1 Techniques to control noise and fading l Noise and fading are the primary sources of distortion in communication channels l Techniques to reduce noise and fading are usually implemented at the receiver l The most common mechanism is to have a receiver filter that can cancel the effects of noise and fading, at least partially l Digital technology has made it possible to have adaptive filters l Noise and fading are the primary sources of distortion in communication channels l Techniques to reduce noise and fading are usually implemented at the receiver l The most common mechanism is to have a receiver filter that can cancel the effects of noise and fading, at least partially l Digital technology has made it possible to have adaptive filters

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

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

4 Equalization model-Correction +Equalizer DecisionMaker ReconstructedSignal EquivalentNoise n b (t)

5 Equalizer System Equations Detected signal y(t) = x(t) * f(t) + n b (t) => Y(f) = X(f) F(f) + N b (f) Output of the Equalizer ^ d(t) = y(t) * h eq (t)

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

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

8 Equalizer Operating Modes l Training l Tracking l Training l Tracking

9 Training and Tracking functions l 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 l The equalizer uses training sequence to adjust its frequency response H eq (f) and is optimally ready for data sequence l Adjustment goes on dynamically, it is adaptable equalizer l 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 l The equalizer uses training sequence to adjust its frequency response H eq (f) and is optimally ready for data sequence l Adjustment goes on dynamically, it is adaptable equalizer

10 Block Diagram of Digital Equalizer Z -1 ∑ w 0k w 1k w 2k w Nk Adaptive Algorithm ∑ + -

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

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

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

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

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

16 …Principle of diversity l 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) Consider a fading channel (Rayleigh) Input s(t) Output r(t) Input s(t) Output r(t) Input-output relation Input-output relation r (t) =  (t) e -j  (t) s (t) + n (t) r (t) =  (t) e -j  (t) s (t) + n (t) l Average value of signal to noise ratio ___ ___ SNR =  = (E b / N o )  2 (t) Consider a fading channel (Rayleigh) Consider a fading channel (Rayleigh) Input s(t) Output r(t) Input s(t) Output r(t) Input-output relation Input-output relation r (t) =  (t) e -j  (t) s (t) + n (t) r (t) =  (t) e -j  (t) s (t) + n (t) l Average value of signal to noise ratio ___ ___ SNR =  = (E b / N o )  2 (t) Channel

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

19 Average Snr Improvement Using Diversity l Average SNR improvement using selection Diversity,

20 l 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.  = 20 dB => 100. Threshold γ = 10 dB = 10. Threshold γ = 10 dB = 10. l 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.  = 20 dB => 100. Threshold γ = 10 dB = 10. Threshold γ = 10 dB = 10.

21 …Example…Example Prob [γ i > γ] = 1 – (1 – e – γ /  ) M For M = 5, Prob = 1 – (1 – e – 0.1 ) 5 = For M = 1(No Diversity), Prob = 1 – (1 – e – 0.1 ) = Prob [γ i > γ] = 1 – (1 – e – γ /  ) M For M = 5, Prob = 1 – (1 – e – 0.1 ) 5 = For M = 1(No Diversity), Prob = 1 – (1 – e – 0.1 ) = 0.905

22 Maximal Ratio Combining (MRC) l 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 G i, r M = total signal envelope = l 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 G i, r M = total signal envelope =

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

24 Average SNR Improvement

25 EXAMPLE : Repeat earlier problem for MRC case

26 …Example…Example e -0.1

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

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

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

30 Block Diagram Of Rake Receiver α 1 α 1 M1 M2 M3 α 2 r(t) α M Z’ Z α 1 α 1 M1 M2 M3 α 2 r(t) α M Z’ Z Correlator 1 Correlator 2 Correlator M Σ  (  )dt ><>< m’(t)

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

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