Techniques to control noise and fading. Noise and fading are the primary sources of distortion in communication channels Techniques to reduce noise and fading are usually implemented at the receiver
Message signal x(t)
Detected signal y(t)
Equalizer System EquationsDetected signaly(t) = x(t) * f(t) + nb(t)=> Y(f) = X(f) F(f) + Nb(f)Output of the Equalizer ^ d(t) = y(t) * heq(t)
Equalizer System EquationsDesired output ^ D(f) = Y(f) Heq(f) = X(f) => Heq(f) X(f) F(f) = X(f)=> Heq(f) F(f) = 1Heq(f) = 1/ F(f) => Inverse filter
MSE Error =
Aim of equalizer: To minimize MSE error
The equalizer weights are varied until convergence is reached.
Input s(t) Output r(t)
r (t) = (t) e -j q(t) s (t) + n (t)
SNR = = (Eb / No) 2 (t)
where (γi 0 ) and γi = instantaneous SNR
= 20 dB => 100.
Threshold γ = 10 dB = 10.
Prob[γi>γ] = 1 – (1 – e – γ/ )M
For M = 5,
Prob= 1 – (1 – e – 0.1)5 = 0.9999
For M = 1(No Diversity),
Prob= 1 – (1 – e – 0.1)= 0.905
rM = total signal envelope
… assuming each branch has some average noise power N, total noise power NT applied to the detector is,
EXAMPLE : Repeat earlier problem for MRC case
M1 M2 M3α2
r(t) αM Z’ Z