Analog Noise

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Noise Analysis - AM, FM
The following assumptions are made: • Channel model – distortionless – Additive White Gaussian Noise (AWGN) • Receiver Model (see Figure 1) – ideal bandpass filter – ideal demodulator

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Modulated signal s(t)

x(t)

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Demodulator

Σ

BPF

w(t)

Figure 1: The Receiver Model • BPF (Bandpass filter) - bandwidth is equal to the message bandwidth B • midband frequency is ωc . Power Spectral Density of Noise • and is defined for both positive and negative frequency (see Figure 2). %
N0 2 ,

• N0 is the average power/(unit BW) at the front-end of the &

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receiver in AM and DSB-SC.

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N 2

0

−ω c 4π B

ω 4π B

c

ω

Figure 2: Bandlimited noise spectrum The filtered signal available for demodulation is given by:

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' x(t) = s(t) + n(t) n(t) = nI (t) cos ωc t −nQ (t) sin ωc t nI (t) cos ωc t is the in-phase component and nQ (t) sin ωc t is the quadrature component. n(t) is the representation for narrowband noise. There are different measures that are used to define the Figure of Merit of different modulators: • Input SNR: Average power of modulated signal s(t) (SN R)I = Average power of noise

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• Output SNR: Average power of demodulated signal s(t) (SN R)O = Average power of noise The Output SNR is measured at the receiver.

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• Channel SNR: Average power of modulated signal s(t) (SN R)C = Average power of noise in message bandwidth • Figure of Merit (FoM) of Receiver: (SN R)O F oM = (SN R)C

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To compare across different modulators, we assume that (see Figure 3): • The modulated signal s(t) of each system has the same average power • Channel noise w(t) has the same average power in the message bandwidth B. m(t) message with same power as modulated wave

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Σ

Low Pass Filter (B)

Output

n(t)

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Figure 3: Basic Channel Model

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Figure of Merit (FoM) Analysis
• DSB-SC (see Figure 4)

s(t) = CAc cos(ωc