Workshop on Novel Waveform and MAC Design for 5G (NWM5G 2016)
Centralised and Distributed Interference Management
in Coordinated Downlink Beam-forming
S. Barman Roy and A. S. Madhukumar
Francois Chin
School of Computer Engineering
Nanyang Technological University
Singapore
Email: {swagato002, asmadhukumar}@ntu.edu.sg
Internet of Things Connectivity
Institute for Infocomm Research
Singapore
Email: chinfrancois@i2r.a-star.edu.sg
Abstract—Traditional cellular systems have depended on coverage areas partitioned into disjoint cells where each user is
served by a single base station, without any cooperation. To deal
with the resulting inter-cell interference, this work combines the
advantages of CoMP along with detection and broadcasting techniques with different channel output suitable for massive MIMO.
Two novel interference management techniques, viz. Centralised
Interference Cancellation (CIC) and Distributed Interference
Cancellation (DIC) to optimise power allocation in a cooperative
framework have been proposed. The schemes point out the
trade off between achievable performance and computational
complexity. Since large number of antennas require mathematical
manipulation of big random matrices, a suboptimal two layer
decoding method is proposed which combines selection diversity
with least mean square filtering.
Keywords—Beam-forming, Coordinated Multipoint Transmission, Duality, Interference Management, Resource Allocation
I.
I NTRODUCTION
T
HE shortage of radio spectrum to meet the exploding
demand for wireless data rate has been a persistent
challenge facing the communication engineering and research
community. With the global tele-traffic growth projected to
grow exponentially, there is an increasing need for innovative
coding and multi-user resource allocation techniques (time slot,
frequency and power) to address the shortfall. To improve
the link performance with constrained power budgets, this
paper incorporates two major paradigm shifts which have been
proposed independently in earlier literature to supplement the
standard cellular system currently in existence.
Cooperative multi-point transmission techniques have been
proposed to blur the cell boundary and explore more efficient forms of inter cell cooperation [1]. In the existing
systems, each user equipment (UE) exchanges data with a
predetermined single base station. The downlink (broadcast)
transmissions at adjacent cells go on independently of each
other, usually separated in time/frequency domains so as to
avoid interference. One of the major drawbacks is the nonuniform service quality, particularly, the poor performance
suffered by users near the cell edge which has been studied
in [2]. Cooperative Beam-forming (CBF) is a special case
CoMP where the transmitting base stations still serve their own
users. However, unlike existing systems in deployment, CBF
entails minimisation of interference caused to other users as a
secondary goal. Different interference management algorithms
have been presented within cooperative frameworks [3], [1].
978-1-4673-8666-1/16/$31.00 ©2016 IEEE
For example, [4] assumes that all the base stations have perfect
cooperation and access to data stream of all users. Hence the
system model becomes equivalent to a multi-user single cell
system with a sum power constraint. Further, a multicellular
system was also considered in [5].
Also, a completely different paradigm of large scale antenna system (LSAS) or massive MIMO with a very high
number of antennas has been proposed in literature [6]. Presence of large number of antennas in the base station supports transmission of multiple data streams along independent
(interference free) spatial dimensions. To exploit this, zero
forcing beam-forming strategies have been proposed in [7], [8].
However, optimal utilisation of a big number of antenna
faces serious challenges in terms of hardware and algorithmic
complexity [9], [10]. Also, most MIMO as deployed in existing
wireless standards such as LTE and IEEE 802.11 etc. typically
cater to single user systems.
The motivation behind this work is to incorporate the
suboptimal two layer decoding [11] of massive MIMO in
cooperative beam-forming and present two novel interference
cancellation methods, i.e, Centralised Interference Cancellation
(CIC) and Distributed Interference Cancellation (DIC). Those
two methods are compared between themselves along with
existing techniques to identify the complexity-performance
trade-off in the design of next generation cellular systems.
A. Notations
Boldface small letters represent vectors and capital letters
represent matrices. {· · · } represents a set in roster form and
2S represents the power set of a set S. ∪ represents the
union of sets. Usually, the index k has been used to denote
users and l is used to denote base stations in multicellular
environments. R and C denote the fields of real and complex
numbers respectively. R++ denotes the set of positive real
numbers. E (•) denotes the expectation of a random variable.
II.
S YSTEM M ODEL AND BACKGROUND
The system model under consideration is a multi-cellular
system where several base stations are serving multiple users
scattered throughout the coverage area. It is shown in Fig. 1
with three cooperating base stations. It is assumed that a cluster
of cooperating base stations use the same time-frequency
resource block (unlike the currently deployed systems) to
transmit downlink data. The other base stations adjacent to the
Fig. 1. System Model: Dotted line indicates interference, continuous line
indicates Signal
cluster are assumed to use different time-frequency blocks and
hence present zero interference. The frequency reuse happens
across different clusters of cooperative cells and because of
geographical distance, we can ignore the effect of inter-cluster
interference. As we can see in Fig. 1, the coverage areas can
overlap with each other and each user is attached to only
one base station, in line with the definition of CBF [12]. The
channel carrying desired information for a user is shown by
continuous line whereas the interfering channels from other
base stations is shown as a continuous line. Because of the
back-haul cooperation (not shown in Fig. 1), each base station
can access the data streams and channel state among other
base station-user pairs, which is important for the proposed
beam-forming procedure.
Fig. 2 gives a schematic representation where each user
is attached to a base station and each base station in the
cooperating cluster is controlled by the central server. Note that
every user has an existing link with every base station, although
some of them are omitted from the figure for clarity. From the
implementation point of view, this is similar to the two layer
schematic diagram for LSAS uplink (multiple-access) channel
discussed in [11]. In Section III, we will improve this idea of
two layer decoding via Successive Interference Cancellation
(SIC) and extend it to broadcast channel.
A. Duality Principle
It is well known that uplink channels render themselves to
simpler analyses and optimisation procedure than broadcast
channels. Fortunately, because of the duality principle [13,
Section II], it is possible to solve any optimisation problem
in a downlink channel using known solutions from an uplink
channel. If for a single cell uplink channel, the achievable
rate region is given by CMAC (p) for user equipment power
constraints p ∈ RK
+ and the downlink rate region is given by
CBC (P ) for base station power constraint P ∈ R, then by
duality principle [13, Section II]
[
CMAC (p) = CBC (P )
P
pi =P
Also, two algorithms have been proposed in [14] to translate
any power allocation in the uplink channel to a power allocation in downlink channel and vice versa, so as to achieve
the same rate region. Henceforth, we will attempt to solve the
beamforming problems in the uplink direction and will assume
that it is possible to transform the solutions to downlink.
Fig. 2.
Schematic of Two Layer Processing System
B. Problem Formulation
We are assuming in each cooperating cluster, there are
•
L base stations each with N antennas and power
constraints Pl ∈ R++ ∀1 ≤ l ≤ L.
•
K single antenna users each attached to a base station
and intends to receive a single data stream xk C∀1 ≤
k ≤ K.
•
A central server with a high speed fibre optic connection with each base station facilitating instant communication of channel state and data signal.
The objective is to find the optimal beamforming vectors
at the base stations required to transmit the data stream while
obeying the power constraints. The optimal solution for single
cell scenarios has been discussed in [13], [15]. However, for
tractable analyses, Section III will propose some suboptimal
solutions and Section IV will compare them graphically with
some existing methods in terms of performance and complexity.
III.
P ROPOSED M ETHODS
Before we discuss the cooperative beam-forming methods,
it is important to discuss the two layer decoding method
proposed in massive MIMO uplink systems [11]. Traditional
zero forcing or MMSE receivers [14] need to find an inverse
or pseudo inverse of a channel matrix for optimal reception.
However, the computational complexity of finding an inverse
varies with the cube of the matrix dimension, which makes
it infeasible for large scale systems. In two layer systems,
the data streams received at a large number of antennas are
divided into different blocks. In the first layer, each individual
block is processed using zero forcing or MMSE technique, in
the second layer the results from the first block are processed
using selection diversity.
A. Two Layer with SIC
In this work, as part of our process to formulate the beamforming methods for downlink channel, we propose a two
layer decoding method for the uplink channel, with single
base station but antennas partitioned into blocks. The system
is similar to Fig. 2 where each base-station is replaced by a
block in the same base station. They cooperate with each other
via the server to provide optimal performance.
Following this decoding method, the rate obtained for user
k (after cancellation of interference by previous users) is given
by


!−1
K
X

rk = log 1 + pk max hkl I +
pi hil hH
hH
il
kl
Fig. 3.
l
Block Diagram for Two Layer System
i=k+1
(2)
Since each of the L blocks have N antennas, let the channel
from user k to block l be denoted by hkl ∈ CN , ∀1 ≤ k ≤ K
and 1 ≤ l ≤ L. The signal transmitted by user k is xk ∈ C and
the signal received at block l is yl . If we assume individual user
power constraints as p1 , p2 , · · · , pK , that means E |xk |2 =
pk .
yl =
K
X
hkl xk + η ∈ CN , ∀1 ≤ l ≤ L
(1)
k=1
where
η is centralised independent Gaussian noise with
E ηη H = I.
The major difference with previous works on uplink channel is because of the presence of multiple blocks with different
channel outputs to choose from. When this diversity is combined with SIC, that implies, after decoding each user, we
subtract that user’s signal from the received signals yl so as to
avoid propagation of the interference. If we assume a decoding
order 1 → 2 → · · · → K −1 → K, that means user k does not
face interference from users 1 to k − 1. Hence, while decoding
user k, the interferences come only from users k + 1 to K.
So the covariance matrix of noise and interference as seen in
block l is given by
Skl = I +
K
X
pi hil hH
il .
i=k+1
If MMSE reception is used, it can be shown that at block l, the
−1
SINR is given by pk hH
kl Skl hkl . After the first layer processing
by MMSE, we employ selection diversity at the second layer
to choose the block with highest SINR and after decoding,
we update the covariance matrix to subtract the component
because of pk .
B. Downlink Interference Cancellation
Now the two layer method for uplink reception method
will be extended to downlink beam-forming. While discussing
downlink channels in single cell, we assume that the noise at
each user has the same power. If the powers are the different,
then the corresponding channel vector can be normalised by
division with the standard deviation, making the noise variable
having unit power.
Keeping that in mind, to maximise the sum rates constrained by individual base station powers P1 , P2 , · · · , PL , it
is necessary to optimise the following parameters
•
User Ordering
•
Base station ordering
•
User association with base station
•
Power allocation and beam-forming
Clearly, for K users and L base stations, there can be K!
and L different orders respectively. In this work, for the sake
of mathematical tractability, we assume that a specific ordering
is decided upon by some external criteria. Based on the
given user/base station orderings, two interference cancellation
methods will be proposed.
1) Centralised Interference Cancellation: In this scenario,
a specific user ordering is decided by the central server out
of L! possibilities. After that, each user is associated with the
base station which has the strongest channel (as determined
by the L2 norm). Let the channel vector between user k and
base station l is given by hkl . Without loss of generality, let
us assume the user ordering is given by 1 → 2 → · · · → K.
Consider an association function φ, where
φ : {1, 2, · · · , K} → {1, 2, · · · , L}.
The decoding method is shown in the form of a block
diagram in Fig. 3. The corresponding algorithm is presented
in Algorithm 1. In Algorithm 1, the subscript k is omitted
from Sl for the sake of brevity, since it is updated after each
decoding.
φ(k) ≡ argmaxl |hkl |2 represents the base station which
is attached to user k. Also consider the inverse association
function
Algorithm 1 : Two Layer Decoding with SIC
N
Require: p ∈ RK
and
++ , h11 , · · · , hkl , · · · , hKL ∈ C
y1 , y2 · · · yL
1: for 1 ≤ l ≤
PL
K
H
2: Sl ← I +
i=2 pi hil hil end
3: for 1 ≤ k ≤ K
−1
4: l∗ ← argmax1≤l≤L hkl Sl hH
kl
5: Decode user k from antenna cluster l∗
6: for 1 ≤ l ≤ L
7: Sl ← Sl − pk hkl hH
kl end end
which gives the set of users attached to any base station.
Obviously in the case of CIC, there is no ordering of base
stations since any two consecutive users can belong to two
different base stations.
φ−1 : {1, 2, · · · , L} → 2{1,2,··· ,K} .
To find the required beam-forming vectors, let us assume
the vector transmitted by base station l is given by xl ∈
CN ∀1 ≤ l ≤ L. Hence the received signal at user k is
yk =
L
X
l=1
hH
kl xl + ηk
(3)
where E |ηk |2 = 1. Now, among all possible xl , only
xφ(k) contains the useful data signal for k. The rest constitute
interference. However, because the base station are cooperating
with the central server, base station φ(k) is already aware of the
interferences caused by signals for users 1, 2, · · · , k − 1, coming from base stations φ(1), φ(2), · · · , φ(k−1) respectively. So
these interferences can be pre-subtracted before transmission
by dirty paper coding [16]. Hence for user k, the interferences
will be coming from users (k + 1), · · · , K which must be
treated as noise. Let the variance of this additional Gaussian
interference be denoted by σk2 . In that case the total variance
of noise and interference for user k is σk2 + 1 . The effective
h
channel can be constructed as √kφ(k)
.
2
Fig. 4.
Inter-cellular noise cancellation with DPC
σk +1
Hence for base station l, the problem is to find the power
allocation and beam-forming vectors for users φ−1 (l). Since
each user has different noise covariance, the channels must
be normalised. Hence it becomes a power allocation problem
for single antenna users in a single cell downlink channel,
performed independently at each base station according to
power constraints Pl . It has been solved using duality principle
and a norm balancing method in the authors’ earlier work [13].
base station, the received signal can be written as
yk =
L
X
∀k ∈ φ−1 (l)
hH
ki xi + ηk
(4)
i=l
= hH
kl xl +
L
X
hH
ki xi + ηk
i=l+1
In summary, the steps for power allocation in CIC
where the second term represent inter-cell interference from
other base stations with higher priorities.
•
All users are ordered according to pre-defined criteria
by the server, out of K! possibilities.
•
Each user is associated with the base station which
offers the strongest channel.
•
Normalise the user channels with the noise and interference levels.
The power allocation and beam-forming problem can be
solved as the sum rate maximisation problem in a single cell
downlink channel with added inter-cell interference [13]. However, in the dual uplink channel, the sum rate is independent of
the decoding order. So the base station l can use the appropriate
decoding order not to maximise its own sum rate, but to
minimise interference to users φ−1 (1), · · · , φ−1 (l − 1).
•
Each base station will allocate power to maximise the
sum rate according to the given noise levels using
duality [14] and the algorithm proposed in [13].
To illustrate, let us assume the base station l transmits a
vector xl . In that case, the inter-cell interference signals from
BS l to other users is given by
Note that the last step in the procedure automatically cancels
both the inter-cell interference (among users under the same
base station) and intra-cell interference (from other base stations).
2) Distributed Interference Cancellation: In this scenario,
the central server performs an ordering of the base station
out of L! possibilities. The users are associated with the base
station in the same way as CIC and we will continue to use
the functions φ and φ−1 to denote the user association.
However, the key difference with CIC is the autonomous
decisions are taken at the base stations to order their users and
cancel the inter-cell interference. The inter-cell interference
cancellation can be achieved using dirty paper coding as shown
for a two cell cluster in Fig. 4. In the figure, BS l serves the
group of users φ−1 (l) for l = 1, 2. However, BS 2 has higher
priority than BS 1, which allows BS 2 to pre-subtract the
interference from BS 1 to φ−1 (2), as illustrated by the absence
of connecting lines. But this does not stop the interference
from BS 2 to φ−1 (1) which is indicated by the dotted lines.
For an L cell cluster, when the base station ordering is given
by 1 → 2 → · · · → L then for base station l, the interferences
come from base stations l + 1 to L. Hence for users under a
hH
kl xl
∀k ∈
l−1
[
φ−1 (i)
i=1
In this work, the goal is to minimise the total interference
power given by
X
2
H
Pl =
|hH
(5)
kl xl | = xl Al xl
k∈
Sl−1
i=1
φ−1 (i)
where
X
Al ≡
k∈
Sl−1
i=1
hkl hH
kl
φ−1 (i)
Since the positive definite matrix Al depends solely on the
channels and is independent of any beam-forming strategy, the
base station l has to find
argminxl xH
l Al xl
Now the optimisation parameter xl can be taken only from
a finite set of arguments, which we can find using the uplinkdownlink transformation [14, Section IV–B]. After that it is
possible to use brute force method to evaluate (5) for each
resulting xl and find the minimum. However, this step can
TABLE I.
Scheme
CIC
DIC
C OMPARISON OF C ENTRALISED AND D ISTRIBUTED I NTERFERENCE M ANAGEMENT
Power Allocation
Performed by base station
Base station Ordering
Results automatically from user ordering
Done by base station from L! possibilities
be performed only if the available computational resources at
each base station satisfies it.
Total Throughput (bit/transmission)
115
In summary, steps for power allocation in DIC
•
•
•
•
Base stations are ordered according to pre-defined
criteria by the server, out of L! possibilities.
Each user is associated with the base station which
offers the strongest channel.
110
105
100
95
Two Layer Decoding with SIC
Decoding Method As Proposed in [11]
Without Massive MIMO enabled base station
90
85
10
20
30
40
50
60
Sum Power of Users (in Watt)
70
80
90
100
Each base station will construct a dual multiple access
channel [14] according to the given noise levels.
Fig. 5.
Allocate the power to maximise the sum rate according to the base station power constraint Pl and using
norm balance algorithm [13].
a single base station with 200 antenna, which does not allow
the selection diversity employed at the second layer.
[Optional: Depending on complexity] The user ordering is done by the base stations to minimise the determinant of interference covariance matrix according
to duality.
Note that the power allocation to maximise sum-rate is
done exclusively to cancel the known intra-cell interference
among the users. However the optional last step seeks to minimise inter-cell interference with trade-off on the algorithmic
front.
Both CIC and DIC can be conceptualised as extension of
the two layer method in uplink to a cooperative downlink channel, where the roles of the antenna blocks [11] are replaced
by individual base stations. The key difference between CIC
and DIC have been summarised in Table I.
IV.
S IMULATION AND C OMPARISON
This section compares the proposed algorithms graphically
with existing results in the literature and among themselves.
The simulation was carried out using matlab and simulink in
linux platform.
Fig. 5 shows the performance of the two layer decoding
system enabled by massive MIMO and enhanced by the SIC
technique outlined in Section III-A. The rates obtained from
SIC are plotted according to 2. Two comparison benchmarks
are the earlier two layer processing (proposed in [11]) and
the data rate achievable by an ordinary base station without
the aid of massive MIMO. For simulation purpose, a system
consisting of 100 users is considered, along with a base station
containing 1000 antenna divided into five blocks of 200 each.
(For such high number of antennas with uncorrelated channels,
typically a millimetre range system is required [17].) Since the
achievable data rate increases monotonically with power (with
a diminishing marginal effect), the comparison is done for an
appropriate range only for illustration purpose.
The advantage of SIC along with two layer decoding is
clear. Also, the last line indicates the data rate achievable for
Comparison of Achievable Sum Rates.
Further, in Fig. 6, we compare the best possible outcomes
of CIC and DIC. Since there is a sub-optimality involved
in determining the order of users in CIC and order of base
stations in DIC, the algorithms have been run using brute force
techniques to go through all possible orders and select the
base possible one. For algorithmic efficiency, the minimisation
of (5) in DIC has been omitted and each base station has
ordered the user according to the user index. It is clear that for
the best possible scenarios, CIC outperforms DIC. However,
the search space for CIC consists of K! elements whereas
for DIC, the search space has L! elements, as pointed out
in Table I. The comparison benchmarks also includes the
conventional resource allocation strategy in downlink virtual
MIMO, as pointed out in [18] . According to the framework
proposed in [18], each base station allocates power without
cooperation (to cancel inter-cell interference) and without dirty
paper coding (to cancel intra-cell interference). The advantage
of the proposed CIC and DIC is evident from the achievable
throughputs.
18
Total Throughput (Bit/Transmission)
•
User Ordering
Performed by server from K! possibilities
Performed by each base station
16
14
12
10
8
6
Centralised Interference Cancellation
Distributed Interference Cancellation
4
Without Interference Cancellation [18]
2
1
Fig. 6.
2
3
4
5
6
7
Sum Power of Basestations (in Watt)
8
8
10
11
Comparison of Interference Cancellation Techniques.
The computational trade off has been illustrated in Fig. 7
where the time requirements to execute the algorithms (in a
64 bit linux system) have been plotted against the number of
users (problem size). Although the exact values are system
dependent, the trend is evident from the growth rates of
algorithms. Hence DIC gives us a suboptimal result but with
superior algorithmic efficiency.
[5]
3.5
Time Requirements (in ms)
3
2.5
DIC Without Base Station Optimisation
Centralised Interference Cancellation
[6]
2
1.5
[7]
1
0.5
0
0
Fig. 7.
50
100
Number of Users in the cell Cluster
150
[8]
Time Complexity of Interference Cancellation Techniques.
[9]
V.
C ONCLUSION
The important objective of the paper has been to identifies
the performance–complexity trade off by proposing several algorithms to allocate resources. Because of certain assumptions,
the proposed techniques are sub-optimal from a performance
point of view. However, the assumptions are necessary to
maintain analytical tractability and reduce the complexity.
The proposed algorithms have been compared with several
earlier methods to show the performance improvement where
applicable. The work can be extended in the directions of
further optimisation of the sub-optimally allocated parameters.
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