مخابرات سیّار (626-40) چند مسیری دانشکده مهندسی کامپیوتر مخابرات سیّار (626-40) چند مسیری نیمسال اوّل 94-93 افشین همّت یار

Handling Changes in Channel (1) 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 (2) 2 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 (3) 2 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 (4) 2 Variable Rate Coding Optimum rate, so more suitable for data applications (rather than fixed rate voice communication)

Introduction to Diversity 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 effect. Multiple paths unlikely to fade simultaneously

Diversity Techniques (1) 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 (2) 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.

Fading Effects In fading environments, SNR is random and therefore Pb (Probability of Error) is random too. Performance metrics: Average Pb Outage Probability

Average Probability (1) Average Pb usually 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/N0 will have an exponential distribution of the form: p(γb) = 1/Γ exp(-γb /Γ ) where Γ = (α2)av Eb/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 (2) 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.

Outage Probability (1) Outage Probability is the probability that Pb is 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.)

Outage Probability (2) 2 Pout = p(γb < γ0) where γ0 is 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/Γ exp(-γb /Γ )  Pout = 1- exp(-γ0 /Γ ) where Γ = (α2)av Eb/N0

Outage Probability (3) Pout = 1- exp(-γ0 /Γ ) 2 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. Fd is 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) = 21.4dB So, a fade margin of about 13dB is required.

Combined Outage and Average Probability 2 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.

Performance Improvement 2 Deep fades become rarer.

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

Time Diversity (2) 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.

Frequency Diversity Example: GSM 2 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.

Cooperative Diversity 2 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!

Diversity Options Micro-diversity: 2 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.

Combining Techniques (1) 2 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 (2) 2 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/ Γ exp(-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 (3) 2 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 (4) 2 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 (5) 2 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 = N Σ(Gi)2  Output SNR = (rM)2/NT = 1/N (ΣGiri)2/ Σ(Gi)2 Gi s should be found such that output SNR is maximized: Gi= ri/N  Output SNR = 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.

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

Multiuser Diversity (2) 2 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 (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.

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.

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

Multiuser Diversity (6) 2 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 (7) 2 Higher Mobility and Channel Dynamics Channel varies faster and has more dynamic range in mobile environments.

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