Chapter 5 Effect of Noise on Analog Communication Systems. Outline. Chapter 5 Effect of Noise on Analog Communication Systems 5.1 Effect of Noise on linear-Modulation Systems 5.1.1 Effect of noise on a baseband system 5.1.2 Effect of noise on DSB-SC AM 5.1.3 Effect of noise on SSB AM

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Chapter 5 Effect of Noise on Analog Communication Systems

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Outline • Chapter 5 Effect of Noise on Analog Communication Systems • 5.1 Effect of Noise on linear-Modulation Systems • 5.1.1 Effect of noise on a baseband system • 5.1.2 Effect of noise on DSB-SC AM • 5.1.3 Effect of noise on SSB AM • 5.1.4 Effect of noise on conventional • 5.2 Carrier-Phase Estimation with a phase-Locked Loop (PLL) • 5.2.1 The phase-locked loop (PLL) • 5.2.2 Effect of additive noise on phase estimation • 5.3 Effect of noise on angle modulation • 5..3.1 Threshold effect in angle modulation • 5.3.2 Pre-emphasis and De-emphasis filtering • 5.4 Comparison of analog-modulation systems 2

Outline • 5.5 Effects of transmission losses and noise in analog communication systems • 5.5.1 Characterization of thermal noise sources • 5.5.2 Effective noise temperature and noise figure • 5.5.3 Transmission losses • 5.5.4 Repeaters for signal transmission • 5.6 Further reading 3

5 Effect of Noise on Analog Communication Systems • The effect of noise on various analog communication systems will be analysis in this chapter. • Angle-modulation systems and particularly FM, can provide a high degree of noise immunity, and therefore are desirable in cases of severe noise and/or low signal power. • The noise immunity is obtained at the price of sacrificing channel bandwidth because he bandwidth requirements of angle-modulation systems is considerably higher than amplitude-modulation systems. 4

5.1 Effect of Noise on linear-Modulation Systems(4) Conventional AM Notes: i) Signal and noise components are no longer additive. ii) Signal component is multiple by the noise and is no longer distinguishable. iii) no meaningful SNR can be defined. • It is said that this system is operating below the threshold ==> threshold effect 19

5.2.1 The phase-locked loop (PLL) ) • Loop filter is a lowpass filter, dc is reserved as is removed. • It has transfer function • n(t) provide the control voltage for VCD (see section 5.3.3). • The VCO is basically a sinusoidal signal generation with an instantaneous phase given by where is a gain constant in radians/ volt-sec. 27

5.2.1 The phase-locked loop (PLL) ) • The carrier-phase estimate at the output of VCO is : and its transfer function is . • Double-frequency terms resulting from the multiplication of the input signal to the loop with the output of the VCD is removed by the loop filter PLL can be represented by the closed-loop system model as follows. 28

5.2.1 The phase-locked loop (PLL) ) • In steady-state operation, when the loop is tracking the phase of the received carrier, is small. • With this approximation, PLL is represented the linear model shown below. 30

5.2.1 The phase-locked loop (PLL) ) • The closed-loop system function of the linearized PLL is second order when the loop filter has a signal pole and signal zero. • The parameter determines the position of zero in H(s), while K, and control the position of the closed-loop system poles. 32

5.2.1 The phase-locked loop (PLL) ) • The denominator of H(s) may be expressed in the standard form where : loop-damping factor : natural frequency of the loop 33

5.2.1 The phase-locked loop (PLL) ) • The magnitude response as a function of the normalized frequency is illustrated, with the damping factor as a parameter and . 34

5.2.1 The phase-locked loop (PLL) ) • The one-side noise equivalent bandwidth • Trade-off between speed of response and noise in the phase estimate 35

5.2.2 Effect of additive noise on phase estimation • PLL is tracking a signal as which is corrupted by additive narrowband noise , are assumed to be statistically independent stationary Gaussian noise. 36

5.2.2 Effect of additive noise on phase estimation • Problem 4.29 a phase shift does not change the first two moments of nc(t) and ns(t). i.e. xc(t) and xs(t) have exactly the same statistical characteristics as nc(t) and ns(t). 37

5.2.2 Effect of additive noise on phase estimation is additive at the input to the loop, the variance of the phase error , which is also the variance of the VCO output phase is Bneq : one-sided noise equivalent bandwidth of the loop, given by 40

5.2.2 Effect of additive noise on phase estimation • Note that is the power of the input sinusoid, and is simply proportional to the total noise power with the bandwidth of the PLL divided by the input signal power, hence where is defined as the SNR Thus, the variance of is inversely proportional to the SNR. 41

5.2.2 Effect of additive noise on phase estimation • By computing the autocorrelation and power spectral density of these two noise component, one can show that both components have spectral power in frequency band centered at 2 fc. • Let’s select Bneq << Bbp, then total noise spectrum at the input to PLL may be approximated by a constant with the loop bandwidth. 44

5.2.2 Effect of additive noise on phase estimation • This approximation allows us to obtain a simple expression for the variance of the phase error as where SL is called the squaring loss and is given as since SL<1 , we have an increase in the variance of the phase error caused by the added noise power that results from the squaring operation. • E.g. if the loss is 3dB or equivalently, the variance in the estimate increase by a factor of 2. 45

5.2.2 Effect of additive noise on phase estimation • These terms (signal noise and noise noise) are similar to the two noise terms at the input of the PLL for the squaring method. • In fact, if the loop filter in the Costas loop is identical to that used in the squaring loop, the two loops are equivalent. • Under this condition the pdf of the phase error, and the performance of the two loops are identical. • In conclusion, the squaring PLL and the Costas PLL are two practical methods for deriving a carrier-phase estimation for synchronous demodulation of a DSB-SC AM signal. 50