project summer internship2

SUMMER INTERNSHIP PROJECT REPORT

ON

TO GENERATE PRN/TRUNCATED PRN SEQUENCE AND ANALYSE THE PROPERTIES USING LAB VIEW

AMITY SCHOOL OF ENGINEERING & TECHNOLOGY.

Under the valuable guidance of

Dr. P. Banerjee

AMITY UNIVERSITY,

UTTAR PRADESH

SUBMITTED BY:-

NAME : MANISHA SHARMA

ENROLLMENT NO. :A2326612002

PROGRAMME: M.TECH (W.C.)

CERTIFICATE

On the basis of declaration submitted by MANISHA SHARMA , student of M.Tech (Wireless Communication), we hereby certify that the project titled “TO GENERATE PRN/TRUNCATED PRN AND TO STUDY THE PROPERTIES USING LAB VIEW” which is submitted to

Department of Electronics and Communication, Amity School of Engineering and Technology,

Amity University, NOIDA, Uttar Pradesh in partial fulfilment of the requirement for the award of

the degree of Master of Technology in Wireless Communication, is an original contribution with

existing knowledge and faithful record of work carried out by her under my guidance and

supervision.

To the best of our knowledge this work has not been submitted in part or full for any Degree or

Diploma to this University or elsewhere.

Dr. P. BANERJEE

Dept. Of ECE

ASET

2

ACKNOWLEDGMENT

I , sincerely , acknowledge with sincere thanks contribution of Dr. P. BANERJEE, in guiding

the preparation of Summer Internship Project . I also acknowledge with sincere thanks , to the

contribution of Ms. NEERU AGARWAL who helped and guided me in the finalization of the

Project .

I, sincerely thank them for the guidance and help provided by them in the completion of this

Project .

MANISHA SHARMA

M.TECH. (W.C.)

3

DECLARATION

I, MANISHA SHARMA student of M.Tech (WC) hereby declare that the Summer Internship

Project titled “TO GENERATE PRN/TRUNCATED PRN AND TO STUDY THE PROPERTIES USING LAB VIEW” which is submitted by me to Department Of ECE, Amity School of

Engineering and Technology, Amity University Uttar Pradesh, NOIDA, in partial fulfilment of

requirement for the award of the degree of Master of Technology in Wireless Communication ,

has not been previously formed the basis for the award of any degree, diploma or other similar

title or recognition.

NOIDA

DATE Name and signature of Student

4

ABSTRACT

A very dynamical development of virtual instrumentation in recent years has

caused a very good acceptance of this concept and its use in many applications.

This concept, as one flexible and cost-effective solution for test and

measurement, is used in this project for implementation of maximum length

pseudorandom noise sequences(PRN) and their truncation. Because of their

properties, the pseudorandom binary sequences are often used in development

and improvement of modern pseudorandom position encoders as well as in

testing of some sensors, analog-to-digital converters, etc.

Also the PRN codes act as spreading codes in the spread-spectrum

communications system. Sometimes there is a need to shorten the PRN

sequence to decrease the acquisition time and to match the data field size in

frame structures . Some properties of truncated PRN sequences will be studied

keeping in mind its application in communication system 9 stage shift registers will

be used to implement in Lab View .

Key words: virtual instrument, pseudorandom noise sequence

5

Table Of Contents

S.NO. TITLE PAGE NO.

1. INTRODUCTION 8

2. NI Lab View: A BRIEF VIEW 10

3. GENERATION OF PSEUDORANDOM BINARY SEQUENCE OF MAXIMUM LENGTH

13

4. 511 PN SEQUENCE GENERATION 16

5. TRUNCATED PSEUDO RANDOM NOISE SEQUENCE 18

6. AUTOCORRELATION PROPERTIES 22

6. CONCLUSION 29

7. FUTURE WORK 30

8. REFERNCES 31

6

INTRODUCTION

The vision of virtual instrumentation changed and improved the way engineers

and scientists work, delivering solutions in less development time, with lower

costs, and greater flexibility. It can be noted that virtual instrumentation has had a

constant and extensive development regarding hardware and software and was

widely adopted mostly in test and measurement areas in the last decade. Of

course, the main catalyst of that development is a very dynamical development of

computer techniques and digital electronics. The presence of virtual

instrumentation in industry, education, everyday life etc, is getting wider each day.

The virtual instrument concept offers the possibility for an engineer to use flexible

and powerful software running on a computer combined with instrumentation

hardware to define a custom test and measurement solution. The development of

virtual instrumentation enables a series of new possibilities in the field of

measurement techniques, research work, etc. What is important is the fact that

virtual instruments are significantly cheaper than traditional. They are also very

flexible, i.e. have a possibility of simple modification and upgrading. The good

properties of virtual instruments are modularity and hierarchy, i.e. the possibility of

dividing a complex task into simplier problems and their separate realizations and

testing, and connecting them to complex virtual instrument. Virtual instrumentation

also offers a possibility of communication with traditional instruments through an

appropriate interface, which is widely used in development and during realization

of virtual and remote laboratories.

There are different development tools and environments for realization and design

of virtual instruments. One of the most often used and widespread is LabVIEW, by

National Instruments , which as a graphical development platform enables

7

intuitive and simple development without the need for serious previous

programming knowledge. The programming is performed by a graphical

programming language, which is easier for learning and debugging than textual.

The pseudorandom binary sequences (PRBS) are a useful type of periodic

signals, which have the following properties: 1) the signal is bipolar, series of 1’s

and 0’s; 2) the PRBS is a deterministic repeatable signal; 3) the PRBS exhibits a

uniform power spectral density over a wide frequency band; 4) according to the

“window property” of PRBS of

length 2n-1, any n-bit code word obtained by a window of width n, is unique and

may fully identify the window’s absolute position p relative to the beginning of the

sequence. This is used in pseudorandom absolute encoders.

The area of PRBS application is wide, for example, during design and testing of

pseudorandom position encoders, then for testing of measurement transducers ,

AD converters testing , in the field of communication , measurement of frequency

response , navigation systems, scrambling, cryptographic applications, etc. Other

applications are found in surface characterization and 3D scene modeling, and in

audio applications to measure the properties of loudspeakers.

The generation of pseudorandom binary sequences can be implemented in

different ways, including using a discrete shift register and flip-flops, using a

microprocessor, using a FPGA-based implementation ,MATLAB etc. However,

methods of pseudorandom binary sequences generation based on virtual

instrumentation concept are presented in this project.

8

NI Lab View: A Brief View

LabVIEW is a highly productive development environment that engineers and

scientists use for graphical programming and unprecedented hardware integration

to rapidly design and deploy measurement and control systems. Within this

flexible platform, engineers scale from design to test and from small to large

systems while reusing IP and refining their processes to achieve maximum

performance.

It is a graphical programming language that uses icons instead of lines of text to

create applications. In contrast to text based programming languages, where

instructions determine program execution, LabVIEW uses dataflow programming,

where the flow of data determine execution order.

It consists of two main blocks: BLOCK DIAGRAM & FRONT PANEL.

1. BLOCK DIAGRAM:

Block diagram objects include terminals, subVIs, functions, constants,

structures, and wires, which transfer data among other block diagram

objects.

9

Example of a Block Diagram window

2. FRONT PANEL:

The front panel window is the user interface for the VI.

Example of a Front Panel Window

10

LabVIEW programs are called virtual instruments, or VIs, because their

appearance and operation often imitate physical instruments, such as

oscilloscopes and multimeters. LabVIEW contains a comprehensive set of tools

for acquiring, analyzing, displaying, and storing data, as well as tools to help

troubleshoot code we write.

11

GENERATION OF PSEUDORANDOM BINARY SEQUENCES OF MAXIMUM LENGTH

The pseudorandom binary sequences of maximum length can be generated by

using shift register which is composed of n flip-flops and appropriate feedback

connections. The order of binary zeros and binary ones depends on feedback

configuration.

With a proper selection of feedback, a pseudorandom binary sequence of

maximum length m = 2^n- 1 is generated, where n is the number of stages in the

shift register. Also, it does not matter which state is considered to be initial, if state

"zero" is turned off. In the configuration of pseudorandom sequence generator

using exclusive-OR (XOR) gates is not allowed to appear the state where all

outputs of shift register are zeros, because 0XOR 0 = 0. A properly selected

feedback provides a generation of pseudorandom sequences of maximum length,

m = 2^n- 1. The sequences are deterministic, but exhibit noise properties similar

to randomness.

Example of linear feedback shift register

A PN sequence has three following properties:

· The number of ‘1’s and the number of ‘0’s in a PN sequence are only different by

12

one (BALANCE PROPERTY).

· Run lengths of zeroes or ones are the same as in a coin flipping experiment.

Half of the run lengths are unity, one-quarter are of length two, one-eighth are

of length three and a fraction 1/2n of all runs are of length n (RUN

PROPERTY).

· If the sequence is shifted by any non-zero number of elements, the resulting

sequence will have an equal number of agreements and disagreements with

the original sequence (AUTOCORRELATION PROPERTY).

The BLOCK DIAGRAM of the realized virtual instrument using a LabVIEW 11.0

software environment is shown in Fig.

Here a 15 bit pn sequence is generated using 4 Linear Feedback Shift Registers.

Block Diagram of 15 length PN sequence

13

Following PN code is generated on the Front Panel of the LAB VIEW.

PN CODE:

WAVEFORM:

The above generated pn code is satisfying all the properties of the pn sequence:

1. No. of 1’s (= 8) > No. of 0’s (= 7) , balance property is satisfied.

2. Total no. of runs = 8.

Half the no. of runs (=4) are of length, 1 i.e. 0,1,0,1.

One-quater (=2) are of length 2 ,i.e. 11 & 00.

One-eighth (=1) are of length 3 i.e. 000.

Hence Run property is satisfied.

3. If the sequence is shifted by any non-zero number of elements, the resulting

sequence will have an equal number of agreements and disagreements with

the original sequence.

1 1 1 0 1 0 1 1 0 0 1 0 0 0

14

1 1 1 1 0 1 0 1 1 0 0 1 0 0

a a a d d d d a d a d d a a

Hence Autocorrelation property is satisfied.

NOTE: In the developed solution, for a given length of shift register, the

generation mode of pseudorandom binary sequences can be selected, i.e. if

generation is done by using XOR gates or XNOR gates.

15

511 PN SEQUENCE GENERATION

With reference to the previous 4 bit PN sequence , we will now generate a 9-bit

PN sequence ,which will result in a 511 length sequence.

A nine-element shift register is placed on a While Loop. An exclusive OR gate is

used whose inputs have been wired to Q5 and Q9. The loop index keeps track of

the cycle count, and it stops when the output becomes equal to the initial value.

An initial seed is set at starting of the process and each shift registers on the loop

are initialized.

The parallel output can be observed either on LED indicators or in addition, a

pseudo-random sequence of ones and zeros can be produced at Serial Out.

Following is the block diagram of 9-bit PN sequence.

Block Diagram of 9-bit PN sequence

16

In this code the tapping is done from 4th and 9th shift register and then xoring them

. This output is then fed back to the 1st register . The code length and the seed

value are 511.

The output of the set up is observed on the waveform chart on the Front Panel of

LAB VIEW, as follows.

The 511 PN code is very large to be obtained , hence plotting the waveform is

more convenient and moreover it gives a better view.

This sequence also satisfies all the three basic properties of the PN sequence like

the previous one.

17

TRUNCATED PSEUDO RANDOM NOISE SEQUENCE

The PN sequences are not truly random but these codes have a very good

correlation properties and nearly ideal properties similar to those of a sequence of

independent and identically distributed binary random variables. These properties

are essential components in a wide variety of modern applications like radar

ranging system , code division multiple access in spread spectrum ,error

correction, cryptographic systems, and many others.

However ,the properties of randomness in PRN-sequences are strictly dependent

on their full length. Just cutting out one or few bits from the specified length can

adversely disturb the system performance.

But it may be desirable to shorten the length of sequence in some

applications .For example, for 8-stage PRN sequence the length of the sequence

is 255, whereas for 9-stage it is 511 and for 10-stage is 1023. There is large gap

in the selection of sequence length between 256 and 511 and further between

511 and 1023. Some shorter or intermediate length may be convenient to reduce

the acquisition time and still preserve the advantage of a PRN-sequence . Even

more commomnly, the PRN sequence could be shortened to fit into the data field

size in frame structures . Further , the sequence number which is divisible by 5 or

10, sometimes make the system design less complicated.

To shorten the sequence one has to delete few bits. The resulting sequences may

be called truncated PRN sequences , where the first or last few bits have been

cut. In this project the last 11 bits of 511 length PRN sequence are being removed by

using some additional blocks in that of the generation .

18

Here a “DELETE FROM ARRAY” icon from the fuction pallete is inserted in the

previous diagram and 11 bits are then removed from the 511 sequence to obtain

the 500 length sequence.

Following is the block diagram for the truncation of the last 11 cycles of 511 PN

sequence:

Block Diagram of Truncated PRN sequence

By running the above block diagram we obtain sequence in which last 11 cycles

are removed .It can be seen below the following waveform charts of the normal

PRN sequence and Truncated PRN sequence that waveform in the 2nd chart are

stopped at the 500th sequence .

19

Waveform of normal PRN sequence

Waveform of Truncated PRN sequence

20

AUTOCORRELATION PROPERTIES

After truncating the PN sequence , their autocorrelation properties are studied.

The autocorrelation Rxx(t) of a function x(t) is defined as

where the symbol denotes correlation.

Side Lobes: Side lobes occur on each side of the main lobe and approach zero at

multiples of fs/N from the main lobe.

By varying seed values the autocorrelation of TPRN and PRN sequence varied.Considering 11 bits truncation, following observations were obtained :

Polynomial: 1+D4+D9

Seed value – 000001010

Truncated bits -10010100000

Auto corr of prn seq.

Auto corr of tprn seq.

21

Seed value -001100100

Truncated bits-00001001100

Autocorr of prn seq.

Autocorr of tprn seq.

Like this by varying the seed values different results were obtained.

Also for different seed values , the peak side lobe (rms) values were

obtained .

SEED VALUES

RMS value of 11 bit truncated PRN seq.







000001010 0.0370043 0.0382634 0.0394002 0.0423284 0.0458956 0.0504004 0.065412

000010100 0.0370043 0.0383088 0.0394696 0.0422886 0.0459451 0.0503523 0.064847

000011110 0.0366342 0.0377456 0.0388889 0.0421593 0.0464451 0.0513363 0.0638377

000101000 0.0370917 0.0380528 0.0393035 0.0417395 0.0457326 0.050491 0.0641826

000110010 0.036472 0.0376255 0.0387198 0.0424381 0.0456264 0.0503924 0.064827

000111100 0.0364395 0.0375851 0.0389856 0.0423833 0.046397 0.0509999 0.0640273

001000110 0.0369723 0.0379933 0.0393229 0.0426934 0.0462311 0.0502802 0.0641556

22

001010000 0.0369914 0.0379713 0.0392606 0.0417771 0.0457438 0.0504031 0.063858

001011010 0.036906 0.0380214 0.039337 0.0425284 0.0456424 0.0501757 0.0638987

001100100 0.0365111 0.0375552 0.0386438 0.0418813 0.0455821 0.0505496 0.0638105

001101110 0.0368408 0.0378448 0.03927 0.0418813 0.0460394 0.051276 0.0627224

001111000 0.0367302 0.0381108 0.0393009 0.0423381 0.0457495 0.0506745 0.0645458

010000010 0.0365304 0.0374519 0.0385703 0.0419548 0.0462988 0.0511762 0.0633816

010001100 0.369558 0.037936 0.0393119 0.0428117 0.0461893 0.0502748 0.063593

010010110 0.036879 0.0377969 0.0388005 0.0422405 0.0467077 0.05024 0.0652596

010100000 0.0370017 0.038019 0.0392779 0.0424176 0.0458703 0.0500442 0.0654914

010101010 0.0370013 0.0379575 0.0392684 0.0422501 0.0458385 0.050224 0.06518

010110100 0.0369242 0.0381041 0.0389502 0.0420157 0.0460916 0.0504431 0.0624111

010111110 0.0368786 0.0380066 0.0393569 0.0423847 0.0458413 0.0497261 0.064987

011001000 0.0365488 0.0375788 0.0386449 0.0419035 0.0458862 0.050701 0.0636611

011010010 0.0362836 0.0375668 0.0388535 0.0423147 0.045947 0.0501409 0.0659919

011011100 0.0368138 0.0378835 0.0392758 0.0418646 0.0461018 0.0513965 0.0630117

011100110 0.0365115 0.0376227 0.0386794 0.0421193 0.0459713 0.0510394 0.0643847

011110000 0.0369034 0.0378673 0.0390262 0.0420212 0.0461074 0.0511526 0.06472

011111010 0.0369316 0.0379775 0.039338 0.0424217 0.0458928 0.0499609 0.0649271

100000100 0.0365234 0.0374558 0.0386017 0.0420226 0.0462329 0.0499609 0.0635454

100001110 0.036923 0.0378563 0.0391194 0.0420875 0.046017 0.0508255 0.0651467

100011000 0.0369077 0.0379127 0.039336 0.0427913 0.0462608 0.0502293 0.0638377

100100010 0.0369407 0.0380109 0.039143 0.0416908 0.0456894 0.0505735 0.0631078

10010110 0.0367171 0.038028 0.0391998 0.0421785 0.0458357 0.0505682 0.0647668

23

100110110 0.0363502 0.037806 0.0389444 0.042268 0.0464451 0.0513468 0.0637494

101000000 0.0369896 0.0379985 0.0393135 0.0423037 0.0458067 0.050098 0.065696

101001010 0.0369381 0.0381625 0.039302 0.0422653 0.0460217 0.0502507 0.0648069

101010100 0.0370359 0.0379961 0.0393035 0.0422941 0.0458544 0.0503977 0.0651002

101011110 0.0367899 0.0381545 0.0390294 0.0422254 0.0461679 0.050363 0.0640949

101101000 0.0365422 0.0375263 0.0389133 0.0422625 0.0464857 0.0515611 0.063559

101110010 0.0368343 0.037968 0.0392789 0.0418494 0.0459909 0.0509048 0.0628603

101111100 0.0364092 0.0375962 0.0386209 0.0419534 0.0460357 0.0514514 0.0656631

110000110 0.0367511 0.0379723 0.0391746 0.0420502 0.046167 0.0510578 0.0631215

110010000 0.0365335 0.0375417 0.0386166 0.0420143 0.0460273 0.0510289 0.0634977

110011010 0.0369107 0.0378878 0.0388916 0.0421413 0.046219 0.0510578 0.0655509

110100100 0.0371809 0.0380209 0.0391793 0.0424107 0.0464155 0.0510973 0.0629498

110101110 o.o369654 0.0378524 0.0391593 0.0422116 0.0458254 0.050379 0.0626948

110111000 0.0369914 0.0380499 0.0390346 0.0424491 0.0460254 0.0510605 0.0626948

111000010 0.0367442 0.0380309 0.039227 0.0425038 0.0461642 0.0510815 0.0626948

111001100 0.0365054 0.0376674 0.0387289 0.0421386 0.0460935 0.0510104 0.0639325

111010110 0.0366224 0.0379084 0.0393103 0.0422116 0.0459862 0.0507673 0.065696

111100000 0.0365554 0.0376712 0.0389053 0.0422872 0.0464109 0.051171 0.0650536

111101010 0.0369125 0.037895 0.0391383 0.0423257 0.0458376 0.0499259 0.0645391

From the above results further analysis was being done by plotting graphs

between the truncation and the rms values at different seed values and following

observations were being made.

Considering for few seed values:

24

tprn/

prn

seed-10 seed-

50

seed-

100

seed-

150

seed-

200

seed-

250

seed-

300

seed-

350

seed-

400

seed-

450

500/51

1

0.03700

43

0.036

47

0.0365

11

0.0368

79

0.0365

49

0.0369

32

0.0367

17

0.0367

9

0.0365

34

0.0367

44

480/51

1

0.03826

34

0.037

63

0.0375

55

0.0377

97

0.0375

79

0.0379

78

0.0380

28

0.0381

55

0.0375

42

0.0380

31

460/51

1

0.03940

02

0.038

72

0.0386

44

0.0388

01

0.0386

45

0.0393

38

0.0392 0.0390

29

0.0386

17

0.0392

27

410/51

1

0.04232

84

0.042

44

0.0418

81

0.0422

41

0.0419

04

0.0424

22

0.0421

79

0.0422

25

0.0420

14

0.0425

04

360/51

1

0.04589

56

0.045

63

0.0455

82

0.0467

08

0.0458

86

0.0458

93

0.0458

36

0.0461

68

0.0460

27

0.0461

64

310/51

1

0.05040

04

0.050

39

0.0505

5

0.0502

4

0.0507

01

0.0499

61

0.0505

68

0.0503

63

0.0510

29

0.0510

82

210/51

1

0.06541

2

0.064

83

0.0638

11

0.0652

6

0.0636

61

0.0649

27

0.0647

67

0.0640

95

0.0634

98

0.0626

95

25

Graph:

0 0.5 1 1.5 2 2.5 3 3.5 4

0.04

0.045

0.05

0.055

0.06

0.065

0.07

TRuncation in dB

RMS Value

000001010000010100000011110000101000000110010000111100001000110001010000001011010001100100

Also db plot is obtained:

26

tprn/

prn

seed-

10

seed-

50

seed-

100

seed-

150

seed-

200

seed-

250

seed-

300

seed-

350

seed-

400

seed-

450

0.0945

1

0.0370

04

0.0364

72

0.0365

11

0.0368

79

0.0365

49

0.0369

32

0.0367

17

0.0367

9

0.0365

34

0.0367

44

0.2717

9

0.0382

63

0.0376

26

0.0375

55

0.0377

97

0.0375

79

0.0379

78

0.0380

28

0.0381

55

0.0375

42

0.0380

31

0.4566

3

0.0394 0.0387

2

0.0386

44

0.0388

01

0.0386

45

0.0393

38

0.0392 0.0390

29

0.0386

17

0.0392

27

0.9563

7

0.0423

28

0.0424

38

0.0418

81

0.0422

41

0.0419

04

0.0424

22

0.0421

79

0.0422

25

0.0420

14

0.0425

04

1.5211

8

0.0458

96

0.0456

26

0.0455

82

0.0467

08

0.0458

86

0.0458

93

0.0458

36

0.0461

68

0.0460

27

0.0461

64

2.1705

9

0.0504 0.0503

92

0.0505

5

0.0502

4

0.0507

01

0.0499

61

0.0505

68

0.0503

63

0.0510

29

0.0510

82

3.8620

2

0.0654

12

0.0648

27

0.0638

11

0.0652

6

0.0636

61

0.0649

27

0.0647

67

0.0640

95

0.0634

98

0.0626

95

Graph:

27

0 50 100 150 200 250 300 350

0.04

0.045

0.05

0.055

0.06

0.065

0.07

Truncation

RMS Value

000001010000010100000011110000101000000110010000111100001000110001010000001011010001100100

Hence by observing the above results it can be concluded that the by increasing

the number of bits truncated the peak side lobe level increases but there is less

deviation for different seed values.

28

CONCLUSION

Pseudorandom binary sequences are a type of periodic signals with some useful

properties, and can be generated in different ways. The advantages of using

virtual instrumentation for generation of pseudorandom binary sequences are

pointed out in the project.

The Pseudo Random Binary Noise sequences were successfully generated and

further are truncated in NI Lab View software. The waveforms of both the

sequences are being compared. The realized PRN sequence is very flexible and

can be used widely in various fields of research work. Graphical programming

which is used for implementation of this generation is easier to learn than textual

or VHDL programming.

Autocorrelation properties of both pn and truncated pn sequence are being

studied. As truncation increases the peak side lobes also increases for different

seed valuesbut with very less deviation.

.

29

FUTURE WORK

The PRN sequences and the Truncated PRN are very widely used sequences in

various applications, so there is a lot of scope in the study of these sequences by

modifying them in different ways, like by truncating the pn sequence ,more

number of sequence can be generated, and can be implemented in different

softwares. In Lab View software, by studying the performances of these

sequences can be done and then comparing it with the simple PRN sequence.

After studying the properties further study can be done in the spectrum of these

sequences.

30

REFERENCES

1. Study on Potentiality of Truncated PRN Sequences for Communication –

P.Banerjee* , Ushaben Keshwala and Monika Kaushik

ECE ,ASET ,Amity University, Noida-201303.

2. Marco Baldi, Franco Chiaraluce, Noureddine Bounjnah, Roberto Garello,

“On the Autocorrelation Properties o\f Truncated Maximum-Length

Sequences and Their Effect on the Power Spectrum”

IEEE Trans Signal Processing, vol. 58 , no. 12, December 2010.

3. S.W.Golomb, Shift Register Sequences. Laguna Hills ,CA: Aegean Park

Press, 1981.

4. LabVIEW 8.0, User's Manual, National Instruments, www.ni.com, USA,

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5. Improved Channel Estimation Methods based on PN sequence for TDS-

OFDM ,Ming Liu, Matthieu Crussière, Jean-François Hélard Université

Européenne de Bretagne (UEB) INSA, IETR, UMR 6164, F-35708,

Rennes, France.

6. NI Lab View, Using External Code in Lab View.

7. Fundamentals of Digital Electronics ,March 1998 Edition Part Number

321948A-01 ,by Professor Barry Paton Dalhousie University

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