Midterm and Extra EE359 – Lecture 11 Outline Lecture Announcements Announcements Midterm Wed Nov. 4, 8:45-10:45a in this rm. Open book/notes (bring textbook/calculators) HW due Friday 5pm, no late HWs Covers Chapters 1-7 Midterm announcements Bonus lecture query: extend last lecture? Review Session Sunday 4-5:30pm, rm TBD Average Ps with outage Extra OHs Me: Friday, Monday, Tuesday 2-3pm, Yao TBD Ps due to Doppler and ISI No HW next week Introduction to Diversity Midterms from past 3 MTs posted Combining Techniques 10 bonus points for “taking” a practice exam Solns for all exams given when you turn in practice exam Performance of Diversity in Fading Review of Last Lecture Combined outage and average Ps Outage probability Ps( s) Outage Probability that Ps is above target P s( s) Equivalently, probability below target Pstarget s Used when Tc>>Ts Average Ps in fast fading: Averaged over fast fading distribution Ps( s) Good metric when Tc~Ts Alternate Q function approach greatly simplifies Used in combined shadowing and flat-fading calculations (switch integral order, becomes Laplace Xfm) Ps varies slowly, locally determined by flat fading Fading severely degrades performance Declare outage when Ps above target value Doppler Effects ISI Effects High doppler causes channel phase to Delay spread exceeding a symbol time decorrelate between symbols causes ISI (self interference). 1 2 3 4 5 Leads to an irreducible error floor for differential modulation 0 Ts Tm Increasing power does not reduce error ISI leads to irreducible error floor Increasing signal power increases ISI power Error floor depends on BdTs ISI requires that Ts>>Tm (Rs<<Bc) Introduction to Diversity Combining Techniques Basic Idea Selection Combining Send same bits over independent fading paths Fading path with highest gain used Independent fading paths obtained by time, space, frequency, or polarization diversity Maximal Ratio Combining Combine paths to mitigate fading effects All paths cophased and summed with optimal weighting to maximize combiner output SNR Tb Equal Gain Combining All paths cophased and summed with equal weighting Array/Diversity gain Array gain is from noise averaging (AWGN and fading) t Diversity gain is change in BER slope (fading) Multiple paths unlikely to fade simultaneously Diversity Performance MRC and its Performance Selection Combining (SC) With MRC, = i for branch SNRs i Combiner SNR is the maximum of the branch SNRs. Optimal technique to maximize output SNR Yields 20-40 dB performance gains CDF easy to obtain, pdf found by differentiating. Distribution of hard to obtain Diminishing returns with number of antennas. Can get up to about 20 dB of gain. Standard average BER calculation Pb Pb ( ) p( )d ... Pb ( ) p( 1 ) * p( 2 ) * ... * p( M )d 1d 2 ...d M Maximal Ratio Combining (MRC) Hard to obtain in closed form Optimal technique (maximizes output SNR) Integral often diverges Combiner SNR is the sum of the branch SNRs. Distribution of SNR hard to obtain. MGF Approach .5 M 1 g Can use MGF approach for simplified analysis. Pb Mi ; i d Exhibits 10-40 dB gains in Rayleigh fading. 0 i 1 sin 2 Main Points Doppler spread only impacts differential modulation causing an irreducible error floor at low data rates Delay spread causes irreducible error floor or imposes rate limits Diversity overcomes the effects of fading by combining fading paths Diversity typically entails some penalty in terms of rate, bandwidth, complexity, or size. Techniques trade complexity for performance. MRC yields 20-40 dB gain, SC around 20 dB.
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