1. 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
The most common mechanism is to have a receiver filter that can cancel the effects of noise and fading, at least partially
Digital technology has made it possible to have adaptive filters

2. Principle of Equalization
Equalization is the process of compensation at the receiver, to reduce noise effects
The channel is treated as a filter with transfer function
Equalization is the process of creating a filter with an inverse transfer function of the channel
Since the channel is a varying filter, equalizer filter also has to change accordingly, hence the term adaptive.

3. Equalization Model-Signal detection
Transmitter
Receiver
Front End
Channel
IF Stage
Detector
Carrier
Message signal x(t)
Detected signal y(t)

4. Equalization model-Correction
Reconstructed
Signal
nb(t)
Decision
Maker
Equalizer +
Equivalent
Noise

5. Equalizer System Equations Detected signal Time domain:. y(t) = x(t)
Equalizer System Equations Detected signal Time domain: y(t) = x(t) * f(t) + nb(t) Frequency domain: Y(f) = X(f) F(f) + Nb(f) Output of the Equalizer ^ d(t) = y(t) * heq(t)

6. Equalizer System Equations Desired output. ^
Equalizer System Equations Desired output ^ D(f) = Y(f) Heq(f) = X(f) => Heq(f) X(f) F(f) = X(f) => Heq(f) F(f) = 1 Heq(f) = 1/ F(f) => Inverse filter

7. System Equations Error MSE Error =
Aim of equalizer: To minimize MSE error

8. Equalizer Operating Modes
Training
Tracking

9. Training and Tracking functions
Training sequence is a known fixed bit pattern sent by the transmitter
The user data is sent immediately after the training sequence
The equalizer uses training sequence to adjust its frequency response Heq (f) and is optimally ready for data sequence
Adjustment goes on dynamically, hence it is adaptive equalizer

10. Block Diagram of Digital Equalizer
w0k
w2k
w1k
wNk ∑ - + ∑
Adaptive Algorithm

11. Digital Equalizer equations
Digital systems use time sampling:
t = k T
T is the sampling interval
Equalizer output:

12. The error signal updates the equalizer weights
Error minimization
The adaptive algorithm minimizes error
The error signal updates the equalizer weights
The updating is continued until convergence

13. Diversity techniques
Diversity is a powerful communications technique for minimizing fading effects
It provides wireless link improvement at relatively low cost
Unlike equalization, diversity requires no training overhead
Practical version is the popular Rake receiver

14. Fading effects
Small Scale fading causes rapid amplitude fluctuations in received wireless signal
Fading results in signal loss and distortion

15. Principle of diversity
If we space 2 antennas at 0.5 m, one may receive a null while the other receives a strong signal
By selecting the best signal at all times, a receiver can mitigate or reduce small-scale fading. This concept is Space diversity or Antenna Diversity

16. Space Diversity
Concept of using more than one antenna (or branch )for reception
Parameters
gi = instantaneous SNR
G = Average SNR
g= Threshold SNR

17. SNR Improvement Using Diversity
M diversity branches
Probability [gi > g]
Average SNR improvement

18. Example :
Assume that 5 antennas are used to provide space diversity. If average SNR is 20 dB, determine the probability that the instantaneous SNR will be  10 dB. Compare this with the case of a single receiver.

19. Solution :  = 20 dB => 100 Threshold g = 10 dB = 10
Prob [gi > g] = 1 – (1 – e – g/  )M
For M = 5 branches,
Prob = 1 – (1 – e – 0.1 )5 =
For M = 1 branch (No Diversity),
Prob = 1 – (1 – e – 0.1 ) = 0.905

20. Maximal Ratio Combining (MRC)
MRC uses each of the M branches in co-phased and weighted manner such that highest achievable SNR is available
If each branch has gain Gi,
rM = total signal envelope =

21. SNR Improvement with MRC

22. Example : Repeat earlier problem for MRC case

23. Types of diversity Space Diversity
Either at the mobile or base station
Polarization Diversity
Orthogonal Polarization to exploit diversity
Frequency Diversity
More than one carrier frequency is used
Time Diversity :
Information is sent at time spacings

24. Practical diversity – Rake receiver
CDMA system uses RAKE Receiver to improve the signal to noise ratio at the receiver
Generally CDMA systems do not require equalization due to multi-path resolution.

25. Block Diagram Of Rake Receiverα1
M1 M2 M α2
r(t) αM Z’ Z
Correlator 1
 ()dt
Correlator 2 Σ
Correlator M
>
<
m’(t)

26. Principle Of Operation
M correlators – correlator i is synchronized to strongest multi-path Mi
The weights 1 , 2 ,……,M are based on SNR from each correlator output
Demodulation and bit decisions are then based on the weighted outputs of M correlators