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
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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
Throughput distribution for packet data
Number of users at fixed rate transmission
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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
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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 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
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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
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7. Maximum Weighted Rate Sum
Using duality
Using polymatroid structure of the MAC rate region
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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
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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 :
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10. 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
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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
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12. Classic Cellular Model
MSC
BTS
Gateway
Hexagonal Layout
Uniform User distribution
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13. Simulation Setup 20 users drawn from this CDF
10000 frames with the proportional fair scheduling
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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
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15. Performance for Multiple Receive Antennas
Harder to bridge the gap
GZF technique is sub-optimal even among schemes without DPC
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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
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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
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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
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19. Convex optimization algorithm for achievability
Define
Given a rate vector find
Then is achievable iff
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20. Convex Sets and Separating Hyperplanes
Can quickly determine points outside the rate region
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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
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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
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23. TDMA Vs FCFS (multiple receive antennas)
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24. FCFS Vs Optimal Ordering
MPF – Minimum Power First
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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
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