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) = Ac cos 2πfct; 0 ≤ t ≤ Tb
= 0; otherwise
Bandwidth = 2 × 1/Tb
= 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.
- For binary digit 1, Ac cos 2π fct × Ac cos 2πfct = (A2c /2)[1 + cos 4πfct]
- Output of LPF = (A2c /2)
- For binary digit 0 output of LPF = 0
- In ASK, probability of error (Pe) 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) = Ac cos 2πfct for bit 1
= – Ac cos 2pfct for bit 0
A frequency of the carrier must be a multiple of a bit rate.
Tb = n/fc
Fc = nrb
- 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 + 2fm
Bandwidth = f1 + (1/Tb) – f2 + (1/Tb)
= f1 – f2 + (2/Tb); f1 – f2 = 2Δf
- In case of FSK, Pe 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* (Tb – t)
where, * is represent complex conjugate
Tb = Bit duration
S(t) = Input signal to filter
Probability of error Pe is
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 = mfs and f2 = kfs′ 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
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, PR = 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, Pm = Message signal power, Pc = 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, Ac = Amplitude of carrier wave, μ = Modulation index, and Pmn = 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
where, Pm = message signal power
For FM :
where, (A2c /2) received signal power Pr.
For PM :
where, βP = modulation index of PM system.
where, βf = 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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