ISBN: 378-26-138420-01
INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN ENGINEERING RESEARCH, ICCTER - 2014
Study of Various Effects on Peak to Average Power Reduction using OFDM EM HARINATH Smt. N. PUSHPALATHA M.Tech DECS Student Assistant Professor Department of ECE, AITS, TIRUPATI Department of ECE, AITS, TIRUPATI Hari.810213@gmail.com Pushpalatha_nainaru@gmail.com Annamachrya institute of technology and sciences (AITS),TIRUPATI
Abstract: In this paper the novel method of complex weighting for peak to average power (PAPR) reduction of OFDM is addressed. The Study of various effects on peak to average power reduction using OFDM on this paper. The simulation result are studied about the combination of both different amplitude weighting factors including rectangular , Bartlett , Gaussian , raised cosine , Half-sin , Shannon , and sub carrier masking with phasing of each OFDM Subcarrier using random phase updating algorithm. By using the amplitude weighting factor Bit error performance of weighted multicarrier transmission over a multipath channel is also investigated. In the random phase updating algorithm the phase of each carrier is updated by a random increment until the PAPR goes below a certain threshold level. Further the random phase updating algorithm has been extended by dynamically reducing the threshold level. For an OFDM system with 322 subcarriers and by Gaussian weighting combined with random phase updating, a PAPR reduction gain of 3.2 dB can be reduced. Result show that grouping of amplitudes weights and phase reduce the hardware complexity while not much impacting the PAPR reduction gain of the method. Even further dynamic threshold gives the best results and can reduce the mean power variance of 8-carrier OFDM signal with BPSK modulation by a factor of 7 dB.
1. Introduction: Orthogonal frequency division multiplexing (OFDM) is a parallel transmission method where the input data is divided into several parallel information sequences. And each sequence modulates a subcarrier. OFDM signal has a non constant envelope characteristic since modulated signal form orthogonal subcarriers are summed.
The PAPR problem is occurred when these signals are added up coherently, resulting in a high peak. The high PAPR of OFDM signal is not favorable for the power amplifiers working in non-linear region. Different methods have been proposed to mitigate the PAPR problems of OFDM. These techniques are mainly divided into two categories: signal scrambling and signal distortion techniques. Signal scrambling techniques are all variations on how to modify the phase of OFDM subcarriers to decrease the PAPR. The signal distortion technique is developed to reduce the amplitude of samples whose power exceeds a certain threshold. The Signal scrambling techniques are as follows: Block coding techniques, Block coding scheme with error correction, Selected mapping (SLM), Partial transmit sequence (PTS), Interleaving technique, Tone reservation (TR), Tone injection (TI). The Signal distortion techniques are as follows: Peak windowing, Envelope scaling, Peak reduction carrier, clipping and filtering. This paper addresses the PAPR reduction of OFDM by combination of both signal scrambling and signal distortion techniques.
2.0. Related project work: In this section explain the existing methods of our paper. 2.1. Weighted OFDM for wireless multipath channel 2.2. Random phase updating algorithm for OFDM Transmission with low PAPR The above two existing methods explained below section
2.1. Weighted OFDM for wireless multipath channel 2.1.1. Description:
INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT
76
www.iaetsd.in
ISBN: 378-26-138420-01
INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN ENGINEERING RESEARCH, ICCTER - 2014
OFDM also called multicarrier (MC) technique is a modulation method that can be used for the high speed data communications. In this modulation is scheme transmission is carried out in parallel on the different frequencies. This technique is desirable for the transmission of the digital data through the multipath fading channel. The advantage of this technique is spectral efficiency. In the MC method the spectra of sub channels overlap each other while satisfying orthogonality, giving rise to the spectral efficiency. Because of the parallel transmission in the OFDM technique the symbol duration is increased. Another advantage of this method to work in the channels having impulsive noise characteristics. One more advantage of the MC method is its implementation with the FFT algorithm which provides full digital implementation of the modulator and demodulator.
2.1.2. Weighted modulation:
Where f0 is the lowest frequency, m is the number of carriers and T is the OFDM symbol duration. The weighted MC transmitted signal is ( )=
()
(
)
( −
) (2)
Where α m is the real weighting factor of the m-th carrier, bm (i) is the symbol of the m-th sub channel at time interval iT, which is±1 for BPSK Modulation and (±1 ± )/√2 for QPSK ,p(t) is a rectangular function with amplitude one and duration T.
multicarrier
In this method of weighted OFDM is explained and the PAPR reduction associated with this technique is reported. In serial data transmission, sequence of data is transmitted as a train of serial pulses. However in parallel transmission each bit of a sequence of M-bits modulates a carrier. In the multicarrier technique transmission is parallel. The block diagram to the conventional MC method but with a different that each carrier is weighted by a real factor αm m=0, 1, 2………M-1. In the modulator the input data with the rate R is divided into the M parallel information sequences a weighted subcarrier. In this method the frequency of m-th carrier is =
+
m=0,1,2,……M-1
(1)
2.1.3. Different weighting factors In this section several weighting factors for weighting of the OFDM signal is describe.
Rectangular: This weighting function has Rectangular shape and is expressed by
INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT
77
www.iaetsd.in
ISBN: 378-26-138420-01
INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN ENGINEERING RESEARCH, ICCTER - 2014
0≤
≤ ℎ
−1
( ) = | ( )|
0 (3) Bartlett: This weighting function has simply a triangular shape for 0 ≤ ≤ − 1 1−
, = 0
(10) ( )
Gaussian: These factors are generated based on the Gaussian function
−
)
[ ( )] =
weighting
function
| |
| [
∗]
∗
(
)
(12) The symbols on different carriers are assumed to be independent i.e., therefore, the second term in (13) is zero and accordingly, by using (9) the average power becomes
(6) is
(7) 0 ℎ Shannon: The shape of this weighting factors is the sinc function i.e., sinc(x) = (sin (πx)/ (πx)) , =
|
+
sin
[ ( )] =
|
| =1
(13) The variation of the instantaneous power of OFDM signal from the average is ∆ ( ) = ( ) − [ ( )]
(8) 0
(
)∗
(
(11) Averaging the power P (t) yields E [P (t)]
if 0≤m≤M-1
ℎ
Half-sin: This explained by
|
(5)
0 ℎ Where s= spread or standard deviation of the weighting factors around M/2 Raised cosine: The shape of this function in the interval [0,M-1] is described by 1cos(2πm/M) , =
|
=
+
−
, =
, =
)
(4)
ℎ
0
(
)∗
(
=
ℎ
(
)∗
(
)
2.1.4. PAPR of Weighted OFDM
=
In this section the impact of weighting of OFDM signal on the PAPR is investigated. The OFDM signal of (2) in the time interval of 0 ≤ ≤ can be written as
(14) Averaging of ∆ ( ) over a symbol period of T yields
( )=
()
=
1
∆ ( )
|
=
( )|
(15) Where R cc (i) is the autocorrelation function of the complex sequence cm=bm.α m
(9) For the calculation of PAPR first by using (10) we obtain the instantaneous power of OFDM signal as
()=
∗
(16)
INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT
78
www.iaetsd.in
ISBN: 378-26-138420-01
INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN ENGINEERING RESEARCH, ICCTER - 2014
The parameter ρ is the power variance of the OFDM signal and as is described below is a good measure of the PAPR.
the average is Δp(t)=P(t)-E[P(t)] and accordingly, the power variance (PV) of OFDM signal, denoted by ρ
{ ( )}
=
{ (
=
= max{ ( )} = )} (17)
[ ≤
= =
( 1/ 2
( − 1) 2
(18) Using (18) and (19) it can be easily shown that PAPR has the following relationship with the power variance − ( )=
+
√
=
√
∫
( )=
2.2. Random Phase Updating Algorithm for OFDM Transmission with low PAPR OFDM is the basic technology for a number of communication systems such as Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), HIPERLAN-2,I EEE802.11a and Digital subscriber line. In this random phase updating algorithm we are using the signal scrambling technique. Signal scrambling techniques are all variations on how to modify the phase to decrease the PAPR.
2.2.2. PAPR of OFDM signal can
( )= (21) Where T is the OFDM symbol duration, bm is the symbol of the m-th sub channel, which is ±1 for the BPSK modulation and (±1 ± )/√2 for QPSK modulation and M is the number of carriers. The power of s(t) is ∗
(
( )|
∅
(24) Where 2πφm is the m-th subcarrier phase shift. Adding random phases to each subcarrier will change the power variance of OFDM Signal. In the random phase updating algorithm, the phase of each subcarrier is updated by a random increment as: (∅ ) = (∅ ) + (∆∅ ) (25) Where i is the iteration index and is the phase increment of the m-th subcarrier at ith iteration. Assume the initial phase is zero, consequently a random phase increment is generated and the phase is updated by adding the increment to the phase of that subcarrier. Flow chart of the algorithm for this iterative phase updating is shown in figure. Figure 8a a certain threshold for PV is set and for figure 8b a limited number of iterations is allowed. Two distributions are Gaussian and uniform where the uniform distribution chosen for the distribution of phase increments. A connection between phase shift variance and the number of iteration
2.2.1. Description
( ) = | ( )| =
|
In the random phase updating algorithm for each carrier a random phase is generated and assigned to that carrier. Using (23) the OFDM signal
(20)
The OFDM signal in the period of 0 ≤ ≤ be written as
=
2.2.3. RANDOM PHASE UPDATING ALGORITHM
(19)
∞
(∆ ( ) )
(23) Where Rbb (i) is the autocorrelation function of the sequence bm as ∗ ()=∑
] ) exp −
1
)
(22) The PAPR of the OFDM signal is written as PAPR=Max {P(t)}/Mean{p(t)}. The variation of the instantaneous power of OFDM signal from
INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT
79
www.iaetsd.in
ISBN: 378-26-138420-01
INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN ENGINEERING RESEARCH, ICCTER - 2014
from zero initial phases, the random phase shifts are generated and combined with the symbols, and the threshold is not changed.
2.3. PRAPOSED METHOD: In the above existing methods the high PAPR has been reduced due to this the hardware complexity is increased, so much impact has not been on the reduction of the PAPR and also the above methods have the demerit that has the PAPR reduction gain is very low. So the above two methods clubbed together and creates a new method called as the complex weighted OFDM Transmission with low PAPR. By applying both techniques together will further reduce the PAPR by a factor of 4.8dB. Complex Weighting for Multicarrier modulation The OFDM Signal for one symbol interval 0 ≤ ≤ is written as
s reaching the threshold. Fig.2. Flow chart showing the iterative random phase updating algorithm. A) With threshold. B) With limited number of iterations.
( )=
(
)∗
(
)
(26) Where M is number of subcarriers, BM is modulation data of the m-th subcarrier, T is the OFDM symbol period, and wm is a complex factor defined as = Where a positive real value and φm α m is the phase of m-th subcarrier. The block diagram of an OFDM modulator with complex eighting factors is shown in fig
and receiver.
2.2.4. Phase Updating Dynamic threshold
with
Fig.3. Flowchart of the random phase updating algorithm with dynamic threshold. The selection of random phase increments it is possible to reduce the PV threshold. As illustrated in figure 11 this approach the threshold level of the algorithm is dynamically reduced. The first step of the algorithm is to calculate the PV of the original OFDM symbol, and then set the first threshold to e.g. 10% lower. Then starting
INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT
80
www.iaetsd.in
ISBN: 378-26-138420-01
INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN ENGINEERING RESEARCH, ICCTER - 2014
Fig 5. Block diagram of complex-weighted OFDM modulator
weightings of the OFDM signal are sketched respectively.The CDF of PAPR of OFDM signal with several scenarios of weighting and phasing are depicted in Fig. 1 for M = 32. In Fig. phasing is applied by random phase updating with Uniform distribution (x = 1.0) and power variance threshold ρTh = -4 dB.
3.0. Simulation results: By comparing the above two existing methods with the proposed method the result should be shown below. In the weighted OFDM for the wireless multi path channels
Fig.8. CDF plots of PAPR for different weightings with and without phase c1: rectangular weighting, no phasing , c2: rectangular weighting with phasing , c3: Gaussian weighting (std=M/16) , no phasing , c4: Gaussian weighting (std= M/16) with phasing.
Figure 6 illustrates the CDF of the power variance for different weighting functions. Table 1 for the OFDM signal with 256 carriers and BPSK modulations by applying Gaussian weighting , the ρ is reduced by a factor of 3.2 db and for the QPSK Modulation by a factor of
4.0. Conclusion: In this paper we have addressed the novel method of PAPR reduction for OFDM signal by applying both amplitude weighting and phasing of OFDM subcarriers. This joint application gives more PAPR reduction gain than only weighting or phasing. Employing both weighting and phasing to subcarriers implies more complex implementation. However, the complexity can be reduced by grouping of the subcarriers when weighting or phasing is applied. Furthermore, the complex weighting with dynamic threshold was studied. Combining amplitude weighting, phasing and dynamic thresholding will result in a larger PAPR reduction gain of the proposed algorithm.
6.1 dB Fig .7 the irreducible bit error probability of the OFDM signals with different functions versus rms delay spread of the channel is illustrated. The BPSK and QPSK modulations are considered and simulations are carried out for 5000 symbols weighted by proper weighting functions. In figs.3 and figs.4 the parameter ρ versus number of the messages for BPSK and QPSK modulations and for different
References: [1] T.A.Wilkinson et al," Block coding scheme for Reduction of peak to mean envelope power ratio of Multicarrier
INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT
81
www.iaetsd.in
ISBN: 378-26-138420-01
INTERNATIONAL CONFERENCE ON CURRENT TRENDS IN ENGINEERING RESEARCH, ICCTER - 2014
transmission schemes," Electronics Letters, Vol. 30, No. 25, 1994. [2] R.F.H. Fischer et al," Reducing the peakto-average power ratio of multicarrier modulation by selected mapping," Electronics Letters, Vol. 32, No. 22, 1996. [3] G. Wade et al," Peak-to-average power reduction for OFDM schemes by selective scrambling," Electronics Letters, Vol. 32, No. 21, 1996. [4] S.H.Muller and J.B.Huber," OFDM with reduced peak-to-average power ratio by optimum [5] M.Friese," Multitone signals with low crest factor," IEEE Trans. Commun., Vol. 45, No. 10, 1997. [6] J.Tollado, Multicarrier Modulation with Low PAR, Kluwer Publishers, MA, USA, 2000. [7] G.L.Stuber and D.Kim," Clipping noise mitigation for OFDM by decision aided reconstruction," IEEE Commun. Letters, Vol. 3, No. 1, 1999. [8] R.J.van Nee and A. de Wild," Reducing peak-to average power ratio of OFDM," IEEE Vehicle. Technol. Conf., pp. 2072-2076, 1996.
Distortions of an OFDM system using efficient an Adaptive predistorter," Commun., Vol-2
IEEE
Trans.
[14] K. S. Lidsheim, “Peak-to-Average Power Reduction by Phase Shift Optimization for Multicarrier Transmission,” MSc. thesis, Delft University of Technology, Delft, The Netherlands, April 2001. [15] R. Prasad and R. D. J. van Nee, OFDM for Wireless Multimedia Communications. Boston: Artech House, 1999. [16] H. Nikookar and R. Prasad, “Weighted OFDM for wireless multipath channels,” IEICE Commun. Trans., vol. E83-B, no. 8, pp. 1864-1872,Aug. 2000. [17] H. Nikookar and K. S. Lidsheim, “Random phase updating algorithm for OFDM transmission with low PAPR,” IEEE Broadcasting Trans., vol. 48, no. 2, pp. 123128, Jun. 2002
[9] R.Prasad and R.J. van Nee, OFDM for Wireless Multimedia Communications, Artech House, Boston, 1999. [10] O.Muta et al," Peak power suppression with parity carrier for multicarrier transmission," IEEE Vehicle. Technol. Conf. (VTC'99-Fall), pp. 2923-2928, 1999. [11] H.Nikookar and R.Prasad," Weighted multicarrier modulation for peak-to average power reduction," IEICE, Trans. Commun., Vol. E83-B, No. 8, 2000. [12] X.Wang and T.T.Tjhung," Reduction of peak-toaverage power ratio of OFDM system using companding technique," IEEE Trans. On Broadcasting, Vol. 45, No. 3, 1999. [13] Y.S.Chu et al.," On compensating nonlinear
INTERNATIONAL ASSOCIATION OF ENGINEERING & TECHNOLOGY FOR SKILL DEVELOPMENT
82
www.iaetsd.in