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
04/19/23
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
04/19/23
System Model
Wire-Line Network
h
hh
1
23
'n n nk k ky v h x
( )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
04/19/23
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
04/19/23
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
R
R
1
Ki
i i
R
T
iT
R
04/19/23
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
I H Q H I H Q H
1 2 Kw w w
04/19/23
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
2 2 2
2 2 22 2 2
2 2 2
det( )logdet( ) log
det( )
det( )logdet( ) log
det( )
t tt 1 1 11 1 1 t
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
04/19/23
Convex Optimization Algorithm
Standard convex optimization techniques can be used to perform the maximization
max ( )fAx b
x
*
: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
04/19/23
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
04/19/23
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
04/19/23
Classic Cellular Model
MSC
Gateway
BTS
Hexagonal Layout
Uniform User distribution
04/19/23
Simulation Setup
20 users drawn from this CDF
10000 frames with the proportional fair scheduling
04/19/23
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
04/19/23
Performance for Multiple Receive Antennas
Harder to bridge the gap
GZF technique is sub-optimal even among schemes without DPC
04/19/23
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
04/19/23
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
04/19/23
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
04/19/23
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
04/19/23
Convex Sets and Separating Hyperplanes
Can quickly determine points outside the rate region
04/19/23
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
04/19/23
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
04/19/23
TDMA Vs FCFS (multiple receive antennas)
04/19/23
FCFS Vs Optimal Ordering
MPF – Minimum Power First
04/19/23
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