- Home/
- GATE ELECTRONICS/
- GATE EC/
- Article

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

By BYJU'S Exam Prep

Updated on: September 25th, 2023

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

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_{c}t; 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_{c}t × A_{c}cos 2πf_{c}t = (A^{2}_{c }/2)[1 + cos 4πf_{c}t] - Output of LPF = (A
^{2}_{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_{c}t for bit 1

= – A_{c} cos 2pf_{c}t 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 f
_{1}and for digital data 0 we use frequency f_{2}.

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

Bandwidth = 2Δf + 2f_{m}

Bandwidth = f_{1} + (1/T_{b}) – f_{2} + (1/T_{b})

= f_{1} – f_{2} + (2/T_{b}); f_{1} – f_{2} = 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 ω_{0}t = ± A cos ω_{0}t

**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 f
_{1}and f_{2}are choose such that f_{1}= mf_{s}and f_{2}= 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

**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, N_{0}/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, (A^{2}_{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.

The Candidates who have missed the schedule for **GATE EC 2021 champion study plan** can follow the following link:

**Detailed Schedule For GATE EC 2021 Champion Study Plan**

Candidates can practice 150+ Mock Tests with BYJU’S Exam Prep Test Series for exams like GATE, ESE, NIELIT from the following link:

**Click Here to Avail Electronics Engineering Test Series (150+ Mock Tests)**

Get unlimited access to 24+ structured Live Courses all 150+ mock tests to boost your GATE 2021 Preparation with Online Classroom Program:

### Click here to avail Online Classroom Program for Electronics Engineering

Thanks

#DreamStriveSucceed

**Download BYJU’S Exam Prep, Best gate exam app**

**for Preparation**