Diversity - E CE 5670: DIGITAL COMMUNICATIONS SPRING 2011...

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Unformatted text preview: E CE 5670: DIGITAL COMMUNICATIONS SPRING 2011 Diversity 04/07/2011 Salman Avestimehr School of ECE Cornell University avestimehr@ece.cornell.edu 1 3: Diversity R ayleigh Vs. AWGN Rayleigh vs AWGN Fundamentals of Wireless Communication, Tse&Viswanath 6 2 3: Diversity Typical Error Event Typical Error Event Conditional on h, When When error probability is very small. error probability is large: Typical error event is due to channel being in deep fade rather than noise being large. Fundamentals of Wireless Communication, Tse&Viswanath 7 3 D iversity 4 3: Diversity • Time Diversity Time Diversity Time diversity can be obtained by interleaving and coding over symbols across different coherent time periods. Coding alone is not sufficient! Fundamentals of Wireless Communication, Tse&Viswanath 9 5 3: Diversity S implest Code: Repetition Simplest Code: Repetition After interleaving over L coherence time periods, Repetition coding: for all where and This is classic vector detection in white Gaussian noise. Fundamentals of Wireless Communication, Tse&Viswanath 11 6 3: Diversity E rror Probability Geometry For BPSK Is a sufficient statistic (match filtering). Reduces to scalar detection problem: Fundamentals of Wireless Communication, Tse&Viswanath 12 7 D eep Fades Become Rarer 3: Diversity Deep Fades Become Rarer Fundamentals of Wireless Communication, Tse&Viswanath 13 8 3: Diversity P erformance Performance Fundamentals of Wireless Communication, Tse&Viswanath 14 9 3: Diversity E xample: GSM Example:GSM • • • Amount of time diversity limited by delay constraint and how fast channel varies. In GSM, delay constraint is 40ms (voice). To get full diversity of 8, needs v > 30 km/hr at fc = 900Mhz. Fundamentals of Wireless Communication, Tse&Viswanath 10 10 3: Diversity F requency Diversity Frequency Diversity • Resolution of multipaths provides diversity. • Full diversity is achieved by sending one symbol every L symbol times. • But this is inefficient (like repetition coding). • Sending symbols more frequently may result in intersymbol interference. • Challenge is how to mitigate the ISI while extracting the inherent diversity in the frequency-selective channel. Fundamentals of Wireless Communication, Tse&Viswanath 26 11 3: Diversity O FDM OFDM Fundamentals of Wireless Communication, Tse&Viswanath 35 12 3: Diversity O FDM OFDM OFDM transforms the communication problem into the frequency domain: a bunch of non-interfering sub-channels, one for each sub-carrier. Can apply time-diversity techniques. Fundamentals of Wireless Communication, Tse&Viswanath 36 13 C yclic Prefix Overhead 3: Diversity Cyclic Prefix Overhead • OFDM overhead = length of cyclic prefix / OFDM symbol time • Cyclic prefix dictated by delay spread. • OFDM symbol time limited by channel coherence time. • Equivalently, the inter-carrier spacing should be much larger than the Doppler spread. • Since most channels are underspread, the overhead can be made small. Fundamentals of Wireless Communication, Tse&Viswanath 37 14 3: Diversity E xample: Flash OFDM Example: Flash OFDM • Bandwidth = 1.25 Mz • OFDM symbol = 128 samples = 100 ! s • Cyclic prefix = 16 samples = 11 ! s delay spread • 11 % overhead. Fundamentals of Wireless Communication, Tse&Viswanath 38 15 L imitations Of Time And Frequency D iversity • Time diversity comes from mobility and delay tolerance • Maximum time diversity: delay/Tc • Frequency diversity comes from good delay spread and large BW • Maximum frequency diversity: L= [Td*W] • They may not be always available! 16 3: Diversity A ntenna Diversity Antenna Diversity Receive Transmit Fundamentals of Wireless Communication, Tse&Viswanath Both 19 17 3: Diversity R eceive Diversity Receive Diversity Same as repetition coding in time diversity, except that there is a further power gain. Optimal reception is via match filtering (receive beamforming). Fundamentals of Wireless Communication, Tse&Viswanath 20 18 Transmit Diversity smit Diversity the channel, send: ived SNR by in-phase addition of Simplest scheme: TDMA ver (transmit beamforming). hannel: amforming. 19 3: Diversity Transmit Diversity Transmit Diversity If transmitter knows the channel, send: maximizes the received SNR by in-phase addition of signals at the receiver (transmit beamforming). Reduce to scalar channel: same as receive beamforming. What happens if transmitter does not know the channel? Fundamentals of Wireless Communication, Tse&Viswanath 21 20 3: Diversity S pace Time Codes Space-time Codes • Transmitting the same symbol simultaneously at the antennas doesn’t work. • Using the antennas one at a time and sending the same symbol over the different antennas is like repetition coding. • More generally, can use any time-diversity code by turning on one antenna at a time. • Space-time codes are designed specifically for the transmit diversity scenario. Fundamentals of Wireless Communication, Tse&Viswanath 22 21 3: Diversity A lamouti Scheme Alamouti Scheme Over two symbol times: Projecting onto the two columns of the H matrix yields: •double the symbol rate of repetition coding. •3dB loss of received SNR compared to transmit beamforming. Fundamentals of Wireless Communication, Tse&Viswanath 23 22 3: Diversity S ummary Summary • Fading makes wireless channels unreliable. • Diversity increases reliability and makes the channel more consistent. • Smart codes yields a coding gain in addition to the diversity gain. • This viewpoint of the adversity of fading will be challenged and enriched in later parts of the course. Fundamentals of Wireless Communication, Tse&Viswanath 40 23 B lank 24 ...
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