ABSTRACT There are various types of digital modulation techniques, which include Amplitude Shift

Keying(ASK), Phase Shift Keying (PSK), Frequency Shift Keying (FSK) and Quadrature Amplitude

Modulation (QAM). The objective of digital modulation is to transport data between two or

more nodes. In digital modulation,analog carrier signal is modulated by a discrete signal. In this

lab, we studied about PSK and its’ schemes (BPSK and QPSK). PSK is a digital modulation

scheme that conveys data by changing , or modulating the phase of the reference signal (carrier

wave). BPSK is the simplest form of phase modulation that use two carrier phase. We studied

about its principle and waveform. The waveform is generated in MATLAB. BPSK signal is proven

mathematically by equations. QPSK uses four carrier phases, each representing two bits of data.

QPSK is preferred than BPSK because of it is higher order modulation scheme when improved

spectral efficiency. QPSK principle is studied and its waveform is produced using MATLAB and is

proven with mathematical equations.

INTRODUCTION Phase shift keying (PSK) is another form of angle-modulated, constant amplitude

digital modulation. The output signal for PSK is a binary digital signal and has a limited number

of output phases. In BPSK, the transmitted signal is sinusoid of fixed amplitude. The phase of

the modulated signal itself conveys information ; the demodulator has a reference signal to

compare the received signal phase. The phase of carrier is changed according to input data

signal. The general expression is:

𝑉𝐵𝑃𝑆𝐾=b(t) √2𝑃 cos 2π𝑓𝑐t, where 0<t<T

where b(t)=1 or -1

𝑓𝑐=carrier frequency

𝜔𝑐=radian carrier frequency

𝑇=bit duration

√2𝑃=A=peak value of sinusoidal carrier

There is two output phases in BPSK. One output represents a logic 1 and another is

logic 0. As the input changes, the phase of output carrier shifts between two angles that are

180 oͦut of phase. BPSK is a form of suppressed-carrier, square wave modulation of a

continuous wave (CW) signal. BPSK demonstrates better performance than ASK and FSK.

Quadrature Phase Shift Keying (QPSK) is effectively two independent BPSK system

(I-In phase Q-out of phase) which exhibit similar performance but the bandwidth efficiency is

two times. QPSK is a M-ary technique whereby M=4. QPSK uses two points of constellation

diagram, equispaced around a circle. With 4 phases, QPSK can encode two bits per symbol to

minimize Bit Error Rate (BER). With QPSK, four output phases are possible for a single carrier

frequency. Because there are four different output phases, there must be four different input

conditions. The digital input to a QPSK modulator is a binary signal, if to produce four different

output conditions, it must combine into groups of 2 bits called dibits. With 2 bits there are four

different conditions : 00,01,10,11. Each dibit code generates one of the four possible output

phases. The rate of change at the output (baud rate) is one-half of the input bit rate.

RESULTS AND DISCUSSIONS Task 1:Binary Phase Shift Keying (PSK) MATLAB Code

function bpskd(g,f) %Define variables g and f in the command window

%Input carrier frequency as a multiple of if nargin>2 error('Too many input arguments'); elseif nargin==1 f=1; end

if f<1; error('Frequency must be greater than 1'); end

t=0:2*pi/99:2*pi; cp=[];sp=[]; mod=[];mod=[];bit=[]; for n=1:length(g); if g(n)==0; die=-ones(1,100); se=zeros(1,100);

%Signal else g(n)==1; die=ones(1,100); se=ones(1,100);

%Signal end c=sin(f*t); cp=[cp die];

%Amplitude mod=[mod c];

%Carrier bit=[bit se];

%Binary signal end bpsk=cp.*mod;

%BPSK Signal subplot(2,1,1); plot(bit,'LineWidth',1.5); grid on; xlabel('time');ylabel('Amplitude'); title('binary signal'); axis([0 100*length(g) -2.5 2.5]);

subplot(2,1,2); plot(bpsk,'LineWidth',1.5); grid on; xlabel('time');ylabel('Amplitude'); title('BPSK signal'); axis([0 100*length(g) -2.5 2.5]);

OUTPUT

In this laboratory, it can be seen that MATLAB function bpskd generates waveform

of BPSK signal. In above figure shows BPSK signal for bit sequence of 11001011 with

frequency,f=2.The waveform has a constant envelope like FSK . Also, the frequency is constant.

It can be seen that when the input binary signal changes from value of 1 to 0, the output phase

changes. The phase shift is introduced by the channel. BPSK changes the phase on each

component at the start of each bit-period. The frequency of carrier must be greater than 1

because it must be greater than data bit rate so that the condition is relaxed and resultant BER

performance is negligible. If f=1, the condition is it can ensure minimum error possible. The

output signal is either +1 sin 𝜔𝑐t or -1 sin 𝜔𝑐t. +1 sin 𝜔𝑐t represents a signal that is in phase

meanwhile -1 sin 𝜔𝑐t represents a signal that is 180 oͦut of phase. Mathematically, the output

phase of a BPSK modulator is 1

2 cos (𝜔𝑐-𝜔𝑎)t -

1

2 cos (𝜔𝑐+𝜔𝑎)t. The received signal has

the form 𝑉𝐵𝑃𝑆𝐾=± √2𝑃 cos (2π𝑓𝑐t + ϴ) , , where ϴ is the phase shift introduced by the

channel.

The truth table is:

Binary Input Output phase

Logic 0

Logic 1

180 ͦ

0 ͦ

Phasor and constellation diagrams are shown respectively:

i) 90 ͦ

cos 𝜔𝑐t

-sin 𝜔𝑐t sin 𝜔𝑐t

180 ͦ 180 ͦ

Logic 0 Logic 0

-90 ͦ

-cos 𝜔𝑐t

cos 𝜔𝑐t

ii)

±180 ͦ 0 ͦ Reference

-cos 𝜔𝑐t

Task 2: Quadrature Phase Shift Keying

MATLAB

function qpskd(g,f) if nargin > 2 error('Too many input arguments'); elseif nargin==1 f=1; end if f<1 error('Frequency must be bigger than 1'); end l=length(g); r=l/2; re=ceil(r); val=re-r; if val~=0; error('Please insert a vector divisible for

2'); end t=0:2*pi/99:2*pi; cp=[];sp=[]; mod=[];mod1=[];bit=[]; for n=1:2:length(g); if g(n)==0 && g(n+1)==1; die=sqrt(2)/2*ones(1,100); die1=-sqrt(2)/2*ones(1,100); se=[zeros(1,50) ones(1,50)]; elseif g(n)==0 && g(n+1)==0; die=-sqrt(2)/2*ones(1,100); die1=-sqrt(2)/2*ones(1,100); se=[zeros(1,50) zeros(1,50)]; elseif g(n)==1 && g(n+1)==0; die=-sqrt(2)/2*ones(1,100); die1=sqrt(2)/2*ones(1,100); se=[ones(1,50) zeros(1,50)]; elseif g(n)==1 && g(n+1)==1; die=sqrt(2)/2*ones(1,100); die1=sqrt(2)/2*ones(1,100); se=[ones(1,50) ones(1,50)]; end c=cos(f*t); s=sin(f*t); cp=[cp die]; sp=[sp die1]; mod=[mod c]; mod1=[mod1 s]; bit=[bit se]; end qpsk=cp.*mod+sp.*mod1; subplot(2,1,1); plot(bit,'LineWidth',1.5); grid on; xlabel('Time'); ylabel('Amplitude'); title('Binary Signal') axis([0 50*length(g) -1.5 1.5]); subplot(2,1,2); plot(qpsk,'LineWidth',1.5); grid on; xlabel('Time');

OUTPUT WAVEFORMS

grid on; xlabel('Time'); ylabel('Amplitude'); title('Binary Signal') axis([0 50*length(g) -1.5 1.5]); subplot(2,1,2); plot(qpsk,'LineWidth',1.5); grid on; xlabel('Time'); ylabel('Amplitude'); title('QPSK signal') axis([0 50*length(g) -1.5 1.5]);

In this laboratory, it can be seen that MATLAB function qpskd generates waveform

of QPSK signal. In above figure shows QPSK signal for bit sequence of 11001011 with frequency,

f=2. The frequency of carrier must be greater than 1 because it must be greater than data bit

rate so that the condition is relaxed and resultant BER performance is negligible. If f=1, the

condition is it can ensure minimum error possible. Like BPSK, the waveform has a constant

envelope and discontinuous phase at symbol boundaries (from logic 1 to 0, or vice versa).

However, the symbol interval is two times the BPSK. QPSK transmits data twice as fast as BPSK

does if the transmission rate of the symbols is the same for both BPSK and QPSK. With QPSK,

the input data are divided into two channels and is equal to one-half of the input data rate. The

mathematical expressions form of QPSK signal is:

s(t)=A cos (2𝜋𝑓𝑐𝑡 + 𝛳𝑖) 0≤t≤T , i=1,2,3,4

where 𝛳𝑖= (2𝑖−1)𝜋

4 . The initial signal phases are

𝜋

4 ,

3𝜋

4 ,

5𝜋

4 ,

7𝜋

4 .

The truth table is:

Binary Input

Q I

QPSK Output Phase

0 1 -135 ͦ

0 1 -45 ͦ

1 0 +135 ͦ

1 1 +45 ͦ

Phasor and constellation diagrams are shown respectively:

i)

cos 𝜔𝑐t

Q I Q I

cos 𝜔𝑐t - sin 𝜔𝑐t cos 𝜔𝑐t + sin 𝜔𝑐t

1 0 1 1

sin (𝜔𝑐t + 135 ͦ) sin (𝜔𝑐t + 45 ͦ)

- sin 𝜔𝑐t sin 𝜔𝑐t (0 ͦ reference)

Q I -cos 𝜔𝑐t Q I

-cos 𝜔𝑐t - sin 𝜔𝑐t -cos 𝜔𝑐t + sin 𝜔𝑐t

0 0 0 1

sin (𝜔𝑐t - 135 ͦ) sin (𝜔𝑐t – 45 ͦ)

cos 𝜔𝑐t

ii)

10 11

-sin 𝜔𝑐t sin 𝜔𝑐t

00 01

-cos 𝜔𝑐t

CONCLUSIONS

In this laboratory, it can be concluded that M-PSK waveform is successfully generated

by using MATLAB. The basic principles of digital modulation techniques are studied in this lab

that is PSK through MATLAB coding. PSK modulation schemes that are studied in this lab are

BPSK and QPSK. BPSK demonstrates better performance than ASK and FSK. Binary data are

represented by two signals with different phases in BPSK. These two phases are 0 and π. The

phase of carrier is changed according to input data signal. It has the minimum error possibility

with the same Eb/No. Next, QPSK does not suffer from BER degradation while the bandwidth

efficiency increases. In a QPSK system, data bits are divided into groups of two bits called dibits

(00,01,10,11). Unlike BPSK, the output signal for QPSK has a constant envelope than BPSK.

The performance between BPSK and QPSK is analyzed. QPSK is better in terms of data rate

and bandwidth. QPSK transmits data twice as fast as BPSK. QPSK has high data rate which is 2

bits per bit interval. QPSK does not suffer from BER degradation while the bandwidth efficiency

is increased. Only two different phases are used to represents two different binary values

whereby each element only represents one bit in BPSK meanwhile four different phases are

used to represent two binary values in QPSK whereby each signal element represents in two

bits. For the same bit error rate the bandwidth required by QPSK is reduced half than BPSK.

Applications for QPSK in digital communications include CDMA system, Iridium Satellite

Communication System, Digital Video Broadcasting Satellite. QPSK is also used for satellite

transmission of MPEG-2 videos. It also used in cable modems, video conferencing and in cellular

phone systems and other forms of digital communications over an RF carrier.

REFERENCES

1) B.P. Lathi : Modern Digital and Analog Communication, Oxford University Press, New

York, 1998

2) Wayne Tomasi : Electronics Communications System, Prentice Hall, New Jersey, 2004

3) Madhow: Fundamentals of Digital Communication, Cambridge University Press, New

York, 2008

4) Ibrahim Omar, Volunteer at IEEE Zagazig Student Branch :

http://www.slideshare.net/Hema91/digital-modulation-14204950?from_search=1,

Digital Modulation, 7 Sep 2012

5) Park J. H.,Jr., “On Binary DPSK detection” IEEE Trans Comm. , vol. 26, no.4, April 1978