Techniques to control noise and fading

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 Carrier Transmitter Channel Receiver Front End IF Stage Message signal x(t) Detector Detected signal y(t)

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

5. 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)

6. 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

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

8. Equalizer Operating Modes • Training • Tracking

9. Training and Tracking functions • The Training sequence is a known pseudo-random signal or a 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, it is adaptable equalizer

10. Block Diagram of Digital Equalizer Z-1 Z-1 Z-1 w2k w0k w1k wNk ∑ - + ∑ Adaptive Algorithm

11. Digital Equalizer equations • In discrete form, we sample signals at interval of ‘T’ seconds : t = k T; • The output of Equalizer is:

12. Error minimization • The adaptive algorithm is controlled by the error signal, The equalizer weights are varied until convergence is reached.

13. Types of equalizers • Linear Equalizers. • Non Linear Equalizers.

14. Diversity techniques • Powerful communications receiver technique that provides wireless link improvement at relatively low cost. • Unlike equalization, diversity requires no training overhead.

15. Principle of diversity • Small Scale fading causes deep and rapid amplitude fluctuations as mobile moves over a very small distances.

16. …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 Antenna Diversity.

17. Diversity Improvement • Consider a fading channel (Rayleigh) Input s(t) Output r(t) • Input-output relation r (t) =  (t) e -j q(t) s (t) + n (t) • Average value of signal to noise ratio ___ SNR =  = (Eb / No) 2 (t) Channel

18. Average SNR Improvement Using Diversity • p.d.f., p(γi) = (1 /  ) e – γi /  where (γi 0 ) and γi = instantaneous SNR Probability [γiγ] • M diversity branches, Probability [γi>γ]

19. Average Snr Improvement Using Diversity • Average SNR improvement using selection Diversity,

20. Example : Assume that 5 antennas are used to provide space diversity. If average SNR is 20 dB, determine the probability that the SNR will be  10 dB. Compare this with the case of a single receiver. Solution :  = 20 dB => 100. Threshold γ = 10 dB = 10.

21. …Example 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

22. 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 =

23. …Maximal Ratio Combining (MRC) … assuming each branch has some average noise power N, total noise power NT applied to the detector is,

24. Average SNR Improvement

25. EXAMPLE : Repeat earlier problem for MRC case

26. …Example e-0.1

27. Types of diversity • Space Diversity • Either at the mobile or base station. • At base station, separation on order of several tens of wavelength are required. • Polarization Diversity • Orthogonal Polarization to exploit diversity

28. …Types of diversity • Frequency Diversity : • More than one carrier frequency is used • Time Diversity : • Information is sent at time spacings • Greater than the coherence time of Channel, so multiple repetitions can be resolved

29. Practical diversity receiver – rake receiver • CDMA system uses RAKE Receiver to improve the signal to noise ratio at the receiver. • Generally CDMA systems don’t require equalization due to multi-path resolution.

30. Block Diagram Of Rake Receiver α1 M1 M2 M3α2 r(t) αM Z’ Z Correlator 1  ()dt Correlator 2 Σ Correlator M > < m’(t)

31. Principle Of Operation • M Correlators – Correlator 1 is synchronized to strongest multi-path M1. The correlator 2 is synchronized to next strongest multipath M2 and so on. • The weights 1 , 2 ,……,M are based on SNR from each correlator output. ( is proportional to SNR of correlator.) • M Z’ = M ZM m =1

32. …Principle Of Operation • Demodulation and bit decisions are then based on the weighted Outputs of M Correlators.