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.

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