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PAPR Reduction of OFDM Signal by Using Huffman Coding over Rayleigh Fading Environment

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PAPR Reduction of OFDM Signal by Using Huffman Coding over Rayleigh Fading Environment
Mashhur Sattorov, Heau-Jo Kang (correspondent author)Division of IT Engineering, Graduate School, Mokwon University, Korea.mashhurs@yahoo.com, hjkang@mokwon.ac.kr
Abstract
: As we know an OFDM isgetting popular currently at transmissionthe data in high rate. In order to achieve better result, some disadvantageous points are being still discussed. One of the major problem related to the OFDMsystem, the signal peak to average power ratio (PAPR) reduction solutions play animportant role to improve performanceof OFDM that peak occurs after symbolsfed to FFT to produce time domainsignal, adding signals up coherently.However, for this problem, 4G projectscan find enough approaches to reduce itin this manner. In this paper, our approach to PAPR over a fading channel proposes one of coded mapping methodthat maintains not only decreasing it, butalso contributes to high data ratetransmission.
Keywords
: PAPR, Huffman coding,Rayleigh fading channel.
I. Introduction
It is obvious, a special case of FDM iscalled OFDM (orthogonal frequencydivision modulation) has an adequateamount of QoS in 4G communicationsystems [1]. To understand them easily,let’s peer at the figure 1 below.
a)shipment b) 5 subcarriersFigure 1. a) FDM transportation, b) OFDMtransportation
As analogy, FDM looks like to a bigship container, in contrast OFDM is inshape of little ship. The advantage inhere, the probability of crashes is 1/5 onsame shipment amount. This schemeuses subcarriers instead of one and intime domain, even though it is couldn’tfeel the orthogonality of signals, infrequency domain they have a bigdifferences each other as shown in figure2. In addition, we could surely witnesssystem’s robustness on fixing ISI, ICI problems due to guard period insertionin [2].
Figure 2. Orthogonality of OFDM signals infrequency domain.
On the other hand, after FFT process,summing up the signals brings other looks angrily puzzle called PAPR thathave came as a hot topic in wireless
communication area, particularly, inOFDM. Next chapter turns into theseissue characteristics, while explanationof helpful solutions for it. The 3
rd
partimplements Huffman coding techniqueover Rayleigh fading channel and performances are superimposed insimulation results of IV section.
II. PAPR problem in OFDM
To mitigate PAPR, several ideas can bedone, such as:1. Clipping – clip the signals at desired powers level [3];2. Selective Mapping – coded srcinaldata by a coding technique goes throughthe IFFT, and then selects satisfactionPAPR factor;3. Partial IFFT – separating signals toclusters do IFFT on each then combinethese [4].Suppose, we have got the result on IFFTin following signal:
∑
−=
=
102
1)(
N k JN kt jk
e s N t x
π
(1)where
k
s
denotes the data to betransmitted, N complex symbol block, Jsampling factor and t should be in limitof 1<t<JN. Then PAPR can be written as
]|)([|
|)(|max
22
t x E t x PAPR
=
.(2)Here, E[] identifies expectation.So that, we should take in a count probability that the signal transcendingat a certain threshold which given by
N
e PAPR
)1(1}Pr{
λ
λ
−
−−=>
[5].(3)This relationship between thresholdvalue and threshold level on differentsubcarriers is depicted in Figure 3.
Figure 3. Maximum threshold values onthreshold levels by subcarriers
III. System Model
The received signal is
)()(*)()(
t nt xt z t r
+=
(4)where
)(
)()(
t j
et t z
θ
α
=
denotes thecomplex channel gain [6]. Then,consider an OFDM system with Nsubcarriers utilize QAM modulation.The transmitted and received symbolsare can be
T
N x x x x
)]1().....1(),0([
−=
and
T
N r r r r
)]1().....1(),0([
−=
respectively. Over multipathenvironment the received symbol comeout by rewrite equation of (4).
)()(*)(
t nt xGt r
+=
(5)where G is a matrix of g.
∑∑
−=−=−−−
=
1010/2/)(2
),(1),(
N n Ll N ql j N q pn j
eel nh
N q p g
π π
(6)Then, we will implement channelestimation and time-frequency selectivechannel processes as shown in [7].Figure 4 illustrates system scheme andadditionally, guard period is alsoincluded by 20% of symbol durationwhich is higher than delay spread.Huffman coding realization part isdescribed in our previous paper [8].
Figure 4. Huffman coded OFDM system over Rayleigh fading channel.
IV. Simulation Results
To verify the validity of the expressionfor the PAPR of a system obtained in the preceding section, we implemented asimulation for the case of coded, withoutcoded and theoretical conditions using arectangular 16 point QAM signalconstellation over Rayleigh fading for chart 5.
Figure 5. Comparison of coded and withoutcoded channel BER on 16-QAM scheme over Rayleigh fading.Figure 6. PAPR Estimation.
The Figure 6 illustrates PAPR estimation(2) formula simulation of two coded anduncoded signals that by looking at, wecan easily can see PAPR decreasing at-3-4db and same result obtained at figure7 by simulating its probabilitydistribution function.
Figure 7. PAPR probability Estimation.
V. Conclusion and future works
In conclusion, we can notice that byimplementation of Huffman coding, wehave reached valuable BER and PAPR decreasing results for -3db at least. For future works, we are going to analyzeour ideas not only over Rayleigh, butalso include Rician or something likethat fading channel to estimate performance of OFDM.REFERENCES[1]Hui Liu and Guoqing Li“OFDM- Based Broadband Wireless Networks”, p. 5, 2005.[2]Shinsuke Hara and RamjeePrasad “Multicarrier Techniques for 4GMobile Communications”, p. 34, 2003.[3]X. Li and L. J. Cimini Jr.,“Effects of clipping and filtering on the performance of OFDM”, IEEECommunication Letter, pp. 131-133,May 1998.
[4]Charan Langton “Intuitive Guideto Principles of Communications”, p. 20,2004.[5]Abdulla A. Abouda “PAPR Reduction of OFDM signal using turbocoding and selective mapping”, 2004.[6]Ola Jetlund, Geir E.Øien andKjell J.Hole “Adaptive Gallager codedmodulation on Rayleigh fadingchannels”, IEEE, 2003.[7]Jin-Goog Kim, Tae-Joon Kim,Jae-Seang Lee, and Jong-Tae Lim“Channel estimation for OFDM over fastRayleigh fading channels”, 2007.[8]Sattorov Mashhur, Heau-Jo Kang“Huffman coding approach to performance of 16-QAM/OFDM”, 2009.

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