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

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Characterization of rate region using duality used for
computations
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
Block Fading
Wire-Line
Network
h (t ) h(t  1) h(t  2) h(t  3)
h1
h3
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Each interval has
sufficient number of
symbols to achieve
capacity
h2
ykn  h'k x n  vkn
Other-cell
interference +
AWGN
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
K
–
max  log(Ti ) where Ti is the long term average
i 1
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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On-line scheduling algorithm

In each frame we assign rate vector
R R
that maximizes
K
Ri

i 1 Ti
where

Ti is the moving average of the throughput
The rate region
R depends on the the transmission strategy
– DPC rate region when known interference cancellation is
employed
– Rate region from beam forming

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We have to solve the weighted rate sum maximization in each
frame to determine the throughput
Maximum Weighted Rate Sum

Using duality
K
max
RR BC ( P )

w R
i 1
i
i

K
R
max
K
P:  Pi  P
i 1
R MAC ( P )
w R
i 1
i
i
Using polymatroid structure of the MAC rate region
w1  w2 
 wK
i
K




t
t
max
(
w

w
)log
det
I

H
Q
H

w
log
det
I

H
Q
H

i
i 1
K
  l l l
  l l l
K
l 1
l 1




Qi : tr ( Qi )  P i 1
K 1
i 1
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Simple proof of optimal ordering

For any set of covariance matrices
t
t
det(
I
+
H
Q
H

H
1 1 1
2Q 2 H 2 )
log det(I + H1t Q1H1 )  log
det(I + H1t Q1H1 )
t
t
det(
I
+
H
Q
H

H
t
1 1 1
2Q 2 H 2 )
 log det(I + H 2Q 2 H 2 )  log
det(I + H t2Q 2 H 2 )

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Since R1  R2  const independent of the decoding order,
we should pick the user with least weight to see the most
interference w1  w2
Convex Optimization Algorithm

Standard convex optimization techniques can be used to
perform the maximization
Optimization :
max f (x)
Axb
x
: Covariance matrices
Linear Constraint : Power Constraint
Iterative Algorithm
Linear Optimization:
x*  arg max f (x( n))  x
x : Ax=b
Line Search :
t *  arg max f  tx(n)  (1  t )x* 
t
Update :
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x(n  1)  t *x(n)  (1  t * )x*
Beam Forming Scheme

Separately encode each user’s signal with zero-forcing beam
forming

Rate Region for a subset of users (| S |  M )

R ZF (S )  R : Rk  log det (I + Hk Qk Hkt ), k S


Max weighted rate sum within the subset is weighted waterfilling

Computing max weighted rate sum over all subsets of users is
very complex even for 4 antennas

Approx: First select a subset T of users with the highest
individual metrics and implement max weighted rate sum only
over this subset of users

Complexity depends on the size
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KT of the set T
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

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Similar approximation algorithm as in ZF case for computing
maximum weighted rate sum
Classic Cellular Model
MSC
BTS
Gateway
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
weight vector w* such that
optimization max w*  R*
R*
R* there exists
is the solution to the
– Cannot iterate on the weights to determine the equal rate
point
–
R* is indeed unique whenever w is such that
wi  w j for all i  j

All points of the rate region may not be achievable without ratesplitting or time-sharing

For capacity evaluation we need only an algorithm to test if a
rate vector is achievable
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Convex optimization algorithm for achievability

Define
g (  )  max   R
RR

Given a rate vector
R* find
 *  arg min g (  )    R*
 i 1
:
i

Then
R* is achievable iff
g (  * )   *  R*  0
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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

6/30/2016
Scenarios where inter-cell coordination becomes feasible
should be investigated for potentially larger gains