Note for Principles of Communication Systems - PCS by Manjunatha P

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Chapter 1 Noise in Analog Modulation Syllabus • Introduction, Receiver Model • Noise in DSB-SC receivers • Noise in AM receivers, Threshold effect • Noise in FM receivers, Capture effect, FM threshold effect, FM threshold reduction. • Pre-emphasis and De-emphasis in FM. (Chapter 6 of Text) Text : Simon Haykins & Moheri, “Communication Systems”, 5th Edition, John Willey, India Pvt. Ltd, 2010, ISBN 9788126521517. Note: While preparing this material Text book Simon Haykins & Moheri “Communication Systems”, 5th Edition is used and most of the Figures are redrawn and some of the Figures and material is used from the Internet. Some concepts are directly downloaded from the Internet. All the concepts may be of from Text book or it may be from Internet. 1

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1.1. INTRODUCTION: 1.1 Chapter 1. Noise in Analog Modulation Introduction: • To analyse the noise in continuous wave modulation systems, a receiver model is required. • In a receiver model it is assumed that noise (channel noise) is additive, white, and Gaussian in nature. • This assumption help us to obtain a basic understanding of the way in which noise affects the performance of the receiver. • The block diagram of the receiver model is as shown in Figure 1.1. Modulated signal s(t) Band-pass filter + Output signal s(t) x(t ) Demodulator w(t ) Noise Figure 1.1: Block diagram of the receiver model • Consider a modulated signal s(t) is transmitted through the channel and in the channel the noise w(t) is added to the transmitted signal s(t). • It is assumed that the noise w(t) is a sample function of the white Gaussian noise process with the two sided spectral density of N2o • In multiple access communication system when more than two transmitters use the same common channel to transmit information, then interference will occurs and this will limits the performance of the system. • The input to the demodulator is given by x(t) = s(t) + n(t) where n(t) is the sample function of a bandlimited (narrowband) white noise process n(t) with the power spectral density N2o . • The bandwidth of band-pass filter is equal to the bandwidth of the modulated signal s(t) (Transmitter bandwidth BT ) and its mid-frequency is equal to the carrier frequency fc and fc  BT . • The ideal characteristic of the bandpass filter is as shown in Figure 1.2. • The noise n(t) is represented in the canonical form as: n(t) = nI (t)cos(2πfc t) − nQ (t)sin(2πfc t) Dr. Manjunatha P Professor Dept of E&CE, JNN College of Engineering, Shivamogga 2

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1.1. INTRODUCTION: Chapter 1. Noise in Analog Modulation • where where nI (t) is the in-phase noise component and nQ (t) is the quadrature noise component, with respect to the unmodulated carrier wave Ac cos(2πfc t)). SN ( f ) N0 2 − fc 0 BT fc f Figure 1.2: Ideal characteristic of the bandpass filter • The phasor diagram for noise is as shown in Figure 1.3 (t ) r t an t l su nQ (t ) Re Ψ (t ) nI (t ) Figure 1.3: Ideal characteristic of the bandpass filter • Bandpass noise can also be expressed in envelope-and-phase form as n(t) = r(t)cos[2πfc t + Ψ(t)] • where r(t) is the envelope r(t) = h i −1 nq (t) tan nI (t) q n2I (t) + n2q (t) and Ψ(t) is the phase of the noise. Ψ(t) = • The average noise power at the demodulator input is = Average noise power per unit Bandwidth × Bandwidth = N0 BT • Input signal-to-noise ratio (SN R)I = Average power of modulated signal Average power of f iltered noise n(t) • Output signal-to-noise ratio (SN R)O = Average power of demodulated signal Average power of noise at the receiver output Dr. Manjunatha P Professor Dept of E&CE, JNN College of Engineering, Shivamogga 3

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1.1. INTRODUCTION: Chapter 1. Noise in Analog Modulation • Channel signal-to-noise ratio (SN R)C = Average power of modulated signal Average power of noise in the message bandwidth Figure of merit: • For comparing different modulation systems, Figure of Merit (FoM) criteria is used, which is defined as the ratio of output signal-to-noise ratio to the channel signal-to-noise ratio. = (SN R)O (SN R)C • The value of the figure of merit may equal one, less than one, or be greater than one, depending on the type of modulation scheme. • As the figure of merit value is higher then the receiver performance is better. Dr. Manjunatha P Professor Dept of E&CE, JNN College of Engineering, Shivamogga 4