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

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 11/7/2018

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 Throughput distribution for packet data Number of users at fixed rate transmission 11/7/2018

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 11/7/2018

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 will assume the backlogged scenario where each user has infinite amount of data to send Simplifying assumption Can still obtain reasonable estimate of the gain 11/7/2018

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 11/7/2018

Maximum Weighted Rate Sum Using duality Using polymatroid structure of the MAC rate region 11/7/2018

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 11/7/2018

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 : 11/7/2018

Beam Forming Scheme Separately encode each user’s signal with zero-forcing beam forming 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 11/7/2018

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 11/7/2018

Classic Cellular Model MSC BTS Gateway Hexagonal Layout Uniform User distribution 11/7/2018

Simulation Setup 20 users drawn from this CDF 10000 frames with the proportional fair scheduling 11/7/2018

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 11/7/2018

Performance for Multiple Receive Antennas Harder to bridge the gap GZF technique is sub-optimal even among schemes without DPC 11/7/2018

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 11/7/2018

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 11/7/2018

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 11/7/2018

Convex optimization algorithm for achievability Define Given a rate vector find Then is achievable iff 11/7/2018

Convex Sets and Separating Hyperplanes Can quickly determine points outside the rate region 11/7/2018

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 11/7/2018

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 11/7/2018

TDMA Vs FCFS (multiple receive antennas) 11/7/2018

FCFS Vs Optimal Ordering MPF – Minimum Power First 11/7/2018

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 11/7/2018