scispace - formally typeset
Search or ask a question
Proceedings ArticleDOI

Peak-to-average power-ratio reduction for OFDM systems based on method of conditional probability and coordinate descent optimization

TL;DR: Two new algorithms for PAPR reduction are developed by applying the so-called method of conditional probability (MCP) and coordinate descent optimization (CDO) and it is demonstrated that they outperform several existing algorithms.
Abstract: A new constellation extension technique for peak-to-average power-ratio reduction (PAPR) in orthogonal frequency-division multiplexing systems is proposed. Two new algorithms for PAPR reduction are developed by applying the so-called method of conditional probability (MCP) and coordinate descent optimization (CDO). Our simulations demonstrate that the proposed algorithms outperform several existing algorithms and the performance can be further improved by combining the MCP, CDO, and the selective mapping algorithms.

Summary (2 min read)

Introduction

  • Orthogonal frequency-division multiplexing (OFDM) has recently been used for data transmission in a number of communication systems [1][2].
  • A major problem associated with OFDM is its large peak-to-average power-ratio (PAPR) which renders system performance sensitive to distortion introduced by nonlinear devices, e.g., power amplifiers (PAs).
  • Recently, a number of algorithms [3]-[5] have been proposed to reduce the PAPR of the transmit signal before it enters the PAs.
  • A new constellation is proposed whereby the data are represented either by points in the original constellation or by extended points.
  • The performance of the proposed algorithms can be further improved by combining them with the selective mapping (SLM) algorithm [3].

II. PAPR REDUCTION VIA CONSTELLATION EXTENSION

  • Consider an N -subcarrier OFDM transmitter as illustrated in Fig. 1, where S/P, P/S, and D/A represent serialto-parallel, parallel-to-serial, and digital-to-analog converter, respectively, and the block labeled as “Amp.” represents a power amplifier.
  • A 16-QAM modulation is adopted for each subcarrier and its constellation is shown in Fig. 2a.
  • The proposed constellation extension scheme is illustrated in Fig. 2b where any data point with a value greater than or equal to 4 and less than 12 can be represented by a pair of two possible constellation points.
  • The authors objective is to obtain an optimal representation of the data points by either the exterior or the extended points such that the PAPR of the OFDM symbol X is minimized.
  • For this reason, a reasonable suboptimal solution to the PAPRreduction problem in (3) can be obtained by solving the problem in (6).

B. Algorithm Based on Coordinate Descent Optimization

  • The idea of CDO [8] can be applied to reduce the value of f(s) iteratively where only one element of the sign vector s is allowed to switch in each iteration.
  • Since the value of f(s) is monotonically reduced in each iteration, the CDO technique can be applied to enhance the performance of the MCP algorithms proposed in Secs. III.A and B.

C. Combination of the Proposed and the SLM Algorithms

  • In the proposed algorithms only one data set has been utilized for PAPR reduction.
  • The performance can be improved by combining the proposed algorithms with the SLM algorithm, as illustrated in Fig.
  • First, multiple candidate data sets are generated at the transmitter.
  • Second, for each of the data sets the proposed MCP algorithm is applied and the one with the least PAPR is selected.
  • Third, the selective rotation (SR) [5] and CDO algorithms are applied to the data set selected in the second stage for further PAPR reduction.

D. Computational Complexity Analysis

  • Note that compared with the scheme in Fig. 2c, the scheme in Fig. 2b requires fewer extended points for PAPR reduction.
  • Statistically, the number of variables in (6) associated with the scheme in Fig. 2b is two thirds that associated with the scheme in Fig. 2c.
  • Since the computation complexity of the MCP and CDO algorithms is propotional to the number of variables in problem (6), the computation required by the algorithms using the scheme in Fig. 2b is only about two thirds that required by the algorithms using the scheme in Fig. 2c.

IV. SIMULATIONS

  • The proposed algorithms were applied to an OFDM system with 64 subcarriers and the performance was evaluated and compared with that of the algorithms proposed in [4][5].
  • In order to approximate the analog signal accurately, oversampling was applied as in [5].
  • Applying the proposed algorithms to the extended constellations in Fig. 2b and 2c, the clipping probabilities versus various power threshold values are plotted as the solid and dash curves in Fig. 4, respectively, also known as Example.
  • Second, it can be observed from Fig. 5 that the performance can be further improved by combining the proposed algorithms with the SLM algorithm.
  • The CPU time required by the former scheme is only about two thirds that required by the latter one.

V. CONCLUSIONS

  • Two new algorithms for PAPR reduction based on a new constellation extension scheme have been proposed.
  • Simulations have demonstrated that the proposed algorithms outperform the SLM algorithm in [4] in terms of PAPR reduction and the algorithm in [5] in terms of computational complexity.

Did you find this useful? Give us your feedback

Content maybe subject to copyright    Report

Peak-to-Average Power-Ratio Reduction for OFDM
Systems Based on Method of Conditional
Probability and Coordinate Descent Optimization
Y. J. Kou, W.-S. Lu, and A. Antoniou
Department of Electrical and Computer Engineering, University of Victoria
P.O. Box 3055, Victoria, B.C., Canada V8W 3P6
Email:
{ykou, wslu}@ece.uvic.ca, aantoniou@ieee.org
Abstract A new constellation extension technique for peak-to-
average power-ratio reduction (PAPR) in orthogonal frequency-
division multiplexing systems is proposed. Two new algorithms
for PAPR reduction are developed by applying the so-called
method of conditional probability (MCP) and coordinate descent
optimization (CDO). Our simulations demonstrate that the pro-
posed algorithms outperform several existing algorithms and the
performance can be further improved by combining the MCP,
CDO, and the selective mapping algorithms.
I. INTRODUCTION
Orthogonal frequency-division multiplexing (OFDM) has
recently been used for data transmission in a number of com-
munication systems [1][2]. A major problem associated with
OFDM is its large peak-to-average power-ratio (PAPR) which
renders system performance sensitive to distortion introduced
by nonlinear devices, e.g., power amplifiers (PAs). Recently,
a number of algorithms [3]-[5] have been proposed to reduce
the PAPR of the transmit signal before it enters the PAs.
In this paper, a new constellation is proposed whereby
the data are represented either by points in the original
constellation or by extended points. Two new algorithms
are then developed by applying the so-called method of
conditional probablity (MCP) [6]-[7] and coordinate descent
optimization (CDO) [8], which can be used to find the op-
timal representation of the OFDM signal. Design examples
are presented which demonstrate that significant reduction in
PAPR as well as reduced computational effort can be achieved
by the proposed algorithms over several existing algorithms.
The performance of the proposed algorithms can be further
improved by combining them with the selective mapping
(SLM) algorithm [3].
II. PAPR R
EDUCTION VIA CONSTELLATION EXTENSION
Consider an N-subcarrier OFDM transmitter as illustrated
in Fig. 1, where S/P, P/S,andD/A represent serial-
to-parallel, parallel-to-serial, and digital-to-analog converter,
respectively, and the block labeled as Amp.”represents
a power amplifier. A 16-QAM modulation is adopted for
each subcarrier and its constellation is shown in Fig. 2a.
The proposed constellation extension scheme is illustrated in
Fig. 2b where any data point with a value greater than or
equal to 4 and less than 12 can be represented by a pair of
two possible constellation points. For example, the data point
D
k
=11(or 1011 in binary form) can be represented by either
X
0
k
= 1 3j or X
1
k
= 1+5j where the superscript of
X
k
is used to identify which constellation point is selected
to represent D
k
, i.e., X
0
k
indicates that an exterior point of
the conventional constellation is used to represent D
k
;onthe
other hand, X
1
k
indicates that a corresponding extended point
is used to represent D
k
. For the purpose of comparison, the
constellation extension scheme proposed in [5] is shown in
Fig. 2c.
The 16-QAM modulated symbol X
k
is referred to as
the subsymbol at the kth subcarrier, and vector X =
[X
0
··· X
N1
] is referred to as the OFDM symbol.The
discrete complex baseband representation of the nth sample
of the OFDM symbol is given by
x
n
=
1
N
N1
k=0
s
k
X
k
e
j2πkn
N
for n =0, ..., N 1 (1)
If we let x =[x
0
··· x
N1
]
T
, the PAPR of signal x can be
defined as
PAPR =
x
2
E[x
2
2
]/N
(2)
where E[·] denotes expectation. Our objective is to obtain an
optimal representation of the data points by either the exterior
or the extended points such that the PAPR of the OFDM
symbol X is minimized. For the sake of a fair comparison
with other PAPR-reduction algorithms, the peak power of
the transmit signal will be used as a performance measure
in the computer simulations presented in Sec. IV. Denoting
the number and index set of subcarriers which are applicable
to constellation extension as K and I = {i
1
,i
2
, ...,i
K
},
respectively, and letting
¯
X =[X
i
1
···X
i
K
]
T
,thePAPR-
reduction problem can be formulated as
minimize
¯
X
max
0nN1
N1
k=0,k∈I
X
k
e
j2πkn
N
(3a)
subject to:X
k
∈{X
0
k
,X
1
k
} for k ∈I (3b)

If we let
Y
k
=
X
0
k
+ X
1
k
2
and Z
k
=
X
0
k
X
1
k
2
for k ∈I (4a)
then we have
X
0
k
= Y
k
+ Z
k
and X
1
k
= Y
k
Z
k
for k ∈I (4b)
where the variables in (3) and (4) are complex. If we define
c
n
=
Re
N1
k=0,k /I
X
k
e
j2πkn
N
+
K
k=1
Y
i
k
e
j2πi
k
n
N
0 n N 1
Im
N1
k=0,k /I
X
k
e
j2πk(nN )
N
+
K
k=1
Y
i
k
e
j2πi
k
(nN )
N
N n 2N 1
(5a)
and
d
nk
=
Re
Z
i
k
e
j2πi
k
n
N
0 n N 1
Im
Z
i
k
e
j2πi
k
(nN )
N
N n 2N 1
(5b)
then the problem in (3) can be relaxed to
minimize
s
max
0n2N1
c
n
+
K
k=1
s
k
d
nk
(6a)
subject to: s
k
∈{1, 1} for k =1, ..., K (6b)
where the variables involved are real. It can be shown that
the solution of the problem in (6) can be regarded as a good
approximation of the solution of the problem in (3). For
this reason, a reasonable suboptimal solution to the PAPR-
reduction problem in (3) can be obtained by solving the
problem in (6).
X
x
P/S
Inverse
DFT
channel
Amp.D/AS/P Modulation
stream
bit
Fig. 1. Block diagram of a typical OFDM transmitter.
III. PAPR-REDUCTION ALGORITHMS
The minimax optimization problem in (6) is an integer
programming problem which can be solved by using the MCP
along with the pessimistic estimator reported in [6][7] or
by using the CDO reported in [8].
A. Algorithm Based on Method of Conditional Probability
Consider sign vector s =[s
1
···s
K
] where s
1
, ..., s
K
are
treated as random variables which can assume the values of
1 or 1 with equal probability. Let A
λ
n
be the event that
c
n
+
K
k=1
d
nk
s
k
λ and let Pr
A
λ
n
be the probability
that event A
λ
n
occurs. For the problem in (6), a pessimistic
estimator is defined as an upper bound of the conditional
probability Pr
A
λ
n
|s
1
, ..., s
j
and can be characterized by
Pr
A
λ
n
|s
1
, ..., s
j
U
n
(λ, s
1
, ...,s
j
) (7)
1000 1100
0000 0100
0111
1111
0011
1011 1010
0010 0110
1110
(a)
0110
1110
1100
1000
0010
1001
0101
0111
1111
X
X
Y
k
0
k
k
k
k
1
Z
−Z
0100
0110
0100
(c)
1110
1100
1010
1000
0000
1010
1001
0001
0011
1011
1101
0101
0111
1101
10111111
1001
0110
0100
(b)
1010
1000
0000
1010
Y
k
X
k
1
X
k
0
1001
1101
0101 0001
0001
0011
1011
1101
0101
0111
1011
0100
0110
1110
1100
1000
0010
1001
0101
0111
1111
−Z
Z
k
k
Fig. 2. (a) 16-QAM constellation with Gray code bit mapping. (b) An 8-
point extension scheme for 16-QAM constellation. (c) A 12-point extension
scheme for 16-QAM constellation.
for j =1, ..., K, where the following condition is satisfied
min
s
j
∈{1,1}
2N1
n=0
U
n
(λ, s
1
, ..., s
j1
,s
j
)
2N1
n=0
U
n
(λ, s
1
, ..., s
j1
) (8)
Let us assume that λ is chosen such that
2N1
n=0
U
n
(λ) < 1 (9)
where U
n
(λ) denotes the upper bound of Pr
A
λ
n
with all
the components of s,i.e.,s
1
, ..., s
K
treated as random
variables. If the first component of the optimal sign vector
is taken to be s
1
=1, a suboptimal sign vector s
can be
obtained sequentially as
s
j
=arg
min
s
j
∈{1,1}
2N1
n=0
U
n
λ, s
1
, ..., s
j1
,s
j
= sign
2N1
n=0
U
n
λ, s
1
, ...,s
j1
, 1
2N1
n=0
U
n
λ, s
1
, ...,s
j1
, 1
(10)
for j =2, ..., K. Consequently, we have
2N1
n=0
U
n
λ, s
1
, ..., s
j1
,s
j
2N1
n=0
U
n
λ, s
1
, ..., s
j1
(11)

which in conjunction with (7), (8), and (9) implies that
2N1
n=0
Pr
A
λ
n
|s
1
, ..., s
K
2N1
n=0
U
n
(λ, s
1
, ..., s
K
)
< 1 (12)
With the vector s
known, the probability Pr
A
λ
n
|s
1
,
..., s
K
) for each n is either zero or one. Hence, it can be
inferred from (12) that Pr
A
λ
n
|s
1
, ..., s
K
=0for n =
0, ..., 2N 1, which means that
c
n
+
K
k=1
s
k
d
nk
.
In other words, the sign vector s
=[s
1
···s
K
] obtained
using (10) can be regarded as a suboptimal solution for which
the objective function in the problem in (6) is guaranteed to
be smaller than λ.
In what follows, a pessimistic estimator is derived based
on the Chernoff bound [9] which can be described by the
inequality
Pr(Y δ) e
γδ
E(e
γY
) (13)
where γ is a nonnegative parameter to be optimized. By
applying the Chernoff bound to the conditional probability,
we obtain
Pr
A
λ
n
|s
1
, ..., s
j
2e
γλ
cosh
γc
n
+ γ
j
k=1
s
k
d
nk
·
N
k=j+1
cosh(γd
nk
) (14)
where the fact that the random variables s
j+1
, ..., s
K
are
independent and assume the values of 1 or 1 with equal
probability has been used. Using the above analysis, a pes-
simistic estimator can be derived as
U
n
(λ
,s
1
, ..., s
j
)=2e
γ
λ
cosh
γ
c
n
+ γ
j
k=1
s
k
d
nk
·
N
k=j+1
cosh (γ
d
nk
) (15)
for j =1, ..., K,where λ
=
2ε log(4N )
=
λ
/ε, and ε =
max
0n2N1
c
2
n
+
K
k=1
d
2
nk
. By using (10)
and (15), a suboptimal solution s
for the problem in (6) can
be obtained as
s
j
= sign
2N1
n=0
sinh
γ
c
n
+ γ
j1
k=1
s
k
d
nk
· sinh (γ
d
nk
)
K
k=j+1
cosh (γ
d
nk
)
(16)
for j =2, ..., K. Using (4b) and (16), the optimized OFDM
symbol X
can be obtained as
X
k
=
X
k
for k/ I
Y
k
+ s
l
Z
k
for k I
(17)
where l is the index of element k in set I in case that k I.
It can be shown that the peak power of the optimized OFDM
symbol X
is guaranteed to be smaller than 2λ
2
.
B. Algorithm Based on Coordinate Descent Optimization
Define f (s)=max {f
n
(s) for 0 n 2N 1} where
f
n
(s)=
c
n
+
K
k=1
s
k
d
nk
for n =0, ..., 2N 1
The idea of CDO [8] can be applied to reduce the value of
f(s) iteratively where only one element of the sign vector s
is allowed to switch in each iteration. First, the value of f
n
(s)
after the sign switch of element s
k
c
can be obtained as
f
n
(s,k
c
)=
c
n
+
K
k=1,k=k
c
s
k
d
nk
s
k
c
d
nk
c
for n =0, ..., 2N 1 and k
c
=1, ..., K.Let
f
be the
change in the value of f ,i.e.,
f
(k
c
)=f(s)
max
0n2N1
f
n
(s,k
c
) for k
c
=1, ..., K
and
ˆ
k
c
be the index that yields the maximum of
{
f
(k
c
), 1 k
c
K}.If
f
(
ˆ
k
c
) where is a pre-
defined tolerance, then a local minimum of function f (s) is
achieved and the algorithm terminates. Otherwise, the sign
of s
ˆ
k
c
is switched and the sign vector can be updated as
s =[s
1
··· s
ˆ
k
c
1
s
ˆ
k
c
s
ˆ
k
c
+1
... s
K
]. Since the value
of f(s) is monotonically reduced in each iteration, the CDO
technique can be applied to enhance the performance of the
MCP algorithms proposed in Secs. III.A and B.
C. Combination of the Proposed and the SLM Algorithms
In the proposed algorithms only one data set has been
utilized for PAPR reduction. The performance can be improved
by combining the proposed algorithms with the SLM algo-
rithm, as illustrated in Fig. 3. First, multiple candidate data sets
are generated at the transmitter. Second, for each of the data
sets the proposed MCP algorithm is applied and the one with
the least PAPR is selected. Third, the selective rotation (SR)
[5] and CDO algorithms are applied to the data set selected
in the second stage for further PAPR reduction.
P/SDACAmp.
channel
Modulation
PAPR
Select
Least
MCP Algorithm
Representation
Signal
Multiple
bit
stream
MCP AlgorithmModulationModulation
SR
CDO
&
CP
Insertion
DFT
Inverse
D
1
U
D
0
x
N
−1
1
x
X
X
U
Fig. 3. Combination of the proposed and the SLM algorithms.
D. Computational Complexity Analysis
Note that compared with the scheme in Fig. 2c, the scheme
in Fig. 2b requires fewer extended points for PAPR reduction.
Statistically, the number of variables in (6) associated with the
scheme in Fig. 2b is two thirds that associated with the scheme
in Fig. 2c. Since the computation complexity of the MCP and
CDO algorithms is propotional to the number of variables in

problem (6), the computation required by the algorithms using
the scheme in Fig. 2b is only about two thirds that required
by the algorithms using the scheme in Fig. 2c.
IV. S
IMULATIONS
The proposed algorithms were applied to an OFDM system
with 64 subcarriers and the performance was evaluated and
compared with that of the algorithms proposed in [4][5].
In order to approximate the analog signal accurately, over-
sampling was applied as in [5]. In the case where multiple
candidate sequences are used, the number of sequences is
denoted as U. In the case where the proposed MCP algorithm
is combined with the SR algorithm, the number of rotations
is denoted as K and the rotation angles θ assume the values
θ =0, π/K, ..., (K 2)π/K, (K 1)π/K.
Example: Applying the proposed algorithms to the extended
constellations in Fig. 2b and 2c, the clipping probabilities
versus various power threshold values are plotted as the solid
and dash curves in Fig. 4, respectively. For the SLM algo-
rithm, a 16-QAM constellation was adopted. For the sake of
comparison, the clipping probabilities obtained using the SLM
algorithm and for the original OFDM signal are plotted in the
same gure as dot-dashed curves. First, it can be observed
from Fig. 4 that by combining the SR and the CDO algorithms
with the MCP algorithm, significant PAPR reduction can be
achieved over that obtained with the SLM algorithm. For
example, for the MCP algorithm using the scheme in Fig. 2b
with K =4for a clipping probability of 10
3
, a 0.5-dB
improvement can be achieved compared with the performance
of the SLM algorithm with U =16. Second, it can be observed
from Fig. 5 that the performance can be further improved by
combining the proposed algorithms with the SLM algorithm.
For example, a 1.5-dB improvement can be achieved by using
the combined algorithm with U =4,K=2over the SLM
algorithm with U =16. Third, it can be observed from Figs. 4
and 5 that the performance of the algorithms using the scheme
in Fig. 2b is quite close to that of the algorithms using the
scheme in Fig. 2c. However, the CPU time required by the
former scheme is only about two thirds that required by the
latter one.
V. C
ONCLUSIONS
Two new algorithms for PAPR reduction based on a new
constellation extension scheme have been proposed. Simula-
tions have demonstrated that the proposed algorithms outper-
form the SLM algorithm in [4] in terms of PAPR reduction
and the algorithm in [5] in terms of computational complexity.
ACKNOWLEDGEMENT
The authors are grateful to Micronet, NCE Program, and the
Natural Sciences and Engineering Research Council of Canada
for supporting this work.
R
EFERENCES
[1] ETSI, “Radio broadcasting systems: digital audio broadcasting
to mobile, portable and fixed receivers, European Telecommu-
nication Standard, ETS 300-401, Feb. 1995.
[2] IEEE 802.11, “IEEE Standard for Wireless LAN Medium Ac-
cess Control (MAC) and Physical Layer (PHY) Specifications,
Nov. 1997.
[3] S. Mueller, R. Baeuml, R. Fischer, and J. Huber, “OFDM
with reduced peak-to-average power ratio by multiple signal
representation, Annals of Telecommunications, Feb. 1997.
[4] M. Breiling, S. Mueller-Weinfurtner, and J. Huber, “Distortion-
less reduction of peak power without explicit side information,
Proc. IEEE GLOBECOM, pp. 1494-1498, 2000.
[5] Y. Kou, W.-S. Lu, and A. Antoniou, “New peak-to-average
power-ratio reduction algorithm for OFDM systems using con-
stellation extension, Proc. IEEE Pacific Rim Conference on
Communications, Computers, and Signal Processing, pp. 514-
517, Victoria, BC, Aug. 2005.
[6] P. Raghavan, “Probabilistic construction of deterministic algo-
rithms approximating packing integer program, J. Computer
and System Sciences, vol. 37, pp. 130-143, 1988.
[7] J. Spencer, Ten Lectures on the Probabilistic Method,SIAM,
Philadelphia, 1987.
[8] J. Luo, K. Pattipati, and P. Willett, A class of coordinate descent
methods for multiuser detection, Proc. IEEE ICASSP,vol.5,
pp. 2853-2856, Jun. 2000.
[9] J. G. Proakis, Digital Communications, 4th ed., McGraw Hill,
2000.
5 6 7 8 9 10 11 12
10
−3
10
−2
10
−1
10
0
OFDM signal
SLM (U=4)
SLM (U=16)
12 points, MCP, CDO (K=1)
12 points, MCP, CDO (K=4)
8 points, MCP, CDO (K=1)
8 points, MCP, CDO (K=4)
Clipping Probability (Pr(s
2
(t)>s
0
2
)
10log
10
(s
2
0
) (dB)
Fig. 4. Performance of the proposed algorithms.
4 5 6 7 8 9 10 11 12
10
−3
10
−2
10
−1
10
0
10log
10
(s
0
2
) (dB)
Clipping Probability (Pr(s
2
(t)>s
0
2
)
OFDM signal
SLM (U=4)
SLM (U=16)
12 points, Combined (U=4,K=1)
12 points, Combined (U=4,K=2)
8 points, Combined (U=4,K=1)
8 points, Combined (U=4,K=2)
Fig. 5. Performance of the proposed algorithms which are combined with
the SLM algorithm.
References
More filters
01 Nov 1985
TL;DR: This month's guest columnist, Steve Bible, N7HPR, is completing a master’s degree in computer science at the Naval Postgraduate School in Monterey, California, and his research area closely follows his interest in amateur radio.
Abstract: Spread Spectrum It’s not just for breakfast anymore! Don't blame me, the title is the work of this month's guest columnist, Steve Bible, N7HPR (n7hpr@tapr.org). While cruising the net recently, I noticed a sudden bump in the number of times Spread Spectrum (SS) techniques were mentioned in the amateur digital areas. While QEX has discussed SS in the past, we haven't touched on it in this forum. Steve was a frequent cogent contributor, so I asked him to give us some background. Steve enlisted in the Navy in 1977 and became a Data Systems Technician, a repairman of shipboard computer systems. In 1985 he was accepted into the Navy’s Enlisted Commissioning Program and attended the University of Utah where he studied computer science. Upon graduation in 1988 he was commissioned an Ensign and entered Nuclear Power School. His subsequent assignment was onboard the USS Georgia, a trident submarine stationed in Bangor, Washington. Today Steve is a Lieutenant and he is completing a master’s degree in computer science at the Naval Postgraduate School in Monterey, California. His areas of interest are digital communications, amateur satellites, VHF/UHF contesting, and QRP. His research area closely follows his interest in amateur radio. His thesis topic is Multihop Packet Radio Routing Protocol Using Dynamic Power Control. Steve is also the AMSAT Area Coordinator for the Monterey Bay area. Here's Steve, I'll have some additional comments at the end.

8,781 citations


"Peak-to-average power-ratio reducti..." refers methods in this paper

  • ...The minimax optimization problem in (6) is an integer programming problem which can be solved by using the MCP along with the pessimistic estimator reported in [6][7] or by using the CDO reported in [8]....

    [...]

Book
01 Jan 1987
TL;DR: The Janson Inequalities as discussed by the authors allow accurate approximation of extremely small probabilities, and have been shown to be useful for the probabilistic method in many problems. But they do not cover the complexity of the Janson inequalities.
Abstract: This is an examination of what is known about the probabilistic method. Based on the notes from the author's 1986 series of ten lectures, this edition features an additional lecture: The Janson Inequalities. These inequalities allow accurate approximation of extremely small probabilities.

485 citations


"Peak-to-average power-ratio reducti..." refers methods in this paper

  • ...PAPR-REDUCTION ALGORITHMS The minimax optimization problem in (6) is an integer programming problem which can be solved by using the MCP along with the pessimistic estimator reported in [6][7] or by using the CDO reported in [8]....

    [...]

  • ...Two new algorithms are then developed by applying the so-called method of conditional probablity (MCP) [6]-[7] and coordinate descent optimization (CDO) [8], which can be used to find the optimal representation of the OFDM signal....

    [...]

Journal ArticleDOI
TL;DR: In this article, two methods are proposed to reduce the facteur de crete, i.e., the ratio of the probability of a facteur of crete to the probability that it exists, by combining two sequences transmises partielles.
Abstract: Deux methodes sont proposees pour reduire la puissance de crete ďun signal ofdm. Elles sont efficaces, souples et sans distorsion et elles apportent un accroissement faible de la complexite des calculs. De plus elles fonctionnent avec des nombres quelconques. La premiere methode produit plusieurs signaux multiporteurs et choisit celui qui a la plus faible puissance de crete pour la transmission. La seconde combine des sequences transmises partielles pour minimiser le facteur de crete. Apres ľanalyse theorique, les performances sont evaluees par simulation.

301 citations

Proceedings ArticleDOI
Prabhakar Raghavan1
27 Oct 1986
TL;DR: A methodology for converting a probabilistic existence proof to a deterministic approximation algorithm that mimics the existence proof in a very strong sense is developed.
Abstract: We consider the problem of approximating an integer program by first solving its relaxation linear program and "rounding" the resulting solution. For several packing problems, we prove probabilistically that there exists an integer solution close to the optimum of the relaxation solution. We then develop a methodology for converting such a probabilistic existence proof to a deterministic approximation algorithm. The methodology mimics the existence proof in a very strong sense.

289 citations

Frequently Asked Questions (1)
Q1. What have the authors contributed in "Peak-to-average power-ratio reduction for ofdm systems based on method of conditional probability and coordinate descent optimization" ?

In this paper, a new constellation extension technique for peak-to-average power ratio reduction ( PAPR ) in orthogonal frequency division multiplexing systems is proposed.