Introduction to Satellite FM Communications

EEL 4518 Satellite CommunicationsRev-J

Frequency Modulation Review

FM Modulator

Modulation voltage

CW Carrier

€

V(t)FM = cAcos[Φ(t)]AcCos(2π fc t)

m(t)

The signal (m(t) is contained in the frequency of the carrier

Frequency Modulation Review - 2•  FM Signal

e(t)= AC  cos(2π  ωi  t)where, ωi = 2π fi

i f = the instanteous carrier frequency

Frequency Modulation Review - 2•  Instantaneous Freq:

i f = the instanteous carrier frequency

if =

cf + (k f ∗m(t))

where c f = the "unmodulated" carrier freq

m(t) = the analog (voltage) message k f = FM modulator index, Hz/Volt

i( f )max =  cf ±  Δf

= the peak (max) instanteous carrier frequency                               excursion Δf = the peak deviation of the carrier freq                   = k f ∗m(t)peak

Frequency Modulation Review - 3

•  FM Signal

€

fi = dΦ(t)dt

V (t)FM = cA cos[Φ( t )]where,

Φ(t) = 2πfc + 2π k f m(t)[ ] dt + φo , radians0

t

∫

V(t)FM

Frequency Modulation Review - 4•  FM Signal -Tone Modulation: m(t) = Am cos(ωmt)

e(t) = Ac cos(ωc  t +2π k f Am cosωm t 'dt '0

t

∫ )

= Ac cos(ωc  t +2π Δfωm( )sinωm t )

β =2π Δfωm

=Δffm

where  fm = the maximum freq in the message spectrumso that:e(t) = Ac cos(ωc  t +β sinωm  t )which can be expanded in a Bessel function Fourier series

Frequency Modulation Review - 5•  FM Signal -Tone Modulation

V (t)FM = Ac cos(ωc  t +β sinωm  t )which can be expanded in a Bessel function Fourier seriesV (t)FM = Re{A e jΦ(t )} = Re{A e j (ωct ) e jβ sin(ωmt )}but

e jβ sin(ωmt ) = Jn (β) n=−∞

∞

∑ e j (nωmt )

= Re{A e j (ωct ) Jn (β) n=−∞

∞

∑ e j (nωmt )}

= A Jn (β) n=−∞

∞

∑ cos(ωc + nωm ) t

FM spectrum is a series of spectral lines that are harmonics of the fm

Amplitude of FM Spectral Lines are J-type Bessel Functions

Bessel functions are damped sinusoids

FM Spectrum - Tone Modulation β = Δf/fm

β = 1Fixed fm Fixed Δf

β = 2

β = 5

β  = 1.0

β  = 2.0

β  = 5.0

Spacing between spectral lines = fm

FM Spectrum - Tone Modulation β = Δf/fm

β = 1Fixed fm Fixed Δf

β = 2

β = 5

Spacing between spectral lines = fm , which varies with β

FM Spectrum - Tone Modulation β = Δf/fm

β = 1Fixed fm Fixed Δf

β = 2

β = 5

The carrier BW varies with the type of β

For SatCom, we are primarily interested in the Bandwidth of the FM Signal

•  FM Spectral Bandwidth (BW)– Carson’s Rule

– Commercial FM Broadcast•  Δf = 75 KHz and fm = 15 KHz •  BW = 180 KHz•  Spacing between stations on the FM radio = 200 KHz

€

Bandwidth = 2∗(Δf pk +mf ) , Hz

FM Modulation/De-modulation Process

*Kf *1/Kf

m(t)

Freq Modulation(voltage-to-freq)

Freq De-modulation(freq-to-voltage)

Recovered FM baseband signal

Vdemod(t) = Δf*1/Kf = Kf*m(t)*(1/Kf) = m(t)

Δf = Kf*m(t)

Δf

Vdemod(t)

Freq Modulation in Sat Comm•  FM was the original modulation scheme for the

transmission of analog (telephone voice & TV) signals •  Today most telephone signals are transmitted by digital

techniques using phase-shift keying carrier modulation•  Video signal distribution for the cable TV industry in

now the only remaining analog FM satellite service–  FM is used because it provides an improvement in the

baseband S/N ratio relative to the downlink (C/N)overall

–  Typical satellite links have 5 db < (C/N)o < 25 dB; however analog systems require S/N ≥ 50 dB

–  In general, S/N = (C/N)o + FM improvement, dB

FM Signal to Noise Ratio

€

CN

is constant in the receiver = SN" # $

% & ' in

= A2

2( )KTsysB( )

SN" # $

% & ' out

= GFM ∗ SN" # $

% & ' in

Gfm = FM signal processing gain

FM Receiver

Antenna

FM Descriminator

C/N (S/N)in (S/N)out

Noise Output of FM Discriminator

Frequency Frequency

Noi

se P

ower

Noi

se V

olta

ge

Noise power density is proportional to freq2

Noise voltage density is proportional to freq

Noise Output of FM Discriminator

Frequency Frequency

Noi

se P

ower

Noi

se V

olta

ge

Noise power density is proportional to freq2

Noise voltage density is proportional to freq

Noise power spectral density at the output of an FM demodulator, Figure 5.1 (p. 160)

€

Nout = 2No

K f

A"

# $ %

& '

2

f 2df0

fmax

∫ = 2No

K f

A"

# $ %

& '

2

( fmax

3 ) / 3

where No = KTsys

Nout

Δf =

FM Descriminator (S/N)out for Test Tone

(FM Signal)out = (K f Δfpeak )2 / 2 , Watts

for baseband signal, f1 ~ zero Hz and the

total noise output power = 2No

K f

A"

#$

%

&'

2

(fmax3 ) / 3

SN( )

out= C N( )∗ 3

2∗Bfmax( )∗ Δfpk

fmax

)

*+

,

-.

2

where B = the RF bandwidth (Carson's rule) Δfpk = the peak deviation of the RF carrier fmax = the max frequency in the baseband output

FM Descriminator (S/N)out for Test Tone

€

SN( )

out= CN( ) +10 * log(3

2) +10* log Bfmax

" # $ %

& '

+10* log Δf pkfmax

"

# $

%

& '

2

, dB

= CN( ) +10* log B

fmax

" # $ %

& ' +10* log Δf pk

fmax

"

# $

%

& '

2

+ 1.8 , dB

FM Processing Gain

•  The FM processing gain (Gfm) is the improvement in the output S/N over the C/N

•  Gfm is proportional to fm deviation ratio Ø  β = D = Δfpk/fmax

however, the RF bandwidth B = 2(Δfpk + fmax) = 2fmax( D + 1)

•  This is spectrally inefficient but is used in all analog FM satellite links

Pre-emphasis and De-emphasis ���for S/N improvement

Noise Output of FM Discriminator

Frequency Frequency

Noi

se P

ower

Noi

se V

olta

ge

Noise power density is proportional to freq2

Noise voltage density is proportional to freq

���For de-emphasis, the noise voltage at FM detector output is passed through a de-emphasis filter with characteristic. Figure 5.2 (p. 163 ) ���

De-emphasis filter roll-off = b/f (linear) = - 6 dB/octave (dB)

FM Demodulator

De-emphasis Filter

Input Output

fd Frequency

Transfer Function dB

���Resulting noise voltage at output of de-emphasis filter is a constant for freq > fd Figure 5.2 cont. ���

De-emphasis limits the noiseVoltage to a constant

The de-emphasis filter also reduces the output signal voltage; so distortion will occur. To prevent this, a pre-emphasis filter

is used to boost the input signal voltage to compensate for the de-emphasis filter reduction. Figure 5.2 (cont.) ���

fd Frequency

Transfer Function dB

fd Frequency

Transfer Function dB

Pre-emphasis Filter De-emphasis Filter

De-emphasis filter roll-off = b/f (linear) = - 6 dB/octave (dB)

Pre-emphasis filter boost = f /b (linear) = + 6 dB/octave (dB)

Pre- & Post Emphasis Gain

•  G(f)pe = (1/b)*fb

•  G(f) = G(f)pe * G(f)de = (fb / b) * (b / fb) = 1With pre/post-emphasis, the S/N becomes:

Where typical values of pre- & post-emphasis gain is P = :

9 db for NTSC video 5 - 10 db for analog FM voice transmission

€

SN = C

N( ) +10* log Bfmax

" # $ %

& ' +10* log Δf pk

fmax

"

# $

%

& '

2

+ 1.8 + P , dB

5.2 Analog FM Transmission of TV

Spectra of NTSC baseband TV signals transmitted by U.S. domestic satellites: (a) Baseband video TV signal (b) The composite (video plus audio) signal. Figure 5.3

Max Modulation freq = 4.2 MHz

Satellite TV Broadcast•  Δf = 10.75 MHz •  fm = 4.2 MHz•  BW = 29.9 MHz (Carson’s rule)

Typical FM threshold extension demodulator for TV reception. FM threshold is C/N = 9 dB, where the S/N at the demodulator output has fallen 1 dB below the straight line. Figure 4.9 (p. 119)

1 dB

Satellite television distribution system. ���Figure 4.11 (p. 133)

FM Satellite TV Transmission

Where typical values of: P = 9 dB pre/de-emphasis improvement for NTSC videoQ = 8 dB subjective improvement or weighting factor

€

SN = C

N( ) +10* log Bfmax

" # $ %

& ' +10 * log Δf pk

fmax

"

# $

%

& '

2

+ 1.8

+ P + Q , dB

•  Baseband video bandwidth: 4.2 MHz•  Transponder bandwidth: 30 MHz•  C/N = 15 dB•  De-emphasis improvement: 9 dB•  Subjective nimprovement factor: 8 dBCalc S/N for video signal1)  Use Carson’s rule to find the peak freq deviation Brf = 30 MHz = 2(Δfpk + fmax)

Δfpk = Brf / 2 - fmax = 15 - 4.2 = 10.8 MHz2)  Use equat 5.22 to calc S/N

Example 5.2.1 NTSC Sat TV Transmission

€

SN = C

N( ) +10* log Bfmax

" # $ %

& ' +10 * log Δf pk

fmax

"

# $

%

& '

2

+ 1.8

+ P + Q , dB

S/n = 15 + 10log(30/4.2) + 10 log(10.8/4.2)2 + 1.8 + 9 + 8= 15 + 8.5 + 8.2 + 18.8 = 50.5 dB

FM processing gain (S/N improvement) = 50.5 - 15 = 35.5 dB

Without the subjective weighting (8 dB), the unweighted improvement = 35.5 - 8 = 27.5 dB

For TV transmission a S/N = 55 dB, no perceptible noise, studio quality signal= 50 dB, very good quality, noise just preceptible in background= 45 dB, good quality, some noise visible but not annoying= 40 dB, poor quality, lots of noise visible= 35 dB, bottom limit for picture quality, high noise, very annoying

Example 5.2.1 NTSC Sat TV Trans cont.

€

SN = C

N( ) +10* log Bfmax

" # $ %

& ' +10* log Δf pk

fmax

"

# $

%

& '

2

+ 1.8

+ P + Q , dB

5.2 Single Carrier per Channel (SCPC) FM Links

•  SCPC links have been widely used for voice and also for data xmissions by amateur sat community

–  Earth stations transmit at an assigned freq–  Threshold for narrow band threshold extension FM demodulators ~ 5 dB

SCPC FM Transmission

Where typical values of: P = 7 dB pre/de-emphasis improvement for baseband voice€

SN = C

N( ) +10* log Bfmax

" # $ %

& ' +10 * log Δf pk

fmax

"

# $

%

& '

2

+ 1.8

+ P , dB

SCPC ExampleA SCPC-FM sat link has an RF chan bandwidth of 45 KHz and a baseband max freq of 3.4 KHz. De-emphasis provides a subjective S/N improvement = 7 dB. For receiver C/N = 13 dBCalc the baseband S/NThe peak FM deviation is

Baseband S/N

€

BRF = 2(Δfpk + fmax ) = 45 KHzΔfpk = 45/2− 3.4 =19.1KHz

€

S /N( )FM −voice= C /N +10log(BRF

fmax)+10log(Δfpk fmax

)2 +1.8+P

= 13+10log(45 3.4)+10log(19.2

3.4)2 +1.8+ 7

= 13−11.2+15.0+8.8 = 48 dB

This is an acceptable S/N

SCPC Example contAssuming the FM demod threshold = 6 dB, what is the link margin?If the link suffers rain atten, the link will be operational until the C/N = 6 dB, so the Link margin = 13 - 6 = 7 dB

Since the demod is operating at threshold, there is an additional 1 dB loss in S/N; so the

S/N = 48 - 7 - 1 = 40 dBwhich is at the lower limit of acceptable voice quality.