Downlink Capacity Evaluation of Cellular Networks with Known Interference Cancellation

1. Downlink Capacity Evaluation of Cellular Networks with Known Interference Cancellation Howard Huang, Sivarama Venkatesan, and Harish Viswanathan Lucent Technologies Bell Labs

2. Motivation • Significant advance on known interference cancellation for MIMO broadcast channels • Natural fit with downlink of a cellular system • Most base stations already equipped with 2~4 antennas • Additional processing at the base station is economically reasonable • Asymmetric bandwidth requirement for data traffic can justify channel feedback required for known interference cancellation • Goal: How much do we really gain? • Best effort packet data • Delay sensitive streaming applications • Characterization of rate region using duality used for computations

3. Model • Mobile receives signal from a single cell and interference from surrounding cells • Phase coordination across multiple cells in outdoor wide area wireless networks appears impractical • Complexity of computing the gains grows with the number of cells • Block fading channel model • Mobile feeds back channel conditions from the desired base station in each frame • Ideal noiseless feedback • Performance Metrics • Throughputdistribution for packet data • Number of users at fixed rate transmission

4. System Model Block Fading Wire-Line Network h Each interval has sufficient number of symbols to achieve capacity 1 h 2 h 3 Other-cell interference + AWGN

5. Packet Data Throughput • In a cellular system different users are at different distances from the base station • Sum rate is a poor metric for comparing gains • A scheduler is used to arbitrate the resources and guarantees some notion of fairness • We will use the proportional fair scheduler • where is the long term average throughput achieved • We willassume thebacklogged scenario where each user has infinite amount of data to send • Simplifying assumption • Can still obtain reasonable estimate of the gain

6. On-line scheduling algorithm • In each frame we assign rate vector that maximizes where is the moving average of the throughput • The rate region depends on the the transmission strategy • DPC rate region when known interference cancellation is employed • Rate region from beam forming • We have to solve the weighted rate sum maximization in each frame to determine the throughput

7. Maximum Weighted Rate Sum • Using duality • Using polymatroid structure of the MAC rate region

8. Simple proof of optimal ordering • For any set of covariance matrices • Since independent of the decoding order, we should pick the user with least weight to see the most interference

9. Convex Optimization Algorithm • Standard convex optimization techniques can be used to perform the maximization : Covariance matrices Optimization : Linear Constraint : Power Constraint Iterative Algorithm Linear Optimization: Line Search : Update :

10. Beam Forming Scheme • Separately encode each user’s signal with zero-forcing beamforming • Rate Region for a subset of users ( ) • Max weighted rate sum within the subset is weighted water-filling • Computing max weighted rate sum over all subsets of users is very complex even for 4 antennas • Approx: First select a subset of users with the highest individual metrics and implement max weighted rate sum only over this subset of users • Complexity depends on the size of the set

11. Group ZF Beam Forming for Multiple Receive Antennas • Similar to group multi-user detection • Covariance matrices are chosen such that multiple streams can be transmitted to each user on separate beams • Orthogonality of ZF beam forming preserved only across users • The multiple streams for a given user are not orthogonal • Similar approximation algorithm as in ZF case for computing maximum weighted rate sum

12. Classic Cellular Model MSC BTS Gateway Hexagonal Layout Uniform User distribution

13. Simulation Setup 20 users drawn from this CDF 10000 frames with the proportional fair scheduling

14. Performance for Single Receive Antenna Factor of 2 improvement w.r.t simple beam forming at 50% point Optimum selection of users with beam forming reduces the gap significantly

15. Performance for Multiple Receive Antennas Harder to bridge the gap GZF technique is sub-optimal even among schemes without DPC

16. Optimality in a Large Symmetric System • Consider a system with large number of users with identical fading statistics • With high probability there will be a subset of users that are orthogonal with high SNR in each scheduling interval • Symmetry implies sum rate maximization in each scheduling interval should be optimal • Sum rate is maximized by transmission to subset that is orthogonal with high SNR • Optimal even when joint coding is allowed since sum rate is maximized by transmission to orthogonal subset

17. Fixed Rate Evaluation Model • For delay sensitive applications we have to guarantee a fixed rate independent of channel conditions • Assume the same rate requirement for all users • Translates to determining the equal rate point on the rate region • Goal: Evaluate the CDF of number users that can be supported at a given fixed rate (user locations and channel instances are random) • Optimum known interference cancellation • Known interference cancellation with FCFS order • TDMA

18. Equal Rate Point on the DPC Region • Unable to establish that for any rate vector there exists weight vector such that is the solution to the optimization • Cannot iterate on the weights to determine the equal rate point • is indeed unique whenever is such that • All points of the rate region may not be achievable without rate- splitting or time-sharing • For capacity evaluation we need only an algorithm to test if a rate vector is achievable

19. Convex optimization algorithm for achievability • Define • Given a rate vector find • Then is achievable iff

20. Convex Sets and Separating Hyperplanes Can quickly determine points outside the rate region

21. FCFS Algorithm • Users arrive in some order with the rate requirement • Allocate power to the users assuming entire bandwidth is allocated to each user • Use known interference cancellation to remove the new user from interfering existing users • Existing users are interference to new user • The arrival order can be sub-optimal • Performance will be better than TDMA because of known interference cancellation

22. TDMA Vs FCFS (Single Receive Antenna) 50% gain at the 10% point for 4 transmit antennas Gain is not significant for 1 and 2 transmit antennas

23. TDMA Vs FCFS (multiple receive antennas)

24. FCFS Vs Optimal Ordering MPF – Minimum Power First

25. Summary • Duality results were used to determine the maximum gain when using a proportional fair scheduler • Factor of 2 gain relative to TDMA strategy with single beam • Single receive antenna case the beam forming can come close to Known Interference Cancellation • Algorithm to determine the fixed rate capacity was proposed • 50% improvement relative to TDMA with single beam • TDMA with multiple beams could potentially narrow this gap • Optimum order is comparable to FCFS at the 10% outage level • Scenarios where inter-cell coordination becomes feasible should be investigated for potentially larger gains