Resource Allocation for Mobile Multiuser Orthogonal Frequency Division

Resource Allocation for Mobile Multiuser Orthogonal Frequency Division Multiplexing Systems Prof. Brian L. Evans Embedded Signal Processing Laboratory Dept. of Electrical and Computer Engineering The University of Texas at Austin July 5, 2006 bevans@ece. utexas. edu Featuring work by Ph. D students Zukang Shen (now at TI) and Ian Wong Collaboration with Prof. Jeffrey G. Andrews and Prof. Robert W. Heath

Outline § Introduction § Resource allocation in wireless systems § Multiuser OFDM (MU-OFDM) § Resource allocation in MU-OFDM § MU-OFDM resource allocation with proportional rates § Near-optimal solution § Low-complexity solution § Real-time implementation § OFDM channel state information prediction § Comparison of algorithms § High-resolution joint estimation and prediction § Multiuser OFDM resource allocation using predicted channel state information 2

Resource Allocation in Wireless Systems § Wireless local area networks (WLAN) 54 --108 Mbps § Metropolitan area networks (Wi. MAX) ~10 --100 Mbps § Limited resources shared by multiple users Transmit power Frequency bandwidth Transmission time Code resource Spatial antennas frequency code/spatial § § § Resource allocation impacts § Power consumption § User throughput § System latency user 4 user 1 user 5 user 2 user 6 user 3 time 3

Orthogonal Frequency Division Multiplexing § Adopted by many wireless communication standards § IEEE 802. 11 a/g WLAN § Digital Video Broadcasting – Terrestrial and Handheld § Broadband channel divided into narrowband subchannels § Multipath resistant § Receiver equalization simpler than single-carrier systems magnitude § Uses static time or frequency division multiple access channel subcarrier frequency Bandwidth OFDM Baseband Spectrum 4

Multiuser OFDM § Orthogonal frequency division multiple access (OFDMA) § Adopted by IEEE 802. 16 a/d/e standards § 802. 16 e: 1536 data subchannels with up to 40 users / sector § Users may transmit on different subcarriers at same time § Inherits advantages of OFDM § Exploits diversity among users User 1 User 2 . . . frequency Base Station (Subcarrier and power allocation) 5 User K

Exploiting Multiuser Diversity § Downlink multiuser OFDM § Users share subchannels and basestation transmit power § Users only decode their own data Resource Allocation Static Adaptive Users transmission order Predetermined Dynamically scheduled Channel state information Not exploited Well exploited System Performance Poor Good 6

Multiuser OFDM Resource Allocation Objective Advantage Disadvantage Best sum capacity No data rate proportionality among users Equal user data rates Inflexible user data rates distribution Data rate fairness adjustable by varying weights No guarantee for meeting proportional user data rates Max sum capacity [Jang et al. , 2003] Max minimum user’s capacity [Rhee et al. , 2000] Max weighted sum capacity [Cendrillon et al. , 2004] : user k’s capacity (bits/s/Hz) as continuous function for single cell 7

Outline § Introduction § § MU-OFDM resource allocation with proportional rates § § Near-optimal solution Low-complexity solution Real-time implementation OFDM channel state information prediction § § § Resource allocation in wireless systems Multiuser-OFDM (MU-OFDM) Resource allocation in MU-OFDM Comparison of algorithms High-resolution joint estimation and prediction Multiuser OFDM resource allocation using predicted channel state information 8

MU-OFDM with Proportional Rates § Objective: Sum capacity § Constraints B Transmission bandwidth K # of users N # of subchannels pk, n power in user k’s subchannel n hk, n channel gain of user k’s subchannel n N 0 AWGN power density Rk User k’s capacity System parameter for proportional rates § Total transmit power § No subchannel shared by multiple users § Proportional rate constraints § Advantages § Allows different service privileges and different pricing 9

Two-Step Near-Optimal Solution § Subchannel allocation step § Greedy algorithm – allow user with least allocated capacity/proportionality to choose best subcarrier [Rhee & Cioffi, 2000] § Modified to incorporate proportional rates § Computational complexity O(K N log N) K - # users N - # subchannels n - # iterations § Power allocation step [Shen, Andrews & Evans, 2005] § Exact solution given a subcarrier allocation § General case § Solution to set of K non-linear equations in K unknowns § Newton-Raphson methods are O(n K) where n is no. of iterations § Special case: High channel-to-noise ratio § Solution finds a root of a polynomial with O(n K) complexity § Typically 10 iterations in simulation 10

Lower Complexity Solution § In practical scenarios, rough proportionality is acceptable § Key ideas to simplify Shen’s approach [Wong, Shen, Andrews & Evans, 2004] § Relax strict proportionality constraint § Require predetermined number of subchannels to be assigned to simplify power allocation § Power allocation 10 8 7 4 § Solution to sparse set of linear equations § Computational complexity O(K) Example § Advantages [Wong, Shen, Andrews & Evans, 2004] § Waives high channel-to-noise ratio assumption of Shen’s method § Achieves higher capacity with lower complexity vs. Shen’s method § Maintains acceptable proportionality of user data rates 11

Simulation Parameters Parameter Value Number of Subcarriers (N) 64 Channel Model Number of Users (K) 4 -16 Maximum 5 ms Delay Spread Bit Error Rate Constraint 10 -3 Doppler Frequency 12 6 -tap exponentially decaying power profile with Rayleigh fading 30 Hz

Total Capacity Comparison N = 64 subchannels SNR = 38 d. B SNR Gap = 3. 3 d. B Based on 10000 channel realizations Wong’s Method Shen’s Method 13 Proportions assigned randomly from {4, 2, 1} with probabilities [0. 2, 0. 3, 0. 5]

Proportionality Comparison Proportions Wong’s Method Shen’s Method Based on the 16 -user case, 10000 channel realizations per user Normalized rate proportions for three classes of users using proportions {4, 2, 1} 14

Real-time Software Prototype Lab. VIEW 7. 0 Matlab 6. 5 Lab. VIEW handles the interface between Matlab and the DSP and automates allocation tests. Matlab generates a frequencyselective Rayleigh channel for each user. TMS 320 C 6701 Digital Signal Processor (DSP) The DSP receives Channel State Information and performs resource allocation algorithm. 15

Computational Complexity 22% average improvement Code developed in floating point C Run on 133 MHz TI TMS 320 C 6701 DSP EVM board 16

Memory Usage Memory Type *Shen’s Method *Wong’s Method Program Memory Subcarrier Allocation 1660 2024 Power Allocation 2480 1976 Total Data Memory 4140 System 8 KN+4 K Variables O(KN) Subcarrier 4 N+8 K Allocation O(N+K) Power 4 N+24 K Allocation O(N+K) * All values are in bytes 17 4000 8 KN+4 K O(KN) 4 N+12 K O(N+K) 4 N+28 K O(N+K)

Performance Comparison Summary Performance Criterion Shen’s Method Wong’s Method Subcarrier Allocation Computational Complexity O(K N log N) Power Allocation Computational Complexity O(N + n. K), n~9 O(N+K) Memory Complexity O(NK) Achieved Capacity Higher Adherence to Proportionality Tight Loose Assumptions on Subchannel SNR High None 18

Outline § Introduction § § MU-OFDM resource allocation with proportional rates § § Near-optimal solution Low-complexity solution Real-time implementation OFDM channel state information prediction § § § Resource allocation in wireless systems Multiuser-OFDM (MU-OFDM) Resource Allocation in MU-OFDM Comparison of algorithms High-resolution joint estimation and prediction Multiuser OFDM resource allocation using predicted channel state information 19

Delayed Channel State Information Internet Back haul t=0: Mobile estimates channel and feeds this back to base station t= : Base station receives estimates, adapts transmission based on these Channel mismatch [Souryal & Pickholtz, 2001] Higher BER Lower bits/s/Hz 20 mobile t=0 t=

Prediction of Wireless Channels § Use current and previous channel estimates to predict future channel response § Overcome feedback delay § Adaptation based on predicted channel response § Reduce amount of feedback § Predicted channel response may reduce how often direct channel feedback is provided h(n-p ) 21 h(n) … h(n- ) h(n+ ) ?

Related Work § Prediction on each subcarrier [Forenza & Heath, 2002] § Each subcarrier treated as a narrowband autoregressive process [Duel-Hallen et al. , 2000] § Prediction using pilot subcarriers [Sternad & Aronsson, 2003] § Used unbiased power prediction [Ekman, 2002] § Prediction on time-domain channel taps [Schafhuber & Matz, 2005] § Used adaptive prediction filters Pilot Subcarriers … … IFFT Data Subcarriers Time-domain channel taps 22

OFDM Channel Prediction Comparison § Compared three approaches in unified framework [Wong, Forenza, Heath & Evans, 2004] § Analytical and numerical mean squared error comparison § All-subcarrier and pilot-subcarrier methods have similar mean squared error performance § Time-domain prediction performs much better than the two other frequency domain prediction methods § Complexity comparison § All-subcarrier > Pilot-subcarrier ¸ Time-domain 23

High-resolution OFDM Channel Prediction § Combined channel estimation and prediction [Wong & Evans, 2005] § Outperforms previous methods with similar order of computational complexity § Allows decoupling of computations between receiver and transmitter § High-resolution channel estimates available as a by-product of prediction algorithm 24

Deterministic Channel Model § Outdoor mobile macrocell scenario § Far-field scatterer (plane wave assumption) § Linear motion with constant velocity § Small time window (a few wavelengths) § Channel model n k § Used in modeling and simulation of wireless channels [Jakes 1974] § Used in ray-tracing channel characterization [Rappaport 2002] 25 OFDM symbol index subchannel index

Prediction via 2 -D Frequency Estimation § If we accurately estimate parameters in channel model, we could effectively extrapolate the fading process § Estimation and extrapolation period should be within time window where model parameters are stationary § Estimation of two-dimensional complex sinusoids in noise § Well studied in radar, sonar, and other array signal processing applications [Kay, 1988] § Many algorithms available, but are computationally intensive 26

Two-step 1 -D Frequency Estimation § § Typically, many propagation paths share the same resolvable time delay We can thus break down the problem into two steps 1. Time-delay estimation 2. Doppler-frequency estimation 27

IEEE 802. 16 e Simulation 28

Mean-square Error vs. SNR Prediction 2 ahead ACRLB – Asymptotic Cramer-Rao Lower Bound CRLB – Cramer-Rao Lower Bound 29

Mean-square Error vs. Prediction Length SNR = 7. 5 d. B ACRLB – Asymptotic Cramer-Rao Lower Bound CRLB – Cramer-Rao Lower Bound 30

Performance Comparison Summary L - No. of paths M - No. of rays per path 31

MU-OFDM Resource Allocation with Predicted Channel State Infomation (Future) § Combine MU-OFDM resource allocation with long-range channel prediction § Using the statistics of the channel prediction error, we can stochastically adapt to the channel § Requires less channel feedback § More resilient to channel feedback delay § Improved overall throughput 32

Conclusion § Resource allocation for MU-OFDM with proportional rates § Allows tradeoff between sum capacity and user rate “fairness” to enable different service privileges and pricing § Derived efficient algorithms to achieve similar performance with lower complexity § Prototyped system in a DSP, showing its promise for real-time implementation § Channel prediction for OFDM systems § Overcomes the detrimental effect of feedback delay § Proposed high-performance OFDM channel prediction algorithms with similar complexity § Resource allocation using predicted channels is important for practical realization of resource allocation in MU-OFDM 33

Embedded Signal Processing Laboratory § Director: Prof. Brian L. Evans § § http: //www. ece. utexas. edu/~bevans/ Wi. MAX (OFDM) related research § § Algorithms for resource allocation in Multiuser OFDM Algorithms for OFDM channel estimation and prediction Key collaborators: Prof. Jeffrey Andrews and Prof. Robert Heath Key graduate students: Aditya Chopra Youssof Mortazavi Marcel Nassar 34 Hamood Rehman Ian Wong

Backup 35

Subchannel Allocation § Modified method of [Rhee et al. , 2000], but we keep the assumption of equal power distribution on subchannels § Initialization (Enforce zero initial conditions) Set , for. Let § For § § § to Find Let While § § § (Allocate best subchannel for each user) satisfying for all and update , (Iteratively give lowest rate user first choice) Find satisfying For the found , find For the found and update for all satisfying , Let for all , and Back 36

Power Allocation for a Single User § Optimal power distribution for user § Order § Water-filling algorithm § How to find for K # of users N # of subchannels pk, n power in user k’s nth assigned subchannel Hk, n Channel-to-noise ratio in user k’s nth assigned subchannel Nk # of subchannels allocated to user k Pk, tot Total power allocated to user k Water-level subchannels 37

Power Allocation among Many Users § Use proportional rate and total power constraints where § Solve nonlinear system of K equations: § Two special cases § Linear case: § High channel-to-noise ratio: /iteration , closed-form solution and 38 Back

Comparison with Optimal Solution Back 39

Comparison with Max-Min Capacity 40

Comparison with Max Sum Capacity 41

Summary of Shen’s Contribution § Adaptive resource allocation in multiuser OFDM systems § Maximize sum capacity § Enforce proportional user data rates § Low complexity near-optimal resource allocation algorithm § Subchannel allocation assuming equal power on all subchannels § Optimal power distribution for a single user § Optimal power distribution among many users with proportionality § Advantages § § Evaluate tradeoff between sum capacity and user data rate fairness Fill the gap of max sum capacity and max-min capacity Achieve flexible data rate distribution among users Allow different service privileges and pricing 42

Wong’s 4 -Step Approach 1. Determine number of subcarriers Nk for each user 2. Assign subcarriers to each user to give rough proportionality 3. Assign total power Pk for each user to maximize capacity 4. Assign the powers pk, n for each user’s subcarriers (waterfilling) 43 O(K) O(KNlog. N) O(K) O(N)

Simple Example N = 4 subchannels K = 2 users Ptotal = 10 10 8 Desired proportionality among data rates 1 = 3/4 7 4 2 = 1/4 9 6 3 5 44

Step 1: # of Subcarriers/User Nk 3 10 8 1 1 = 3/4 7 4 2 = 1/4 9 6 3 1 2 5 3 N = 4 subchannels K = 2 users Ptotal = 10 4 45

Step 2: Subcarrier Assignment Rk 10 8 10 7 log 2(1+2. 5*10)=4. 70 8 7 4 9 6 3 1 2 9 5 3 4 1 Rtot 2 3 4 46 log 2(1+2. 5*8)=4. 39 log 2(1+2. 5*7)=4. 21 13. 3 log 2(1+2. 5*9)=4. 55 Nk 3/4 3 1/4 1

Step 3: Power per user 10 1 8 2 7 3 9 4 P 1 = 7. 66 P 2 = 2. 34 N = 4 subchannels; K = 2 users; Ptotal = 10 47 Back

Step 4: Power per subcarrier • Waterfilling across subcarriers for each user P 1 = 7. 66 P 2 = 2. 34 10 1 8 2 7 3 p 1, 1= 2. 58 p 1, 2= 2. 55 p 1, 3= 2. 53 p 2, 1= 2. 34 9 4 Nk 3/4 3 1/4 1 Data Rates: R 1 = log 2(1 + 2. 58*10) + log 2(1 + 2. 55*8) + log 2(1 + 2. 53*7) = 13. 39008 Back R 2 = log 2(1+ 2. 34*9) = 4. 46336 48

Pilot-based Transmission § Comb pilot pattern § Least-squares channel estimates … f Df Dt 49 t

Prediction over all the subcarriers § Design prediction filter for each of the Nd data subcarriers § Mean-square error 50

Prediction over the pilot subcarriers § Design filter on the Npilot subcarriers only § Less computation and storage needed § Npilot << Nd (e. g. Npilot = 8; Nd = 192 for 802. 16 e OFDM) § Use the same prediction filter for the data subcarriers nearest to the pilot carrier Pilot Subcarriers … … Data Subcarriers 51

Prediction on time-domain channel taps § Design filter on Nt · Npilot time-domain channel taps § Channel estimates typically available only in freq. domain § IFFT required to compute time-domain channel taps § MSE: 52

Simulation Parameters (IEEE 802. 16 e) Parameter Value N 256 Bandwidth 5 MHz Guard Carriers (7) [0 -27] & [201: 256] Fcarrier 2600 MHz Channel Model ETSI Vehicular A Mobile Velocity 75 kmph Prediction Order 75 Downsampling rate 25 (4*fd) 53

Prediction Snapshot 54

NMSE vs. Channel Estimation Error 55

NMSE vs. Prediction Horizon 56

Step 1 – Time-delay estimation § Estimate autocorrelation function using the modified covariance averaging method [Stoica & Moses, 1997] § Estimate the number of paths L using minimum description length rule [Xu, Roy, & Kailath, 1994] § Estimate the time delays using Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) [Roy & Kailath, 1989] § Estimate the amplitudes cp(l) using least-squares § Discrete Fourier Transform of these amplitudes could be used to estimate channel § More accurate than conventional approaches, and similar to parametric channel estimation method in [Yang, et al. , 2001] 57

Step 2 – Doppler Frequency Estimation § Using complex amplitudes cp(l) estimated from Step 1 as the left hand side for (2), we determine the rest of the parameters § Similar steps as Step 1 can be applied for the parameter estimation for each path p § Using the estimated parameters, predict channel as 58

Prediction as parameter estimation § Channel is a continuous non-linear function of the 4 Mlength channel parameter vector 59

Cramer-Rao Lower Bound (CRLB) 60

Closed-form expression for asymptotic CRLB § Using large-sample limit of CRLB matrix for general 2 -D complex sinusoidal parameter estimation [Mitra & Stoica, 2002] § Much simpler expression § Achievable by maximum-likelihood and nonlinear least-squares methods § Monte-Carlo numerical evaluations not necessary 61

Insights from the MSE expression Amplitude & Doppler phase error frequency & phase cross variance covariance § Linear increase with 2 and M Doppler frequency error variance Time-delay & phase cross covariance Time-delay error variance § Dense multipath channel environments are the hardest to predict [Teal, 2002] § Quadratic increase in n and |k| with f and estimation error variances § Emphasizes the importance of estimating these accurately § Nt, Nf, Dt and Df should be chosen as large as possible to decrease the MSE bound 62

Selected Wireless Standards § Selected wireless data communication standards. § On June 8, 2006, IEEE suspended its 802. 20 Mobile Broadband Wireless Access standard activities. § IEEE 802. 20 is intended to operate at carrier frequencies below 3. 5 GHz Standard Primary Use Carrier Frequency Transmission Bandwidth Channels Bluetooth Personal Area Network 2. 4 GHz 1 MHz 79 IEEE 802. 11 a Wireless LAN (Wi-Fi) 5. 2 GHz 20 MHz 12 IEEE 802. 11 b Wireless LAN (Wi-Fi) 2. 4 GHz 22 MHz 3 IEEE 802. 11 g Wireless LAN (Wi-Fi) 2. 4 GHz 30 MHz 3 IEEE 802. 11 n High-Speed Wireless LAN (expected July 2007) 2. 4 GHz 30 MHz 3 IEEE 802. 16 e Mobile Broadband Wireless Access (Wi-Max) Varies by maker: 2. 5– 2. 69 GHz, 3. 3– 3. 8 GHz, or 5. 725– 5. 850 GHz 1. 25 – 20 MHz Varies by maker 7 – 400 63