Noise in Digital Communication | Communication System - Electronics and Communication Engineering (ECE) PDF Download

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

h(t) = S* (T_b – t)

where, * is represent complex conjugate

Tb = Bit duration

S(t) = Input signal to filter

Probability of error P_e is

where,

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

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

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

Classification of Noise

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:

Where is the Hilbert transform of n(t)

Quadrature noise component

where, n (t) represents the filtered noise

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

OR

N= (n/2) x 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

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

SNR of baseband system: 

Effect of Noise on DSBSC AM

For coherent receiver, SNR at the output is:

where, P_m = Message signal power, P_c = Carrier signal amplitude, and

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

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

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

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

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: 

where, P_m = message signal power

For FM :

where, (A²_c /2) received signal power P_r.

For PM : 

where, β_P = modulation index of PM system.

For FM:

where, β_f = 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.

PYQs: Competitive Exams

Q1: A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is 40 dB. The minimum number of bits per sample needed to achieve the desired SQNR is __________ .     (GATE 2017)
Ans: 7
Sol:
SNR (Signal to Noise Ratio) for a sinusoidal message signal Quantized uniformly with ‘n’ bits in given by;  SNR_AB = 6n + 1.8
Calculation: Given, SNR = 40 dB, required at the output;
So, 40 ≤  6n + 1.8
6n ≥  40 – 1.8
n ≥  6.366
So, the minimum number of bits per sample needed to achieve the derived SQNR is 7 bits 

Q2: A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8 dB, the number of levels in the quantizer is ________.     (GATE 2015)
Ans: 32
Sol:
In a PCM system with sinusoidal input, The SNR is given by 6n+1.8 dB. where n is a number of bits used for encoding the samples.
the number of quantization levels = L = 2ⁿ

Application: The SNR is given by 6n+1.8 = 31.8dB
⇒ n = 5 bits
Thus, the number of quantization levels L = 2ⁿ = 2⁵=32