1. Generation & Analysis of BPSK from Truncated PRN
Sequence
*Manisha Sharma & Neeru Agarwal
Department of ECE, ASET,
Amity University, Noida
India
*Email:
Abstract— In this paper the pseudo random noise sequence is
generated in Lab View software using 9 bit LFSR and then these
are truncated and then with different seed values, different
truncation bits, the change in the properties of the sequence are
also observed with mathematical and graphical analysis. Also
with both the normal and truncated PN sequences obtained
BPSK is also simulated and its power spectral density is also
obtained.
Keywords— PRN Sequence, Truncated PRN Sequence, peak
side lobes(rms), bpsk, power spectral density, seed value, taps,
LFSR, LabView software.
I. INTRODUCTION
Linear Feedback Shift Registers (LFSR) 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 beneficial in
terms of acquisition time and some applications. As length of
9th
stage PN sequence is 511 and that of 10th
stage is 1023, so
there is huge difference between these selections. Hence
experiments are being conducted by selecting some length in
between the large gap such that the properties of the resulting
truncated sequence are preserved along with the acquisition
time being reduced [1].
In this paper the normal p-n sequence along with the
truncated sequence is being generated in LabView software
using 4 stage and 9 stage LFSR . Also mathematical studies
are 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 benefits
as it can be used in communication and also 11 bit truncation
from 511 bit sequence resulting in length of 500 will be much
easier to handle for calculation purposes.
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), and these
sequences are being tested for many applications like in the
analysis of optical DPSK transmissions modeling [3]. The
PRN sequences can be generated by numerous ways like it can
be generated using algebraic 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.
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
primitive polynomial 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.
II. GENERATION OF NORMAL & TRUNCATED PRN SEQUENCE
A. Generation of Normal PRN Sequence:
In this paper simulation model is created in LabView to
generate the sequences. Following is the block diagram of 4
stage PRN sequence.
Figure 1: Block Diagram of 4 stage PRN sequence Generator.

2. This resulted PN code is shown in figure 2 & resulted
waveform is depicted in figure3.
Figure 2: Resulted PN code
Figure 3: Resulted 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 or EXNOR gates. Here we have
implemented this using EXOR gates on the block diagram of
the virtual instrumentation. The front panel is representing the
code and the waveform is 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 [6]. 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 [6]. Following is the resulting
waveform of 511 length PRN sequence.
Figure 4: Resulting Waveform of 511 length PRN sequence.
This sequence satisfies all the properties of a normal PN
sequence like balance, run and autocorrelation properties.
B. Generation of Truncated PRN Sequence:
A truncated sequence of 500 bits length can be generated by
removing last 11 bits from the above sequence which in this
simulation is achieved by using a 'delete from array' block. In
this block we can delete any number of last elements of the
initial array.
Figure 5: Truncated Sequence
III. MATHEMATICAL ANALYSIS
Observations are being made by varying the seed values
and seeing their effect on the different amount of truncation of
bits. Example: 11, 31, 51, 101, 151, 201, 301 etc. This is
shown in table 1. This analysis shows how the root mean
square value or the peak side lobes generation is being
affected as we change seed values for different number of bits
being truncated from the end of the normal sequence .
In the second table observations are carried out such that
as the truncation is increased with respect to the normal PRN
sequence the performance is affected i.e. The RMS values
with respect to some seed values taken into consideration (it
gives the nutshell of the previous analysis). As it is observed
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 is shown below using
MATLAB tool. Figure 6 is showing Matlab plot that with
increase in truncation with respect to the normal sequence
RMS values increases for each seed value but there in not
much variation in slope as seed changes. Fig. 7 showing the
dB plot of the same observation.
0 50 100 150 200 250 300 350
0.04
0.045
0.05
0.055
0.06
0.065
0.07
Truncation
RMSValue
000001010
000010100
000011110
000101000
000110010
000111100
001000110
001010000
001011010
001100100
FIGURE 6: Matlab Plot
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
RMSValue
000001010
000010100
000011110
000101000
000110010
000111100
001000110
001010000
001011010
001100100
Figure 7: dB Plot

3. IV. GENERATION OF BPSK
From both the normal and truncated PRN sequences we
simulated the BPSK signal and observed their respective
power spectral densities.
FIGURE 8: Block for BPSK Generation
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.
V. RESULTS & DISCUSSIONS
One random data stream (A) is selected from square wave
generator and then the normal PN sequence is multiplied with
that data stream resulting in a sequence in (D). Finally BPSK
is obtained from this sequence and one sinusoidal carrier
signal with changing phase at the transitions (E). Power
spectral density for the resulting BPSK is plotted in graph (F).
Same procedure is followed with the 11 bit truncated PRN
sequence and its PSD is also plotted (I). It can be clearly seen
from both the spectral densities that as bits are truncated the
spectral performance goes poor resulting in more side lobes.
A. Selected Data Stream:
B. Sinusoidal Carrier Signal:
C. Normal PN sequence of length 511 bits:
D. Sequence Generated on multipling PN sequence with data:
E. Generated BPSK:
F. Power SpectralDensity (PSD):
G. 11 Bit Trancated PN Sequence:
H. Generated BPSK:
I. Power Spectral Density (PSD) of Trancated PN sequence:
.

4. VI. CONCLUSION
In virtual instrumentation simulation environment the pseudo
random noise sequences are simulated along with the
truncation by different bits. This made us to observe the
comparison between the amount of truncation increases the
peak side lobe level also increases but does not vary much for
different amount of truncation of bits. Then with the both
sequences BPSK signal is generated and its respective power
spectral densities are also plotted and it is observed that as we
truncate the sequence the PSD expands and side lobe levels are
also increased leading to change in system performance.
ACKNOWLEDGMENT
Manisha Sharma, is highly thankful to Prof. (Dr) P
Bannerjee & Prof (Dr) M.K.Dutta, Department of ECE,
ASET, Amity University Noida, India, for their valuable
support.
REFERENCES
[1] Banerjee P, Keshwala U & Kaushik M, “Study on Potentiality of
Truncated PRN Sequences for Communication”, International
Conference on Communications, Devices & Intelligent Systems, 2012,
pp 409-412.
[2] Ahmed A & Abri D, “Design of a Pseudo-Random Binary Code
Generator via a Developed Simulation Model”, ACEEE Int. J. on
Information Technology, Vol. 02, No. 01, March 2012, pp 33-36.
[3] Hadjia Badaoui, Yann Frignac & Mohammed Feham, “Pseudo
Random Binary Sequences Analysis for the Modeling of Optical DPSK
Transmission Systems”, International Journal of Computer Science &
Communication, Vol. 1, No. 2, July-December 2010, pp. 369-372.
[4] Mark Goresky and Andrew Klapper, “Pseudo-noise Sequences based on
Algebraic Feedback Shift Registers”, IEEE Transaction on Information
Theory, VOL. 52, No: 4, 2006, pp 1649-1662.
[5] R.N. Mutagi, “Pseudo noise sequences for engineers”, Electronics &
Communication Engineering Journal,1996, pp 79-87.
[6] Goran S. Miljković, Ivana S. Stojković & Dragan B. Denić,
“Generation and Application of pseudorandom binary sequences using
virtual Instrumentation”, Automatic Control and Robotics, FACTA
UNIVERSITATIS, Vol. 10, No 1, 2011, pp. 51 – 58.
TABLE I
SEED
VALUES
RMS value of
11 bit
truncated PRN
seq.
RMS value of
31 bit
truncated PRN
seq.
RMS value of
51 bit
truncated PRN
seq.
RMS value of
101 bit
truncated PRN
seq.
RMS value of
151 bit
truncated PRN
seq.
RMS value of
201 bit
truncated PRN
seq.
RMS 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
TABLE II
seed-> 000001010 000110010 001100100 010010110 011001000 100000100 100110110 101101000 110011010
Tprn/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