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 Total Downloads : 969
 Authors : Krishna Kumar, Garima Saini
 Paper ID : IJERTV1IS10471
 Volume & Issue : Volume 01, Issue 10 (December 2012)
 Published (First Online): 28122012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Ber Performance Analysis of Daubechies Wavelet In DvbT For Rayleigh Channel
Krishna Kumar, Garima Saini
Astt. Prof. LKCE Ghaziabad, Astt. Prof. NITTTR Chandigarh
ABSTRACT:
In todays scenario of communication technology, the demand for high speed data rate and bandwidth has increased to the extent, that it has become very difficult to manage the communication system. To increase the speed of operation, the data is transmitted parallel and for this purpose Orthogonal Frequency Division Multiplexing (OFDM) technique is used which also has high spectral containment required for wireless communication systems. The fundamental principle of OFDM is to decompose the high rate data stream (bandwidth W) into N parallel lower rate data streams or channels, one for each subcarrier. Each subcarrier is modulated with a conventional modulation scheme (such as Quadrature Amplitude Modulation or PhaseShift Keying) at a low symbol rate, maintaining total data rates similar to conventional single carrier modulation schemes in the same bandwidth. In OFDM, Fourier Transform (FT) is used as a modulation technique, but this concept creates an Inter Symbol Interference (ISI) because of the time dispersive nature of the channel. To reduce this effect, a Cyclic Prefix is used but this reduces its spectral efficiency too. Orthogonal Wavelet Division multiplexing (OWDM) scheme has been proposed in this paper for wireless (DVBT) communication which outperforms OFDM and has a lower computational complexity and increased flexibility. Key words: OFDM, Bit Error Rate, FFT, DWT, AWGN, Rayleigh Channel, DVBT.

INTRODUCTION:
The scarcity of radio spectrum has become problem in many applications that utilize the higher Radio Frequencies (RF). It is therefore, important that this resource is carefully managed to avoid waste. To help optimize the RF spectrum, in 1997, The United Kingdom launched the worlds first commercial digital terrestrial television service with the ultimate aim to switch off in the analogue services between 2008 and 2012 [] thus potentially freeing up a large number of RF channels for either more television services or for other applications. Because the UK was eager to release the analogue bandwidth as soon as possible (meaning the government had to start to migrate quickly), the UK adopted the 2K version of DVBT due to commercial hardware restrictions at the time (the 8K system was too expensive for use in consumer devices). Those countries moving over to digital television recently have tended to go straight to the 8K system because the technology is now commercially viable
and because of all the advantages the 8K system has to offer. OFDM is the underlying technology of the DVBT standard and comprises of an Inverse Fast Fourier Transform (IFFT) at the transmitter (and an FFT at the receiver) which performs the frequency division multiplex (unlike wideband communications which tend to use time division multiple). It is the size of these IFFTs and FFTs that determines whether the system is in the 2K or 8K mode.
The implementation of such large FFT cores was the main cause for delay for implementing OFDM in Consumer devices although OFDM was used in military applications long before this time as there are minimal budget constraints in military hardware. In 1997, the 2K core was just becoming commercially viable with a SetTop Box (STB) costing the consumer in the region of Â£200300. Today, most STBs are dual core (implementing both systems) and can cost as little as Â£30 for a basic system. If the technology could be further simplified, then it would be of significant benefit to the Manufacturing community as it would contribute to a drop in production costs that impact on the consumer market. Even with its inherent advantages, there is a drawback to OFDM being the inflexibility of the system. With OFDM, there are a small number of parameters that can be changed to suit the channel but the choice has to apply across a whole OFDM symbol it is not possible to code different parts of the symbol in different ways as it is in the Japanese Integrated Services Digital Broadcast (ISDB) standard. The use of filters in the wavelet domain has been predominantly used for multiresolution analysis of time varying signals. An alternative, however, is to use the wavelet domain to separate the sub band components in the same way that OFDM does. This system is termed Orthogonal Wavelet Division Multiplex (OWDM). The big difference between OFDM and OWDM is that in OFDM, the FFT performs sub band decomposition with a specific number of sub bands at well defined intervals. With OWDM, it is possible to dynamically allocate the number of sub bands and the bandwidth of each. Of course, if there were sufficient levels, the OWDM would start to resemble the OFDM Symbol. With all this in mind, this paper will propose an alternative to using OFDM in DVBT which employs a true time frequency division multiplex using wavelets which may provide a more flexible environment that can be tailored to suite signal and channel conditions and of lower financial and computational cost.
Standard DVBT uses two modes of operation i.e. 2K and 8K. The 2K mode provides the best mobile reception conditions because of its larger inter career spacing.
However, it is only suitable for smallsize SFNs (Single Frequency Network) and DVBH networks. The 8K mode can be used both in SFNs and MFNs (Multiple) networks. It provides a Doppler tolerance allowing for highspeed reception.
This paper is focussed on the implementation of OWDM (Orthogonal Wavelet Division Multiplexing) in place of OFDM (Orthogonal Frequency Division Multiplexing) in DVBT. This paper also examine the performance of Wavelet Modulation (WM) in time varying channels. Results for Rayleigh fading channels are compared to the AWGN channel
where and are the lowpass and highpass filters.
g [n]
2
h [n]
s [n]
2
Figure 1: Block Diagram of Filter Analysis
IFF T
Outer Coder/
Quadra ture
Outer Coder/ Interle
MPEG 2
Multipl
First the samples are passed through a low pass filter (LPF) and high pass filter (HPF) with impulse response g and h respectively, resulting in a convolution of the two.
= = = [ ]
(5)
Gau ssia
= = = [ ]
(6)
MPEG
2
Multip
Outer Decod er/
Outer Decode r/
The output of the HPF gives the detail coefficient and the output of LPF gives the approximation coefficient. The wavelet transform divides the signal into the approximation coefficient and detail coefficient.
FF T
Quadr ature
The DWT analyses the signal at different frequency bands with different resolutions by decomposing the signal into
Figure.2. ETSI EN 300 744 DVBT Block Diagram [2]

DWT AND WAVELET MODULATION A wavelet is a waveform of limited duration that has an average value of zero [4]. Unlike sinusoids that theoretically extend from minus to plus infinity, wavelets have a beginning and an end. The basic idea of the wavelet transform is to represent any arbitrary function s as a superposition of a set of such wavelets or basis functions. These basis functions or baby wavelets are obtained from a single prototype wavelet called the mother wavelet, by dilations or contractions (scaling) and translations (shifts). The Discrete Wavelet Transform of a finite length signal s(n) having N components, for example, is expressed by an N x N matrix. Wavelets ar known to have compact support (localization) both in time and frequency domain, and possess better orthogonality. The DWT of a signal s is calculated by passing it through a series of filters.
The discrete wavelet transform (DWT) of a signal s is given by
an approximation containing coarse and detailed information. The original signal s[n] is first passed through a halfband high pass filter g [n] and a halfband low pass filter h [n]. A halfband low pass filter removes all frequencies that are above half of the highest frequency, while a halfband high pass filter removes all frequencies that are below half of the highest frequency of the signal. The low pass filtering halves the resolution, but leaves the scale unchanged. The signal is then subsampled by two since half of the number of samples is redundant, according to the Nyquists rule.
MPE G2
Multi
Outer Coder
Outer Coder/
Quad ratur
Wavelet Synthesi
Gaussi an + Raylei
Figure
Quadra ture
Outer Decoder/
Outer Decoder
MPE G2
Multi
Wavele t Decom
.3.
+
2
= 2
(2
)
(1)
= + +
+ 2 2 2 (2)
Proposed System Block Diagram
=
=
where is the wavelet function [6]. Mallats fast wavelet transform (FWT) provides a computationally efficient, practical, discrete time algorithm for computing the DWT. The scaling and wavelet coefficients at scales
m can be computed from the scaling coefficients at the next finer scale m+1, using
The DWT based system replaces the IFFT and FFT blocks by IDWT (Inverse Discrete Wavelet Transformation) and DWT blocks respectively.
= 2 +1
(3)
= 2 +1
(4)
III Wavelet Modulation
Wavelet modulation has a novel multirate diversity strategy that offers improved message recovery over conventional modulation techniques: if the message is not recovered at one rate due to channel disturbances, it can be received at another where the channel is clear.
S
/ P
C
o n s t e l l a
I D W
T
CHANNEL
C
o n s t e l l a
t
D W T
P
/
S
:
Figure.4 DWTOFDM
One of the advantages of using wavelet transform is that due to the overlapping nature of wavelet properties, the wavelet based OFDM does not need cyclic prefix to deal with delay spreads of the channel. As a result, it has higher spectral containment than that of Fourierbased OFDM [6]. The input data is processed as per FFTOFDM. However, the difference is that the system does not require CP to be added to the OFDM symbol.
The output of the inverse discrete wavelet transform (IDWT) can be represented as:

Fading and Multipath:
Fading occurs due to multipath components in a channel. In the wireless propagation channel there is no single direct link between the transmitter and the receiver; rather the transmitted signal undergoes multiple reflections, refractions, diffractions and scattering. The effect can cause time spreading of the signal and results in fluctuations in the received signals amplitude,:phase, and: angle of arrival, giving rise to the terminology multipath fading. It is possible that either or both the transmitter and receiver are moving. These moments cause Doppler shifts in the received signal and hence result in intercarrier
interference. The: construc:tive (or destructive) interference results in random fluctuation in the
received signal.
Figure 3: Multipath reception of a signal
Rayleigh fading model:
The Rayleigh fading is primarily caused by multipath
2 2 2 7
=0 =0
where are the wavelet coefficients and (t) is the
wavelet function with compressed factor m times and shifted n times for each subcarrier (number k, 0 k N 1). The wavelet coefficients are the representation of signals in scale and position or time. Xm At the receiver side, the process is inversed. The output of discrete wavelet transform (DWT) is
reception [6]. Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal. It is a reasonable model for troposphere and ionospheres signal propagation as well as the effect of heavily builtup urban environments on radio signals. Rayleigh fading [7] is most applicable when there is no line of sight between the transmitter and receiver.

Simulation Parameter and Results:

1
= 2
=0
2 2 8
In the OWDM system, the performance of BER as a
function of Eb/No (SNR) is examined. Simulation has been carried out to compare the performance of Daubechis
Multiresolution analysis of wavelet theory allows to
represents wavelet and scaling functions by high and low pass filters (HPF and LPF), respectively with impulse responses and . therefore the wavelet transformation can be easily implemented using discrete time filters.
In this Paper, The Wavelet of interest is Daubechies wavelet, because only this wavelet proves to be the wavelet of shortest duration during simulation.
(N= 2, 4,6,8,16,32) wavelet over Rayleigh fading channels. The study and comparisons are based on simulation done using MATLAB. The BER performance as a function of SNR is examined for Rayleigh fading and frequency selective fading with Doppler frequency (fd = 10Hz). Digital Video Broadcasting Terrestrial (DVBT) communication system with 16QAM modulation is implemented using Matlab programming. The simulation time of different wavelets is also calculated and found that Daubechies wavelet is a wavelet of shortest duration.
Table1: Simulation Parameters[1]
Parameter 
2K Mode 

Elementary Period T 
7/64 s 

Number of carriers K 
1705 

Value of carrier number Kmin 
0 

Value of carrier number Kmax 
1704 

Duration Tu 
224 s 

Spacing between carriers Kmin and Kmax =(K1)/Tu 
7.61 MHz 

Carrier Spacing 1/Tu 
4464 Hz 

Allowed guard interval /Tu 
1/4 
1/8 
1/16 
1/32 

Duration of symbol part Tu 
2048xT 224 s 

Duration of guard interval 
512xT 56 s 
256xT 28 s 
128xT 14 s 
64xT 7 s 

Symbol duration Ts= + Tu 
2048xT 280 s 
2304xT 252 s 
2176xT 238 s 
2112xT 231 s 
The choice of a suitable wavelet for digital wireless communication depends on its length and shape of the signal. The chosen wavelet must be of shortest duration and close to the analysed signal.
Table 2: Summary of the elapsed time in simulation.
Wavelet 
Gaussian Channel 
Rayleigh Channel 
Db2 
39.057933 
44.601987 
Sym2 
40.678816 
44.804060 
Coif2 
46.71725 
53.078534 
Db4 
42.342866 
48.086294 
Sym4 
42.231923 
48.302867 
Coif4 
50.99034 
56.72645 
From the above table it is concluded that Daubechies (N = 2, 4) wavelets generate waveforms of shortest
duration for both Gaussian and Rayleigh fading channels, that is why, BER performance of different Daubechies wavelets is analysed through MATLAB Code.

BER Vs EbNo plot of different Daubechies Wavelets for Gaussian and Rayleigh Channel in DVBT.
Probability of reduced bit error rate (increased performance) is a very important key to measure the noise robustness of OWDM communication scheme. The relationship of BER as a function of EbNo performance for different levels of noise is a useful performance tool. The wavelet family that results in a high performance gain is selected for optimum performance of the OWDM.
0
10
1
10
FFTOFDM DWTOFDM
Bit error probability curve for DWT QAM usinVgoOlF.D1MIssue 10, December 2012
0
10
db4 Gaussian
1 db4 Rayleigh
10
2
2 10
10
X: 16
Y: 0.00361
BER
3
BER
3 10
10
4
10
4
10
5
10
5
10
6
10
0 5 10 15 20 25 30 35 40
6
10
0 5 10 15 20 25 30
Eb/No
Eb/No
Figure 4: BER Performance Comparision of DWT OFDM and FFTOFDM in AWGN in 16QAM Modulation
DWT based OFDM gives better performance than that of FFT based OFDM in Gaussian
Figure 5:BER Vs Eb/N0 for db4 in Gussian and Rayleigh fading channels
db2
db4
db6
db8
db16
db32
Bit error probability curve for DWT QAM using OFDM
1.374
10
0 Bit error probability curve for DWT QAM using OFDM 10
1.376
10
db32 Gaussian
10
1 d32 Rayleigh
1.378
BER
10
10
2 X: 16
Y: 0.003533
BER
3
10
4
10
5
10
1.38
10
1.382
10
1.384
10
4.975 4.98 4.985 4.99 4.995 5 5.005 5.01 5.015 5.02 5.025
Eb/No
10
6 Figure 7: BER Vs Eb/N0 at 5 Db for Daubechies in
0 5 10 15 20 25 30
Eb/No
Figure 6: BER Vs Eb/N0 for db4 in Gussian and Rayleigh fading channels
Channel. Wavelet based OFDM system was found having small bit error rate probability than that of the Fourier transform system.
Gussian and Rayleigh fading channels

Performance Analysis
We analyze in this section the performance of OWDM in the propagation channels. The results have been obtained by simulations only, due to the fact that no analytical expressions are available for wavelet and wavelet filters. The different levels of decomposition of the Daubechies wavelet that are used, are (N= 2, 4,6,8,16,32). Wavelet Modulation (WM) performance in an AWGN channel is the best at all SNRs than that of Rayleigh channels.
3.6
10
3.7
10
BER
3.8
10
3.9
10
Bit error probability curve for DWT QAM using OFDM
db2
db4
db6
db8
db16
db32
Table 4 values of min. BER at different EVboNl.o1 oIsfsDuea1u0b,eDcehcieems ber 2012
Wavelets
EbNo
(dB)
Minimum BER
(dB)
Daubeccies
Wavelet
0
0.105
db4
5
0.04172
db2
10
0.01442
db2
15
0.004529
db6
20
0.00139
db16
25
0.000444
db16
30
0.000127
db8
28.2 28.4 28.6 28.8 29 29.2 29.4 29.6 29.8 30
Eb/No
Figure 8 BER Vs Eb/N0 at 30 Db for Daubechies in Gussian and Rayleigh fading channels Table3: Values of BER at different EbNo of Daubechies Wavelet
BER
BER
BER
BER
BER
BER
min BER
EbNo
db2
db4
db6
db8
db16
db32
0
0.1056
0.105
0.1056
0.1056
0.1054
0.1052
0.105
5
0.04172
0.0418
0.04193
0.04184
0.04204
0.0419
0.04172
10
0.01442
0.01444
0.01454
0.01454
0.01442
0.01458
0.01442
15
0.004621
o.oo4628
0.004529
0.004556
0.004537
0.004571
0.004529
20
0.001424
0.001462
0.001433
0.001431
0.00139
0.001473
0.00139
25
0.000461
0.000446
0.000444
0.000462
0.000444
0.000472
0.000444
30
0.000161
0.000161
0.001382
0.000127
0.000157
0.000144
0.000127
Figure 9: Performance of Daubechies Wavelet at different values of EbNo
Figure 10: Graph between EbNo Vs Daubechies wavelet in Rayleigh fading channel

Results
References
Vol. 1 Issue 10, December 2012
Wavelets use to give improved message recovery over channel disturbances. This has become possible because of the multidiversity behaviour of the wavelets. The results obtained above by simulation, justifies the multidiversity behaviour if the wavelet, which means that if the message is not received at one rate due to channel disturbances, it can be received another rate where the channel is clear
BER performances of Daubechies N=2,4,6,8,16 and
32 in Rayleigh fading channel with Doppler spread of 10 Hz is analysed whose outcomes are.

For EbNo of 0dB, db4 is more noise resilient, followed by db32.

For EbNo of 5dB and 10 dB, db2 is more noise resilient, followed by db4 and db16 respectively.

For EbNo at 15 dB, db6 is more noise resilient, followed by db16.

For EbNo at 20dB and 25dB, db6 and db16 are equally noise resilient, followed by db4.

For EbNo at 30 dB, db8 is more noise resilient, followed by db6.
The paper compares the performance of the system using 16QAM only, whereas the future work may include the implementation of other modulation schemes and different channel scenarios for performance evaluation of any OFDM based system.
Conclusion and Future works
Over all, the performance results of wavelet based OFDM and its ability to fulfil the wide range of requirements of tomorrows ubiquitous wireless communications leads to a conclusion that this mew modulation technique is a viable alternative to conventional OFDM to be considered in future wireless communication systems
Because of the selective nature of wavelets, different order of the Daubechies wavelet should be selected for the enhanced performance of the system. Daubechies wavelet also generates a wave form of shortest duration. Short waveforms require less memory, limit the modulation demodulation delay and require less computation which helps to implement fast wavelet transform less computational complex wavelet based OFDM scheme. This leads to conclude that Daubechies wavelet family can be a viable alternative suitable basis for OFDM to be considered for future OFDM communication scheme.
The paper compares the performance of the system using 16QAM only, whereas the future work may include the implementation of other modulation schemes and different channel scenarios for performance evaluation of any OFDM based system. Diversity Scheme on Wavelet based OFDM: improved transmission integrity may be achieved with aid of diversity. Space, time, frequency diversities are the most physical diversities to be exploited.

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