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8/10/2019 Bfsk, Dpsk,Ask,Error Control
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*Signal space diagram of QPSK signal
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BFSK
Binary Frequency Shift Keying
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*Principle of BFSK
1, 0symbols1 bit
1&0 - distinguished by transmitting waves that differ in frequency.
Tb- bit duration= symbol duration
Eb- Energy of bit = symbol energy
Transmitted signals are
where
elsewhere,0
0,2cos2
bib
b
i
TttfT
E
ts
2,1;
iT
inf
b
ci
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symbol 1f1
symbol 0f2
S1(t) -transmitted signal ,represents symbol 1
S2(t)transmitted signal , represents symbol 0
There are two basis functions written as
elsewhere,0
0,2cos2
1
1
b
b
TttfTt
elsewhere,0
0,2cos2
2
2
b
b
TttfTt
elsewhere,0
0,2cos
2
11 b
b
b
TttfT
E
ts
elsewhere,0
0,2cos
2
2 2 bb
b
TttfT
E
ts
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1 = 2 =
As a result, the signal vectors are
b
b
E
E 0and
021 ss
t1
t2
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*Signal space diagram of BFSK
Distance between two points ,
= 2
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Symbol 1- f1frequency say, f1= 2fb
Symbol 0f2frequency say, f2= fb
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TRANSMITTER
1. Generation of coherent BFSK signal / Modulator
*MODEMS of BFSK
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Onoff level encoder
Unipolar
Converts 00
1
For Symbol 1,
On off level encoder o/p = =
Upper channel o/p = m(t)
= = s1(t)Lower channel o/p = ()
=0 = s2(t)S(t) = s1(t) + s2(t) = s1(t)
t1
t1
t2
For Symbol 0
On off level encoder o/p = 0
= 0Upper channel o/p = 0= s1(t)
()= ()Lower channel o/p = ()
= s2(t)
S(t) = s1(t) + s2(t) = s2(t)
t2
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RECEIVER
2. Detection of coherent BFSK signal/ Demodulator
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Noisy received signal, = (t) + w(t)
Two matched filters with 1 and 2observationvectors
= () (t) dt = () (t) dt
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For symbol 1 ,
=
()
(t) dt =
= () (t) dt = 0 = 1 2=
For symbol 0,
= () (t) dt = 0= () (t) dt = = 1 2= -
Decision device output,
If y>0 : symbol 1
If y
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*Bandwidth of BFSK
If Tbis the bit duration & fb=
= bit rate
Symbol 1 , Centered at f12fb
Symbol 0, Centered at f22fb
Total bandwidth = 4fb
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* Probability of bit error = probability of symbol
error
Symbol 1 : x(t) = s1(t) + w(t)
Symbol 0: x(t) = s2(t) +w(t)
Two decision regions : z1and z2
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Receiver decision in favour of 1:
When 1 > 2 falls under 1region =
Receiver decision in favour of 0:
When 1 < 2 falls under 2region =
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Mean of y , when symbol 1 was transmitted,
Mean of y , when symbol 0 was transmitted,
Variance of Y,
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Conditional probability density function of y
= ?
Suppose symbol 0 transmitted,
CPDF =
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Prob of error, for 0 transmitted, 1 received
P10 =
Substitute ,
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Similarly
0
0122
1
N
EerfcP b
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Average probability of symbol error = bit error
rate for BFSK,
022
1
NEerfcP be
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Amplitude Shift Keying
(ASK)
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On- off keying
Symbol 1pulse transmitted
Symbol 0no pulse
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* Principle of ASK
Transmitted signal Symbol 1: (0t )
Symbol 0 : (0
t
)
S(t) = 0
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Orthonormal basis function:
For symbol 1:
For symbol 0:
S(t) = 0
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* Signal constellation for ASK
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* Detection of ASK signal
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Noisy received signal, = (t) + w(t)
matched filter o/p: 1 observation vector
= () (t) dt
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*Bandwidth of ASK
Bandwidth = 2fb
fb = bit rate = 1/Tb
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*Probability of error
Received signal ,
= + : 0
0
Matched filter o/p ,
= () (t) dt
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When symbol 1 transmitted,
1 =
[1] =
[1] = 0/2
When symbol 0 transmitted,[1] =0 [1] = 0/2
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Conditional probability density function or
random variable x1 = ?
Symbol 1 transmitted,
Cpdf=
Symbol 0 transmitted,Cpdf =
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Cases of Error
Symbol 1 transmitted,
s/g falls under
2region
Ie : 1 <
Symbol 0 transmitted,
s/g falls under 2regionIe : 1 >
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Probability of error ,
P01
=
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Substitute
= 1
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P01 = P10 =erfc(
)
= average probability of symbol error = BER
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DPSK
Non coherent version of PSK
Eliminate the need of coherent reference
signal at the receiver side
Combination of
1) Differential encoding of input binary wave
2) Phase shift keying
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Send symbol 1,
No phase change
Send symbol 0,
Phase advances by 180 degree
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DPSK transmitter
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Illustration of generation of DPSK
signal
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*detection of DPSK signal
BPF- removes undesired frequency components
Decoding : bk = + 1: xnor operation
dk-1 1 1 0 1 1 0 1 1
dk 1 1 0 1 1 0 1 1 1
bk 1 0 0 1 0 0 1 1
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Case 1: symbol 1, symbol 1
1 =
Case 2: symbol 1, symbol 0
1 = Receiver decision: 1 > 0: 1 1
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* Bandwidth of DPSK
BW= fb
Since,2Tb is the symbol duration
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Erfc(u)= 1-erf(u)
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Error control coding
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Channel encoding
Accepts msg bits
Add parity bits along with msg bit
Parity generation
Channel decoding
- Parity checking for detecting msg signal
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Channel encoder
Block code
Sending information as blocks
No memory requirement
Convolutional code
Bit by bit
Serially
With memory
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Block codes
Linear block codes
Cyclic codes
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Channel decoder
Syndrome decoder
Block codes
Viterbi decoder
Convolutional codes
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Block code
General representation
: (n, k) block codes
n ->no: of code words
k>no: of msg bits
n-k ->no: of parity bits added
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Linear block code
A code is said to be linear if any two code
words in the code can be added in modulo-2
arithmetic to produce a third code word in the
code
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Modulo-2 arithmetic
Xor operation
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Linear Block Codes
A vector notation is used for the msg bitsand codewords, Dataword m = (m0m1.mk-1)
Codeword c = (c0c1..cn-1) Parity bits b= (b0b1..bn-k-1)
the code rate, Code rate = k/n
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Linear Block Code - Example
msg length k = 4
Codeword length n = 7
This is a (7,4) block code with code rate = 4/7
For example, m = (1101), c = (0011101)
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b- linear combination of msg bits
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Structure of a lbc
Matrix representation
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Considering p as the co-efficient k x (n-k)
matrix
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Block diagram representation of generator
equation
Parity check equation for lbc
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Parity check equation for lbc
Take H, as parity check matrix orthogonal to
G(generator matrix)
Parity
check
equation
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Indicates transmitted vector received correctly
or not.