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Instructor: Eng. Nada Khatib
Website: http://www.philadelphia.edu.jo/academics/nkhatib/
Digital Communication (650533) CH 6_4
Passband Data Transmission
Philadelphia University/Faculty of Engineering
Communication and Electronics Engineering
Frequency Shift Keying
• In a binary FSK system, symbols 1 and 0 are distinguished from each other by transmitting one of two sinusoidal waves that differ in frequency.
Where i =1,2
Eng. Nada Khatib 2 Ch 6- lecture 2/4
Continuous Frequency Shift Keying
• Abrupt phase changes at the bit-transition instants are avoided; FSK schemes where phase continuity is maintained are known as continuous phase FSK (CP-FSK).
• These schemes have rapid spectral roll-off and improved efficiency. (4)
• A binary FSK signal with continuous phase does not produce as much as interference outside the signal band of interest as a corresponding FSK signal with discontinuous phase does.
Eng. Nada Khatib Ch 6- lecture 2/4 3
Required Tone Spacing for Orthogonal FSK
• FSK is usually implemented as orthogonal signaling, but not all FSK signaling is orthogonal (3).
• Tone spacing for orthogonal coherent FSK is
• Where h is the digital modulation index (6)
Eng. Nada Khatib Ch 6- lecture 2/4 4
bT
hf 2
Minimum Tone Spacing for Orthogonal FSK
• Represents the minimum frequency separation between adjacent signals for orthogonality; FSK using this value of 2∆f is known as minimum-shift keying (MSK) or fast frequency shift keying. (4)
Eng. Nada Khatib Ch 6- lecture 2/4 5
Tff
2
101
Signal Space
• Two dimensional (N=2) with two message points (M=2)
• Orthonormal basis functions are
• Where i =1,2
• The Two message points are defined by the:
Eng. Nada Khatib 6 Ch 6- lecture 2/4
Eng. Nada Khatib Ch 6- lecture 2/4 7
Euclidean distance =
Signal Space Diagram
FSK generation
The two oscillators are synchronized with each other
Alternatively, we may use a voltage-controlled oscillator, in
which case phase continuity is automatically satisfied Eng. Nada Khatib 8 Ch 6- lecture 2/4
FSK detection
• The FSK can be viewed as two interleaved ASK signals with carrier frequencies wco and wc1 respectively. Therefore, FSK can be detected coherently or noncoherently.
Eng. Nada Khatib 9 Ch 6- lecture 2/4
Coherent BFSK receiver
r(t)
r1
r2
Eng. Nada Khatib 10 Ch 6- lecture 2/4
Probability of error
• The average probability of bit error for binary FSK using coherent detection is (7)
• For orthogonal FSK , then
)4(sinc,))1(
( b
o
bb fT
N
EQP
0
Eng. Nada Khatib 11 Ch 6- lecture 2/4
Comparison
• To maintain the BER for a binary FSK receiver the same as in binary PSK receiver, the bit energy-to-noise density ratio (Eb/No)has to be doubled.
Eng. Nada Khatib Ch 6- lecture 2/4 12
)2
(o
b
BPSKeN
EQp )(
o
b
BFSKeN
EQp
Noncoherent BFSK Detection
r(t)
Eng. Nada Khatib 13 Ch 6- lecture 2/4
• Binary CP-FSK has lower sidelobes than binary PSK
• The bandwidth of FSK is higher than of ASK or PSK.
Power spectral density
Eng. Nada Khatib 14 Ch 6- lecture 2/4
• The approximate transmission bandwidth for the FSK signal is given by:
• If a raised cosine rolloff premodulation filter is used, the transmission bandwith of the FSK signal becomes (6)
Power spectral density
bRfWB 22.
bRrfWB )1(2.
Eng. Nada Khatib 15 Ch 6- lecture 2/4
M-ary FSK
• The transmitted signals for M-ary version of FSK are defined as:
• For orthogonal M-ary FSK signals, the individual signal frequencies are separated by
Eng. Nada Khatib Ch 6- lecture 2/4 16
TttfT
EtS ii 0)2cos(
2)(
T
hf 2
Signal Space
• The M-ary FSK is described by an M-dimensional signal-space diagram.
Eng. Nada Khatib Ch 6- lecture 2/4 17
The minimum distance between a signal vector and any of the
decision boundaries remain fixed as M increases.
Optimum Receiver
Eng. Nada Khatib Ch 6- lecture 2/4 18
φ1(t)
φ2(t)
φM(t)
Decis
ion
Lo
gic
: W
hic
h o
ne is
larg
est
at
t=K
T
T=kTs
Probability of error
• Using Union bound to place an upper bound on the average probability of symbol error for M-ary FSK, we get:
Eng. Nada Khatib Ch 6- lecture 2/4 19
)()1(o
bN
EQMP
• As the number of states, M, is increased, the error performance is improved at the expense of bandwidth.
Eng. Nada Khatib Ch 6- lecture 2/4 20
The probability of bit error for coherent
MFSK over a Gaussian channel
Bandwidth Efficiency
• When the orthogonal signals of an M-ary FSK signals are detected coherently, the adjacent signals need only be separated from each other by a frequency difference 1/2T so as to maintain orthogonality.
• Hence the channel bandwidth required to transmit M-ary FSK signals is
Eng. Nada Khatib Ch 6- lecture 2/4 21
M
MR
T
MWB b
2log22..
Bandwidth Efficiency
• The bandwidth efficiency of M-ary signal is therefore
• Increasing the number of levels M tends to decrease the bandwidth efficiency of M-ary FSK signals.
Eng. Nada Khatib Ch 6- lecture 2/4 22
M
MB 2log2
Comparison
• The bit error rates for all the systems decrease monotonically with increasing values of Eb/No.
Eng. Nada Khatib Ch 6- lecture 2/4 23
Comparison
• For any value of Eb/No, coherent binary PSK, QPSK and MSK produce a smaller bit error rate than DPSK, coherent binary FSK and noncoherent binary FSK.
Eng. Nada Khatib Ch 6- lecture 2/4 24
Eng. Nada Khatib Ch 6- lecture 2/4 25
For any value of Eb/No, the schemes using coherent
detection produce a smaller BER than those using
noncoherent detection.
Eng. Nada Khatib Ch 6- lecture 2/4 26
Coherent binary PSK and DPSK require an Eb/No that is 3
dB less than the corresponding values for conventional
coherent BFSK and noncoherent BFSK, respectively to
realize the same bit error rate.
At high values of Eb/No, DPSK
and noncoherent BFSK perform
almost as well as a coherent
BPSK and coherent BFSK,
respectively, for the same bit
rate and signal energy per bit.
Comparison
• M-ary FSK behaves in an opposite manner to that of M-ary PSK; in M-ary FSK and for a fixed probability of error, increasing M results in a reduced power requirement. However, this reduction in transmitted power is achieved at the cost of increased channel bandwidth.
Eng. Nada Khatib Ch 6- lecture 2/4 27
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