DWT OFDM SYSTEMS WITH REDUCED PAPR FOR NEXT

GENERATION MOBILE NETWORKS

Mr Y. A. LAFTA 1 and Dr. P. JOHNSON

2

School of engineering, Liverpool John Moores University, Byrom Street, Liverpool, L3 3AF,

UK

Y.Lafta@2008.ljmu.ac.uk

ABSTRACT

Peak to power average ratio (PAPR) is a

serious issue in OFDM systems. Several

techniques have been proposed by

researchers to reduce PAPR. A technique

proposed, by Tellambura applies real-

valued modulation schemes to reduce

PAPR in systems using a limited number

of subcarriers. However, the technique has

not been evaluated for its performance of

bit error rate using discrete time

approximations of the continuous-time

PAPR. On other hand, Wong proposed a

technique that applies complex modulation

as a practical technique for computing the

continuous-time peak-to-average to power

ratio (PAPR) of OFDM. However, this

technique does not consider coherent

multilevel modulation scheme. Khalid and

Shah have proposed to select the best

wavelet packet basis function to decrease

the PAPR. This technique results in no less

than 1-2 dB reduction in PAPR. Jiang

proposed a new companding transform for

PAPR reduction in OFDM systems, which

was shown to improve PAPR by no less

than 2.2 dB. In this paper, combination of

DWT OFDM with 64DAPSK is proposed

for better BER performance and improved

PAPR and interference values. It is

demonstrated that including companding

with this system results in further

reduction of PAPR.

Correspondence should be addressed to YHYA LAFTA on

Y.Lafta@2008.ljmu.ac.uk

KEYWORDS

Orthogonal Frequency-Division

Multiplexing (OFDM), Discrete Wavelet

Transformer (DWT), Inverse Discrete

Wavelet Transformer (IDWT), Differential

Amplitude and Phase Shift Keying

(DAPSK), Additive Wight Gaussian Noise

(AWGN), Rayleigh channel Peak to power

average ratio (PAPR).

1 INTRODUCTION

1.1 Orthogonal Frequency Division

Modulation (OFDM) Systems

Service providers working towards

4G communication systems are

continuously met with the challenge of

accommodating more and more users

within a limited available bandwidth [5].

The main advantage of the OFDM systems

is that they are immune to multi path

fading [7]. However, their major

disadvantage is that the transmitted signal

has a high peak-to-average power ratio

(PAPR). Many research investigations

have lead to the conclusion that the

wavelet based OFDM is more

advantageous than the Fourier based

OFDM [1], [12], [3]. One of the main

reasons being Fourier based OFDM

systems require allocation of guard bands

between subcarrier frequencies to avoid

inter symbol interference, however

wavelet based OFDM systems do not

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require such guard bands and therefore the

overall system bandwidth is increased.

The OFDM scheme provides an

efficient means to handle high speed data

streams. This is because an OFDM is a

multi carrier modulation (MCM) technique

which divides the entire data stream into

several small number of lower data-rate

subcarrier data streams, thus reducing the

effect of frequency selective fading [8].

Using a large number of sub

carriers to narrow down the spectrum for

each sub carrier is the most straightforward

way to spread the data across a wider

spectrum. However, this increases system

complexity and the cost. This also

increases the sensitivity to Doppler Effect

and demands higher accuracy of frequency

synchronization.

A set of cosinusoidal functions

, n=0,1,….., N-1

representing the signal can be used on

orthogonal basis to achieve the multi

carrier modulation (MCM) scheme that

can be synthesized using a discrete cosine

transform (DCT) [14]. The minimum

frequency spacing required to satisfy the

DCT based OFDM is [16]. The

baseband DCT-OFDM signal x (t) is still a

real value when the data symbols are

obtained using real valued modulation

formats, such as pulse amplitude

modulation (PAM) and binary phase shift

keying ( BPSK).

The discrete wavelet transform

(DWT) is represented by a function of a

countable set of wavelet coefficients, i.e.

individual wavelet functions localized in

space [Zhang, H. et al 2007]. The wavelets

are a family of functions constructed from

translation and dilation of signal

function called the mother wavelet. Due

to an extremely high spectral containment

property of the wavelet filters and the fact

that extremely less energy is contained in

the side lobes, the amount of interference

between carriers in wavelet systems is

much lower than that in Fourier systems

[12]. Therefore, even in the absence of

guard bands, DWT-OFDM can combat

narrowband interference better than the

traditional discrete Fourier transform

systems and is inherently more robust in

terms of ICI (DFT-OFDM) [2]. This

research work proposes a combination of

DWT with DAPSK modulation scheme in

anticipation that this system should have

reduced PAPR compared to the existing

systems.

1.2 Organization of The paper

The organization of this paper is as

follows: section 1.3 reviews the QAM

modulation scheme and 1.4 reviews related

work in the area of DCT (DWT) –OFDM

systems with QAM modulation for high

data rate next generation communication

networks. Finally, section 2 presents the

simulation and the results of the proposed

combination of DWT system with DAPSK

modulation scheme and compares to that

with QAM modulation schemes. The

performance from the system is evaluated

against metrics such as Eb/No, ISI and

PAPR and compared with that of DCT

system.

1.3 Modulation Schemes

Quadrature amplitude modulation

(QAM) is more attractive for the highly

mobile radio environment (e.g., in a car or

a train), which is a high-order and non-

coherent modulation scheme, employed as

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a potential means to give further

improvement to the spectral efficiency.

QAM scheme does not require

complicated channel estimation and

equalization to be detected by the receiver.

Use of pilot symbol can be avoided to

more efficiently transmit the information-

bearing data. Moreover, the non-coherent

modulation can preferably withstand the

Doppler Effect caused by the high mobility

of the transmitter and receiver [10]. The

16QAM has a more efficient signal

distribution than the 16DAPSK, in terms

of the relative power saving in an AWGN

channel [13]. Since highly accurate carrier

recovery and phase tracking are required in

the receiver, applying coherent detection in

the mobile radio environment is a very

difficult task. It is also important to

accurately track the fading envelope for

systems such as 16QAM.

The coded bits are mapped to form

symbols which use gray coding in the

constellation map. The coding rate is (1/2)

for the 16QAM modulation scheme. When

the symbol is normalized, the average

power is unity irrespective of the

modulation scheme used. The data are

converted by the process to corresponding

value of M-ary constellation, which is a

complex word, constituting real and

imaginary parts. The bandwidth B =1/ is

divided into N equally spaced subcarriers

at frequencies (kΔf), k=0, 1, 2… N-1 with

Δf=B/N and as the sampling interval.

Grouping and mapping information bits

into complex symbols will be carried out

at the transmitter. Inverse wavelet

Transform IDWT or inverse discrete

cosine IDCT will be used to modulate

spread data symbol on the orthogonal

carriers, as in conventional OFDM.

1.4 Related work

As a candidate for the 3rd generation

mobile telecommunication system the

OFDM systems have attracted

considerable research attention. The

OFDM system has successfully been

implemented [9] in the wireless

broadcasting applications such as Digital

Video Broadcasting (DVB) and Digital

Audio Broadcasting (DAB). The above

mentioned systems use data rates in the

range of 25Mbits/s, the ETSI-BRAN

system employs this transmission

technique for HIPERLAN 2 (high

performance local area networks), and also

for the extension of the IEEE 802.11

standard for the 5-GHz frequency range.

Future mobile communication systems

with data rates far beyond universal mobile

telecommunication system (UMTS) can be

realized using OFDM as a suitable

transmission technique.

2 2 SIMULATION AND

ANALYSIS

The results of the simulation carried out

on DWT and DCT-OFDM systems with

64DAPSK/64QAM modulation schemes

with AWGN and Rayleigh transmission

channels, and random binary stream input

data are presented in this section in figures

1 to 4. The number of samples for the sub

carrier N is 64, and the number of samples

for the symbols is 1000. If the number of

samples for the sub carriers and symbols

were larger, the time for running the

simulations will be longer. Also, it has

been verified that a larger value than the

present value for the symbols does not

make significant difference to the results.

The figures 1a to 1c represent the

power spectral density of the received

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signal for DWT (and DCT)-OFDM

systems with 64QAM

Fig1a Power spectral densities for DWT and DCT

systems with 64QAM modulation schemes via

AWGN channel

Fig1b Power spectral densities for DWT and DCT

systems with 64QAM modulation schemes via

Rayleigh (Gaussian) channel

Fig1c Power spectral densities for DWT and DCT

systems with 64QAM modulation schemes via

Rayleigh (Jakes) channel

modulation schemes using AWGN

channel with Gaussian spectrum and

Rayleigh channel with Jakes spectrum.

The simulation results indicate that the

DWT-OFDM with 64QAM scheme has

higher signal power than that for the DCT

based OFDM system using the same

modulation scheme. It is also clearly seen

that the power spectral density (PSD) for

DWT-OFDM is approximately (20-

40dB/rad/sample) better than the DCT-

OFDM system when using the 64QAM

scheme modulation via AWGN

transmission channel type. This huge

difference in PSD between the received

signals which were transmitted with the

same input power leads to the observation

that DWT system has much better signal to

noise ratio. Whereas, the DWT-OFDM

system with 64QAM using Rayleigh with

Jakes spectrum demonstrates to have

higher bandwidth efficiency when

compared to the DCT OFDM system

under exactly same conditions. The DCT-

OFDM seems to have better than PSD

signal using the AWGN and Rayleigh with

Gaussian spectrum. This means that the

spectrum for this system will have smaller

side-lobes and so will be immune to inter-

symbol interference (ISI).

Fig1d Power spectral densities for DWT system

with 64DAPSK modulation schemes via AWGN

channel

Fig1e Power spectral densities for DWT system

with 64DAPSK modulation schemes via Rayleigh

(Jakes) channel

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Fig1f Power spectral densities for DWT system

with 64DAPSK modulation schemes via Rayleigh

(Gaussian) channel

The figures 1d to 1f represent the

power spectral density of the received

signal for DWT -OFDM systems with

64DAPSK modulation scheme using

AWGN or Rayleigh channels with

Gaussian and Jakes spectrum respectively.

The DWT-OFDM system with 64DAPSK

has 75dB higher PSD than that of the

DWT-OFDM system with 64QAM

scheme, though with less bandwidth

efficiency .

The PSD of the DWT and DCT

OFDM systems were also simulated with

and without -law companding, and

exponential transforms. The results are

shown in figures 2a and 2b. Figure 2a

representing the DWT-OFDM system with

64DAPSK scheme using Rayleigh

Channel shows that the signal with no-

companding suffers from out-of-band

interference (OBI) compared to the signal

that has gone through companding or

exponential transforms.

Fig.2a PSD for DWT with 64DAPSK channel

Raleigh ( Jakes and Gaussian)

Fig.2b PSD for DWT with 64DAPSK channel

AWGN

The DWT-64DAPSK system in Fig.2a

using Rayleigh channel with Jakes or

Gaussian spectrum is shown to have at

least 32dB lower PSD with or without

companding when compared to that with

exponential transform. Fig.3 represents

DCT-OFDM system with 64QAM scheme

using Rayleigh Channel and AWGN

channels, the DCT-64QAM is shown to

have at least 15dB lower PSD with

exponential transform when compared to

that with or without companding.

Fig.3 PSD for DCT with 64QAM Rayleigh’s

channel (Jakes and Gaussian) and AWGN

Fig.4 CCDF for DWT/DCT with

64DAPSK/64QAM for no companding,

companding and exponential signals

In figure 4, the continuous line

graphs represent the complementary

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cumulative distribution (CCDF) vs. PAPR

performance for DWT systems, whereas

the dashed lines represent the same for

DCT systems. It can be observed from the

graph that both DCT and DWT systems

with companding have at least 1.9 dB less

PAPR than the systems without

companding and the systems with

exponential transform have 1.3 dB less

PAPR than that without any transform.

3 CONCLUSIONS

In conclusion, the huge difference (20-

40dB/rad/sample) in PSD between the

received signals which were transmitted

with the same input power leads to the

observation that DWT system has much

better signal to noise ratio. Moreover, the

DWT-OFDM system with 64QAM using

Rayleigh with Jakes spectrum

demonstrates to have higher bandwidth

efficiency when compared to the DCT

OFDM system under exactly same

conditions. However, the DCT-OFDM

seems to have better than PSD signal

using the AWGN and Rayleigh with

Gaussian spectrum. This means the

spectrum for this system will have smaller

side-lobes and so will be immune to inter-

symbol interference (ISI). Significant

reduction of PAPR was obtained in

systems using companding signal, i.e. 1.9

dB less PAPR than the systems without

companding. Also, systems using

exponential transform achieved1.3 dB less

PAPR than without any transform. These

performance figures lead us to believe that

the proposed combination of DWT-

DAPSK system with companding or

exponential transforms should be best

suited for the next generation mobile

communication networks.

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