College of Telecommunication – MCSNational University of Sciences and
Technology - NUST
Instructor: Dr. M. Arif [email protected]
AdvanceDigital Communications
206:35 PM
What are we studying ?
Adv Digital Comm - Dr. M. Arif Wahla
Digital Communications Systems
• Base Band Modulation Schemes Sampling (PAM) . . . Baseband & Bandpass
Systems Quantization (PCM) . . . Uniform and Non-
uniform PCM Waveforms . . . Line Coding Time Division Multiplexing T1/E1 Standards
Baseband Detection/Demodulation Matched Filter and Correlators Threshold Detection ISI and Equalization• Band pass Modulation Techniques
306:35 PMAdv Digital Comm - Dr. M. Arif Wahla
ModulationModulation is the process of facilitating the transfer of information over a medium
Amplitude Shift Keying (ASK)
Frequency Shift Keying (FSK)
Phase Shift Keying (PSK)
On-Off Keying (OOK)
Ai
0( ) ( ) cos[ ( ) cos[ ( )] General forms t A t t A t t t
406:35 PMAdv Digital Comm - Dr. M. Arif Wahla
The study of signal spaces provides us with a geometric method of conceptualizing the modulation process.
Signal Spaces
In a physical space when we describe a vector by its coordinates (x, y); the vector is being described by a linear combination of two functions (1, 0) and (0, 1).
Any vector can be written as a linear combination of these two functions. These functions are called ‘Basis functions’ and are orthogonal to each other.
Basis functions should
Have unit energyshould be orthogonal to
every other function
506:35 PMAdv Digital Comm - Dr. M. Arif Wahla
Basis Functions
An important example of terrific basis functions is the pair of sine and cosine waves of unit amplitude. This special basis set is used as carriers in all real communications systems.
Sine and cosine, two orthogonal functions are the basis set for all modern communications
Sine Cosine
606:35 PMAdv Digital Comm - Dr. M. Arif Wahla
Basis FunctionsThe concept of I and Q Channels
I and Q projections Polar form
706:35 PMAdv Digital Comm - Dr. M. Arif Wahla
Binary Phase Shift Keying (BPSK) modulationLet’s give these two symbols names of s1 and s2. Simplest thing is to have the symbol stand for just one bit. We define two little packets of the cosine wave, one with zero phase and second one with a 180 degree different phase.
Symbol Energy =
806:35 PMAdv Digital Comm - Dr. M. Arif Wahla
Creating a BPSK carrierA bit sequence 0111 0101 0010 1011
s1 s2 s2 s2 s1 s2 s1 s2 s1 s1 s2 s1 s2 s1 s2 s2
16 symbols are required since each BPSK symbol stands for one bit
What is a transition?
906:35 PMAdv Digital Comm - Dr. M. Arif Wahla
Quadrature Phase Shift Keying (QPSK) modulationThe dimensionality of a modulation is defined by the number of basis functions used.Therefore, QPSK a two-dimensional signal. Not because it sends two bits per symbol,but because it uses two independent signals (a sine and a cosine) to create the symbols.
QPSK signal is an extension of the BPSK signal. Both of these are a type of M-ary signals.
M = 2, makes this a BPSK, M = 4 is QPSK, M = 8, 8PSK and so on.
M-PSK modulations, a. BPSK, b. QPSK, c. also QPSK, d. 8PSK
2 2 ( 1)( ) cos , 0 , 0,1,2,.... 1i c
E is t t t T and i M
T M
• Analytical expression can be written as
where– m(t) = transmitting signal pulse shape– A = amplitude of the signal– = carrier phase
• The range of the carrier phase can be determined using
• For a rectangular pulse, we obtain
( ) ( ) cos[ ( )], 0 , 1, 2,....,i c i bs t Am t t t t T i M
2( ) , 0 ;m t t T and assume A E
T
2 ( 1)( ) 0,.... 1i
it i M
M
Adv Digital Comm - Dr. M. Arif Wahla 1006:35 PM
2 2 ( 1)( ) cos , 0 , 0,1,2,.... 1i c
E is t t t T and i M
T M
• We can now write the analytical expression as
• In PSK the carrier phase changes abruptly at the beginning of each signal interval while the amplitude remains constant
1106:35 PM
carrier phase changes abruptly at the beginning of each signal interval
Constant envelope
2 2 ( 1)( ) cos , 0 , 0,1,2,.... 1i c
E is t t t T and i M
T M
Adv Digital Comm - Dr. M. Arif Wahla
• Also can be written as
• Furthermore, si(t) may be represented as a linear combination of two orthogonal functions ψ1(t) and ψ2(t) as follows
Where
1206:35 PM
M
it
T
Ets ci
)1(2cos
2)(
2 2 ( 1) 2 ( 1)cos cos sin sinc c
E i it t
T M M
)()1(2
sin)()1(2
cos)( 21 tM
iEt
M
iEtsi
]sin[2
)(]cos[2
)( 21 tT
tandtT
t cc
Adv Digital Comm - Dr. M. Arif Wahla
• Using the concept of the orthogonal basis function, we can represent PSK signals as a two dimensional vector
• For M-ary phase modulation M = 2k, where k is the number of information bits per transmitted symbol
• In an M-ary system, one of M ≥ 2 possible symbols, s1(t), …, sm(t), is transmitted during each Ts-second signaling interval
• The mapping or assignment of k information bits into M = 2k possible phases may be done in many ways, e.g. for M = 4
1306:35 PM
1 2
2 ( 1) 2 ( 1)( ) cos , sini
i is t E E
M M
Adv Digital Comm - Dr. M. Arif Wahla
• A preferred assignment is to use “Gray code” in which adjacent phases differ by only one binary digit such that only a single bit error occurs in a k-bit sequence
• It is also possible to transmit data encoded as the phase change (phase difference) between consecutive symbols– This technique is known as Differential PSK (DPSK)
• There is no non-coherent detection equivalent for PSK
1406:35 PM
𝜙𝜙4
Adv Digital Comm - Dr. M. Arif Wahla
• Two BPSK in phase quadrature• QPSK (or 4PSK) is a modulation technique that transmits 2-bit of
information using 4 states of phases• For example
• General expression:
1506:35 PM
2-bit Information ø
00 0
01 π/2
10 π
11 3π/2
Each symbol corresponds
to two bits
scs
sQPSK Tti
M
itf
T
Ets
04,3,2,1,)1(2
2cos2
)(
Adv Digital Comm - Dr. M. Arif Wahla
1606:35 PMAdv Digital Comm - Dr. M. Arif Wahla
M-ary PSK modulation . . .
Modulation equation called the quadrature form
• So a phase modulated signal is a combination of two quadrature signals, the amplitude of which changes in response to the phase change. The modulating signal can be seen as a vector with I and Q as its x and y components
• We need a way to create a signal packet of a particular phase when needed out of a free-running sine or cosine. This is where Quadrature Modulation with I and Q channels come into play. • I and Q channels are not just concepts but also how modulators are designed. However, the signal created by I and Q channels is not what is transmitted, it is the sum or the difference (makes no difference as long the polar form is consistent) of these two, and that is the real modulated signal.
1 2
2 ( 1) 2 ( 1)( ) cos , sini
i is t E E
M M
1706:35 PMAdv Digital Comm - Dr. M. Arif Wahla
M-ary PSK modulation . . .How the bits are mapped to the possible phases ?Number the bits such a way that each adjacent phase means just one bit difference. So that when a phase mistake is made and the most likely one is the nearest phase, then only one bit is decoded incorrectly. This is called Gray coding.
1806:35 PMAdv Digital Comm - Dr. M. Arif Wahla
M-ary PSK modulation . . .
Constellation diagram
1906:35 PMAdv Digital Comm - Dr. M. Arif Wahla
0 3 2 0 3 3 2
1 -1 1 1 -1 -1 1
1 -1 -1 1 -1 -1 -1
M-ary PSK modulation . . .
2006:35 PMAdv Digital Comm - Dr. M. Arif Wahla
M-ary PSK modulation . . .
The quadrature form of modulation using I and Q channels
2106:35 PMAdv Digital Comm - Dr. M. Arif Wahla
8 PSK modulation . . .
2206:35 PMAdv Digital Comm - Dr. M. Arif Wahla
16 QAMIn PSK all points lie on a circle so the I and Q values are related to each other. PSK signals are constant envelope and all points have the same amplitude. If we allow the amplitude to change from symbol to symbol, then we get a modulation called Quadrature amplitude modulation (QAM).
M = 16, so that we have 16 symbols, eachrepresenting a four bit word
The signal points lie in rectangle instead of a circle
1 2
2 ( 1) 2 ( 1)( ) cos , sini
i is t E E
M M
2306:35 PMAdv Digital Comm - Dr. M. Arif Wahla
16 QAM . . .
2406:35 PMAdv Digital Comm - Dr. M. Arif Wahla
3
3
-3
31 3
-3
1
-1 -3 -3
1
-1 -3
16 QAM . . .
2506:35 PM
Amplitude Shift Keying
• Modulation Process– In Amplitude Shift Keying (ASK),
the amplitude of the carrier is switched between two (or more) levels according to the digital data
– For BASK (also called ON-OFF Keying (OOK)), one and zero are represented by two amplitude levels A1 and A0
cos( ), 0 1( )
0, 0 0i o
i
A t t T binarys t
t T binary
0( ) ( ) cos[ ( ) cos[ ( )] General forms t A t t A t t t
• Adv Digital Comm - Dr. M. Arif Wahla
2606:35 PM
• 4.2.4 ASK - Analytical Expression:
where Ai = peak amplitude
Hence,
where
)cos(2)cos(2)cos()( 02
00 tAtAtAtsrmsrms
0 0
22 cos( ) cos( )
EP t t
T
0
2 ( )cos( ), 0 1
( ) , 1,2,......
0, 0 0
i
i
E tt t T binary
s t i MTt T binary
1,......2,0,)(0
2 MidttsET
i
cos( ), 0 1( )
0, 0 0i o
i
A t t T binarys t
t T binary
• Adv Digital Comm - Dr. M. Arif Wahla
2706:35 PM
• Where for binary ASK (also known as ON OFF Keying (OOK))
• Mathematical ASK Signal Representation– The complex envelope of an ASK signal is:
– The magnitude and phase of an ASK signal are:
– The in-phase and quadrature components are:
the quadrature component is wasted.
1( ) ( ) cos( ), 0 1o os t A m t t t T binary
( ) ( )og t A m t
00,0)(0 binaryTtts
( ) ( ), ( ) 0oA t A m t t
( ) ( )ox t A m t
,0)( ty
• Adv Digital Comm - Dr. M. Arif Wahla
2806:35 PM
• It can be seen that thebandwidth of ASK
modulated is twice thatoccupied by the source
baseband stream
• Bandwidth of ASK– Bandwidth of ASK can be found from its power spectral density– The bandwidth of an ASK signal is twice that of the unipolar NRZ line
code used to create it., i.e.,
• This is the null-to-null bandwidth of ASKb
b TRB
22
• Adv Digital Comm - Dr. M. Arif Wahla
2906:35 PM
• If raised cosine rolloff pulse shaping is used, then the bandwidth is:
• Spectral efficiency of ASK is half that of a baseband unipolar NRZ line code– This is because the quadrature component is wasted
• 95% energy bandwidth
2(1 ) bB r R
bb
RT
B 33
• Adv Digital Comm - Dr. M. Arif Wahla
3006:35 PM
4.2.3 Frequency Shift Keying (FSK)
• In FSK, the instantaneous carrier frequency is switched between 2 or more levels according to the baseband digital data– data bits select a carrier at one of two frequencies– the data is encoded in the frequency
• Until recently, FSK has been the most widely used form of digital modulation;Why?– Simple both to generate and detect– Insensitive to amplitude fluctuations in the channel
• FSK conveys the data using distinct carrier frequencies to represent symbol states• An important property of FSK is that the amplitude of the modulated wave is
constant• Waveform
2( ) cos( ), 1,....i i
Es t t i M
T
Adv Digital Comm - Dr. M. Arif Wahla
3106:35 PM
Binary FSK
• In BFSK, 2 different frequencies, f1 and f2 = f1 + ∆ f are used to transmit binary information
• Data is encoded in the frequencies• That is, m(t) is used to select between 2 frequencies:• f1 is the mark frequency, and f2 is the space frequency
0 1
2( ) cos 2 ( ), 0b
bb
Es t f t T
T
1 2
2( ) cos 2 ( ), 0b
bb
Es t f t T
T
𝜙𝜙
• Adv Digital Comm - Dr. M. Arif Wahla
3206:35 PM
1
2
cos( ), ( ) 1 1( )
cos( ), ( ) 1 0c n
c n
A t when m t or Xs t
A t when m t or X
• Binary Orthogonal Phase FSK
• When w1 an w2 are chosen so that f1(t) and f2(t) are orthogonal, i.e.,
– form a set of K = 2 basis orthonormal basis functions1 2( ) ( ) 0t t
𝜙
𝜙
2 ( )t¿ ¿
¿ ¿
• Adv Digital Comm - Dr. M. Arif Wahla
% Matlab script for generating FM via Phase modulation
clear all;close all;
t0=.15; % signal duration
ts=0.0005; % sampling interval
fc=200; % carrier frequency
kf=100; % Modulation index
fs=1/ts; % sampling frequency
t=[0:ts:t0]; % time vector
df=0.25; % required frequency resolution
%message signal
m=[ones(1,t0/(3*ts)),-1*ones(1,t0/(3*ts)),ones(1,t0/(3*ts)+1)];
int_m(1)=0;
for i=1:length(t)-1 % Integral of m
int_m(i+1)=int_m(i)+m(i)*ts;
end
u=cos(2*pi*fc*t+2*pi*kf*int_m); % phase modulating with the % integral of the signal
3306:35 PMAdv Digital Comm - Dr. M. Arif Wahla
0 0.05 0.1 0.15-1
-0.5
0
0.5
1
The message signal
0 0.05 0.1 0.15
-1
-0.5
0
0.5
1
Time
The modulated signal
3406:35 PMAdv Digital Comm - Dr. M. Arif Wahla
Top Related