)N
zeros. After partitioning the signal and
performing the IFFT for each part, then the phase factors v
j
v
b e ,v 1,2 ,...,V
 are used to
optimize the v
S. In time domain the OFDM signal can be expressed as:
V
vv
v1
s(b) b s
(17)
where T
01 NF1
s(b) [s (b),s (b),...s (b)]

. The objective is to find the optimum signal s(b)
with
the lowest PAPR. Notice that here NKL
which means that there is no change in the
length of the input signal after the addition of dummy sequence. The subblock partition
type here is based on interleaving which is the best choice for PTS OFDM in terms of
computational complexity reduction as compared to adjacent and pseudo-random method,
however it gives the least PAPR reduction among them.
Then, the process is continued by choosing the optimization parameter b
with the following
condition:
V
vv,k
0kNF1
v1
b arg min( max b s )

(18)
After finding the optimum b
then the optimum signal s(b)
is transmitted to the next block.
Then the PAPR of s(b)
is checked whether it lies in the range of the PAPR threshold
(th
PAPR ). After this additional task, the signal is transmitted otherwise it is returned to the
DSI block to generate the dummy sequence again. This process will continue until the PAPR
is less than the th
PAPR .
Fig. 7 shows the CCDF curves of conventional PTS and DSI-PTS techniques. We assume
here that the number of dummy sequence insertion ( L) is 55 which bears no significant
Advanced Transmission Techniques in WiMAX
228
effect on the transmission efficiency (TE = 100% ). These results are obtained after 10
iteration (I). It can be observed that the PAPR reduction of our proposed PTS scheme
outperforms the conventional PTS scheme with an improvement by 2 and 1 dB respectively
at CCDF = 0.01% , when V2,4
respectively. Even though this reduction seems minor the
complexity according to Table 1 is reduced significantly.
Fig. 7. CCDF of the PAPR of conventional PTS and DSI-PTS technique (L=55, I=10).
Fig. 8 shows the result for different length of dummy sequence. As discussed earlier the
maximum length of dummy sequence that can be applied is 55 and this figure shows that
with this length the reduction obtained is slightly better than when is 30. It is observed that
the reductions of PAPR at CCDF = 0.01% are 1 dB, 1.5 dB and 2 dB for dummy length of 5,
30 and 55 respectively.
Fig. 9 shows the effect of different iteration number on the PAPR performance. From this
figure maximum PAPR reduction is achieved which is 7 dB at CCDF = 0.01% at 100
iterations with L=55. But increasing the number of iterations will reduce the data rate.
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
229
Fig. 8. CCDF of PAPR of DSI-PTS technique for different length of dummy sequence when
I=10.
Fig. 9. CCDF of PAPR of DSI-PTS technique for different number of iterations when the
L=55
Advanced Transmission Techniques in WiMAX
230
There is about 0.5 dB improvement in PAPR reduction when the number of iteration is 100
compared to 10 iteration for both cases of V2,4
as shown in Fig. 9.
Fig. 10. CCDF of PAPR of DSI-PTS technique compared to DSI when the number of
iterations is 10 and V=2.
Fig. 10 demonstrates the PAPR reduction capacity in DSI and DSI-PTS techniques. It should
also be highlighted on that. The DSI-PTS technique offers about 1.5 dB further reduction in
PAPR compared to DSI when the number of dummy sequence L=55and V2
.
3.6 Dummy Sequence Insertion with Enhanced Partial Transmit Sequence (DSI-EPTS)
The block diagram of this technique is shown in Fig. 11. Here as in DSI described
previously, the complex valued dummy signals are first generated and then added to the
vector of data subcarriers. The new vector in the frequency domain is then constructed from
K-data and L-dummy subcarriers, respectively. L can be any number less than K. The new
vector U is given by:
kl
UX,W
(19)
where kk,0k,1k,NL1
X [ X ,X ,...,X ], k 1,2,...,K

is the data subcarrier vector and
ll,0l,1l,L1
W [W ,W ,..., W ], l 1, 2,...,L
 is the dummy signals vector.
After generation of the optimum OFDM signal, PAPR is checked with the acceptable
threshold that has been predefined before. If the PAPR value is less than the threshold then
the OFDM signal will be transmitted otherwise the dummy sequence is generated again as
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
231
shown by the feedback loop in Fig. 11. This process is one iteration. The number of iterations
can be increased to achieve the desired PAPR ( th
PAPR ) reduction but the processing time
will also increase likewise and cause the system performance to drop. From the block
diagram in Fig. 11, X is the input signal with length N. After that dummy sequence is added
which causes an increase in the IFFT length.
Fig. 11. Block diagram of the proposed DSI-EPTS scheme
The same procedure similar to the one discussed in section 3.5 for DSI-PTS scheme is
performed here except the phase sequence is taken from the EPTS scheme discussed earlier
in section 3.5.
3.6.1 Computational complexity
The total complexity of the C-PTS with oversampling factor F=1, is given by (Baxley and
Zhou, 2007):
V1
CPTS
T3VN/2lo
g
N2VW N
 (20)
Whereas for the Enhanced PTS this value is:
EPTS
T3/4VNlogNPVN
(21)
where P is the number of iterations and V is the number of subblocks.
In (Varahram, et al. 2010), the complexity is calculated only for IFFT section, but here we
require the total complexity. Hence the total complexity for the DSI-PTS method is given by:
Advanced Transmission Techniques in WiMAX
232
V1
DSI PTS
T3/4VNlo
g
N2VNW QL

(22)
The total complexity of DSI-EPTS is given by;
DSI EPTS
T3/4VNlogNPVNQL
 (23)
where Q is the number of iterations for the DSI loop.
It can be observed that (22) and (23) consist of two parts; the first part is actually the
complexity of the IFFT itself and the second part is the complexity of the searching
algorithm. Most of the papers did not consider the second part which causes wrong
calculation of the complexity. It should be noted that the number of IFFT in (24) and (25) is
halved which basically is concluded from the simulation results. From the simulation results
given in the following section the PAPR performance of the proposed method when the
number of IFFT is half of the C-PTS, is almost the same. This is shown for different number
of subblocks which proves that in the DSI-EPTS the number of IFFT is halved compared to
the C-PTS but gives the same PAPR performance.
No. of
Subblocks C-PTS DSI-PTS CCRR
Total Complexity
V=4 60416 46760 22.6%
V=8 1103872 1076392 2.4%
Table 1. Computational Complexity of the DSI-PTS and the conventional PTS when N=512
and W=2, Q=3, L=56
No. of
Subblocks C-PTS
DSI-EPTS CCRR (%)
D=1 D=2 D=1 D=2
Total
Complexity
V=4 60416 30376 46760 49.7 22.6
V=8 1103872 552104 1076392 49.6 2.7
Table 2. Computational Complexity of the DSI-EPTS and the conventional PTS when N=512
and W=2, Q=3, L=56
The computational complexity reduction ratio (CCRR) of the proposed technique over the
C-PTS is defined as (Baxley and Zhou, 2007):
Com
p
lexit
y
o
f
theDSI EPTS
CCRR (1 )
Complexity of theC PTS
 100%
(24)
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
233
Table 1 presents the computational complexity of C-PTS and DSI-PTS, for N=512 and W=2.
Table 2 presents the computational complexity of C-PTS and proposed DSI-EPTS, for the
same value of N and W, while D is the coefficient that can be specified based on the PAPR
reduction and complexity according to equation (12).
It is clear from Table 2, that CCRR is improved for both V=4 and V=8. It should be noted
that when D increases, the complexity reduction becomes less while PAPR performance
improves, as shown in the simulations.
3.6.2 Side information
The other important factor in studying the PAPR reduction method is the side information
which has to be transmitted to the receiver to extract the original signal. One method is that
the side information can be transmitted in a separate channel but this comes at the expense
of spectrum efficiency degradation.
The number of required side information bits in C-PTS is
V1
2
log W
where W is the number of allowed phase factors and the sign
indicates the floor of y. In
DSI-EPTS, the side information can be allocated in the dummy signals and therefore does
not have impact on spectrum efficinecy and data rate loss; however, the only drawback of
this method is that, because of the increase in the phase sequence matrix, higher memory
space is required.
3.6.3 System performance
In C-PTS, even though an OFDM signal does not experience distortion the signal after
power amplifier could exhibit distortions if PAPR is higher than the expected value. In this
case the power amplifier should back off which degrades the efficiency of the system. In
DSI-EPTS, the addition of dummy sequences causes the transmission efficiency to change as
follows:
K
TE 100[%]
KL

(25)
where K is the length of subcarriers and L is the length of dummy sequences. In actual
applications where the cost of the system is the main issue, the other block also have to be
considered, the digital predistortion (DPD) (Varahram and Atlasbaf, 2005), (Varahram, et al.
2005). By applying DPD technique, it is possible to increase the linearity of the power
amplifier and as a result, higher peak signals can be transmitted by the power amplifier and
the performance of the PAPR can be improved. This also increases the efficiency of the
power amplifiers and decreases the cost of the system.
Fig. 12 shows the CCDF comparison of PAPR of DSI-EPTS with C-PTS. It is clear that by
applying the DSI-EPTS when D=2, the PAPR performance is more superior over that of C-
PTS for both V=4 and V=8 respectively. But PAPR reduction when D=1 is almost the same
as C-PTS for V=4 and V=8 respectively.
Advanced Transmission Techniques in WiMAX
234
Fig. 12. CCDF comparison of PAPR of the DSI-EPTS and C-PTS
Fig. 13. CCDF comparison of PAPR of the DSI-EPTS and DSI-PTS when L=56
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
235
The highest PAPR reduction is achieved when D=2 and V=4. From table 2, the complexity
reduction is minimum when D=2. There is always a trade off between PAPR reduction
performance and complexity reduction.
Fig. 13 shows the CCDF comparison of PAPR of the DSI-EPTS and DSI-PTS when L=56. The
results are shown for V=2 and V=4. The CCDF results show that PAPR of the DSI-EPTS
outperforms DSI-PTS for both V=2 and V=4 respectively.
Fig. 14 shows a comparison of Bit Error Rate (BER) performance of the conventional PTS
and the proposed EPTS and DSI-EPTS method in Additive White Gaussian Noise (AWGN)
channels. The length of dummy sequence and iterations is L=56. From this figure, we can
see that the BER is slightly increased with DSI-EPTS method compared to conventional PTS,
but PAPR is much improved according to the result of Fig. 13. The performance of the
system shows improvement at the cost of BER.
Fig. 14. Comparison of BER performance of the conventional PTS and DSI-PTS technique in
AWGN channels.
Advanced Transmission Techniques in WiMAX
236
4. Conclusion
In this chapter we have studied and discussed several PAPR redcution techniques. Their
advantages and disadvantages have been analyzed and by performing the simulation
results, the PAPR performance of those techniques have been compared. Also the
complexity of each technique has been computed and finally compared. These PAPR
techniques is ideal for the latest wireless communications systems such as WiMAX and long
term evolution (LTE).
5. Acknowledgment
This work was supported by Universiti Putra Malaysia under the Research University Grant
Scheme (No. 0501090724RU).
6. References
Al-Azoo W. F., Ali B. M, Khatun S., Bilfagih S. M, and Noordin N. K., “Addition of
Gaussian random signals for peak to average power ration reduction in OFDM
systems,” IEEE ICCCE’08 International conference, PP. 1344-1347, 2008.
Bauml R. W., Fischer R. F. H. and Huber J. B., "Reducing the peak-to-average power ratio of
multicarrier modulationby selected mapping," Electron. Lett., vol. 32, pp. 2056-2057,
1996.
Bauml v, Fischer R. F. H. and Huber J. B., "Reducing the peak-to-average power ratio of
multicarrier modulationby selected mapping," Electron. Lett., vol. 32, pp. 2056-2057,
1996.
Baxley R. J. and Zhou T., “Comparing slected mapping and partial transmit sequence for
PAPR reduction”, IEEE Trans. Broadcast., vol. 53, no. 4, pp.797-803, December
2007.
Cimini L. J. and Sollenberger N. R., “Peak-to-average power ratio reduction of an OFDM
signal using partial transmit sequences,” IEEE Commun. Lett., vol. 4, no. 3, pp. 86–
88, March. 2000.
Han S. H. and Lee J. H., “An overview of peak-to-average power ratio reduction techniques
for multicarrier transmission,” IEEE Wireless Commun., vol. 12, no. 2, pp. 56-65, Apr.
2005.
Hao M. and Liaw C., "A companding technique for PAPR reduction of OFDM systems,"
IEICE Trans. Commun., vol. E91-B, pp. 935-938, 2008.
Foomooljareon P. and Fernando W. A. C., "Input sequence envelope scaling in PAPR
reduction of OFDM," in 2002.
Jayalath v and Tellambura C.. (2000, Reducing the peak-to-average power ratio of
orthogonal frequencydivision multiplexing signal through bit or symbol
interleaving. Electron. Lett. 36(13), pp. 1161-1163.
Krongold B. S. and Jones D. L., "PAR reduction in OFDM via active constellation extension,"
IEEE Trans. Broadcast., vol. 49, 2003.
Kwon U., Kim D. and Im G., "Amplitude clipping and iterative reconstruction of MIMO-
OFDM signals with optimum equalization," IEEE Transactions on Wireless
Communications, vol. 8, pp. 268-277, 2009.
Peak-to-Average Power Ratio Reduction in
Orthogonal Frequency Division Multiplexing Systems
237
Mohammady S., Varahram P., Sidek R. M., Hamidon M. N. and Sulaiman N., “Efficiency
improvement in microwave power amplifiers by using Complex Gain
Predistortion technique,IEICE Electronics Express (ELEX), vol. 7, no. 23, pp.1721-
1727, Oct. 2010.
Muller S. H. and Huber J. B., "A novel peak power reduction scheme for OFDM," in Personal,
Indoor and Mobile Radio Communications, 1997.'Waves of the Year 2000'. PIMRC'97.,
the 8th IEEE International Symposium on, 1997.
Nikookar H. and Lidsheim K. S., "Random phase updating algorithm for OFDM
transmission with low PAPR," IEEE Trans. Broadcast., vol. 48, pp. 123-128, 2002.
Qian H., "Power Efficiency Improvements for Wireless Transmissions," Power Efficiency
Improvements for Wireless Transmissions, 2005.
Ryu H. G., Lee J.E. and Park J.S., “Dummy sequence insertion (DSI) for PAPR reduction in
the OFDM communication system,” IEEE Trans. Consumer Electr., vol. 50, no. 1, pp.
89-94, Feb. 2004
Tellado J., Multicarrier Modulation with Low PAR: Applications to DSL and Wireless. Kluwer
Academic Pub, 2000.
Tan C. E. and Wassell I. J., "Data bearing peak reduction carriers for OFDM systems,"
Information, Communications and Signal Processing, 2003 and the Fourth Pacific Rim
Conference on Multimedia. Proceedings of the 2003 Joint Conference of the Fourth
International Conference on, vol. 2; 2, pp. 854-858 vol.2, 2003.
Van Nee R. and De Wild A., "Reducing the peak-to-average power ratio of OFDM," in 48th
IEEE Vehicular Technology Conference, 1998. VTC 98, 1998.
Varahram P., Mohammady S., Hamidon M. N., Sidek R. M. and Khatun S., “Digital
Predistortion Technique for Compensating Memory Effects of Power
Amplifiers in Wideband Applications”, Journal of Electrical Engineering, vol. 60,
no. 3, 2009.
Varahram P., Mohammady S., Hamidon M. N., Sidek R. M. and Khatun S., “Power
amplifiers linearization based on digital predistortion with memory effects used in
CDMA applicationsm,” 18th European Conference on Circuit Theory and Design
ECCTD, pp. 488 – 491, 2007.
Varahram P., Atlasbaf Z., “Adaptive digital predistortion for high power amplifiers with
memory effects,” Asia-Pacific Microwave Conference Proceedings, APMC. 3(1606627),
2005.
Varahram P., Azzo W. A., Ali B. M., “A Low Complexity Partial Transmit Sequence Scheme
by Use of Dummy Signals for PAPR Reduction in OFDM Systems,” IEEE Trans.
Consumer Electron, vol. 56, no. 4, pp. 2416-2420, Nov. 2010.
Varahram P., Atlasbaf Z., Heydarian N., “Adaptive digital predistortion for power
amplifiers used in CDMA applications,” Asia-Pacific Conference on Applied
Electromagnetics, APACE Proceedings, (1607810):215-21, 2005.
Vijayarangan V. and Sukanesh D., "AN OVERVIEW OF TECHNIQUES FOR REDUCING
PEAK TO AVERAGE POWER RATIO AND ITS SELECTION CRITERIA FOR
ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING RADIO SYSTEMS,"
pp. 25, 2009.
Advanced Transmission Techniques in WiMAX
238
Wilkison T. A. and Jones A. E., "Minimazation of the peak to mean envelope power ratio of
multicarrier transmission schemes by block coding," in IEEE Vehicular Technology
Conference, 1995.
... An important benefit about this group of techniques is that they do not need to transfer extra information to the receiver to inform about the modification performed on the signal at the transmitter. For many coding based techniques, such as [15,16], SLM [17], or PTS [18,19] based algorithms, the receiver has to be informed about the modifications performed on the signal at the receiver side, and generally, a compensation block has to be added to the receiver side to reverse the process, and this normally effects the symbol error rate (SER), and error vector magnitude (EVM). Moreover, informing the receiver normally involves transmitting extra bits as side information. ...
... It should be noted that if an algorithm requires complex multiplications, or complex divisions, they all have to be transformed into real multiplications and additions. For example, as mentioned earlier about SLM based techniques [17,20,36], at the receiver, a compensation block including a complex division is required in order to extract the original transmitted signal [37]. The second parameter that plays an important role in implementing a PAPR reduction technique in hardware is the the memory that is required. ...
... It should be noted that for techniques of PTS [18,[38][39][40], SLM based techniques [20,36,41], the set ups of the algorithms are considered in a way that the PAPR reduction performance is comparable with the PSI technique. This means that number of IDFT processed in both mentioned categories, is considered to be 16, and the length of the signal is considered to be 1024, which indicates the number of bts for storing the phases that are multiplied into the input signal [17,41]. Table 4. Computational complexity comparison. ...
Article
Full-text available
Orthogonal frequency division multiplexing (OFDM) has become an indispensable part of waveform generation in wideband digital communication since its first appearance in digital audio broadcasting (DAB) in Europe in 1980s, and it is indeed in use. As has been seen, the OFDM based waveforms work well with time division duplex operation in new radio (NR) systems in 5G systems, supporting delay-sensitive applications, high spectral efficiency, massive multiple input multiple output (MIMO) compatibility, and ever-larger bandwidth signals, which has demonstrated successful commercial implementation for 5G downlinks and uplinks up to 256-QAM modulation schemes. However, the OFDM waveforms suffer from high peak to average power ratio (PAPR), which is not desired by system designers as they want RF power amplifiers (PAs) to operate with high efficiency. Although NR offers some options for maintaining the efficiency and spectral demand, such as cyclic prefix based (CP-OFDM), and discrete Fourier transform spread based (DFT-S-OFDM) schemes, which have limiting effects on PAPR, the PAPR is still as high as 13 dB. This value increases when the bandwidth is increased. Moreover, in LTE-Advance and 5G systems, in order to increase the bandwidth, and data-rate, carrier aggregation technology is used which increases the PAPR the same way that bandwidth increment does; therefore, it is essential to employ PAPR reduction in signal processing stage before passing the signal to PA. In this paper, we investigate the performance of an innovative peak shrinking and interpolation (PSI) technique for reducing peak to average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) based signals at waveform generation stage. The main idea behind the PSI technique is to extract high peaks, scale them down, and interpolate them back into the signal. It is shown that PSI technique is a possible candidate for reducing PAPR without compromising on computational complexity, compatible for existing and future telecommunication systems such as 4G, 5G, and beyond. In this paper, the PSI technique is tested with variety of signals in terms of inverse fast Fourier transform (IFFT) length, type of the signal modulation, and applications. Additional work has been carried out to compare the proposed technique with other promising PAPR reduction techniques. This paper further validates the PSI technique through experimental measurement with a power amplifier (PA) test bench and achieves an adjacent channel power ratio (ACPR) of less than –55 dBc. Results showed improvement in output power of PA versus given input power, and furthermore, the error vector magnitude (EVM) of less than 1 % was achieved when comparing of the signal after and before modification by the PSI technique.
Article
Full-text available
Multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) has become a promising candidate for next generation broadband wireless communications. However, like a single-input single-output (SISO)-OFDM, one main disadvantage of the MIMO-OFDM is the high peak-to-average power ratio (PAPR), which can be reduced by using an amplitude clipping. In this paper, we propose clipped signal reconstruction methods for the MIMO-OFDMs with spatial diversity, such as space-time and space-frequency block codes (STBC/SFBC). The proposed methods are based on the technique called iterative amplitude reconstruction (IAR) for SISO-OFDM. It is shown that the IAR can be easily employed for the STBC-OFDM, but it cannot be directly applied to the SFBC-OFDM, because the transmitted sequences over different antennas are dependent due to the use of space-frequency code. We propose a new SFBC transmitter for clipped OFDM, which has approximately half the computational complexity of conventional SFBC-OFDM. The proposed clipping preserves the orthogonality of transmitted signals, and the clipped signals are iteratively recovered at the receiver. Further, we theoretically analyze the performance of IAR with optimum equalization, and also provide highly accurate channel estimation of the OFDM with amplitude clipping. Simulation results show that the proposed receivers effectively recover contaminated OFDM signals with a moderate computational complexity.
Article
Full-text available
Many communications signal formats are not power efficient because of their large peak-to-average power ratios (PARs). Moreover, in the presence of nonlinear devices such as power amplifiers (PAs) or mixers, the non-constant-modulus signals may generate both in-band distortion and out-of-band interference. Backing off the signal to the linear region of the device further reduces the system power efficiency. To improve the power efficiency of the communication system, one can pursue two approaches: i) linearize the PA; ii) reduce the high PAR of the input signal. In this dissertation, we first explore the optimal nonlinearity under the peak power constraint. We show that the optimal nonlinearity is a soft limiter with a specific gain calculated based on the peak power limit, noise variance, and the probability density function of the input amplitude. The result is also extended to the fading channel case. Next, we focus on digital baseband predistortion linearization for power amplifiers with memory effects. We build a high-speed wireless test-bed and carry out digital baseband predistortion linearization experiments. To implement adaptive PA linearization in wireless handsets, we propose an adaptive digital predistortion linearization architecture that utilizes existing components of the wireless transceiver to fulfill the adaptive predistorter training functionality. We then investigate the topic of PAR reduction for OFDM signals and forward link CDMA signals. To reduce the PAR of the OFDM signal, we propose a dynamic selected mapping (DSLM) algorithm with a two-buffer structure to reduce the computational requirement of the SLM method without sacrificing the PAR reduction capability. To reduce the PAR of the forward link CDMA signal, we propose a new PAR reduction algorithm by introducing a relative offset between the in-phase branch and the quadrature branch of the transmission system. Ph.D. Committee Chair: Zhou, Tong; Committee Member: Feeney, Robert; Committee Member: Kenney, James; Committee Member: Li, Ye; Committee Member: Pan, Ronghua
Article
Power Amplifiers (PAs) are important parts of the transmitters. They amplify the signals that are going to be transmitted. With increasing the input power of the PA, it creates the nonlinearity at the output. The nonlinearity causes out of band distortion and in band distortion. To overcome these effects the power amplifier should be backed off but it will reduce the efficiency of the PA. To increase the efficiency, the Complex Gain Memory Predistortion (CGP) is added to the system. Experimental results with the Mini Circuit power amplifier show an improvement of 7% in Power Added Efficiency (PAE) when the CGP method is applied.
Article
The application of digital predistortion in base band signal is an extended method of amplifier linearization to reduce the Adjacent Channel Interference (ACI) in those systems in which a varying envelope modulation scheme like OFDM and MQAM is used. Digital baseband predistortion is a highly cost-effective way to linearize Power amplifiers (PAs), but most existing architectures assume that the PA has a memoryless nonlinearity. For wider bandwidth applications such as wideband code-division multiple access (WCDMA), wideband orthogonal frequency-division multiplexing (W-OFDM) and worldwide interoperability for microwave access (WiMAX), PA memory effects can no longer be ignored. In this paper a novel technique for compensating such effects is proposed. This technique is a combination of two techniques, memory polynomial predistortion and the gain based predistorter method. This method is compared with the other technique, memory polynomial method and validated using a Mini-Circuit power amplifier and QPSK signal with 1 MHz bandwidth. Simulations and results show improvement in ACLR reduction and EVM with applying this method. K e y w o r d s: digital predistortion, memory effects, ACLR, power amplifier, WCDMA
Conference Paper
This paper investigates the problem of peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) system. It presents a new PAPR reduction method based on addition of power of random signals in a complex Gaussian distribution form to the data constellation points in frequency domain. The added signals alter the constellation shape by shifting the constellation points from their original positions into new positions. This change in shape is accompanied by changes in the statistical properties and reduction in the PAPR value. There is no need to send side information to the receiver for signal recovery. This scheme significantly reduces the PAPR value without decrease in the bit rate or BER performance. Moreover, there is no out-of-band distortion resulted. For 64-PSK OFDM system using 128 data sub-carriers, >4 dB reduction in the PAPR value is achieved by using the proposed PAPR reduction method.
Article
In this paper a novel technique for reducing the peak to average power ratio (PAPR) in OFDM systems by using the combination of the dummy sequence insertion (DSI) and partial transmit sequence (PTS) is proposed. In DSI increasing the number of dummy sequence decrease the transmission efficiency (TE) and in PTS the complexity increases when the number of subblock increases. Unlike the conventional PTS which needs several inverse fast fourier transform (IFFT) operations, the proposed DSI-PTS technique requires half IFFT operations only, while the PAPR performance is even better. So, it can remarkably reduce the computational complexity. Simulation results are examined with IEEE 802.16-2004 standard. By applying the DSI-PTS method about 0.5 dB reduction in PAPR at complementary cumulative distribution function (CCDF) of 0.01% is achieved compared to the conventional PTS while the complexity is reduced.
Article
Orthogonal frequency division multiplexing (OFDM) is an attractive technique for achieving high-bit-rate wireless data transmission. However, the potentially large peak-to-average power ratio (PAP) of a multicarrier signal has limited its application. Two promising techniques for improving the statistics of the PAP of an OFDM signal have previously been proposed: the selective mapping and partial transmit sequence approaches. Here, we summarize these techniques and present suboptimal strategies for combining partial transmit sequences that achieve similar performance but with reduced complexity
Article
A companding technique using the hyperbolic tangent transform is proposed for reducing the peak-to-average-power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. This technique is practical and can be implemented easily in analog integrated circuit design. The PAPR value of an OFDM system and the optimal companding coefficient to attain the minimum quantization error are derived. Error probability performance of the system after the companding is evaluated, which then is compared to the systems with the mu-law and A-law companding techniques.
Conference Paper
Digital predistortion of a baseband signal is a well-known method of power amplifier (PA) linearization used to reduce adjacent channel interference (ACI) in a non constant envelope modulation system. This paper discusses the application of adaptive digital baseband predistortion linearization to radio frequency (RF) power amplifiers (PAs) that exhibit memory effects. This technique is a highly cost- effective way to linearize Power amplifiers (PAs), but most existing architectures assume that the PA has a memoryless nonlinearity. For wider bandwidth applications such as wideband code-division multiple access (WCDMA) or wideband orthogonal frequency-division multiplexing (W- OFDM), PA memory effects can no longer be ignored. In this paper a new technique for adaptation of digital predistorter that considers memory effects in power amplifiers is proposed. This method is a combination of two techniques, memory polynomial predistortion and slope-dependent method. This new technique is validated by using a 1.9 GHz 60 W LDMOS power amplifier and various signals such as 2- carrier CDMA and 3-carrier CDMA.