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