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

VIEW

Abstract:

In this paper the pseudo random noise sequence were generated in LabView software usning 9 bit LFSR and then these were truncated and then with different seed values ,different truncation bits the change in the properties of the sequence were also observed with mathematical and graphical analysis. Also with both the normal and truncated pn sequences obtained bpsk was also simulated and it's power spectral density was also abtained .

Index Terms:PRN Sequence, Truncated PRN Sequence, peak side lobes(rms), bpsk, power spectral density, seed value, taps, LFSR, LabView software.

Introduction:Linear Feedback Shift Registers with one or more feedbacks from the output are used to generate the PRN sequences. For a n stage shift registers a sequence will be generated which will repeat itself after a length of L= 2^n-1. Performance can be affected by truncating last few bits of the normal pn sequence but sometimes it can be benificial in terms of acquisition time and some applications. As length of 9 stage pn sequence is 511 and that of 10 stage is 1023 , so there is huge difference between this selection [1]. Hence experiments are being conducted by selecting some length in between the large gap such that properties of the resulting truncated sequence is preserved along with the acquisition time being reduced [1].

In this paper also the normal pn sequence along with the truncated sequence is being generated in LabView software using 4 stage and 9 stage LFSR .Also mathematical studies were conducted to compare their resulting autocorrelation and peak side lobe value(rms) for different seeds. Truncated prn sequences can show properties near to that of normal sequence for a particular seed value, which has many benifits as it can be used in communication and also 11 bit truncation from 511 bit sequence resulting in length of 500 will be much more easier to handle for calculation purposes [1].

LFSRs are very much important for the generation of the prn sequences, hence their models are also being extensively studied which can provide transition states of different bits of LFSR and is also capable to switch to any possible feedback connections(i.e polynomial) [2]. Many fields in communication require pseudo random sequences like error detection ,direct sequence spread spectrum (DSSS), this sequences are bein also tested for many applications like in the analysis of optical DPSK transmissions modelling [3]. The prn sequences can be generated by numerous ways like it can be generated using algebric feedback shift registers[4] , series-parallel method to generate sequence at high speeds with low-speed devices, which interests hardware designers[5]. In

mathematical terms it is the generator polynomial(primitive) of variable x that represents any LFSR to produce a maximal length sequence [6].a) M-sequence :A linear shift-register binary sequence whose length is N= 2 m − 1, where m is the degree of the generator polynomial.b) Primitive Polynomial :It is the generator polynomial of m-sequence . If g(x) is a primitivepolynomial of degree m and if the smallest integer n for which g(x) divides x^ n + 1 is n = 2 ^m − 1. g ( x ) = x^ 5 + x^ 4 + x^ 2 + x + 1 is a primitive. But g( x ) = x^5 + x^ 4 + x^3 + x^ 2 + x + 1 is not primitive as x ^6 + 1 = ( x + 1 )( x ^5 + x^ 4 + x^ 3 + x^ 2 + x + 1 ) , hence least value of n is 6 [7].

Generation of normal and truncated prn sequences:in this paper simulation model was created in LabView to generate the sequences. Following is the block diagram of 4 stage prn sequence.

This resulted in the following pn code:

and the folowing waveform:

In this generation, for a given length of shift register, the mode to generate pseudorandom

binary sequences can be done either by using EXOR gates orEXNOR gates. Here we

implemented this using EXOR gates on the block diagram of the virtual instrumentation .

The front panel is representing the code and the waveform generated respectively.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. Similarly a 511 length pn

sequence can be generated using 9 stage shift register[8]. In this a nine-element shift register

is placed on a While Loop. An EXOR gate is used whose inputs have been wired to Q5 and

Q9. The loop index keeps track of the count of loop cycle, 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 [8]. Following is the resulting waveform of 511

length prn sequence.

This sequence satisfies al the properties of a normal pn sequence like balance ,run and

autocorrelation properties. Now we can generate a truncated 500 length sequence by

removing last 11 bits from the above sequence whic in this simulation was achieved by

using a 'delete from array' block[9]. In this block we can delete any number of last elements

of the initial array.

This waveform as we can see has last bits being removed i.e. Truncated.

Mathematical Analysis:

Observations were being made by varrying the seed values and seeing their effect on the

different amount of truncation of bits eg. 11, 31, 51, 101, 151, 201, 301 etc. .

SEED RMS RMS value RMS value RMS value RMS value RMS value RMS

VALUES value of 11 bit truncated PRN seq.

of 31 bit truncated PRN seq.

of 51 bit truncated PRN seq.

of 101 bit truncated PRN seq.

of 151 bit truncated PRN seq.

of 201 bit truncated PRN seq.

value of 301 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

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

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 0.0369654 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 above analysis some of the seed values were selected to observe the effect on truncation versus normal length of the prn sequences.

seed-> 000001010

000110010

001100100

010010110

011001000

100000100

100110110

101101000

110011010Tprn/

prn

500/511 0.037004

0.03647 0.036511

0.036879

0.036549

0.03693 0.036717

0.0367 0.03653

480/511 0.03826 0.0376 0.03755 0.037797

0.037579

0.03797 0.038028

0.03815 0.03754

460/511 0.039400

0.03872 0.038644

0.038801

0.038645

0.0393 0.0392 0.03902 0.03861

410/511 0.0423 0.04244 0.0418 0.0422 0.041904

0.042422

0.042179

0.04222 0.04201

360/511 0.045895

0.04563 0.045582

0.046708

0.045886

0.045893

0..045836

0.04616 0.04602

310/511 0.050400

0.05039 0.05055 0.05024 0.050701

0.049961

0.050568

0.05036 0.05102

210/511 0.065412

0.065483

0.0638 0.0652 0.063661

0.064927

0.064767

0.06409 0.06349

The graphical representation of the above mathematical analysis is shown below. As we can see that for different seed values there is not much variation in the slope of the different truncation with respect to the normal 511 length sequence. Also the dB plot was also plotted as shown below

.

0 50 100 150 200 250 300 350

0.04

0.045

0.05

0.055

0.06

0.065

0.07

Truncation

RMS V

alue

000001010000010100000011110000101000000110010000111100001000110001010000001011010001100100

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 V

alue

000001010000010100000011110000101000000110010000111100001000110001010000001011010001100100

BPSK geneation:From both the normal and truncated prn sequences we simulated the bpsk signal and observed their respective power spectral densities

The above block diagram the bpsk is simulated as, phase of a carrier (a selected signal from waveform generator) is converted to two values according to the binary signal level. The information of the stream is contained at the point where phase changes occur in the transmitted signal.

Results Obtained:

One stream of data was selected:

and a sinusoidal carrier signal :

a) Results from normal PN sequence of length 511:

PN SEQUENCE :

SEQUENCE GENERATED ON MULTIPLYING PN SEQUENCE WITH DATA:

BPSK GENERATED:

POWER SPECTRAL DENSITY :

b) Results from 11 bit truncated pn sequence:

11BIT TRUNCATED PN SEQUENCE:

BPSK :

PSD of truncated pn sequence

Conclusion :In virtual instrumentation simulation environment the pseudo random noise sequences were simulated along with the truncation by different bits. This made us to observe the comparison between the amount of truncation as increased the pesk side lobe level aslo increased but does not vary much for diffrent amount of truncation of bits. Then with the both sequences BPSK signal was generated and its respective power spectral densities were also plotted an it was observed that as we truncate the sequence the psd expands and side lobe levels are also increased leading to change in system performance.

References:

1. P.Banerjee*, Ushaben Keshwala and Monica Kaushik “Study on Potentiality of Truncated PRN Sequences for Communication”.2. A. Ahmad and D. Al-Abri “Design of a Pseudo-Random Binary Code Generator via a Developed Simulation Model”.3. Hadjia Badaoui1, Yann Frignac2 & Mohammed Feham “Pseudo Random Binary Sequences Analysis for the Modeling of Optical DPSK Transmission Systems”.4. Mark Goresky Member and Andrew Klapper Senior Member “Pseudo-noise Sequences based on Algebraic Feedback Shift Registers”.5. R.N. Mutagi “Pseudo noise sequences for engineers”.6. www.cs.huji.ac.il/course/2002/vlsilab/files/ prbs / PRBS . pdf .7. paginas.fe.up.pt/~hmiranda/cm/Pseudo_Noise_Sequences.pdf .8. facta.junis.ni.ac.rs/acar/acar201101/acar2011-05.pdf.