![9
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![10
The probability that all M independent diversity branches Rx
signal which are simultaneously less than some specific SNR
threshold γ
The pdf of :
Average SNR improvement offered by selection diversity
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Lecture 9
- 1. 1 Lecture 9: Diversity Chapter 7 – Equalization, Diversity, and Coding
- 2. 2 I. Introduction MRC Impairments: 1) ACI/CCI → system generated interference 2) Shadowing → large-scale path loss from LOS obstructions 3) Multipath Fading → rapid small-scale signal variations 4) Doppler Spread → due to motion of mobile unit All can lead to significant distortion or attenuation of Rx signal Degrade Bit Error Rate (BER) of digitally modulated signal
- 3. 3 Three techniques are used to improve Rx signal quality and lower BER: 1) Equalization 2) Diversity 3) Channel Coding Used independently or together We will consider Diversity and Channel Coding
- 4. 4 These techniques improve mobile radio link performance Effectiveness of each varies widely in practical wireless systems Cost & complexity are also important issues Complexity in mobile vs. in base station
- 5. 5 III. Diversity Techniques Diversity : Primary goal is to reduce depth & duration of small-scale fades Spatial or antenna diversity → most common Use multiple Rx antennas in mobile or base station Why would this be helpful? Even small antenna separation ( λ ) changes phase of∝ signal → constructive /destructive nature is changed Other diversity types → polarization, frequency, & time
- 6. 6 Exploits random behavior of MRC Goal is to make use of several independent (uncorrelated) received signal paths Why is this necessary? Select path with best SNR or combine multiple paths → improve overall SNR performance
- 7. 7 Microscopic diversity → combat small-scale fading Most widely used Use multiple antennas separated in space At a mobile, signals are independent if separation > λ / 2 But it is not practical to have a mobile with multiple antennas separated by λ / 2 (7.5 cm apart at 2 GHz) Can have multiple receiving antennas at base stations, but must be separated on the order of ten wavelengths (1 to 5 meters).
- 8. 8 Since reflections occur near receiver, independent signals spread out a lot before they reach the base station. a typical antenna configuration for 120 degree sectoring. For each sector, a transmit antenna is in the center, with two diversity receiving antennas on each side. If one radio path undergoes a deep fade, another independent path may have a strong signal. By having more than one path one select from, both the instantaneous and average SNRs at the receiver may be improved
- 9. 9 Spatial or Antenna Diversity → 4 basic types M independent branches Variable gain & phase at each branch → G θ∠ Each branch has same average SNR: Instantaneous , the pdf of 0 bE SNR N = Γ = 1 ( ) 0 (6.155) i i ip e γ γ γ − Γ = ≥ Γ iSNR γ= iγ [ ] 0 0 1 Pr ( ) 1 i i i i ip d e d e γ γ γ γ γ γ γ γ γ − − Γ Γ ≤ = = = − Γ∫ ∫
- 10. 10 The probability that all M independent diversity branches Rx signal which are simultaneously less than some specific SNR threshold γ The pdf of : Average SNR improvement offered by selection diversity [ ] [ ] / 1 / Pr ,... (1 ) ( ) Pr 1 ( ) 1 (1 ) M M M M i M e P P e γ γ γ γ γ γ γ γ γ − Γ − Γ ≤ = − = > = − = − − γ ( ) 1 ( ) ( ) 1 M M M d M p P e e d γ γ γ γ γ −− Γ − Γ = = − Γ ( ) 1 0 0 1 ( ) 1 , 1 Mx x M M k p d Mx e e dx x k γ γ γ γ γ γ ∞ ∞ −− − = = = Γ − = Γ = Γ ∫ ∫ ∑
- 11. 11
- 12. 12 Space diversity methods: 1) Selection diversity 2) Feedback diversity 3) Maximal radio combining 4) Equal gain diversity
- 13. 13 1) Selection Diversity → simple & cheap Rx selects branch with highest instantaneous SNR new selection made at a time that is the reciprocal of the fading rate this will cause the system to stay with the current signal until it is likely the signal has faded SNR improvement : is new avg. SNR Γ : avg. SNR in each branch γ
- 14. 14
- 15. 15 Example: Average SNR is 20 dB Acceptable SNR is 10 dB Assume four branch diversity Determine that the probability that one signal has SNR less than 10 dB
- 16. 16
- 17. 17 2) Scanning Diversity scan each antenna until a signal is found that is above predetermined threshold if signal drops below threshold → rescan only one Rx is required (since only receiving one signal at a time), so less costly → still need multiple antennas
- 18. 18 3) Maximal Ratio Diversity signal amplitudes are weighted according to each SNR summed in-phase most complex of all types a complicated mechanism, but modern DSP makes this more practical → especially in the base station Rx where battery power to perform computations is not an issue
- 19. 19 The resulting signal envelop applied to detector: Total noise power: SNR applied to detector: 1 M M i i i r G r = = ∑ 2 1 M T i i N N G = = ∑ 2 2 M M T r N γ =
- 20. 20 The voltage signals from each of the M diversity branches are co-phased to provide coherent voltage addition and are individually weighted to provide optimal SNR ( is maximized when ) The SNR out of the diversity combiner is the sum of the SNRs in each branch. iγ Mr NrG ii /=
- 21. 21 The probability that less than some specific SNR threshold γ Mγ
- 22. 22 gives optimal SNR improvement : Γi: avg. SNR of each individual branch Γi = Γ if the avg. SNR is the same for each branch 1 1 M M M i i i i Mγ γ = = = = Γ = Γ∑ ∑
- 23. 23
- 24. 24 4) Equal Gain Diversity combine multiple signals into one G = 1, but the phase is adjusted for each received signal so that The signal from each branch are co-phased vectors add in-phase better performance than selection diversity
- 25. 25 IV. Time Diversity Time Diversity → transmit repeatedly the information at different time spacings Time spacing > coherence time (coherence time is the time over which a fading signal can be considered to have similar characteristics) So signals can be considered independent Main disadvantage is that BW efficiency is significantly worsened – signal is transmitted more than once BW must ↑ to obtain the same Rd (data rate)
- 26. 26 If data stream repeated twice then either 1) BW doubles for the same Rd or 2) Rd is reduced by ½ for the same BW
- 27. 27 RAKE Receiver Powerful form of time diversity available in spread spectrum (DS) systems → CDMA Signal is only transmitted once Propagation delays in the MRC provide multiple copies of Tx signals delayed in time
- 28. 28 attempts to collect the time-shifted versions of the original signal by providing a separate correlation receiver for each of the multipath signals. Each correlation receiver may be adjusted in time delay, so that a microprocessor controller can cause different correlation receivers to search in different time windows for significant multipath. The range of time delays that a particular correlator can search is called a search window.
- 29. 29 If time delay between multiple signals > chip period of spreading sequence (Tc) → multipath signals can be considered uncorrelated (independent) In a basic system, these delayed signals only appear as noise, since they are delayed by more than a chip duration. And ignored. Multiplying by the chip code results in noise because of the time shift. But this can also be used to our advantage, by shifting the chip sequence to receive that delayed signal separately from the other signals.
- 30. 30 ** The RAKE Rx is a time diversity Rx that collects time-shifted versions of the original Tx signal **
- 31. 31 M branches or “fingers” = # of correlation Rx’s Separately detect the M strongest signals Weighted sum computed from M branches faded signal → low weight strong signal → high weight overcomes fading of a signal in a single branch
- 32. 32 In outdoor environments the delay between multipath components is usually large, the low autocorrelation properties of a CDMA spreading sequence can assure that multipath components will appear nearly uncorrelated with each other.
- 33. 33 In indoor environments RAKE receiver in IS-95 CDMA has been found to perform poorly since the multipath delay spreads in indoor channels (≈100 ns) are much smaller than an IS-95 chip duration (≈ 800 ns). In such cases, a RAKE will not work since multipath is unresolveable Rayleigh flat-fading typically occurs within a single chip period.