Introduction System model and performance Extension - with Relays Conclusions Weighted CDF-based Scheduling for an OFDMA Relay Downlink with Partial Feedback Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego November 14, 2012 Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model and performance Extension - with Relays Conclusions Outline Introduction 1 System model and performance 2 System model Analysis Weights setting Experimental results Extension - with Relays 3 Fast fading Slow fading Conclusions 4 Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model and performance Extension - with Relays Conclusions Outline Introduction 1 System model and performance 2 System model Analysis Weights setting Experimental results Extension - with Relays 3 Fast fading Slow fading Conclusions 4 Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model and performance Extension - with Relays Conclusions OFDMA system - Multiuser diversity Frequency selective fading 2 10 1 10 0 10 −1 10 |h| 2 −2 10 −3 10 Best of 30 users −4 10 User 1 User 2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Frequency (MHz) Effects of fading on channels of users Multiuser diversity and frequency selectivity Multiuser diversity: channels to different users are different Frequency selectivity: channels on different frequency are different Goal: Exploit the diversity to improve system’s performance Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model and performance Extension - with Relays Conclusions Performance measures vs. Challenges Measures of System’s Performance Throughput Fairness: meet users’ requirements OFDM: N RB resource blocks Feedback constraint resource resource block 4 Challenges block 1,6 Voice SMS A large number of users ….. resource Multimedia block 2,3,5 News A large number of resource blocks Pictures ….. Diversity in users’ characteristics Relay node Web surfing Email Download Youtube Users’ location: different channel gain ….. and channel statistic... Users’ requirements: types of service, Figure: A multiuser system power, data rate, delay tolerance,... At first, we introduce the system model Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model System model and performance Analysis Extension - with Relays Weights setting Conclusions Experimental results Outline Introduction 1 System model and performance 2 System model Analysis Weights setting Experimental results Extension - with Relays 3 Fast fading Slow fading Conclusions 4 Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model System model and performance Analysis Extension - with Relays Weights setting Conclusions Experimental results System, Feedback and Scheduling System: Groups of users with different on resource bock r Selected user priority weighted w 1 Group 1 Groups of macro users Base Station Users provide feedback Groups of cell edge users, each group is weighted w i served by a relay Group i OFDM with Partial feedback best M=2 Users feed back the best M among channels on N resource blocks N=5 resource blocks On resource block r , there are subset of users to feed back Scheduling f 3 f 4 f 5 f 1 f 2 Users are selected based on weighted W cdf of the SNR. Figure: partial feedback in an Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model System model and performance Analysis Extension - with Relays Weights setting Conclusions Experimental results Weighted CDF scheduling How weighted CDF work [5] From SNR Y k i of user k i Obtain u k i = F Y ki ( x ) , Uniformly distributed in [ 0 , 1 ] Identical for all users Compare and prioritize users Select the user with the largest weighted CDF k ∗ = arg max k { F Y ki ( x ) } 1 wi Advantage: can control precisely selection probability of all the users [5] D. Park, H. Seo, H. Kwon, and B. Lee, “Wireless packet scheduling based on the cumulative distribution function of user transmission rates", IEEE Trans on Communications , Nov. 2005. Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model System model and performance Analysis Extension - with Relays Weights setting Conclusions Experimental results System’s performance - average sum rate The average system sum rate is N R = 1 � E log ( 1 + X r ) = E log ( 1 + X r ) (1) N r = 1 where X r is SNR to the selected user on resource block r Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model System model and performance Analysis Extension - with Relays Weights setting Conclusions Experimental results Performance analysis Steps in analyzing system performance [4] Framework CQI feedback Random variable Output Step 1 Z k , r : CQI at a receiver F Z k Step 2 Y k , r : SNR seen at a transmitter F Y k Step 3 X r : SNR of a selected user F X | cond Step 4a F X = E cond F X | cond Step 4b E cond E X r [ log ( 1 + X r ) | cond ] k: user index, r: block index [4] Seong-Ho Hur, and Bhaskar Rao, “Sum rate analysis of a reduced feedback OFDMA system employing joint scheduling and diversity", IEEE Transactions on Signal Processing , 2011. Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model System model and performance Analysis Extension - with Relays Weights setting Conclusions Experimental results Performance analysis Theorem In an OFDMA system where all equipments have a single antenna, with L groups of users, each group i has K i users, if only CQI on M best among N resource blocks is fed back, the CDF of system’s throughput is K j L L � � � F R ( ζ ( x )) = Pr {| S r , j | = n j } l = 1 n j = 0 j = 1 j = 1 ,..., L ;¯ n � = 0 � Nt − m � � ∞ t = 1 e 3 ( α l , t ) � t ( M − 1 ) n l w l x e 2 ( m ) F Z k α l � = 1 � L m = 0 j = 1 n j w j ρ × , � N − m � � M − 1 m = 0 e 1 ( m ) � N − m x k = 0 F Z k α l = 1 ρ (2) Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model System model and performance Analysis Extension - with Relays Weights setting Conclusions Experimental results Performance analysis where ζ ( x ) = log ( 1 + x ) � � x F Z k is CDF of SNR from the BS to user k ρ � K l � � M � n l � � K l − n l 1 − M Pr {| S r , l | = n l } = n l N N � L j = 1 w j n j α l = ; n l w l e 1 ( m ) = � M − 1 M − i M ( N m )( − 1 ) i − m i )( i i = m � min ( M − 1 , m ) 1 e 2 ( 0 ) = e 1 ( 0 ) t ; e 2 ( m ) = ( kt − m + k ) e 1 ( k ) e 2 ( m − k ) ; me 1 ( 0 ) k = 1 � i e 3 ( α l , t ) = � ∞ � ( − 1 ) i − t . i = t ( α l i ) t Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model System model and performance Analysis Extension - with Relays Weights setting Conclusions Experimental results Weights for groups of users Set ǫ = 10 − 10 The probability of selection of user k l is w l n l � K 1 Target P alloc = [ 0 . 2 , 0 . 8 ] � Pr { k ∗ r = k l } = � n 1 � L K l j = 1 n j w j π (¯ Found weight n ) � � L � � L j = 1 n j � j = 1 ( K j − n j ) w = [ 0 . 318 , 0 . 682 ] after 4 � � M � K L 1 − M (3) . n L iterations N N P alloc , 1 P alloc , L Iteration Norm � φ ( w ) � 2 Initialize w ( 0 ) = [ ] which is , . . . , K l K L 0 2.4691512e-001 the weights for the full feedback case. 1 6.2304622e-002 Solving δ w ( t ) φ ( w ( t )) = −∇ φ ( w ( t )) . 2 3.0325582e-003 Update w ( t + 1 ) = w ( t ) + δ w ( t ) . Normalize 3 7.4881615e-006 w so that � w � 2 = 1 which does not change 4 4.5758897e-011 φ ( w ) . Table: Convergence behavior End � φ ( w ) � 2 < ǫ . Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Introduction System model System model and performance Analysis Extension - with Relays Weights setting Conclusions Experimental results Experimental results We consider an OFDMA system with on resource bock r Selected user N = 10 resource blocks and groups of weighted w 1 users with different priority Group 1 Base Station Group 1 Group 2 K 1 = 10 users, weight w 1 = 0 . 4, located at d 1 = 414m weighted w 2 Group 2 - cell edge K 2 = 5 users, weight w 2 = 0 . 6, located at d 2 = 834m Figure: A partial feedback OFDMA system Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego
Recommend
More recommend
