noise performance of cw system

02/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 1

Noise performance of CW system


Narrow band noise

Narrow Band BPF Hn(f)

Pass band 2B

Channel

white noise w(t)Narrow band

Noise n(t)

Receiverdemodulator

LPF cut off W

fc-B fc fc+B-fc-B -fc -fc+B

Sn(f)

fc-B fc fc+B-fc-B -fc -fc+B

Hn(f) Sw(f)

• First stage at the receiver end is BPF of pass band 2B to limit the noise. • spectral density of white Noise Sw(f) at input of BPF is constant (/2)• spectral density of Noise Sn(f) at output of BPF is narrow band


Narrow band noiseFrom the narrow band spectral density function of noise , it is evident that narrow band noise n(t) is approximately a sinusoidal function of frequency fc with amplitude and phase varying randomly.

= Where In phase component of narrow band noise, And quadrature phase component of narrow band noise,

Thus narrow band noise can be viewed as sum of In-phase component of noise modulated on carrier signal and quadrature phase component of noise modulated with quadrature shifted version of carrier signal


Narrow band noiseProperties of narrow band noise• If and has zero mean• • Both and has same power spectral density which is related to spectral density of

narrow band noise, as ==+ Thus

f

𝑆𝑛𝐼 ( 𝑓 )𝑜𝑟 𝑆𝑛𝑄 ( 𝑓 )

B-Bfc-B fc+B

𝜂2

𝑆𝑛 ( 𝑓 )

f-fc-B -fc+B


Noise performance of DSB-SC system (coherent detection)

For DSB-SC, Input to demodulator, Signal power at input, Noise power at input,

Input of multiplier =Output of the multiplier=cos()


Pass band 2W

Channel

white noise w(t)

s(t)+n(t)

Receiver

LPF cut off W

s(t) +nw(t) demodulator

cos(2fct)

sd(t)+nd(t)Si

Ni

So

No

s(t)



Output of the multiplier=Output of Low pass filter=• It can be observed that message component and in phase component of noise appear in the

output with half magnitude• Quadrature component of noise is fully rejected by coherent receiverat the output, Signal power , Noise power,



noise figure of DSB-SC receiver, Figure of merit of DSB-SC receiver =1/ F 2• Noise figure of DSB-SC receiver implies that noise power is reduced by half. IT eliminates

quadrature component of noise power


Noise performance of SSB-SC system (coherent detection)

For SSB-SC, , +ve sign for LSB and –ve sign for USBInput to demodulator, Signal power at input, or, as [ is Hilbert transform of m(t)]Thus signal power is half of that in DSB-SCNoise power at input,


Pass band W

Channel

white noise w(t)

s(t)+n(t)

Receiver

LPF cut off W

s(t) +nw(t) demodulator

cos(2fct)

sd(t)+nd(t)Si

Ni

So

No

s(t)



Input of multiplier =Output of the multiplier

Output of Low pass filter=at the output, Signal power , , Noise power,



noise figure of SSB-SC receiver, Figure of merit of DSB-SC receiver =1/ F 1• It implies that noise performance of SSB-SC is inferior to DSB-SC. • But closer examination reveals that signal power and bandwidth at the input of SSB-

SC is half of that in DSB-SC (due to one sideband removed in filtering method).• coherent receiver rejects quadrature component of noise. Also message and in

phase component of noise appear in the output with half magnitude . • Thus for same average input power and same transmission bandwidth performance

of both DSB-SC and SSB-SC receivers will be same


Noise performance of AM system (Envelope detector)

For AM, Input to demodulator, Signal power at input, or, Noise power at input,


Pass band 2W

Channel

white noise w(t)

s(t)+n(t)

Receivers(t) +nw(t)

demodulator

Si

Ni

So

No

s(t) Envelope detector



Input of multiplier = can be represented in polar form as

where is envelope of AM wave

And is phase angle



𝐴𝑐+𝑘𝑎m( t) 𝑛𝐼(𝑡)𝑛𝑄 (𝑡)𝑅 (𝑡 )𝑒(𝑡)

𝜓 (𝑡) 𝜃(𝑡)

small noise

Small noise caseIn this case, Under this condition e(t) can be approximated as‘Ignoring higher order terms being very small

Or output of envelope detector. and



Signal power at the output Noise power at the output Noise figure As (modulation index is less than 100 %), noise figure of AM receiver is always greater than 1For single tone message , Noise figure where m is modulation indexFor maximum modulation (m=1), noise figure will be minimum i.e. Minimum • Noise figure of AM with envelope detector (small noise) is same as that of Noise

figure of AM with coherent detector



𝐴𝑐+𝑘𝑎m( t) 𝑛𝐼(𝑡)

𝑛𝑄 (𝑡 )𝑅 (𝑡)𝑒(𝑡)

𝜓 (𝑡) 𝜃(𝑡 )

Large noise

Large noise caseIn this case, Under this condition e(t) can be approximated as‘Ignoring higher order terms being very small and using

Or output of envelope detector. As the term containing message is multiplied by noise term, message signal can not be recovered.


Noise performance of FM system

For FM, , where Also narrow band noise, Where and Signal power at input, Noise power at input, Input to demodulator, Envelope ofis of no interest and any variation in envelope will be removed by hard limiter, while relative phasor is of the interest.


Pass band BT

Channel

white noise w(t)

s(t)+n(t)

Receivers(t) +nw(t)

demodulator

Si

Ni

So

No

s(t) Hard limiter

12𝜋

𝑑𝑑𝑡

LPFCutoff Wsd(t) +nd(t)


Noise performance of FM system Small noise case In this case, Choosing as reference for phasor diagram. Relative phase angle [for small . tan = ] The differentiator output The signal component will pass through LPF, so signal power in the output

𝐴𝑐

𝑅 (𝑡)𝑒(𝑡)

𝜓 (𝑡 )−𝜙 (𝑡) 𝜃 (𝑡 )−𝜙 (𝑡 )


Noise performance of FM system Noise component As is random and uniformly distributed, so it can be fairly assumed that is uniformly distributed over 2. So noise component will be independent of message signal.

So noise component Thus noise component at differentiator output. can be obtained passing through a system whose frequency response is given as

Power spectral density of noise component is given as Where =+


Noise performance of FM system

𝜂2

𝑆𝑛 ( 𝑓 )

f

f

𝑆𝑛𝑄 ( 𝑓 )

−𝐵𝑇

2𝐵𝑇

2

f

( 𝐵𝑇

2 𝐴𝑐)2

𝑆𝑛𝑑 ( 𝑓 )

−𝐵𝑇

2𝐵𝑇

2

f

(𝑊𝐴𝑐 )2

𝑆𝑛𝑜 ( 𝑓 )

−𝑊 𝑊

Again Output noise power, Or


Noise performance of FM systemNoise figure For single tone message . modulation index and and So, For NBFM, , For WBFM, , Thus FM improves noise performance with increase in modulation index


Noise performance of FM systemBest noise figure obtained in AM is 1.5 (for m=1), for better noise performance of FM than AM, NBFM noise figure must be less than AM noise figure i.e. <1.5 or Thus for noise performance of FM is similar to AM while for higher noise performance of FM is superior to AM and In FM SNR improves with increase in modulation index.FM Threshold Effect: Above results were based on assumptions that carrier component is much lather than noise component.If input signal is decreased input SNR will also decrease, resulting in decrease in SNR improvement. There will be a point below which if input SNR decreases, output SNR will decrease more rapidly. That value of input SNR is referred as FM threshold. FM threshold is 13 dB or 20i.e . Input SNR implies that carrier power at the input


Threshold improvement in FM: Pre-emphasis de-emphasis

• In practical signals amplitude decreases with increase in frequency. This implies lower SNR (more effect of noise) for high frequency components of message.

• High frequency component may suffer from FM threshold effect.• High frequency components have lower amplitude but are most

important for quality of message.This difficulty can be solved by use of Pre-emphasis de-emphasis.Pre emphasis: High frequency components are boosted (amplified) before modulation.

De emphasis: After demodulation High frequency components are de-boosted to restore original signal.

dB

f

Pre-emphasis gaindB

fDe-emphasis gain

noise performance of cw system

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