Downlink Capacity Evaluation of Cellular Networks with Known Interference Cancellation

Howard Huang, Sivarama Venkatesan, and Harish Viswanathan

Lucent Technologies Bell Labs

04/19/23

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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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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System Model

Wire-Line Network

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1

23

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( )th ( 1)t h ( 2)t h ( 3)t h

Block Fading

Each interval has sufficient number of symbols to achieve capacity

Other-cell interference + AWGN

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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

1

max log( )K

ii

T iT

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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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R

1

Ki

i i

R

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iT

R

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Maximum Weighted Rate Sum

Using duality

Using polymatroid structure of the MAC rate region

:1

R ( ) R ( )1 1

max maxBC MAC

KP P Pii

K K

i i i iR P R Pi i

w R w R

1

1

11 1 1: ( )

max ( ) logdet logdetK

i ii

K i Kt t

i i l l l K l l li l ltr P

w w w

Q Q

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1 2 Kw w w

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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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2 2 22 2 2

2 2 2

det( )logdet( ) log

det( )

det( )logdet( ) log

det( )

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1 1 1

t tt 1 1 1

t

I + H Q H H Q HI + H Q H

I + H Q H

I + H Q H H Q HI + H Q H

I + H Q H

1 2w w

1 2R R const

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Convex Optimization Algorithm

Standard convex optimization techniques can be used to perform the maximization

max ( )fAx b

x

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:arg max ( ( ))f n

x Ax=bx x x

* *arg max ( ) (1 )t

t f t n t x x

* * *( 1) ( ) (1 )n t n t x x x

Optimization :

Iterative Algorithm

Linear Optimization:

Line Search :

Update :

x : Covariance matrices

Linear Constraint : Power Constraint

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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

( ) : logdet ,ZFkR R k t

k k k(I + H Q H )

R S S

| | MS

T

TK T

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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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Classic Cellular Model

MSC

Gateway

BTS

Hexagonal Layout

Uniform User distribution

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Simulation Setup

20 users drawn from this CDF

10000 frames with the proportional fair scheduling

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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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Performance for Multiple Receive Antennas

Harder to bridge the gap

GZF technique is sub-optimal even among schemes without DPC

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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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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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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

*R*w

* *max w R

*R

*R w

for all i jw w i j

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Convex optimization algorithm for achievability

Define

Given a rate vector find

Then is achievable iff

( ) maxR

g R

R

*R

* *

: 1

arg min ( )i

i

g R

*R

* * *( ) 0g R

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Convex Sets and Separating Hyperplanes

Can quickly determine points outside the rate region

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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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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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TDMA Vs FCFS (multiple receive antennas)

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FCFS Vs Optimal Ordering

MPF – Minimum Power First

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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