Analog Noise
'
$
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
&
%
'
Modulated signal s(t)
x(t)
$
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 &
'
receiver in AM and DSB-SC.
$
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:
&
%
' 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
$
&
%
'
• Output SNR: Average power of demodulated signal s(t) (SN R)O = Average power of noise The Output SNR is measured at the receiver.
$
• 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
&
%
'
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
$
Σ
Low Pass Filter (B)
Output
n(t)
&
Figure 3: Basic Channel Model
%
'
$
Figure of Merit (FoM) Analysis
• DSB-SC (see Figure 4)
s(t) = CAc cos(ωc
$
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
&
%
'
Modulated signal s(t)
x(t)
$
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 &
'
receiver in AM and DSB-SC.
$
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:
&
%
' 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
$
&
%
'
• Output SNR: Average power of demodulated signal s(t) (SN R)O = Average power of noise The Output SNR is measured at the receiver.
$
• 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
&
%
'
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
$
Σ
Low Pass Filter (B)
Output
n(t)
&
Figure 3: Basic Channel Model
%
'
$
Figure of Merit (FoM) Analysis
• DSB-SC (see Figure 4)
s(t) = CAc cos(ωc