I. Introduction
Orthogonal frequency division multiplexing (OFDM) technique has been accepted for many applications such as mobile and indoor wireless communications. One of the major problems of OFDM signal that may strictly limit its application is its high peak-to-average power ratio (PAPR). If the OFDM signal is amplified by the high power amplifier (HPA) with nonlinear characteristics, the resultant spectrum may exhibit severe in-band and out-of-band radiation of the distortion components.
Inst. of Ind. Sci., Univ. of Tokyo, Japan
Hideki Ochiai (S'97—M'01) received the B.E. degree in communication engineering from Osaka University, Osaka, Japan, in 1996 and the M.E. and Ph.D. degrees in information and communication engineering from the University of Tokyo, Tokyo, Japan, in 1998 and 2001, respectively.
Since April 2001, he has been with the Department of Information and Communication Engineering, the University of Electro-Communications, Tokyo, Japan. From 1994 to 1995, he was with the Department of Electrical Engineering, University of California, Los Angeles, under the scholarship of the Ministry of Education, Science and Culture. His current research interests include modulation and coding techniques in mobile communications.
Dr. Ochiai was a recipient of a Student Paper Award from the Telecommunications Advancement Foundation in 1999 and the Ericsson Young Scientist Award in 2000.
Hideki Imai (M'74—SM'88—F'92) was born in Shimane, Japan, on May 31, 1943. He received the B.E., M.E., and Ph.D. degrees in electrical engineering from the University of Tokyo in 1966, 1968, and 1971, respectively.
From 1971 to 1992, he was on the faculty of Yokohama National University. In 1992, he joined the faculty of the University of Tokyo, where he is currently a Full Professor in the Institute of Industrial Science. His current research interests include information theory, coding theory, cryptography, spread spectrum systems and their applications.
Dr. Imai received Excellent Book Awards from IEICE in 1976 and 1991.
He also received the Best Paper Award (Yonezawa Memorial Award) from IEICE in 1992, the Distinguished Services Award from the Association for Telecommunication Promotion in 1994, the Telecom System Technology Prize from the Telecommunication Advancement Foundation and Achievement Award from IEICE in 1995. In 1998 he was awarded Golden Jubilee Paper Award by the IEEE Information Theory Society. In 1999 he was awarded Honor Doctor Degree from Soonchunhyang University, Korea. He was elected an IEEE Fellow for his contributions to the theory of coded modulation and two-dimensional codes in 1992. He chaired several committees of scientific societies and chaired many international conferences such as IEEE-ITW, IEEE-ISIT, AAECC, PKC, FSE and WPMC. Dr. Imai was on the board of IEICE (1992–1994, 1996–1999), the IEEE Information Theory Society (1993–1998), Japan Society of Security Management (1988-present) and the Society of Information Theory and Its Applications (SITA, 1981–1997). He served as the president of SITA (1997), IEICE Engineering Sciences Society (1998–1999) and as the chairman of CRYPTREC (Cryptography Techniques Research and Evaluation Committee of Japan) (2000-present).
1.
R. W. Bäuml, R. F. H. Fischer, J. B. Huber, "Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping", Electron. Lett., vol. 32, pp. 2056-2057, Oct. 1996.
For example, selective mapping or transformation [1], [2] may statistically reduce the PAPR with a relatively simple implementation cost, but there is a severe limit in a PAPR reduction capability [3].
Since the PAPR reduction by the Nyquist-rate clipping is not so significant, additional PAPR reduction by combining another simple yet efficient method such as that in [1] and [2] was proposed.
2.
D. J. G. Mestdagh, P. M. P. Spruyt, "A method to reduce the probability of clipping in DMT-based transceivers", IEEE Trans. Commun., vol. 44, pp. 1234-1238, Oct. 1996.
For example, selective mapping or transformation [1], [2] may statistically reduce the PAPR with a relatively simple implementation cost, but there is a severe limit in a PAPR reduction capability [3].
Since the PAPR reduction by the Nyquist-rate clipping is not so significant, additional PAPR reduction by combining another simple yet efficient method such as that in [1] and [2] was proposed.
3.
H. Ochiai, H. Imai, "Performance of the deliberate clipping with adaptive symbol selection for strictly band-limited OFDM systems", IEEE J. Select. Areas Commun., vol. 18, pp. 2270-2277, Nov. 2000.
The winter Limited Pullover Sweater Boutique For example, selective mapping or transformation [1], [2] may statistically reduce the PAPR with a relatively simple implementation cost, but there is a severe limit in a PAPR reduction capability [3].
The problem arises, however, that low-pass filtering the clipped OFDM signal samples results in considerable regrowth of peak power [3], [11], [15] in addition to a certain amount of degradation in bit-error performance.
In our previous work [3], the digital clipping was performed on the OFDM signals sampled at the Nyquist rate, which we refer to as Nyquist-rate clipping, followed by the ideal low-pass filter (LPF) for its simple implementation.
Also in practice,
JN
should be chosen as a power of two such that the fast Fourier transform (FFT) algorithm can be employed for computational reduction. and the clipping system with
J=1
is called the Nyquist-rate clipping, which is the case exclusively discussed in [3].
Now, assuming that the OFDM signal is complex Gaussian, which may be valid in the case of OFDM signals with large
NDressy Boutique Design Shorts Express Studio q8pPft
, the amplitude
rn
is Rayleigh distributed and it can be easily shown that the average output power is given by [3], [25] .
Following [3], for convenience of notation, we define
γ=0
as a hard (constant) envelope limiter and
γ=∞
as an ideal system without clipping.
Applying the special case of Price's theorem for Gaussian inputs [16], known as Bussgang's theorem, one can write the output as [25] (see also [31]) where the distortion term
dn
is uncorrelated with
SnBoutique Boutique Columbia Columbia Khaki Khaki Columbia Shorts Shorts Khaki Boutique Boutique Shorts r4ZqrwH
and the attenuation factor
α
is calculated for the soft envelope limiter as [3], [25] .
In order to incorporate the hard envelope limiter as a special case, we rewrite
SDRk
as where a normalized attenuation factor
Kγ
is defined as [3] Note that for the hard envelope limiter,
Kγ
is given by its limit
limγ→∞Kγ=π/4
, while for an ideal channel
limγ→∞Kγ=1
.
In the case of the Nyquist-rate clipping (the clipping without oversampling), i.e.,
J=1Sweater Boutique Limited The winter Pullover
, the distortion term is equally distributed within the entire bandwidth and the
SDRk
can be given in the following closed-form expression [3]: and thus (41) further reduces to [3] Therefore in this case the channel capacity is given by .
4.
S. H. Müller, R. W. Bäuml, R. F. H. Fischer, J. B. Huber, "OFDM with reduced peak-to-average power ratio by multiple signal representation", Ann. Télécommun., vol. 52, pp. 58-67, Feb. 1997.
In [4]–[6], a variety of algorithms for PAPR reduction using some redundant subcarriers or signal constellations have been proposed.
5.
M. Friese, "OFDM signals with low crest-factor", Proc. IEEE GLOBECOM '97, vol. 1, pp. 290-294, 1997-Nov.
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Full Text: PDF (466KB)
In [4]–[5][6], a variety of algorithms for PAPR reduction using some redundant subcarriers or signal constellations have been proposed.
6.
J. Tellado, J. Cioffi, "Peak power reduction for multicarrier transmission", Proc. IEEE CTMC GLOBECOM '98, pp. 219-224, 1998-Nov.
In [4]–[6], a variety of algorithms for PAPR reduction using some redundant subcarriers or signal constellations have been proposed.
7.
R. D. J. van Nee, "OFDM codes for peak-to-average power reduction and error correction", Proc. IEEE GLOBECOM '96, pp. 740-744, 1996-Nov.
Systematic coding techniques [7]–[9] may be attractive since they can deterministically bound the PAPR with little computational cost at the transmitter, but designing the low PAPR codes while maintaining a reasonable coding rate becomes quite difficult as the number of subcarriers increases.
8.
J. A. Davis, J. Jedwab, "Peak-to-mean power control in OFDM Golay complementary sequences and Reed-Muller codes", IEEE Trans. Inform. Theory, vol. 45, pp. 2397-2417, Nov. 1999.
Systematic coding techniques [7]–[8][9] may be attractive since they can deterministically bound the PAPR with little computational cost at the transmitter, but designing the low PAPR codes while maintaining a reasonable coding rate becomes quite difficult as the number of subcarriers increases.
9.
H. Ochiai, H. Imai, "Block coding scheme based on complementary sequences for multicarrier signals", IEICE Trans. Fundamentals, vol. E80-A, pp. 2136-2143, Nov. 1997.
Systematic coding techniques [7]–[9] may be attractive since they can deterministically bound the PAPR with little computational cost at the transmitter, but designing the low PAPR codes while maintaining a reasonable coding rate becomes quite difficult as the number of subcarriers increases.
10.
R. O'Neill, L. B. Lopes, "Envelope variations and spectral splatter in clipped multicarrier signals", Proc. PIMRC '95, vol. 1, pp. 71-75, 1995-Sept.
Probably simplest for the PAPR reduction is digital clipping and filtering of the OFDM signal [10]–[14].
However, exhaustive simulations have shown that the PAPR reduction capability will be considerably enhanced if the oversampled OFDM signal is digitally clipped and filtered [10], [14].
Furthermore, the degradation in bit-error performance will be also alleviated [10], [14].
11.
X. Li, L. J. Cimini Jr., "Effects of clipping and filtering on the performance of OFDM", Proc. VTC '97, pp. 1634-1638, 1997-May.
Probably simplest for the PAPR reduction is digital clipping and filtering of the OFDM signal [10]–[11][14].
The problem arises, however, that low-pass filtering the clipped OFDM signal samples results in considerable regrowth of peak power [3], [11], [15] in addition to a certain amount of degradation in bit-error performance.
12.
D. Wulich, L. Goldfeld, "Reduction of peak factor in orthogonal multicarrier modulation by amplitude limiting and coding", IEEE Trans. Commun., vol. 47, pp. 18-21, January 1999.
Probably simplest for the PAPR reduction is digital clipping and filtering of the OFDM signal [10]–[12][14].
13.
D. Kim, G. L. Stüber, "Clipping noise mitigation for OFDM by decision-aided reconstruction", IEEE Commun. Lett., vol. 3, pp. 4-6, Jan. 1999.
Probably simplest for the PAPR reduction is digital clipping and filtering of the OFDM signal [10]–[13][14].
14.
R. Dinis, A. Gusmão, "On the performance evaluation of OFDM transmission using clipping techniques", Proc. IEEE VTC '99 Fall, pp. 2923-2928, 1999-Sept.
Probably simplest for the PAPR reduction is digital clipping and filtering of the OFDM signal [10]–[14].
However, exhaustive simulations have shown that the PAPR reduction capability will be considerably enhanced if the oversampled OFDM signal is digitally clipped and filtered [10], [14].
Furthermore, the degradation in bit-error performance will be also alleviated [10], [14].
Based on this approach, the effects of nonlinearity of the high power amplifier (HPA) or ideally predistorted limiter on the OFDM signal have been analyzed in the recent literature, e.g., [14], [18]–[22].
However, as a consequence of the central limit theorem that may hold for large classes of even dependent variables [32], we empirically assume
Dk
as Gaussian in the sequel, which is the common assumption when
N
is large [14], [18]–[22].
15.
C. Tellambura, " Use of
m
-sequences for OFDM peak-to-average power ratio reduction ", Electron. Lett., vol. 33, pp. 1300-1301, July 1997.
The problem arises, however, that low-pass filtering the clipped OFDM signal samples results in considerable regrowth of peak power [3], [11], [15] in addition to a certain amount of degradation in bit-error performance.
16.
R. Price, "A useful theorem for nonlinear devices having gaussian inputs", IRE Trans. Inform. Theory, vol. IT-4, pp. 69-72, June 1958.
With this Gaussianity of the OFDM signals, the clipping can be treated as a memoryless nonlinear transformation of the Gaussian processes, where Price's theorem can be applied [16], [17].
Applying the special case of Price's theorem for Gaussian inputs [16], known as Bussgang's theorem, one can write the output as [25] (see also [31]) where the distortion term
dnBoutique The Sweater winter Limited Pullover
is uncorrelated with
Sn
and the attenuation factor
α
is calculated for the soft envelope limiter as [3], [25] .
17.
R. Deutsch, Nonlinear Transformations of Random Processes, NJ, Englewood Cliffs:Prentice-Hall, 1962.
With this Gaussianity of the OFDM signals, the clipping can be treated as a memoryless nonlinear transformation of the Gaussian processes, where Price's theorem can be applied [16], [17].
18.
G. Santella, F. Mazzenga, "A hybrid analytical-simulation procedure for performance evaluation in M-QAM-OFDM schemes in presence of nonlinear distortions", IEEE Trans. Veh. Technol., vol. 47, pp. 142-151, Feb. 1998.
Based on this approach, the effects of nonlinearity of the high power amplifier (HPA) or ideally predistorted limiter on the OFDM signal have been analyzed in the recent literature, e.g., [14], [18]–[22].
However, as a consequence of the central limit theorem that may hold for large classes of even dependent variables [32], we empirically assume
DkBCBGeneration Boutique BCBGeneration Romper Boutique BCBGeneration Romper Romper Boutique Boutique BCBGeneration tqT6w8x
as Gaussian in the sequel, which is the common assumption when
N
is large [14], [18]–[22].
19.
M. Friese, "On the degradation of OFDM-signals due to peak-clipping in optimally predistorted power amplifier", Proc. IEEE GLOBECOM '98, pp. 939-944, 1998-Nov.
Based on this approach, the effects of nonlinearity of the high power amplifier (HPA) or ideally predistorted limiter on the OFDM signal have been analyzed in the recent literature, e.g., [14], [18]–[19][22].
However, as a consequence of the central limit theorem that may hold for large classes of even dependent variables [32], we empirically assume
Dk
as Gaussian in the sequel, which is the common assumption when
N
is large [14], [18]–[19][22].
20.
E. Costa, M. Midrio, S. Pupolin, "Impact of amplifier nonlinearities on OFDM transmission system performance", IEEE Commun. Lett., vol. 3, pp. 37-39, Feb. 1999.
Based on this approach, the effects of nonlinearity of the high power amplifier (HPA) or ideally predistorted limiter on the OFDM signal have been analyzed in the recent literature, e.g., [14], [18]–[20][22].
However, as a consequence of the central limit theorem that may hold for large classes of even dependent variables [32], we empirically assume
Dk
as Gaussian in the sequel, which is the common assumption when
N
is large [14], [18]–[20][22].
21.
D. Dardari, V. Tralli, A. Vaccari, "A theoretical characterization of nonlinear distortion effects in OFDM systems", IEEE Trans. Commun., vol. 48, pp. 1755-1764, Oct. 2000.
Based on this approach, the effects of nonlinearity of the high power amplifier (HPA) or ideally predistorted limiter on the OFDM signal have been analyzed in the recent literature, e.g., [14], [18]–[21][22].
However, as a consequence of the central limit theorem that may hold for large classes of even dependent variables [32], we empirically assume
Dk
as Gaussian in the sequel, which is the common assumption when
N
is large [14], [18]–[21][22].
22.
P. Banelli, S. Cacopardi, "Theoretical analysis and performance of OFDM signals in nonlinear AWGN channels", IEEE Trans. Commun., vol. 48, pp. 430-441, Mar. 2000.
Based on this approach, the effects of nonlinearity of the high power amplifier (HPA) or ideally predistorted limiter on the OFDM signal have been analyzed in the recent literature, e.g., [14], [18]–[22].
However, as a consequence of the central limit theorem that may hold for large classes of even dependent variables [32], we empirically assume
Dk
as Gaussian in the sequel, which is the common assumption when
N
is large [14], [18]–[22].
23.
C. Berrou, A. Glavieux, "Near optimum error correcting coding and decoding: Turbo-codes", IEEE Trans. Commun., vol. 44, pp. 1261-1271, Oct. 1996.
In particular, the recent advent of powerful forward error correction schemes such as turbo codes [23] enables one to design the system operating near the channel capacity, and thus the channel capacity of the clipped OFDM signals becomes of particular interest both theoretically and practically.
We further justify the argument of channel capacity by computer simulation with the help of near optimal turbo codes [23].
The interleaver size of the turbo codes is 16 378 and both the trellises of the two identical component convolutional codes, each having memory of 4, are terminated and each parity bit of the convolutional code is punctured such that the overall coding rate is approximately 112 [23].
24.
G. L. Stüber, Principles of Mobile Communications, MA, Norwell:Kluwer, 1996.
The discrete-time OFDM signal sampled at time instant
t=nΔt
is then expressed as where
n=0,1,…,JN−1
, and
ϕJ,n
is the frequency offset [24] given by .
25.
H. E. Rowe, "Memoryless nonlinearities with gaussian inputs: Elementary results", Bell Syst. Tech. J., vol. 61, pp. 1519-1525, Sept. 1982.
Now, assuming that the OFDM signal is complex Gaussian, which may be valid in the case of OFDM signals with large
N
, the amplitude
rn
is Rayleigh distributed and it can be easily shown that the average output power is given by [3], [25] .
Applying the special case of Price's theorem for Gaussian inputs [16], known as Bussgang's theorem, one can write the output as [25] (see also [31]) where the distortion term
dn
is uncorrelated with
Sn
and the attenuation factor
α
is calculated for the soft envelope limiter as [3], [25] .
26.
J. G. Proakis, Digital Communications, New York:McGraw-Hill, 1995.
In this paper, we assume that the symbol-wise (i.e., subcarrier-wise) channel interleaver (both in frequency and time domain) is ideal such that the channel is characterized as memoryless and the fading is slow and Rayleigh [26].
27.
S. G. Wilson, Digital Modulation and Coding, NJ, Englewood Cliffs:Prentice-Hall, 1996.
Consequently, at the channel decoder the
Hk
are modeled as real-valued and statistically independent Rayleigh random variables [27] and the index
k
is dropped from
Hk
in the following.
With ideal symbol-wise interleaving and perfect CSI, the channel capacity over a Rayleigh fading channel is given by [27, p. 361] where and
f(H)=2He−H2
is a Rayleigh probability density function (pdf) normalized such that
EBoutique Pullover winter The Sweater Limited [H2]=1
.
28.
H. Ochiai, Analysis and Reduction of Peak-to-Average Power Ratio in OFDM Systems, 2001.
However, these two definitions of the PAPR may converge for large
NPullover winter Limited Sweater Boutique The
[28].
On the other hand, the statistical distribution of the instantaneous power of the clipped and band-limited OFDM signal considered in this paper depends on the time instant
t
, where
0≤t<T,T=ΔTs/N
being the Nyquist interval of the signal, due to the fact that the clipped and band-limited OFDM signal becomes cyclostationary with period
T
[28].
A heuristic explanation for this tendency is described in [28, Ch. 6].
In [28, Ch. 6], [30], a tight lower bound of the complementary cdf of the instantaneous power is derived, which can be numerically calculated.
The reader interested in the distribution of the instantaneous power for this case is referred to [28, Ch. 6], [30].
In [28, Ch. 7], the maximization is performed by the iterative algorithm and it is shown that the gain in channel capacity achieved by the water-filling is practically negligible, compared to the case with the equally distributed allocation of the input power.
29.
H. Ochiai, H. Imai, "On the distribution of the peak-to-average power ratio in OFDM signals", IEEE Trans. Commun., vol. 49, pp. 282-289, Feb. 2001.
Also shown in the figure is the analytical approximation of the complementary cdf of the PAPR without clipping obtained from [29].
30.
H. Ochiai, H. Imai, "On clipping for peak power reduction of OFDM signals", Proc. IEEE GLOBECOM '00, vol. 2, pp. 731-735, 2000-Nov.
In [28], [30], a tight lower bound of the complementary cdf of the instantaneous power is derived, which can be numerically calculated.
The reader interested in the distribution of the instantaneous power for this case is referred to [28], [30].
31.
J. Minkoff, "The role of AM-to-PM conversion in memoryless nonlinear systems", IEEE Trans. Commun., vol. COM-33, pp. 139-144, Feb. 1985.
Applying the special case of Price's theorem for Gaussian inputs [16], known as Bussgang's theorem, one can write the output as [25] (see also [31]) where the distortion term
d_{n} is uncorrelated with
S_{n} and the attenuation factor
\alpha is calculated for the soft envelope limiter as [3], [25] .
32.
W. Feller, An Introduction to Probability Theory and its Applications, New York:Wiley, vol. 1, 1957.
However, as a consequence of the central limit theorem that may hold for large classes of even dependent variables [32], we empirically assume
D_{k} as Gaussian in the sequel, which is the common assumption when
N is large [14], [18]–[22].
33.
R. G. Gallager, Information Theory and Reliable Communication, New York:Wiley, 1968.
The Gaussian distribution corresponds to, in ef-fect, the worst kind of additive noise in view of channel capacity [33, p. 337] and thus assuming the distortion terms Gaussian independent of the input signal may serve as a lower bound in terms of the channel capacity.
Since the received signal can be modeled as a sum of a linearly attenuated signal and the Gaussian noise plus Gaussian distortion, without any constraint on the input signal except the average input power
P_{{\rm in}} the average channel capacity per subcarrier (i.e., per complex dimension) will be given by [33](39), shown at the bottom of the page.
Equation (39) could be maximized via the water-filling principle [33].
The conditional average mutual information given the channel coefficient
H is then expressed as [33] where
h(X\vert Y) is the conditional differential entropy of
X given
{ Y} ‘.
34.
S. Haykin, Communication Systems, New York:Wiley, 1994.
We define the channel SNR [34, p. 316] as a ratio of the average power of the modulated signal (i.e., useful signal plus dis-tortion) to the average power of Gaussian noise over the effective bandwidth both measured at the receiver input, i.e., where
\widehat{P}_{{\rm av}} and
{P_{{{\rm noise}}}} are the average power of the output signal [defined in (16)] and the AWGN at the receiver (i.e., after the rectangular filter), respectively.
35.
T. M. Cover, J. A. Thomas, Elements of Information Theory, New York:Wiley, 1991.
Given the input power of the
kth subcarrier
p_{{\rm in}, k} and without any constraint on the distribution of the signal constellation, the channel capacity of the
kth subcarrier over an AWGN channel is expressed as where
I(X;Y) is the mutual information between
X and
Y and
h(X) denotes the differential entropy of the complex-valued signal
X [35].
36.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, U.K., Cambridge:Cambridge Univ. Press, 1992.
Since the power allocation of each subcarrier is assumed equal, (50) reduces to Carrying out the integration of (47) yields where
E_{n}(x) is the exponential integral defined as [36] .
37.
G. Ungerboeck, "Channel coding with multilevel/phase signals", IEEE Trans. Inform. Theory, vol. IT-28, pp. 55-67, Jan. 1982.
For M-QAM, the conditional average mutual information is given by [37] where the expectation is over
{A_k},{\widetilde{A}_k}, and also
H for a fading channel and
f(X\vert Y) is the conditional pdf of
X given
Y.
Unfortunately, a closed form or convenient expression for numerical calculation has not been found for the above equation and thus we resort to the Monte Carlo method [37].
38.
L. R. Bahl, J. Cocke, F. Jelinek, J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate", IEEE Trans. Inform. Theory, vol. IT-20, pp. 284-287, Mar. 1974.
The maximum
a posteriori (MAP) decoding based on the BCJR algorithm [38] requires the knowledge of the variance of the additive noise and in the simulation it is assumed that the decoder has the knowledge of the variance averaged over all the subcarriers.
39.
S. Okui, Special Functions and Their Applications for Electronic and Communication Engineering, Japan, Tokyo:Morikita Pub, 1997.
1.
Fei Peng, William E. Ryan, "MLSD Bounds and Near-Optimum Receiver Designs for Clipped OFDM Channels", Global Telecommunications Conference 2007. GLOBECOM '07. IEEE, pp. 1688-1692, 2007.
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2.
Fei Peng, William E. Ryan, Jinyun Zhang, "MLSD Bounds for Clipped OFDM Systems Over Frequency-Selective Quasi-Static Fading Channels", Global Telecommunications Conference 2007. GLOBECOM '07. IEEE, pp. 1693-1698, 2007.
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3.
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Hun Seok Kim, Babak Daneshrad, "A Theoretical Treatment of PA Power Optimization in Clipped MIMO-OFDM Systems", Global Telecommunications Conference 2009. GLOBECOM 2009. IEEE, pp. 1-6, 2009.
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7.
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8.
Dov Wulich, Igor Gutman, "Efficient Power Amplification for Wireless Communication Based on Single-Carrier", Global Telecommunications Conference (GLOBECOM 2011) 2011 IEEE, pp. 1-5, 2011.
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9.
Nir Regev, Ilia Iofedov, Dov Wulich, "Maximum Likelihood Detection of Nonlinearly Distorted OFDM Signal", Global Communications Conference (GLOBECOM) 2015 IEEE, pp. 1-6, 2015.
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10.
Ryota Yoshizawa, Hideki Ochiai, "Mutual Information and Coded BER Analysis of PAPR Reduced OFDM System with Active Constellation Extension", Global Communications Conference (GLOBECOM) 2015 IEEE, pp. 1-6, 2015.
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11.
Evgeny Vanin, "Analytical model for optical wireless OFDM system with digital signal restoration", Globecom Workshops (GC Wkshps) 2012 IEEE, pp. 1213-1218, 2012.
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12.
Ashna Kakkar, Sai Nitesh Garsha, Ojasvi Jain, Kritika, "Improvisation in BER and PAPR by Using Hybrid Reduction Techniques in MIMO-OFDM Employing Channel Estimation Techniques", Advance Computing Conference (IACC) 2017 IEEE 7th International, pp. 170-173, 2017.
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13.
Meng Wang, Jun Xiao, Chuanlin Yuan, Yong Tian, Lu Zhang, "A new low-complexity subblock segmentation method for PTS OFDM", Advanced Information Technology Electronic and Automation Control Conference (IAEAC) 2017 IEEE 2nd, pp. 2408-2411, 2017.
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14.
Di-xiao Wu, "Selected mapping and partial transmit sequence schemes to reduce PAPR in OFDM systems", Image Analysis and Signal Processing (IASP) 2011 International Conference on, pp. 1-5, 2011.
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15.
Kashif Sultan, Hazrat Ali, Zhongshan Zhang, "Joint SLM and modified clipping scheme for PAPR reduction", Applied Sciences and Technology (IBCAST) 2016 13th International Bhurban Conference on, pp. 710-713, 2016.
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16.
M. Thanigasalam, P. Dananjayan, "BER analysis of OFDM receiver using MMSE channel estimation and modified PTS combined with interleaving", Advanced Communication Control and Computing Technologies (ICACCCT) 2014 International Conference on, pp. 662-666, 2014.
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17.
Bahubali K. Shiragapur, Uday Wali, Sandeep Bidwai, "Novel technique to reduce PAPR in OFDM systems by clipping and filtering", Advances in Computing Communications and Informatics (ICACCI) 2013 International Conference on, pp. 1593-1597, 2013.
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18.
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1.
Chen, Hangjun; Haimovich, Alexander M, "CLIPPING DISTORTION CANCELLER FOR OFDM SIGNALS"
Inventors:
Chen, Hangjun; Haimovich, Alexander M
Abstract:
Methods and apparatus are provided for reducing clipping noise from an OFDM signal, the methods and apparatus are operable to carry out actions including: (a) transforming a received orthogonal frequency division multiplexed (OFDM) signal from a transmission channel into the frequency domain, the OFDM signal having been subject to a clipping function prior to transmission in order to reduce the peak-to-average power ratio (PAPR); (b) recovering data symbols from the transformed OFDM signal, which include clipping noise; (c) estimating the clipping noise in the frequency domain based on the data symbols; and (d) subtracting the estimated clipping noise from the transformed OFDM signal.
Assignee:
NEW JERSEY INSTITUTE OF TECHNOLOGY
Filing Date:
10 February 2006
Grant Date:
19 July 2011
Patent Classes:
Current U.S. Class:
370208000
Current International Class:
H04J0110000
2.
Scarpa, Carl, "CHANNEL ESTIMATION AND COMPENSATION TECHNIQUES FOR USE IN FREQUENCY DIVISION MULTIPLEXED SYSTEMS"
Inventors:
Scarpa, Carl
Abstract:
Methods and apparatus for performing channel estimate updates in frequency division multiplexed, e.g., (OFDM), systems are described. After generation of initial channel estimates from received pilots, channel estimates corresponding to individual tones are updated using any one of a plurality of update techniques including, e.g., a constant modulus based method and a reduced constellation decision directed update method. The channel estimate update technique to be used with for an individual tone is selected based on a comparison of a signal noise measurement to one or more thresholds. The channel estimate update technique applied to different tones of the OFDM signal at the same time may vary. Over time, as the level of noise is reduced, the channel estimate update technique will switch from an interpolated pilot method, to a constant modulus algorithm based method, to a reduced constellation decision directed method, to a full constellation decision directed update method.
Assignee:
HITACHI LTD
Filing Date:
07 January 2002
Grant Date:
24 April 2007
Patent Classes:
Pullover Limited winter Boutique The Sweater Current U.S. Class:
370206000, 370252000, 370526000, 375235000, 375298000
Current International Class:
H04J0110000, H04J0031200
3.
Scarpa, Carl G., "METHODS AND APPARATUS FOR SPECTRAL FILTERING CHANNEL ESTIMATES"
Patent No. 7173991
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Full Text: PDF
Inventors:
Scarpa, Carl G.
Abstract:
Methods and apparatus for performing spectral filtering of channel estimates corresponding to a communications channel used to transmit a multi-tone signal are described. A channel estimate is examined to identify portions where significant multi-path interference is present. Real, as opposed to complex, low pass filters are used to perform spectral filtering on the channel estimate to produce a filtered channel estimate. Values corresponding to portions of the channel estimate determined to correspond to areas where significant multi-path interference is present are replaced with the original unfiltered channel estimate values to generate a selectively filtered channel estimate. By using unfiltered channel estimate values in areas of multi-path interference, the errors introduced in such areas by real filtering are avoided without the need to resort to complex filtering.
Assignee:
HITACHI LTD
Filing Date:
17 June 2002
Grant Date:
06 February 2007
Patent Classes:
Current U.S. Class:
375350000, 375340000, 375341000
Current International Class:
H04B0011000, H03D0010000, H04L0270600
4.
Scarpa, Carl G., "ROBUST OFDM CARRIER RECOVERY METHODS AND APPARATUS"
Inventors:
Scarpa, Carl G.
Abstract:
Methods and apparatus for estimating and correcting carrier frequency offsets in a bust multi-tone receiver are described. Course and fine carrier frequency estimates are generated from the signal's preamble. Decision directed carrier frequency offset estimates are then generated from the signal field and data fields of the multi-tone signal. Frequency error estimates are generated for each tone of the signal and combined using a weighted average to generate the frequency error estimate used to perform the correction operation. Error estimates corresponding to noisy data tones are weighted less then estimates corresponding to less noisy data tones. In cases of low SNR frequency error estimates corresponding to pilots are weighted by an extra amount as compared to error estimates corresponding to tones used to transmit data symbols. During times of high SNR error estimates corresponding to pilot tones are weighted in the same manner as error estimates corresponding to data tones.
Assignee:
HITACHI LTD
Filing Date:
28 June 2002
Grant Date:
21 November 2006
Patent Classes:
Current U.S. Class:
375344000, 375326000
Current International Class:
H04L0270600
5.
Chen, Hangjun; Haimovich, Alexander M., "CLIPPING DISTORTION CANCELLER FOR OFDM SIGNALS"
Inventors:
Chen, Hangjun; Haimovich, Alexander M.
Abstract:
Methods and apparatus are provided for reducing clipping noise from an OFDM signal, the methods and apparatus are operable to carry out actions including: (a) transforming a received orthogonal frequency division multiplexed (OFDM) signal from a transmission channel into the frequency domain, the OFDM signal having been subject to a clipping function prior to transmission in order to reduce the peak-to-average power ratio (PAPR); (b) recovering data symbols from the transformed OFDM signal, which include clipping noise; (c) estimating the clipping noise in the frequency domain based on the data symbols; and (d) subtracting the estimated clipping noise from the transformed OFDM signal.
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Assignee:
UNASSIGNED
Filing Date:
03 February 2004
Grant Date:
18 April 2006
Patent Classes:
Current U.S. Class:
370208000, 370286000
Current International Class:
H04J0110000
- IEEE Keywords
- INSPEC: Controlled Indexing
- INSPEC: Non-Controlled Indexing
performance analysis, clipped OFDM signals, orthogonal frequency division multiplexing, peak power reduction, channel capacity, baseband OFDM signals, ideal low-pass filter, envelope clipping, peak-to-average power ratio, PAPR, channel coding, signal-to-distortion ratio, band-limited OFDM signal, oversampled OFDM signals, additive white Gaussian noise channels, interleaved Rayleigh fading channels, Gaussian distortion, Casual Pants Camuto winter Boutique Vince zwSqC, optimal coding, information data rate reduction, simulation results, near optimal turbo codes
Channel coding: The road to channel capacity
Daniel J. Costello; G. David Forney
Joint Source-Channel Coding of Sources with Memory using Turbo Codes and the Burrows-Wheeler Transform
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Performance of the deliberate clipping with adaptive symbol selection for strictly band-limited OFDM systems
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Quasi-Elliptic Microstrip Low-Pass Filters Using an Interdigital DGS Slot
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Low-Pass Filtering of Irregularly Sampled Signals Using a Set Theoretic Framework [Lecture Notes]
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Ultra-Wide Stopband Low-Pass Filter Using Multiple Transmission Zeros
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Near-Shannon/Slepian-Wolf performance for unknown correlated sources over AWGN channels
J. Garcia-Frias; Ying Zhao
1.
Although we assume
J
an integer in the following for simplicity, the parameter
J
need not be an integer, as long as
JN
is. Also in practice,
JN
should be chosen as a power of two such that the fast Fourier transform (FFT) algorithm can be employed for computational reduction.
2.
Strictly speaking, the use of channel coding may result in the statistical dependence of the encoded data
A_{k}
.
3.
Since the filter for removal of out-of-band energy is implemented in the baseband process, this filter is actually an LPF. However, it will be referred to as a BPF in the sequel in distinction from the subsequent LPF that performs ideal interpolation. Also, in practice, these two successive filters can be unified into the single DFT processor.
4.
Under the Gaussian assumption of the OFDM signals, the average power after the BPF
{\hat{P}_{{{\rm av}}}}
or, equivalently, the reduction ratio
\beta
can be directly calculated based on the result developed in Section IV , i.e., (33) and (34) , ifnecessary.
5.
We refer to the achievable average mutual information as channel capacity under the assumed channel model in Fig. 2Fig. 2 with the distortion terms
D_{k}
independent Gaussian random variables.