Wireless Communication Diversity

1. Wireless CommunicationDiversity Sharif University of Technology Fall 1395 AfshinHemmatyar

2. Traditional transmission: • Send at higher powers to those who have worse channels (Channel Inversion, similar to power control in CDMA). • This has been always used in the past mainly because the goal has been to transmit voice signals. • For voice, you can not tolerate to lose signal when channel is not in good condition. Handling Changes in Channel (1) 2

3. Channel Inversion • Similar to CDMA power control approach. • Fading inverted to maintain constant SNR and fixed rate. • Also has smaller delay, so better for voice/video applications. • However, greatly reduces capacity for a given TX power or leads to infinite power for nonzero capacity in case of a Rayleigh channel. • Therefore, combine with diversity to increase capacity. • Truncated inversion: • Invert channel above cutoff fade depth. • Truncation greatly increases capacity (Close to optimal). • Constant SNR (fixed rate) above cutoff. • Receiver only needs to know when we are below cutoff. Handling Changes in Channel (2) 2

4. Adaptive Transmission: • If we can tolerate some delay (true for data transmission), we can wait until our desired channel becomes good and then transmit at higher rate. • Send more to those who have better channels (also known as Water-filling in information theory). • New techniques are moving more to this more intelligent choice as we move more to data transmission. Handling Changes in Channel (3) 2

5. Variable Rate Coding Optimum rate, so more suitable for data applications (rather than fixed rate voice communication) Handling Changes in Channel (4) 2

6. Tb • What can be done to improve performance in the • presence of Fading? • Basic Idea: • 1) Obtain diversity “branches”: • Send same bits over independent fading paths. • Independent fading paths obtained by time, space, frequency, polarization, etc. • 2) Combine “branches” properly to mitigate fading • effects. • Multiple paths unlikely to fade simultaneously Introduction to Diversity

7. Spatial Diversity • Basic option: d > λ/2 • (for uniform AOA over [0, 2π]) • fC= 1GHz  d > 15cm • Not valid for Base, where AOAs are not uniform. • Larger distance required at Base locations. • Polarization Diversity • At the Base, narrow angles of arrival, therefore larger distance required for independent paths. • One solution to reduce distance is using polarized antennas (Horizontal and Vertical) at base station. • Polarized paths see different reflection coefficients and therefore result in independent signals. Diversity Techniques (1)

8. Time Diversity • Sending multiple replicas of signal in time • distance larger than TC. • One nice way of doing that: RAKE receiver in CDMA systems. • Interleaving/Coding is also a kind of time diversity. • Frequency Diversity • Send same signals over more than one carrier, separated at least by BC. • Multicarrier techniques such as OFDM also provide some sort of frequency diversity. Diversity Techniques (2)

9. In fading environments, • SNRis random and thereforePb (Probability of Error) is random too. • Performance metrics: • Average Pb • Outage Probability Fading Effects

10. Average Pbusually used when we do not stay in deep fade for long time (TC≈ TS). • In Rayleigh fading, the amplitude α have Rayleigh distribution and so γb= α2Eb/N0will have an exponential distribution of the form: • p(γb) = 1/Γexp(-γb /Γ) • whereΓ=(α2)avEb/N0 • (for non-fading scenario, we assume (α2)av= 1) • Averaging over γb: • Average Pb = 1/2 [1-(Γ /(1+ Γ ))½ ]≈1/(4Γ)for large γb Average Probability (1)

11. So, probability of error is much higher in fading environments especially in high SNRs. • For example, for 10-3 bit error rate, we need 8dB SNR in AWGN, but 24dB SNR in fading!! • So, we need to use • diversity techniques • to reduce fading • effects as much as • possible. • Also, AGC at receiver • input can reduce • flat-fading effects to • some extent. • Although has some • amount of noise enhancement as well. Average Probability (2)

12. Outage Probability (1) • Outage Probabilityis the probability that Pbis above target level. • Equivalently, the probability that SNR is below a • target level. • Used when TC >> TS • (channel variations are slow and so receiver may enter deep fades for many symbols.)

13. Pout = p(γb<γ0) where γ0is the minimum SNR level acceptable for the receiver. • For example, for voice where Pb= 10-3 is acceptable, γ0=7dB is selected. • In Rayleigh fading, • p(γb) = 1/Γexp(-γb /Γ) Pout = 1-exp(-γ0 /Γ) • whereΓ=(α2)av Eb/N0 Outage Probability (2) 2

14. Pout = 1- exp(-γ0/Γ) • Based on the above equation:Γ = (-γ0 / ln (1- Pout)) • So, Γ should exceed γ0 by Fd= -10log(-ln (1- Pout)) • and performance is acceptable more than • 100*(1- Pout)) percent of the time. • Fdis usually called “fade margin” (the margin we should keep to maintain acceptable levels most of the time). • For example, for BPSK modulation, assume we want to achieve Pb< 10-4 (γ0= 8.5dB) for 95% of the time: • Γ = -100.85/ln(1-0.05) = 138 = 21.4dB • So, a fade margin of about 13dB is required. Outage Probability (3) 2

15. Used in combined shadowing and flat-fading. • Pb varies slowly, locally determined by flat-fading. • Declare outage when average Pb is above target value. • In outage areas, bit error is too high to be measured. • Outside outage areas, average Pb is meaningful. Combined Outage and Average Probability 2

16. Improvement by Diversity 2 Deep fades become rarer.

17. Time Diversity can be obtained by interleaving and coding symbols across different coherent time periods. Time Diversity (1) 2

18. Example: GSM • Amount of diversity is limited by delay constraint and how fast channels varies. • In GSM, delay constraint is 40mS (voice). • Full diversity of 8, needs V > 30Km/hr. Time Diversity (2) 2

19. Example: GSM • However, if the mobile is moving slowly (for example a person walking at 3Km/hr), there might not be much time diversity. • Then, GSM can use frequency hopping to get diversity in frequency. • With coherence BW of around a few KHz, GSM can use its 25MHz band to switch to another frequency at different time slots and get diversity in frequency domain. Frequency Diversity 2

20. Different users can form a distributed antenna array to help each other in increasing diversity. • Distributed versions of space time codes may be applicable. • Interesting characteristics: • Users have to exchange information and this consumes bandwidth. • Operation is typically in half-duplex mode. • Broadcast nature of the wireless medium can be exploited. • More on this issue later! Cooperative Diversity 2

21. Micro-diversity: • Use diversity to combat small-scale fading. • Mainly in receiver side. • Recently Tx diversity also proposed through space-time coding • Macro-diversity: • Use diversity to combat large-scale shadowing effects. • Use of multiple base stations and select the one which is not in shadow. • Use of largely separated antennas at Base to improve reverse link. Diversity Options 2

22. Scanning Combining • Use a signal above threshold level and keep it until it is above threshold (less switching). • Selection Combining • Fading path with highest gain is used. • Maximal Ratio Combining (MRC) • All paths co-phased and summed with optimal weighting to maximize combiner output SNR. • Equal Gain Combining (EGC) • All paths co-phased and summed with equal weighting. (less complexity than MRC and not much lower performance.) Combining Techniques (1) 2

23. Selection Combining • Assume M independent Rayleigh fading branches at receiver. • Assume each branch has average SNR = Γ • If each branch has instantaneous SNR = γi, then, since the amplitude α has Rayleigh distribution, fading power α2 will have exponential distribution of the form: • p(γi) = 1/ Γexp(-γi/Γ) • Therefore, the probability that a branch has signal power less than some threshold γ, is given by: • Pr[γi< γ] = 1 – exp(-γ/Γ) Combining Techniques (2) 2

24. Selection Combining • Now, the probability that all branches are below threshold is given by: • Pr[γ1, γ2, …, γM ≤γ]=Pr[γmax<γ] = (1 –exp(-γ/Γ))M • Prob. density function of γ is : • PM(γ) = d/dγ((1 –exp(-γ /Γ ))M) • = M/Γ(1 –exp(-γ/Γ))M-1exp(-γ/Γ) • γav = ∫PM(γ ) dγ = Γ Σ(1/i) , i=1:M • Maximum change in γav is when M changes from 1 to 2. • Therefore most advantage in using diversity comes from 2 antennas and that is what we mostly see at Base Stations. Combining Techniques (3) 2

25. Selection Combining • Example: • for M=1, probability of • output of selection • diversity be more than • γ /Γ =-20dB, is only 99%. • But for M =2, • the probability goes • up to 99.99%. • Up to 20dB gain • with one more antenna. Combining Techniques (4) 2

26. Maximal Ratio Combining • Signals ri from each M diversity branches are • co-phased and individually weighted by Gi optimally to maximize SNR: rM= ΣGiri • Since noise power is also given by: NT = NΣ(Gi)2 •  OutputSNR= (rM)2/NT = 1/N(ΣGiri)2/ Σ(Gi)2 • Gi s should be found such that output SNR is maximized: Gi= ri/N •  OutputSNR = 1/N Σri2= Σγi • (Output SNR = Sum of SNRs of all branches) • γav= MΓ • About 22dB improvement for same scenario • 2 dB improvement compared with selection combining, but at much higher complexity. Combining Techniques (5) 2

27. Diversity in wireless systems arises from independent signal paths. Multiuser Diversity (1) 2

28. Traditional forms of diversity includes time, frequency and antennas. • Multiuser diversity arises from independent fading channels across different users. • Fundamental difference: Traditional diversity modes pertain to point-to-point links, while multiuser diversity provides network-wide benefit. Multiuser Diversity (2) 2

29. Multiuser Diversity (3) 2 • In a large system with users fading independently, there is likely to be a user with a very good channel in any time. • Long term total throughput can be maximized by always serving the user with the strongest channel.

30. Multiuser Diversity (4) 2 • Multiuser diversity provides a system-wide benefit. • Challenges: • Share the benefit among the users in a fair way. • Measure and send back channel condition to TX side.

31. Multiuser Diversity (5) 2 • Mobile measures the channel based on the pilot and predicts the SINR to request a rate.

32. Proportional Fair Scheduler (PFS) • Schedule the user with the highest ratio RK /TK where: • RK= current requested rate of user K • TK= average throughput of user K • in the past time slots. Multiuser Diversity (6) 2

33. Higher Mobility and Channel Dynamics • Channel varies faster and has more dynamic range • in mobile environments. Multiuser Diversity (7) 2

34. Diversity gain reduces with higher mobility. • Can only predict the average of the channel fluctuations, not the instantaneous values. Multiuser Diversity (8) 2