QPSK System Simulation - · PDF file01/08/2010 · QPSK System Simulation Page 3 1.0...

QPSK System Simulation

Dr. Stavros Georgakopoulos

Digital Communication Systems II

Florida International University

April 21, 2011

Jovan Robinson

Hassan Chaudhary

Napalys Juodzevicius

David Sanchez


Table of Contents 1.0 Abstract................................................................................................................................................. 3

2.0 Introduction .......................................................................................................................................... 3

3.0 Theory ................................................................................................................................................... 8

4.0 Project Objectives ............................................................................................................................... 13

5.0 Proposed Methods.............................................................................................................................. 14

6.0 Results................................................................................................................................................. 20

7.0 Conclusion........................................................................................................................................... 27

8.0 References .......................................................................................................................................... 28


1.0 Abstract Digital communications is an emerging industry in today’s engineering world.

Communication methods have been generated and applied since the beginning of time. Since

the invention of the first communication device, telegraph in 1844 by Samuel Morse,

communication has come a long way. With new technologies developed by engineers who

makes the day to day life has become easier. There are two types of communication schemes:

Analog and Digital communication. The difference between these two schemes is that the

analog signal is continuous and digital signal is discrete. Today’s communication engineers try

to find the best way to resolve the scarce resource of frequency spectrum. There are many

advances engineers have made throughout the years. Various types of modulations have been

implemented in current systems. Each of these modulations has different bandwidth

efficiency.

Quadriphase-Shift Keying (QPSK) has a more efficient use of bandwidth since it

transmits data in both phase and quadruture channel. QPSK can be modeled as the sum of two

Binary Phase Shift Keying Modulation (BPSK). Furthermore, both of these systems have the

same bit error rate. The difference is the amount of bandwidth utilized by both systems; BPSK

utilizes twice the bandwidth used by QPSK.

The purpose of this project is to identify the main characteristics of a QPSK system and

implementing them with software simulation. This will give a clear understanding of how the

system functions and the theory behind each component.


2.0 Introduction

The QPSK system can be divided in three different subsystems: Transmitter, Channel

and Receiver. Each of these subsystems completes a different function for the system to be

reliable. First, the transmitter inputs a set of Binary numbers. Then these binary bits enter an

encoder to then convert the series to enter both the in-phase and quadruture channel

multiplying it with the oscillator. The receiver than receives this QPSK signal and multiplies

them with the oscillator with a -90° phase shift. This signal is send to a low pass filter to

attenuate any high frequencies within the system. Moreover, this signal is sampled and goes

through a decision making device. Finally, it converts the signal from parallel to serial to receive

the same signal as intended by the user.

Quadrature Phase-Shift Keying Applications

QPSK modulation is widely used in communications industry. It may be applied

whenever low bit error rate is required and high energy per symbol level is not possible. Three

typical areas of QPSK application are satellite, fiber optics, and Bluetooth technologies.

QPSK in Satellite Communications

Because of its robustness QPSK is well suited for the digital satellite communications.

Digital television standard called Digital Video Broadcasting (DVB) is an internationally adopted

open standard. DVB standards are set by the organization called DVB Project. It contains more

than 270 members worldwide. Though it is not used in the United States, it is widely adopted in

Europe, Asia, and Australia. DVB distribution systems include satellite (DVB-S), terrestrial (DVB-

T2), cable (DVB-C). One of the most common modulation schemes used by these distribution

systems is QPSK.


Figure 1 JXDH-6002-6 QPSK Demodulator

Figure 1 illustrates the component used for receiving and transferring DVB-S

satellitechannels to Transport Stream (TS) signal. Chengdu Jiexun Electronics Co., Ltd.

QPSK in Fiber Optics Communications

Fiber optics technology is crucial for today’s communication systems. Because of its

significant advantages over copper network lines, fiber optics have become the main

technology for the long distance, high capacity core communication lines. Traditionally, fiber

optics until very recently has been using simple On-Off keying to transmit digital information

(zeros and ones), without the need of more advanced modulation schemes often used in other

communication systems. The reason for it was the inherent efficiency and broadband capability

of fiber optic technology. Today, with rapidly increasing demand for more bandwidth, network

engineers are beginning to look at more complex modulation schemes that would allow faster

transmission rates over existing fiber optic lines. This is where QPSK and other modulations are

applied. Specifically, QPSK variant called Dual Polarization QPSK (DP-QPSK) seems to be a

modulation standard applied to the newly developing 100GHz fiber networks. Dual polarization

enables the transmission of more channels on a given fiber by supporting a signal in two


polarizations. It is essentially a combination of two QPSK signals that are transmitted on the

same frequency but they are polarized 90 degrees from each other to minimize their

interaction.

Figure 2 DP-QPSK modulation scheme. NORDUnet A/S

DP–QPSK system requires a coherent receiver. In the past, optical devices recognized

signals by detecting the intensity of the light, which was switched on and off by way of using a

more basic modulation format known as On–Off keying. The typical receiver operates much like

a simple envelope detector AM radio, whereas coherent receiver requires local oscillator. The

oscillator is tuned to the frequency of the incoming signal and only extracts that information.

The coherent receiver has to be able to lock onto both the frequency and phase of the DP–

QPSK signal in order to accurately recover the incoming bits. The great benefit of this system is

its capability to transmit four times the amount of data over existing fiber. In fact, the

equipment would be dealing with a signal that is four times slower than typical, and incoming

information can be processed by commonly available digital signal processing (DSP) technology.


Figure 3 High Performance parallel driver designed for 100 GHz DP-QPSK long haul optical transmitters. Gigoptics, Inc.

QPSK in Bluetooth Communications

Bluetooth technology is a radio signal technology which uses spread spectrum and

frequency hopping. It splits the bandwidth into 79 smaller bands and transmits portions of data

through each channel, thus allowing 2 to 3 Mbps transmission rates. Older Bluetooth versions

were modulated using Gaussian Frequency-Shift Keying, which was later replaced by a QPSK

variant called Differential QPSK (DQPSK). DQPSK is designed to alleviate any phase ambiguity

that might be caused by a phase shift in the transmission channel and it also improved data

throughput from 1Mbps to 2Mbps.

Figure 4 Bluetooth Headset. Nokia Corporation


3.0 Theory

Communication, with respect to the telecommunications field, is process that facilitates

the transmission of a message signal across some medium to a designated receiver. The type of

communication studied in this project is of the digital variety. In this scheme (shown below), a

discrete sequence of 1’s and 0’s representing the original signal is converted (modulated) to a

form that allows it to travel across the medium.

Figure 5

When comparing this method of transmission to its counterpart, analog communications,

digital communication have several key advantages: performance, reliability, integration with

other DSP techniques, security, and efficiency.

Band-pass Assumption

Digital communication schemes generally comprise of a device that transmits a

collection of pulses that represent the digitized information. Ideally, the pulse can be best

modeled with the sinc function (shown below). It is important to note that the main lobe of the

sinc function’s peak is equal to the square of the transmitted signal energy per bit.


Figure 6

Alternatively, we can take the Fourier transform of the sinc pulse to obtain its frequency

response shown below. This ideal pulse shape mirrors that of a band pass filter in principle. This

implies that the overall transmission system has some minimum bit rate, Tb.

Figure 7

Nyquist Channel


As stated above, digital communication schemes take in a bit stream, modulates it, and

sends the modulated wave across the channel. At the receiver, however, a number of things

can occur. Due to imperfections in the frequency response of the filter, deviations between the

sent and received messages can occur. One way of dealing with this involves requiring the

system to have a minimum transmission bandwidth contingent upon the rate at which the bits

are being sent and received. Using the fact that this transmission scheme is of the band pass

variety, we can infer that if we set the bandwidth equal must be chosen in such a way to

prevent the sinc pulses from overlapping. Specifically, the bandwidth must be 1/2Tb where Tb

is the reciprocal of bandwidth.

Phase Shift-Keying

Phase shift-keying (PSK) is a digital band-pass communication method that represents

bits through the phase of a cosine wave. The modulated wave s(t) is sqrt(2E/ Tb)*cos(2*pi*f*t

+phase) where E is the transmitted energy per bit. In general, the PSK is generated by

converting the stream to a constant amplitude using the non-return-to-zero encoder. This

device only allows transitions of the input bits to be between a positive or negative constant.

The converting stream is then modulated with the cosine wave sqrt(2E/ Tb)*cos(2*pi*f*t

+phase) to produce the PSK signal. A General illustration of a PSK modulator is shown below.

This modulator is the simplest variety of the PSK’s—Binary Phase Shift-Keying(BPSK). The

system uses the phases 0 and 180 degrees to represent 0 and 1. The bandwidth minimum

required for this type of transmission is 2/Tb.


Figure 8

Quadrature Phase Shift-Keying (QPSK) is a modulation scheme where 4 phases are used

in the transmission of a 2 bit word (00,01,10,11). This signal is represented by the function

sqrt(2E/ Tb)*cos(2*pi*f*t +phase) where the phase is equal to 45, 135, 225, or 270. In terms of

generation, QPSK is essentially 2 BPSK’s put together. Shown below, the 2 BPSK’s differ by its

amplitude and by the phase 90 degree phase shifted oscillator.

Figure 9


In theory, the QPSK is said to be more efficient than BSK in terms of utilization of the channel.

Specifically, 1 more bit is sampled at the output every sampling instant when u compare it to

BPSK. Hence, the bandwidth of this QPSK is one half of that of the BPSK transmitter.

QPSK Detection

Detection of the QPSK is done so by coherent detection. In this scheme a signal is

product modulated with a local oscillator and then low-pass filtered. From there (shown

below), the

Figure 10

Filtered signals In the In and Q channels are compared to some threshold at a rate equal to the

sampling rate.

Detection of QPSK in Noise

Similar to the above receiver, this receiver takes in the signal multiplies it with a local

oscillilator and filters out the high frequency terms (integrate and dump).


Figure 11

The integrate and dump step takes the product of the I or Q and the local oscillator computer

the integral during the sample period. After it computes the integral, it sends the value to the

threshold comparison and dump(resets) the old value for the next sample period.

4.0 Project Objectives

The team has decided to work with QPSK system and implement a transmitter, channel

and receiver. The team is composed of 4 members of Florida International University Electrical

Engineering graduate program. Each team member will contribute their expertise and the

knowledge attained during their studies and work experience. As a team, we have been asked

to submit a report detailing objectives, theory, design methods, conclusion and references

utilized during the team’s research. This project will enhance each member’s ability to design

the elements of a true communications system. Software implementation will simulate how a

communications system must perform.


5.0 Proposed Methods

In this section, we will implement a QPSK transmitter, channel, and receiver. The proposed

QPSK transmitter can be seen below in Figure 12. Using Matlab’s Simulink environment, we

have designed a digital algorithm which is discrete in time and amplitude. The prerequisites for

this transmitter are such that the user owns an analog to digital converter. For this simulation,

we assume the ADC is an 8-bit ADC.

Figure 12

Information signal such as voice or other communication information, one can use an

analog to digital converter and convert each instance of time into an integer representation

based on the ADC possessed by the user. Once we have this information, we use a cast type

transformer to transform the integer data type and conformity to an unsigned 8-bit integer. At

QPSK Transmitter

EEL5501 - QPSK Project

Hassan Chaudhary


Jovan Robinson

David Sanchez

TX RF Out

bit-2

u(2)

bit-1

u(1)

Unbuffer 8-Bits

Rate Transition1

RT

Rate Transition0

RT

DATA

Ts = 1kHz

@1 Byte (8-bits)Tb=8kHz

Quadrature

Phase

Shift

In -90'

Non-Return

to Zero

Line Encoder

u*2-1

In-Phase

Local Osscilator

Fc = 24kHz

DSP

In-Phase

Frame to Sample

To

Sample

DaTC

uint8

Byte to

Bit-stream

Integer to Bit

Converter

Buffer 2-bits

[2x1]

[2x1]

[2x1]

8

[2x1]


that moment in time, the user now possesses all the information required for RT PSK

transmitter to work. We first start off by taking this integer and converting it into a bit stream.

In an 8-bit integer, we of course will have eight bits to the byte and must initilsile the process

for this to happen. We serialize the byte frame of into singular bits. Once we have serial bits, we

need to transform them into a physical quantity such as voltage. For this to happen, we use a

non-returned to the zero line encoder. At this moment in time we will have the zeros and ones

transformed into 1 V and -1 V respectively. In order to accomplish this in a Matlab simulator

environment we presumed a random data set. The first set of block shows the transformation

all the way through non-returned to zero line encoder. With this information we go ahead and

perform a diabetic transformation to the serial input. We take two serial samples and convert

them into one symbol composed of two bits. We take the first bit, and perform an in-phase

BASK. The in-phase component simply takes the bit signal of 1 V or -1 V and multiplies this by a

local oscillator. In our simulation we used 24 kHz cosine for the QPSK carrier. We derive the

quadrature local oscillator, by base shifting the cosine wave by 90°. Similarly we multiply the

quadrature local oscillator by the secondary input bit which may be -1 V or 1 V. At this point we

subtract the quadrature component from the in-phase component. The output of such a

subtraction provides us with the QPSK signal.


Figure 13

Timing is key to the simulation. Not only is bit-time important, the sampling and rate

transition timing is crucial as well. Figure 14 shows the raw bitstream alongside the buffered

and unbuffered decomposed symbol: bit0 & bit1. Each of these bits has its own QPSK which can

be seen the third plot in Figure 14.

Spectral analysis of the serial bitstream (which is the bit stream before the serial to

parallel conversion) confirms the main frequency component of the bitstream is in 8 kHz pulse

per bit. Harmonics and aliases in the spectrum can be seen from DC all the way through to

infinity. Clear separation of 8 kHz per side lobe can be seen in Figure 14.


Figure 14

Figure 15

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

-70

-60

-50

-40

-30

-20

-10

0

10

20

Input bitstream spectrum

Tb = 8kHz

Frequency (MHz)

Ma

gn

itu

de

-sq

ua

red

,dB

m

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-70

-60

-50

-40

-30

-20

-10

0

10

20

QPSK Output (Spectrum)

Frequency (MHz)

Ma

gn

itu

de

-sq

ua

red

,dB

m


Figure 16

Taking that serial bit stream, we performed the QPSK modulation as described in Figure

13. The output spectral power density can be seen in Figure 15. Clearly the 24 kHz carrier is

visible as well as the infinite side lobes. The side lobe bandwidths are approximately 4 kHz each,

and the primary carrier lobe has a bandwidth of 1/Tb. The following figure, Figure 16, closes in

on the DC through 50 kHz. The spectrum observed is a textbook definition of QPSK.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

-70

-60

-50

-40

-30

-20

-10

0

10

20Fc = 24kHz

QPSK Ouput (Spectrum)

Main Lobe Bandwidth is 8kHz

Frequency (MHz)

Ma

gn

itu

de

-sq

ua

red

,dB

m


Figure 17

Next we implement the QPSK receiver. During the design of this DSP algorithm, we

realized how important it is to have a coherent receiver. If the receiver local oscillator has a

phase shift, phi, the received signal will multiplied by the cos(phi). Similar to the transmitter

receiver takes the incoming modulated QPSK RF and multiplies it by an in phase local oscillator

as well as a quadrature local oscillator. Due to the mathematics of this multiplication, the

cosine at the carrier frequencies will diminish. In the quadrature component, the sine waves,

will also diminish leading a double frequency component. By implementing a one cycle buffer

of the double frequency and integrating or digitally summing those samples we reduces the

double frequency to exactly 0. Once this happens we take each bit which is coming in parallel,

and concatenate them to form a serial vector. This vector will then be unbuffered to conformed

to a serial bitstream. The receiver then goes on to take eight bits and converts them into

integers. In this receiver, we assume that the receiver is exactly coherent and uses some phase


Hassan Chaudhary


Jovan Robinson

David Sanchez

QPSK Reciever

orignal code

1

inPhase

lo

Fc = 24kHz

DSP

buffer 1 cycle.

buffer 1 cycle

Unbuffer

Sum of

Elements2

Sum of

Elements1

QuadraturePhase

Shift

In -90'

Matrix

Concatenate

2

Math

Function

uT

In-Phase

Integrate and dump

Gain

-1

Frame to Samples1

To

Sample

Frame to Samples

To

Sample

8-Bit to Integer

Bit to Integer

Converter

QPSK in

1

[168x1]

[168x1]

[1x2]

[1x2]

[2x1]


locked loop technique or other technique to remain coherent. Figure 17 shows the top-level

implementation of this algorithm.

6.0 Results

For a more detailed analysis, we look to Figure 18. Figure 18 displays three-time scopes:

scope one represents the parallel bits as well as the QPSK modulated RF output from the

transmitter and is received in the receiver. As soon as the RF QPSK is received into the receiver,

the receiver multiplies by the in phase and quadrature local oscillator respectively. The middle

scope shows the original bits with a double frequencies superimposed on them due to the in-

phase and quadrature multiplication. Surprisingly after an integrator (which acts as a low pass

filter at every double frequency time period), the third scope shows the original signals quite

intact. There is however a byproduct of the integration and dump component. There is an

apparent phase shift as seen in the third scope with respect to the first scope. This represents

the information coming into the receiver inducing a timeshift upon exit of the information.


Figure 18


Figure 19

Spectral analysis of the signal after the QPSK is multiplied by the local oscillator on the

receiver can be seen in Figure 19. On the left you can see bits zero and bit one. On the right you

can see the spectrum after the integrate and dump process. We can clearly see a double

frequency component's spike at the spectrum before the integrated dump filter. After only

applying integration in digital domain, we can see a spectrum no longer contains the 48 kHz

double frequency component. We are left with what seems to be an allianced pulse wave. Each

of the two bits clearly has a bit frequency of 4 kHz. Once combined, they will form a timing of

1/8kHz.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-80

-60

-40

-20

0

20

Frame: 17

Bit-0 Power Spectral Density

Bit-1 Power Spectral Density

Frequency (MHz)

Ma

gn

itu

de

-sq

ua

red

,dB

m

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

-80

-60

-40

-20

0

20

Double Frequecy due to cos^2Carrier frequency no longer present

Double Frequecy due to cos^2Carrier frequency no longer present

Frequency (MHz)

0 2 4 6 8 10 12

-10

0

10

20

30

40

50

60

Bit-0: Post Integrate and Dump PSD

Bit-1: Post Integrate and Dump PSD

Frequency (kHz)

Ma

gn

itu

de

-sq

ua

red

,dB

m

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-80

-60

-40

-20

0

20

Frame: 17 Frequency (MHz)

Ma

gn

itu

de

-sq

ua

red

,dB

m

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

-80

-60

-40

-20

0

20

Frame: 17 Frequency (MHz)

Magnitude-s

quare

d,

dB

m

0 2 4 6 8 10 12

-10

0

10

20

30

40

50

60

Frame: 7 Frequency (kHz)

Ma

gn

itu

de

-sq

ua

red

,dB

mDouble Frequecy due to sin^2

Carrier frequency no longer present


We next analyzed the QPSK from a system-level perspective. Until now we have

neglected the issues with noise and assume a perfect transmitter, receiver and channel. In the

following section, we will take into account the effects of an imperfect channel.

Figure 20

The top level diagram of the system can be seen in Figure 20. In a QPSK system, a

symbol is received to the transmitter is then forwarded to a transmit filter. On the receiver, side

a receive filter is also implemented to try and match the original signal and reduce noise and

temporal distortions.

Due to a noisy channel, these filters are necessary to maximize all gains and minimize

errors. The perfect channel would of course be the Nyquist channel, however in this scenario

we take into account a channel with white noise. Such a channel has a constant spectral

density. In our simulations we forced the energy per bit her noise spectral density to be 12 dB,

System Level QPSK


Hassan Chaudhary


Jovan Robinson

David Sanchez

Noisy ChannelForced Eb/N0 = 12dB

Random Symbol

M=4

Random

Integer

QPSK

Transmitter

QPSK

QPSK

Reciver

QPSK

Normalized Raised Cosine

TX Filter

Roll-Off Factor: 0.3

Normal

Normalized Raised Cosine

RX Filter


NormalSymbol

Decoder

Constant (White) Spectral Density

w/ Gaussian Amplitude

AWGN


this way we can scrutinize a poorly received signal with a lot of added white Gaussian noise and

see what the effects are.

The specific filter used for our simulations was a raised cosine transmit and receive

filter. Essentially this is a low pass filter with finite impulse response using a rolloff factor of 0.3.

As opposed to an infinite impulse response filter (IIR) such as Chevychev or Butterworth, a finite

impulse response (FIR Filter), is linear in phase. The said filter’s magnitude response and phase

response can be seen on the left in Figure 21. This is the normalize response of the filter. The

impulse response in the time domain can also be seen on the right.

Figure 21

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-60

-50

-40

-30

-20

-10

0

10

20

Normalized Frequency ( rad/sample)

Magnitude (

dB

)

Magnitude (dB) and Phase Responses

Raised-Cosine Transmit and Recive Filters


-15.8005

-13.7924

-11.7842

-9.7761

-7.768

-5.7599

-3.7517

-1.7436

0.2645

Phase (

radia

ns)

0 10 20 30 40 50 60

-0.2

0

0.2

0.4

0.6

0.8

1

Samples

Am

plitu

de

Impulse Response


Figure 22

Most QPSK systems either use binary coding or grey coding, we used binary coding in

our system due to its simplicity. Figure 22 shows the eye diagrams as well as the constellation

diagrams. After the transmitter receives a specific symbol, it proceeds to output QPSK through

the raised cosine transmit filter. On the left-hand side, both the in-phase/quadrature and polar

representations at the device output of the transmitter are analyzed. Due to a 12dB Eb/No, we

see very noisy eye diagram after the transmitter has passed the modulated signal. Here is

where the receiver raised cosine filter shines the greatest. As a constellation diagrams show,

the trivial scenario with a voltage of -1 V and 1 V portrays an extremely noisy cloud at each of


the four symbols. After the receive filter we see a very tight noise cloud with an extreme

separation per symbol.

Finally, the received symbol is seen after the QPSK demodulator has processed the

received signal. Figure 23 clearly portrays the accuracy and timing of the original signal. There

seems to be a huge transient at the output of the QPSK demodulator possibly due to digital and

filter errors. However overall, the system seems to be performing well with a slight phase shift.

Figure 23


7.0 Conclusion

By doing this project at the digital and sampled level, two important factors clearly rose above

all others.

Firstly, we have now learned firsthand how important it is to have matching filters; especially in

phase modulation techniques like QPSK. One cannot use conventional IIR filters, and must use linear

phase FIR filters such as the ones used in our simulation. The IIR filters may not allow sharp

discontinuities in the carriers phase in QPSK signal. They will induce harmonics and output non-linear

phase shifts making them very difficult to correct via the integrate and dump process. With FIR, the

QPSK demodulator can easily recover the original signal.

The second important factor learned was the importance of coherency. This concept was for us

as a team in class to us, however, we underrated it during class lectures. Without a coherent and stable

local oscillator at the receiver side, there really cannot be any communications. The development of

such a method to lock onto the incoming carrier was underappreciated prior to doing this project. We

now hold this concept with much more esteem. This point cannot be overstated enough.

In conclusion, the team was able to successfully simulate a complete QPSK system with visible

results. This project experience was helpful to all the team members; it provided huge insight of how

communication systems mechanism works. The team clearly understood how each component is

integrated and how each team member provided their specific knowledge for the benefit of the project.

In addition, no major setbacks occurred within the team during the design process. Since the assigned

date everybody had a clear idea of their specific responsibilities.


8.0 References

An introduction to digital and analog communications . 2nd ed. S.l.: Wiley, 2006. Print.

Breach, Tony. "40 G and 100G Overview." NORDUnet. N.p., 20 Mar. 2009. Web. 10 Apr. 2011.

<https://wiki.ndgf.org/download/attachments/10355162/40G+and+100G+Overview+-

+Report.pdf>.

"DVB - Digital Video Broadcasting - Home." DVB - Digital Video Broadcasting - Home. N.p.,

n.d. Web. 10 Apr. 2011. <http://www.dvb.org>.

"Jiexun Electronics." Chengdu Jie Xun Electronics. N.p., n.d. Web. 11 Apr. 2011. <www.jie-

xun.com/en>.

" Nokia USA - world leader in cell phone industry ." Nokia USA - world leader in cell phone

industry . N.p., n.d. Web. 11 Apr. 2011. <http://www.nokiausa.com>.

"Semiconductor Technologies for Optical Interconnection." GigOptix. N.p., n.d. Web. 11 Apr.

2011. <www.gigoptix.com/component/k2/item/download/8.html>.

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