Resource Allocation for Mobile Multiuser OFDM Systems Prof. Brian L. Evans Embedded Signal Processing Laboratory Dept. of Electrical and Computer Engineering The University of Texas at Austin February 17, 2006 bevans@ece.utexas.edu Featuring work by ESPL students Zukang Shen 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 (CSI) prediction Comparison of algorithms High-resolution joint estimation and prediction MU-OFDM resource allocation using predicted CSI 2

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

Orthogonal Frequency Division Multiplexing Adopted by many wireless communication standards IEEE 802.11a/g WLAN Digital Video Broadcasting – Terrestrial and Handheld Broadband channel divided into narrowband subchannels Multipath resistant Receiver equalization simpler than single-carrier systems Uses static time or frequency division multiple access subcarrier frequency magnitude channel Bandwidth OFDM Baseband Spectrum 4

Multiuser OFDM Orthogonal frequency division multiple access (OFDMA) Adopted by IEEE 802.16a/d/e standards 802.16e: 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 frequency Base Station (Subcarrier and power allocation) User 2 . . . User K 5

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 Pre-determined Dynamically scheduled Channel state information Not exploited Well exploited System Performance Poor Good 6

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

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 (CSI) prediction Comparison of algorithms High-resolution joint estimation and prediction MU-OFDM resource allocation using predicted CSI 8

MU-OFDM with Proportional Rates 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 N0 AWGN power density Rk User k’s capacity System parameter for proportional rates Objective: Sum capacity Constraints 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) 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 K - # users N - # subchannels n - # iterations 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 Solution to sparse set of linear equations Computational complexity O(K) 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 10 8 7 4 Example 11

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

Total Capacity Comparison N = 64 subchannels SNR = 38 dB SNR Gap = 3.3 dB Based on 10000 channel realizations Proportions assigned randomly from {4,2,1} with probabilities [0.2, 0.3, 0.5] Wong’s Method Shen’s Method 13

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 LabVIEW 7.0 LabVIEW handles the interface between Matlab and the DSP and automates allocation tests. TMS320C6701 Digital Signal Processor (DSP) Matlab 6.5 Matlab generates a frequency-selective Rayleigh channel for each user. 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 TMS320C6701 DSP EVM board 16

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

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

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 (CSI) prediction Comparison of algorithms High-resolution joint estimation and prediction MU-OFDM resource allocation using predicted CSI 19

Delayed CSI  t=0: Mobile estimates channel and Internet Back haul  mobile t=0: Mobile estimates channel and feeds this back to base station t=: Base station receives estimates, adapts transmission based on these t= t=0 Higher BER Lower bps/Hz Channel Mismatch 20

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

… 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 Data Subcarriers IFFT Time-domain channel taps 22

OFDM Channel Prediction Comparison Compared three approaches in unified framework [Wong, Forenza, Heath & Evans, 2004] Analytical and numerical MSE comparison All-subcarrier and pilot-subcarrier methods have similar MSE 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 Used in modeling and simulation of wireless channels [Jakes 1974] Used in ray-tracing channel characterization [Rappaport 2002] n OFDM symbol index k subchannel index 25

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 Time-delay estimation Doppler-frequency estimation 27

IEEE 802.16e 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 dB 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 Explain last two lines more 31

MU-OFDM Resource Allocation with Predicted CSI (Future Work) 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” Enables 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/ WiMAX (OFDM) related research Algorithms for resource allocation in MU-OFDM Algorithms for OFDM channel estimation and prediction Key collaborators: Prof. Jeff Andrews and Prof. Robert Heath Key graduate students: Zukang Shen, PhD Ian C. Wong, PhD Candidate Kyungtae Han, PhD Candidate Daifeng Wang, MS Student Hamood Rehman, MS Student 34

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 (Allocate best subchannel for each user) Find satisfying for all Let , and update While (Iteratively give lowest rate user first choice) Find satisfying for all For the found , find satisfying for all For the found and , Let , and update 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 subchannels Water-level 37

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

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 Determine number of subcarriers Nk for each user Assign subcarriers to each user to give rough proportionality Assign total power Pk for each user to maximize capacity Assign the powers pk,n for each user’s subcarriers (waterfilling) O(K) O(KNlogN) O(K) O(N) 43

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

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

Step 2: Subcarrier Assignment 10 8 4 7 10 10 8 10 8 7 Rk Rtot 8 4 7 4 7 log2(1+2.5*10)=4.70 log2(1+2.5*8)=4.39 4 log2(1+2.5*7)=4.21 13.3 3 6 5 9 9 log2(1+2.5*9)=4.55 4.55 3 6 5  Nk 3/4 3 1/4 1 1 2 3 4 1 2 3 4 46

Step 3: Power per user P1 = 7.66 P2 = 2.34 10 8 7 9 P1 = 7.66 P2 = 2.34 N = 4 subchannels; K = 2 users; Ptotal = 10 Back 47

Step 4: Power per subcarrier Waterfilling across subcarriers for each user P1 = 7.66 P2 = 2.34 p1,1= 2.58 p1,2= 2.55 p1,3= 2.53 p2,1= 2.34  Nk 3/4 3 1/4 1 1 2 3 4 10 8 7 9 Data Rates: R1 = log2(1 + 2.58*10) + log2(1 + 2.55*8) + log2(1 + 2.53*7) = 13.39008 R2 = log2(1+ 2.34*9) = 4.46336 Back 48

Pilot-based Transmission Comb pilot pattern Least-squares channel estimates t f … Dt Df Get rid of pattern, legend of LS estimates, remind key parameters, Nt nf,… 49

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 pilot subcarriers only Less computation and storage needed Npilot << Nd (e.g. Npilot = 8; Nd = 192 for 802.16e 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 802.16e) 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 4M-length channel parameter vector 59

Cramer-Rao Lower Bound (CRLB) Fix this slide… add legend for notation 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 Add box to equation , legend for notation Nf Nt Dt Df, n, k kbar, add bullet lead in to equation 61

Insights from the MSE expression Amplitude & phase error variance Doppler frequency & phase cross covariance Doppler frequency error variance Time-delay & phase cross covariance Time-delay error variance Linear increase with 2 and M 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 Fix equations, put arrows or animation to explain quadratic increase, say what is new and known, explain some tradeoffs… 62