Chapter 7 Equalization, Diversity

1. Chapter 7Equalization, Diversity

7. Figure Explaining Multi-path Fading

10. Inter Symbol Interference(ISI)

12. Definition Equalization, Diversity & Channel Coding

13. Diversity

15. Diversity Techniques- Highlights

16. Diversity Techniques- Highlights

17. Channel Coding

18. Channel Coding (Cont�d)

19. Fundamentals of Equalization

24. Example 7.3 Consider the design of a Digital carrier cellular system Given F=900 Mhz, mobile velocity = 80 km/hour Symbol rate = 24.3 Kbps Determine The maximum doppler shift The coherence time of the channel Max # of symbols that can be transmitted without updating the equalizer

25. Solution Example 7.3 The max doppler shift = velocity/wavelength Wavelength = 3*10^8/900*10^6 = 0.33 meters Doppler shift = 80 *1000/36000/0.33 = 66.67 Hz Coherence time (using the geometric mean) = 3/(4* doppler shift) *sqrt (1/Pi) = 6.3 4millisecs Symbols transmitted without updating the equalizer = 6.34*24.3*1000 = 154 symbols

26. Working of an Adaptive Equalizer (Cont�d)

27. Block Diagram of Adaptive Equalizer

28. A Generic Adaptive Equalizer

29. Diversity

30. Topics Diversity Space Diversity Selection Diversity Scanning Diversity Maximum Ratio Combining Equal Gain Combining Polarization Diversity Frequency Diversity Time Diversity

31. DIVERSITY A diversity scheme is a method that is used to develop information from several signals transmitted over independent fading paths. It exploits the random nature of radio propagation by finding independent (uncorrelated) signal paths for communication.

32. Diversity Technique

33. MACROSCOPIC DIVERSITY Prevents Large Scale fading. Large Scale fading is caused by shadowing due to variation in both the terrain profile and the nature of the surroundings. Large Scale fading is log normally distributed signal. This fading is prevented by selecting an antenna which is not shadowed when others are, this allows increase in the signal-to-noise ratio. MICROSCOPIC DIVERSITY Prevents Small Scale fading. Small Scale fading is caused by multiple reflections from the surroundings. It is characterized by deep and rapid amplitude fluctuations which occur as the mobile moves over distances of a few wavelength. This fading is prevented by selecting an antenna which gives a strong signal that mitigates this small signal fading effect. Types Of Diversity

34. Space Diversity Principle : A method of transmission or reception, or both, in which the effects of fading are minimized by the simultaneous use of two or more physically separated antennas, ideally separated by one half or more wavelengths. Antenna diversity Antenna diversity

35. Space Diversity Signals received from spatially separated antennas on the mobile would have essentially uncorrelated envelopes for antenna separations of one half wavelength or more. Generalized block diagram of space diversity.

36. Selection Diversity Principle : Selecting the best signal among all the signals received from different braches at the receiving end.

37. Derivation of Selection Diversity Improvement Consider M independent Rayleigh fading channels available at receiver Diversity branch Assumptions: Each branch has the same average SNR Instantaneous SNR for each branch = ?i

38. Selection Diversity The Signal-to-Noise ratio is defined as follows Eb , N0 are constants Where Eb - Average Carrier Energy N0 - Noise power spectral density ? - A random variable used to represent amplitude values of the fading channel with respect to Eb/N0 The instantaneous SNR ( ?i ) can be defined as

39. Selection Diversity (cont�d) For Rayleigh fading channels, a has a Rayleigh distribution and so a 2 and consequently ?i have a chi-square distribution with two degrees of freedom. The probability density function for such a channel is The pdf for a single branch that has SNR less than some threshold ? is This is not a test, but a distribution. The Chi-square distribution, is derived from the Normal distribution. It is the distribution of a sum of squared Normal distributed variables. That is, if all Xi are independent and all have an identical, standard Normal distribution then X^2 = X1*X1 + X2*X2 + X3*X3 + ... + Xv*Xv is Chi-square distributed with v degrees of freedom with mean = v and variance = 2*v. The importance of the Chi-square distribution stems from the fact that it describes the distribution of the Variance of a sample taken from a Normal distributed population.Note that X^2 is a Sum of Squares and should be tested One-Sided only. The distribution of the underlying sample values X has mean = 0 and variance = 1, i.e., is Standard Normal. As a consequence, X^2 has mean equal to the Degrees of Freedom and a variance equal to 2 * Degrees of Freedom. Assumptions:The values from which X^2 is calculated are themselves Normal distributed with unit variance. This is not a test, but a distribution. The Chi-square distribution, is derived from the Normal distribution. It is the distribution of a sum of squared Normal distributed variables. That is, if all Xi are independent and all have an identical, standard Normal distribution then X^2 = X1*X1 + X2*X2 + X3*X3 + ... + Xv*Xv is Chi-square distributed with v degrees of freedom with mean = v and variance = 2*v. The importance of the Chi-square distribution stems from the fact that it describes the distribution of the Variance of a sample taken from a Normal distributed population.Note that X^2 is a Sum of Squares and should be tested One-Sided only. The distribution of the underlying sample values X has mean = 0 and variance = 1, i.e., is Standard Normal. As a consequence, X^2 has mean equal to the Degrees of Freedom and a variance equal to 2 * Degrees of Freedom. Assumptions:The values from which X^2 is calculated are themselves Normal distributed with unit variance.

40. Selection Diversity (cont�d) The probability that all M independent diversity branches receive signals which are less than a threshold ? is If a signal branch achieves SNR > ? then the probability that SNR > ? for one or more branches is

41. Cumulative distribution curves for output signals from selection diversity for various values of M The percentage of total time interval during which a signal is below any given level is called �outage rate� at that level. When M = 1 ?/ ? = 1 10 Log(?/ ? ) = 0

42. Determination of average signal to noise ratio Find the pdf of the fading signal Compute the derivative of PM(?) The mean SNR is Where

43. Evaluating this equation the average SNR improvement using selection can be found

44. Selection Diversity Example Assuming four branch diversity is used, where each branch receives an independent Rayleigh fading signal. If the average SNR is 20 dB, determine the probability that the SNR will drop below 10 dB. Compare this with the case of a single receiver without diversity. ? = 10 dB ? = 20 dB ?/ ? = 0.1 With Selection Diversity Without Diversity

45. Conclusion Selection diversity offers an average improvement in the link margin without requiring additional transmitter power or sophisticated receiver circuitry. Selection diversity is easy to implement because all that is needed is a side monitoring station and an antenna switch at the receiver. However it is not an optimal diversity technique because it does not use all of the possible branches simultaneously. In practice the SNR is measured as (S+N)/N, since it is difficult to measure SNR.

46. Feedback or Scanning Diversity Principle : Scanning all the signals in a fixed sequence until the one with SNR more than a predetermined threshold is identified.

47. Scanning Diversity Explanation Consider M independent Rayleigh fading channels available at receiver.

48. Conclusion This method is very simple to implement, requiring only one receiver. The resulting fading statistics are somewhat inferior to those obtained by the other methods.

49. Maximal Ratio Combining Principle : Combining all the signals in a co-phased and weighted manner so as to have the highest achievable SNR at the receiver at all times.

50. Derivation of Maximum Ratio Combining Improvement Consider M branches which are maximal ratio combined in a co-phased and weighted manner in order to achieve high SNR

51. Assumptions: The voltage signal ?i from each of the M diversity branches are co-phased to provide coherent voltage addition and are individually weighted to provide optimal SNR. Each branch has gain Gi Each branch has same average noise power N

52. Resulting signal envelope applied to the detector is Assuming that all amplifiers have additive noise at their input and that the noise is uncorrelated between different amplifiers. The total noise power NT applied to the detector is the weighted sum of the noise in each branch. Which results in a SNR applied to the detector ?M Using Chebychev�s inequality ?M is maximized when

53. Maximal Ratio Combining The Maximized value is Now We have The E field received envelop The received signal envelope for a fading mobile radio signal can be modeled from two independent Gaussian random variables Tc and Ts each having zero mean and equal variance s2 . Thus the snr out of the Thus the snr out of the

54. Maximal Ratio Combining Hence ?M is a chi-square distribution of 2M Gaussian random variable with variance The resulting pdf for ?M is The probability that ?M is less than some SNR threshold ? is Thus the snr out of the Thus the snr out of the

55. Determination of average signal to noise ratio The before equation is the probability distribution for maximal ratio combining. Hence the mean SNR is

56. Equal Gain Combining Principle : Combining all the signals in a co-phased manner with unity weights for all signal levels so as to have the highest achievable SNR at the receiver at all times.

57. Equal Gain Combining

58. Equal Gain Combining In certain cases it is not convenient to provide for the variable weighting capability. This allows the receiver to exploit signals that are simultaneously received on each branch. The probability of producing an acceptable signal from a number of unacceptable inputs is still retained. The performance is marginally inferior to maximal ratio combining and superior to selection Diversity.

59. Polarization Diversity Principle : Polarization diversity relies on the decorrelation of the two receive ports to achieve diversity gain. The two receiver ports must remain cross-polarized. Many wireless service providers have discussed the adoption of a polarization diversity scheme in place of a space diversity approach. Like space diversity, polarization diversity relies on the decorrelation of the two receive ports to achieve diversity gain. The diversity gain from polarization diversity is maximized if the dual-polarized antenna has receive and receive diversity ports that receive radiation in a cross-polarized fashion over the desired coverage area with equal field strengths. Stated in another way, in a typical sectorized system, the two receive ports must remain cross-polarized (i.e., orthogonal) and capable of tracking one another over the forward 120-degree sector and into the hand-over area. The orthogonality, combined with tracking ability, is necessary if systems using dual-polarized antennas in a polarization diversity scheme with an advanced combining technique are to perform as well as systems employing vertically polarized antennas in a horizontal space diversity format. Many wireless service providers have discussed the adoption of a polarization diversity scheme in place of a space diversity approach. Like space diversity, polarization diversity relies on the decorrelation of the two receive ports to achieve diversity gain. The diversity gain from polarization diversity is maximized if the dual-polarized antenna has receive and receive diversity ports that receive radiation in a cross-polarized fashion over the desired coverage area with equal field strengths. Stated in another way, in a typical sectorized system, the two receive ports must remain cross-polarized (i.e., orthogonal) and capable of tracking one another over the forward 120-degree sector and into the hand-over area. The orthogonality, combined with tracking ability, is necessary if systems using dual-polarized antennas in a polarization diversity scheme with an advanced combining technique are to perform as well as systems employing vertically polarized antennas in a horizontal space diversity format.

60. Polarization Diversity Effective Diversity is obtained with a Correlation Coefficient below 0.7 In order to keep the correlation at this level space diversity at a base station requires antenna spacing of up to 20 wavelengths for the broadside case, and even more for the inline case. Polarization diversity at a base station does not require antenna spacing.

61. Polarization Diversity(cont�d) At the base station, space diversity is considerably less practical than at the mobile because the narrow angle of incident fields requires large antenna spacing. The comparatively high cost of using space diversity at the base station prompts the consideration of using orthogonal polarization. Polarization diversity provides two diversity branches and allows the antenna elements to be considered.

62. Polarization Diversity In the early days of cellular radio, all subscriber units were mounted in vehicles or used vertical whip antennas. Today, however, over half of the subscriber units are portable. This means that most subscribers are no longer using vertical polarization due to hand-tilting when the portable cellular phone is used. This recent phenomenon has sparkled interest in polarization diversity at the base station.

63. Theoretical Model for Polarization Diversity Assuming that a signal is transmitted from a mobile station with vertical( or horizontal) polarization, and is received by a polarization diversity antenna with two branches at the base station. The measured horizontal and vertical polarization paths between a mobile and a base station are uncorrelated. The decorrelation for the signal in each polarization is caused by multiple reflections in the channel between the mobile and base station antenna. This results in signals of different amplitudes and phase reflections. In reality there is some dependence of the received polarization on the transmitted polarization.

64. Theoretical Model for Polarization Diversity(Cont�d) v1 , v2 -Two antenna elements Which make �a angle (polarization angle) with the Y-axis. A mobile station is located in the direction of offset angle � from the main beam direction of the diversity antenna.

65. Theoretical Model for Polarization Diversity(Cont�d) Some of the vertically polarized signals transmitted from the mobile station are converted to the horizontally polarized signal, because of multipath propagation. Horizontally Polarized Component Vertically Polarized Component These signals x and y are received at �= 0 Assuming that r1and r2 have independent Rayleigh distribution, F1 and F2 have independent, uniform distribution. No cross coupling between the diversity antenna elements is assumed.

66. Correlation Coefficient ? The received signal values at v1 and v2 are Substituting x and y Where

67. Theoretical Model for Polarization Diversity (Cont�d) Amplitudes for v1 and v2 are Therefore, The correlation coefficient is defined as follows

68. Theoretical Model for Polarization Diversity (cont�d) Assumptions

69. Polarization Diversity Substituting the values Because r1 and r2 follow Rayleigh distribution Let then ? will be Where ? is the cross polarization discrimination of the propagation path between a mobile and a base station. This implies that rho is determined by three factors Alpha Beta tau This implies that rho is determined by three factors Alpha Beta tau

70. Polarization Diversity :Average Signal loss L The average level of vertically polarized signal level is We have seen before that Hence The signal loss is

71. Three factors determine ? and L Polarization angle a Offset angle � Cross polarization discriminator ? When ?= 0 At a = 500 and �= 330 ? = 0 When ?= 0 dB =1 At a = 450 and �= 900

72. Frequency Diversity Principle : The same information signal is transmitted and received simultaneously on two or more independent fading carrier frequencies.

73. Frequency Diversity The rational behind this technique is that frequencies separated by more than the coherence bandwidth of the channel will not experience the same fade. The probability of simultaneous fade will be the product of the individual fading probabilities. This is often employed in microwave LOS links which carry several channels in a frequency division multiplex mode(FDM).

74. Frequency Diversity This technique not only requires spare bandwidth, but also requires that there be as many receivers as there are channels used for the frequency diversity. However, for critical traffic, the expense may be justified.

75. Time Diversity Principle : The signals representing the same information are sent over the same channel at different times.

76. Time Diversity Time Diversity repeatedly transmits information at time spacing that exceeds the coherence time of the channel. Multiple repetitions of the signal will be received with multiple fading conditions, thereby providing for diversity. A modern implementation of time diversity involves the use of RAKE receiver for spread spectrum CDMA, where multipath channel provides redundancy in the transmitted message.

77. summarysummary

78. References Wireless Communications - Theodore S. Rappaport. Mobile Communication Engineers Theory and application � William C.Y.Lee. Cox, D.C., �Antenna Diversity Performance in Mitigating the effects of Portable Radiotelephone Orientation and Multipath Propagation,� IEEE Transactions on Communications,vol.62, No.9, pp.2695-2712, November 1983. Jakes, W. C., � A Comparison of specific space Diversity Technique for Reduction of Fast Fading in UHF Mobile Radio Systems,� IEEE Transactions on Vehicular Technology, Vol. VT-20, No.4, pp.81-93, November 1971. Lemieux, J. F., Tanany, M., and Hafez, H.M., � Experimental Evaluation of Space/Frequency/Polarization Diversity in the Indoor Wireless Channel,� IEEE Transactions on Vehicular Technology, Vol. 40, No.3, pp.569-574, August 1993.

79. References Rappaport, T.S., and Hawbaker, D.A, �Wide band Microwave Propagation Parameters Using Circular Frequency Reuse Efficiency for the Reverse Channel ,� IEEE Transactions on Vehicular Technology, Vol. 40, No.2, pp.231-242, February 1992. Vaughan , R., � Polarization Diversity in Mobile Communications,� IEEE Transactions on Vehicular Technology, Vol. 39, No.3, pp.177-186, August 1990. Kozono , S., � Base Station Polarization Diversity Reception for Mobile Radio,� IEEE Transactions on Vehicular Technology, Vol. VT-33, No.4, pp.301-306, November 1985. Lee, W.C.Y, � Polarization Diversity System for Mobile Radio,� IEEE Transactions on Communications, Vol. 20, pp.912-922, October 1972.