Noise in Digital Communication GATE Notes | EduRev

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Noise in Digital Communication

In digital communication for better SNR, a matched filter is used whose impulse response h(t) is.

h(t) = S* (Tb – t)

where, * is represent complex conjugate

Tb = Bit duration

S(t) = Input signal to filter

Probability of error Pe is

Noise in Digital Communication GATE Notes | EduRev

Noise in Digital Communication GATE Notes | EduRev

where,

Noise in Digital Communication GATE Notes | EduRev

Note: N/2 is two sided noise power spectral density.

Probability of Error The Probability of error for different digital modulation schemes is given below

Probability of Error Different Types of Digital Modulation Schemes

Noise in Digital Communication GATE Notes | EduRev

  • In case of FSK f1 and f2 are choose such that f1 = mfs and f­2 = kfs′ where m and are integers.
  • Bandwidth efficiency for PSK is:

Noise in Digital Communication GATE Notes | EduRev

Noise: 

In electrical-terms, noise may be defined as an unwanted form of energy which tend to interfere with the proper reception and reproduction of transmitted signals. Conveniently noise can be classified as:

  • External noise
  • Internal noise

Noise in Digital Communication GATE Notes | EduRev

Noise Analysis in Communication System: 

The noise analysis can be done in communication system by calculating the following terms

Figure of Merit: 

Noise analysis in Continuous Wave (CW) modulation is carried out in the form of a parameter known as figure of merit denoted by γ. This parameter figure of merit γ is the ratio of output signal-to-noise ratio to the input signal-to-noise ratio of the receiver.

Signal to Noise Ratio (SNR): 

It is defined as ratio of signal power to noise power.

In-phase noise component:

Noise in Digital Communication GATE Notes | EduRev

Where Noise in Digital Communication GATE Notes | EduRevis the Hilbert transform of n(t)

Quadrature noise component

Noise in Digital Communication GATE Notes | EduRev

Noise in Digital Communication GATE Notes | EduRev

where, n (t) represents the filtered noise

Total noise power (N) = White noise power spectrum density x Bandwidth

or

N= (n/2) * Bandwidth

Thus, the noise has a gaussian distribution.

  • The effect of channel noise may be obtained by simple addition of signal x(t) and noise n (t).
  • The noise performance depends on the relative magnitudes of the signal and noise.

Effect of Noise on a Baseband System

SNR is given by

Noise in Digital Communication GATE Notes | EduRev

Where, PR = is received signal phase, N0 = two sided noise spectral density, and ω = Message signal bandwidth.

SNR of baseband system: Noise in Digital Communication GATE Notes | EduRev

Effect of Noise on DSBSC AM

For coherent receiver, SNR at the output is:

Noise in Digital Communication GATE Notes | EduRev

where, Pm = Message signal power, Pc = Carrier signal amplitude, and

Noise in Digital Communication GATE Notes | EduRev

Noise in Digital Communication GATE Notes | EduRev

In DSBSC, the output SNR is the same as the SNR for a baseband system. Therefore DSBSC does not provide any SNR improvement over a baseband communication system.

Effect of Noise on SSB AM

For coherent receiver, SNR at the output is

Noise in Digital Communication GATE Notes | EduRev

Noise in Digital Communication GATE Notes | EduRev

SNR in case of SSB is same as that of DSBSC and baseband system.

Effect of Noise on Conventional AM

For coherent receiver, SNR at the output is

Noise in Digital Communication GATE Notes | EduRev

where, Ac = Amplitude of carrier wave, μ = Modulation index, and Pmn = Normalized message signal power.

Noise in Digital Communication GATE Notes | EduRev

Noise in Digital Communication GATE Notes | EduRev

SNR of conventional AM is always less than the SNR of a baseband system.

Effect of Noise on Angle Modulation

Noise spectral density at the output of angle modulation receiver is

Noise in Digital Communication GATE Notes | EduRev

where, N0/2 is two sided power spectral density of noise.

  • Effect of noise is independent of frequency for PM systems.
  • Effect of noise is more at higher frequencies and less at small frequencies for FM systems.

For angle modulation system, SNR at output is

for PM: 

Noise in Digital Communication GATE Notes | EduRev

where, Pm = message signal power

For FM :

Noise in Digital Communication GATE Notes | EduRev

where, (A2c /2) received signal power Pr.

For PM : 

Noise in Digital Communication GATE Notes | EduRev

where, β= modulation index of PM system.

For FM:

Noise in Digital Communication GATE Notes | EduRev

where, β= modulation index of FM system.

With increase in β without increasing the transmitter power we can increase SNR at output. Increasing β will increasing the bandwidth requirement for transmission so we can increase SNR by increasing bandwidth.

Note: In both PM and FM systems, output SNR is proportional to the square of modulation index.

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