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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 - PowerPoint PPT Presentation
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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