Modulation Schemes and Decoding-II Study Notes for GATE EC 2022 Exam

In this article, Candidates can find study notes on Modulation Schemes and Decoding-II consists of topics such as Digital Modulation Schemes, Quadrature Amplitude Modulation, Noise in Digital Communication, Noise Analysis in Communication System

Digital Modulation Schemes

This is possible to transmit the analog signal i.e., speech, video etc, in digital format. Some digital modulation schemes are given below

• Digital Carrier Modulation: Commonly used digital modulation schemes are Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK) and Phase Shift Keying (PSK).
• Amplitude Shift Keying (ASK): The amplitude of a high-frequency carrier is varied in accordance with digital data (0 or 1).

S(t) = A_c cos 2πf_ct; 0 ≤ t ≤ T_b

= 0; otherwise

Bandwidth = 2 × 1/T_b

= 2 × bit rate

• For digital input 1 amplitude level is high and for digital input 0 amplitude level is low.
• Signalling used is on-off signalling.

Demodulation of ASK:

• For binary digit 1, A_c cos 2π f_ct × A_c cos 2πf_ct = (A²_c /2)[1 + cos 4πf_ct]
• Output of LPF = (A²_c /2)

• For binary digit 0 output of LPF = 0
• In ASK, probability of error (P_e) is high.
• In ASK, SNR is less.

Phase Shift Keying (PSK):

In phase shift, keying phase of high-frequency carrier is varied in accordance with digital data 1 or 0.

• NRZ signalling is used.

S(t) = A_c cos 2πf_ct for bit 1

= – A_c cos 2pf_ct for bit 0

A frequency of the carrier must be a multiple of a bit rate.

T_b = n/f_c

F_c = nr_b

• In case of PSK, a probability of error is less.
• In case of PSK, SNR is high.
• Mainly used a technique in wireless transmission.

Frequency Shift Keying (FSK):

• In frequency shift keying, a frequency of the carrier is varied in accordance with digital data (1 or 0).
• For digital data 1 we use frequency f₁ and for digital data 0 we use frequency f₂.

• NRZ signalling is used here
• VCO The schematic diagram of VCO is given below

Bandwidth = 2Δf + 2f_m

Bandwidth = f₁ + (1/T_b) – f₂ + (1/T_b)

= f₁ – f₂ + (2/T_b); f₁ – f₂ = 2Δf

Key Points

• In case of FSK, P_e is less but SNR is high.
• Multiplexing is difficult in FSK.

Differential Phase Shift Keying (DPSK): In PSK it needs a complicated synchronising circuit at the receiver, this disadvantage of PSK is removed in DPSK.

A cos ω₀t = ± A cos ω₀t

Note: Advantage of DPSK over PSK is, DPSK does not require a coherent carrier for demodulation.

Comparison of Digital Modulation Schemes

Quadrature Amplitude Modulation (QAM): In QAM, digital information is content in a both amplitude and phase of the signal. It is used in both digital modulation scheme and analog modulation scheme. Digital cable television and in cable modem applications QAM is used.

Noise in Digital Communication: 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

T_b = 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:

1. External noise
2. Internal 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) * 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, _N0/2 = 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. 

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