DIVERSITY TECHNIQUES

Prepared by Deepa.T, Asst.Prof. /TCE Introduction

•Three techniques are used independently or in tandem to improve receiver signal quality •Equalization compensates for ISI created by multipath with

time dispersive channels (W>BC) ¾Linear equalization, nonlinear equalization •Diversity also compensates for channel impairments, and is usually implemented by using two or more receiving antennas ¾Spatial diversity, antenna polarization diversity, frequency diversity, time diversity Diversity

Diversity: It is the technique used to compensate for fading channel impairments. It is implemented by using two or more receiving antennas. While Equalization is used to counter the effects of ISI, Diversity is usually employed to reduce the depth and duration of the fades experienced by a receiver in a flat fading channel. These techniques can be employed at both and mobile receivers. Spatial Diversity is the most widely used diversity technique. Spatial Diversity Technique‐ A Brief Description

In this technique multiple antennas are strategically spaced and connected to common receiving system. While one antenna sees a signal null, one of the other antennas may see a signal peak, and the receiver is able to select the antenna with the best signal at any time. The CDMA systems use Rake receivers which provide improvement through time diversity. Diversity Techniques‐ Highlights

• Unlike Equalization, Diversity requires no training overhead as a transmitter doesn’t require one. •It provides significant link improvement with little added cost. •It exploits random nature of wave propagation by finding independent ( uncorrelated) signal paths for communication. Fundamentals of Equalization

ISI has been recognized as the major obstacle to high speed data transmission over mobile channels. Equalization is a technique used to combat inter symbol interference. As the mobile fading channels are random and time varying, equalizers must track the time varying characteristics of the mobile channel, and thus are called adaptive equalizers. Diversity Techniques‐ Highlights

•It is a very simple concept where in one path undergoes a deep fade and another independent path may have a strong signal. •As there is more than one path to select from, both the instantaneous and average SNRs at the receiver may be improved, often as much as 20‐30 dB Channel Coding

Channel coding: It is the technique which improves mobile communication link performance by adding redundant data bits in the transmitted message. In this technique, the base band portion of the transmitter, a channel coder maps a digital message sequence into another specific containing greater number of bits than originally contained in the message. The coded message is then modulated for transmission in the wireless channel. Channel Coding (Cont’d)

Channel Coding is used by the receiver to detect or correct some or all of the errors introduced by the channel in a particular sequence of message bits. The added coding bits lower these the raw data transmission rate through the channel. There are two types of codes: Block codes and convolutional codes. Operating modes of adaptive equalizer

1) Training mode

2) Tracking Mode DIVERSITY

A is a method that is used to develop information from several signals transmitted over independent fading paths.

It exploits the random nature of by finding independent (uncorrelated) signal paths for communication. Diversity Technique

Objective: Combining the multiple signals in such a fashion so as to reduce the effects of excessive deep fades. Types:

Diversity

Macroscopic diversity Microscopic diversity Diversity Technique Types Of Diversity

MACROSCOPIC DIVERSITY MICROSCOPIC DIVERSITY

• Prevents Large Scale fading. • Prevents Small Scale fading.

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

Space Diversity

Selection Diversity Scanning DiversityMaximal Ratio EqualCombining Gain Combining Selection Diversity

Principle :

Selecting the best signal among all the signals received from different braches at the receiving end. 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 = γi Selection Diversity

The Signal‐to‐Noise ratio is defined as follows

E SNR =Γ= b α 2 Eb , N0 are constants N 0 Where

Eb ‐ Average Carrier Energy

N0 ‐ Noise power spectral density ά‐A random variable used to represent amplitude values of the fading channel with

respect to Eb/N0

The instantaneous SNR ( γi ) can be defined as

γi = Instantaneous signal power per branch Mean noise power per branch Selection Diversity (cont’d)

For Rayleigh fading channels, α has a Rayleigh 2 distribution and so α and consequently γi have a chi‐square distribution with two degrees of freedom.

The probability density function for such a channel is

1 ⎛ γ i ⎞ p γ i )( = exp ⎜ − ⎟ γ i ≥ 0 Γ ⎝ Γ ⎠ The pdf for a single branch that has SNR less than some threshold γ is γ γ 1 γ − γ P γγ=≤ )()( dp γγ= exp( − i d γ 1) −= e Γ ir ∫ ii ∫ i 0 0 Γ Γ Selection Diversity (cont’d) The probability that all M independent diversity branches receive signals which are less than a threshold γ is

γ M ⎡ − ⎤ Γ Pr ( ,...... 1 M γγγ⎢1) −=≤ e ⎥ = PM γ )( ⎣ ⎦ If a signal branch achieves SNR > γ then the probability that SNR > γ for one or more branches is

γ M ⎡ − ⎤ Γ P ir γγ)( =≤ PM γ )(-1 ⎢11 −−= e ⎥ ⎣ ⎦ Selection Diversity 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 γ/ Г = 1 10 Log(γ/ Г ) = 0

− 11 Pr [11 −−= e ] e − 1 === %3636.0 Determination of average signal to noise ratio

• Find the pdf of the fading signal

• Compute the derivative of PM(γ)

γ 1-M γ ⎡ − ⎤ − d M Γ Γ p M γ )( = PM γ = ⎢1)( − ⎥ ee The mean SNR is d γ Γ ⎣ ⎦

∞ ∞ 1-M = p )d( γγγγ 1 −Γ= − x − x dxeeMx ∫ M ∫ [] 0 0 Where γ x = Γ Selection Diversity

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

γ M 1 = ∑ Γ k = 1 k Selection Diversity 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. γ = 10 dB Г = 20 dB γ/ Г = 0.1 With Selection Diversity

− 1.0 4 P 4 [1dB)10( −= e ] = .0000820 Without Diversity

− 11.0 P1 [1dB)10( −= e ] = .0950 Selection Diversity 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. Scanning Diversity 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. 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. Maximum Ratio Combining 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 Maximal Ratio Combining

Assumptions:

• The voltage signal γi 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 Maximal Ratio Combining

Resulting signal envelope applied to the detector is M Assuming that all amplifiers have additive noise at their input and that the noise is M = ∑ rGr ii i =1 uncorrelated between different amplifiers. The total noise power NT applied to the detector is the weighted sum of the noise in each branch. M 2 T = ∑ GNN i i =1 Which results in a SNR applied to the detector γM 2 rM γ M = 2 N T Using Chebychev’s inequality γM is maximized when

r G = i i N Maximal Ratio Combining

The Maximized value is

2 Now r 2 (i ) M 2 M 1 ∑ N 1 ri γ M = 2 2 = 2 = ∑∑ γ i ri N N ∑ ()N 2 i =1 i =1 We have The E field 1 1 γ r 2 == ( received+ TT 22 envelop) i 2 N i 2 N sc 2 2 z = c s )()()()( ==+ rtrtTtTtE i

The received signal envelope for a fading signal can be modeled from two independent Gaussian random variables Tc and Ts each having zero mean and equal variance σ2 . Maximal Ratio Combining

Hence γM is a chi‐square distribution of 2M Gaussian random variable with variance

2 σ = Γ N 22 The resulting pdf for γM is

− γ M γ M −1e Γ p γ )( = M γ ≥ 0for M M M −Γ )1( ! M The probability that γM is less than some SNR threshold γ is

γ −γ M (γ )k −1 P =≤ dp γγγγ1)( −= e Γ Γ {}Mr ∫ M M ∑ 0 k =1 ()k − 1 ! Maximal Ratio Combining Determination of average signal to noise ratio

The before equation is the probability distribution for maximal ratio combining.

Hence the mean SNR is

M M M γγi ∑∑ M Γ=Γ== i =1 i =1 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. Equal Gain Combining

Equal Gain Combining 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. 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. 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. 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. 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. Frequency Diversity

Principle :

The same information signal is transmitted and received simultaneously on two or more independent fading carrier frequencies. 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 LOS links which carry several channels in a frequency division multiplex mode(FDM). 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. Time Diversity

Principle :

The signals representing the same information are sent over the same channel at different times. 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 CDMA, where multipath channel provides redundancy in the transmitted message. Diversity

Polorization Diversity Space Diversity Frequency Diversity Time Diversity

Selection Diversity Scanning Diversity Maximal Ratio Combining Equal Gain Combining References

• Wireless Communications ‐ Theodore S. Rappaport. • Mobile Communication Engineers Theory and application – William C.Y.Lee. • Cox, D.C., “ 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. 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. References

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