Distributed Comp Paper Final

7/31/2019 Distributed Comp Paper Final

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Distributed Precoding with Local Power Negotiation

for Coordinated Multi-Point Transmission

Dennis HuiEricsson Research

200 Holger Way, San Jose, California 95134

Email: [email protected]

Abstract—Coordinated multi-point (CoMP) transmission hasrecently received much attention due to its promise in effectivelymitigating the inter-cell interference in a cellular network. Inthis paper, we compare two different architectures for CoMPtransmission. The first architecture partitions all basestationsin the network into disjoint clusters with signal transmissionswithin each cluster being coordinated independently of oneanother at a centralized location of each cluster. In the secondarchitecture, the processing for coordinated transmission isdistributed among overlapping clusters, each centered around

one cell. For this architecture, we propose a simple methodfor computing linear multi-user precoders for all clusters ina distributed manner, where the precoders are chosen notonly to maximize throughput to the served users but also toreduce interference with other users in overlapping clusters. Alow-complexity iterative algorithm is proposed for negotiatingtransmit power levels among adjacent clusters to ensure thepower constraints at all transmission points are satisfied. Throughsystem simulations using practical channel models, we showthat the distributed architecture substantially outperforms thecluster-wise centralized architecture in maximizing the user datathroughputs in the network.

I. INTRODUCTION

One of the major impediments to achieving higher spectralefficiency in a cellular network is the mutual interference

among users in adjacent cells utilizing the same radio re-

sources. Substantial research efforts have been devoted to re-

ducing the adverse impact of inter-cell interference. In particu-

lar, coordinated multi-point (CoMP) transmission has recently

received much attention in both industry and academia, cf. [1]

[2] [8], due to its promise in effectively mitigating inter-cell

interference through the use of multi-user precoding across the

antennas of multiple basestations (BSs).

A simple architecture for CoMP transmission is to parti-

tion all cells in a cellular network into disjoint independent

groups, referred to as CoMP clusters, as depicted in Fig. 1.

Basestations within each of these fixed CoMP clusters areconnected, forming a coordination set, to a centralized, joint

processing center (JPC) where transmissions to all users within

that cluster are coordinated. In this cluster-wise centralized

architecture, although each CoMP cluster provides an extended

geographical area over which inter-cell interference within

the cluster can be controlled, the users near the edge of

a CoMP cluster can still experience substantially degraded

service quality compared to those near the center of the

CoMP cluster due to the uncoordinated interference from other

neighboring CoMP clusters. This has the potential of creating a

large service quality disparity among users within the network.

In order to reduce the fraction of users being adversely affected

by uncoordinated inter-cluster interference, the number of cells

included in each CoMP cluster is preferred to be large, posing

challenging latency problems over the backhaul connecting

distant cell sites to the JPC, which in turn impose practical

limitations on the maximum size of each CoMP cluster.

Users in

CoMP cluster 1

Users in

CoMP cluster

2

Users in

CoMP cluster 3 Fig. 1. Illustration of a Cluster-wise Centralized CoMP Architecture

I I . DISTRIBUTED FRAMEWORK

In this paper, we propose a distributed architecture for

CoMP transmission where CoMP clusters are allowed to

overlap with each other. In this architecture, each cell is

associated with a cell-specific (CS) CoMP cluster, centered

around the serving cell. Users in any given cell are served

by the set of coordinating BSs in its own CS CoMP cluster.

For example, Fig. 2 shows two overlapping CS CoMP clusters

(green and yellow) whose serving cells are adjacent to each

other and are at the center of their respective CS CoMP

clusters. The precoding weights of each CS CoMP clusterare computed almost independently (as explained later) by a

coordinating processor, which is presumably located at the BS

of its serving cell.

Since the CS CoMP clusters closely mingle with each

another, the interference generated by one CS CoMP cluster

can severely affect many other overlapping clusters. To reduce

its impact on the overall system performance, a geographical

area, termed the region of interference avoidance (RoI), is

associated with each CS CoMP cluster such that (some or



User in

Targeted Cell jSet of Coordinating

Basestaions

for Cell j

Region of

Interference

Avoidance for Cell j

Fig. 2. Illustration of a Distributed CoMP Architecture

all) users in the RoI are taken into account by the CS CoMP

cluster when computing the precoding weights in such a way

that minimizes the interference generated to these users. TheRoI of each cluster is assumed to contain its serving cell.

Since each BS antenna can be used to serve multiple CS

CoMP clusters simultaneously, a mechanism for resolving

potential conflicts in the power requirements among different

CS CoMP clusters is needed to avoid violating the power

constraints of each BS. To this end, we propose a simple itera-

tive distribtuted algorithm for negotiating power requirements

among overlapping CoMP clusters. Convergence properties

of the proposed algorithm will be discussed. Using such

an algorithm, we evaluate the system performance of the

distributed approach of CoMP transmission and compare it

with that of the cluster-wise centralized approach.

III. PRECODER COMPUTATION

In this section, we describe a simple, effective method of

computing the precoding weights of all BSs in a distributed

manner. Let J denote the set of indices of all cells, and their

corresponding CS CoMP clusters, in a cellular network. Based

on the framework described above, consider the situation

where each CS CoMP cluster j ∈ J uses nb,j BSs in its coor-

dination set C j to transmit signal to K j users in its serving (or

center) cell while trying to limit interference to other Lj users

in the RoI. Let nt(i) denote the number of available transmit

antenna for each BS i ∈ C j , and the total number of transmit

antenna for this CS CoMP cluster be nt,j = ∑i∈C jnt(i).

Let S j = {qj(1), qj(2), · · · , qj(K j)} denote the set of globaluser indices for the K j users in the serving cell, and let

Aj = {qj(K j + 1), qj(K j + 2), · · · , qj(K j + Lj)} denote

the set of other Lj user indices in the RoI but not in S j ,

where qj(·) denotes a mapping from the local user indices

within the CS CoMP cluster j to the corresponding global

user indices. For each k ∈ S j ∪ Aj , let Hj,k be the nr,kby nt,j channel response matrix from the transmit antennas

of cooperating BSs in C j to the receiver antennas of user k,

where nr,k denotes the number of receive antennas at user k.

Let Pj,k denote a nt,j-by-ns,k precoding matrix of user k to

be served by the CS CoMP cluster j, where ns,k denotes the

number of data streams transmitted to user k. For notational

simplicity, we let Pj ≡ [Pj,qj(1),Pj,qj(2), · · · ,Pj,qj(Kj)] and

Hj ≡ [HH j,qj(1)

,HH j,qj(2)

, · · · ,HH j,qj(Kj+Lj)

]H . We assume

that the processor of CS CoMP cluster obtains, on a regular

basis, the instantaneous channel state information (CSI) Hj

from all users in its serving cell and all the users to be served

in the RoI either through feedback or through measurement in

the reverse link in a Time-Division Duplex (TDD) system.

To facilitate low-complexity, distributed computation of

{Pj}j∈J , we propose to divide each precoding matrix Pj

into two components: a tentative precoding matrix Pj ≡[Pj,qj(1), Pj,qj(2), · · · , Pj,qj(Kj)] and a power back-off (or

scaling) factor δj . The tentative precoding matrix Pj repre-

sents the desired precoding matrix when no other CS CoMP

cluster in J needs to share the antenna resources of any

BSs in C j . When there is a possible sharing of antenna

resources among overlapping CoMP clusters, a power backoff,

as specified by δj , is used to scale the tentative precoding

weights so that the power requirements of all antenna elementsare satisfied. The overall precoding matrix is simply given by

Pj = δjPj . Given a ns,k-by-1 information-bearing symbol

vector sk (normalized such that E sksH k = 1) for each user

k, the transmitted signal from the coordinating BSs in the CS

CoMP cluster j to all K j users in the serving cell is given by

xj =k∈Sj

Pj,ksk = δjk∈Sj

Pj,ksk. (1)

The main idea here is to let each CS CoMP cluster determines

the tentative precoding matrix Pj independently while using

a low-complexity distributed algorithm to negotiate the power

back-off factor δj among overlapping CS CoMP clusters.

There are many methods of computingPj as a function of

Hj , such as the oft-cited zero-forcing precoding [2] [3], and

the MMSE-based multi-user precoding techniques, cf. [4] [5]

[6] [7]. In our simulations, we adopt the transmit Wiener filter

(TxWF) precoder [7] due to its good performance-complexity

tradeoff and its lack of restriction in the size of Hj . More

precisely, the tentative precoding matrix Pj,qj(i) for user qj(i),

for i = 1, 2, · · · ,K j , is computed as

Pj,qj(i)=H

H j

(HjH

H j +α( j)I

)−1:,mj,i−1+1:mj,i

Λqj(i) (2)

where α( j) ≡ P −1T

∑Lj+Kj

l=1 nr,qj(l) σ2n,qj(l)

. mj,i ≡

∑i

l=1ns,qj(l)

, [A]:,m :n

denotes those columns of the matrix

A positioned between its mth and nth column inclusively,

I denotes the identity matrix, σ2n,k denotes the variance of

noise-plus-interference observed at user k, P T represents the

maximum total transmit power of all antennas in all BSs in

C j , and Λk denotes a matrix for allocating different relative

powers to different data streams.

IV. POWER NEGOTIATION

Once Pj is determined at the serving cell of a CS CoMP

cluster, the corresponding tentative antenna weights, as speci-



fied by Pj , are sent to each BS in the coordination set C j . To

resolve any potential conflicts in power demand among differ-

ent overlapping clusters, we present here a simple algorithm,

which we called iterative sum-min algorithm, for computing a

power back-off factor δj for each CS CoMP cluster by iterative

communications among neighboring serving cells, which is

described as follows and illustrated in Fig. 3.

Compute and

report power margin at each

antenna

Scale weights

by minimum

margin

Processors Antennas

Fig. 3. Graphical Representation of Iterative Sum-Min Algorithm (differentbranch colors represent different CS CoMP clusters)

Let Γ be the global index set of all antennas in the network,

and let B(m) denote the index of the BS where antenna m

resides. Also let[A

]k,ldenote the

(k, l

)element of matrix A.

Iterative Sum-Min Algorithm:

Step 1 (Initialization): Set the iteration index n to 0. Pro-

cessor (located at the serving cell) of the CS CoMP

cluster j computes, for each j in the network, the

initial power requirement π(0)j (m) as

π(0)j (m) =

l

[Pj

]rj(m),l

2 , (3)

for each antenna indexed by m ∈ Γ in the coordi-

nation set C j , where rj(m) denotes the row of the

matrix Pj that corresponds to the antenna m.

Step 2 : Processor sends antenna power requirements{π

(n)j (m)}m to all respective neighboring BSs (or

their associated processors) in the set C j\{ j}.

Step 3 (“Sum”): Upon receipt of the power requirements

{π(n)j (m)}m from neighboring BSs for each antenna

m, the processor whose serving cell possesses the

antenna computes the power margin ∆(n)(m) as

∆(n)(m) =P t(m)∑

j:B(m)∈C jπ(n)j (m)

. (4)

where P t(m) denote the maximum power constraint

of antenna m.

Step 4 : Each processor sends power margins {∆(n)

(m)}mof all the antennas of its serving cell to processors of

neighboring serving cells that utilize these antennas

to transmit signals to their respective users.

Step 5 (“Min”): Upon receipt of the power margins of all

antennas in BSs in C j , the processor of the jth CS

CoMP cluster, for each j, computes the minimum

power margins over all the antennas given by

∆(n)j ≡ min

m:B(m)∈C j∆(n)(m) (5)

and use ∆(n)j to update {π

(n)j (m)}m as

π(n+1)j (m) = ∆

(n)j π

(n)j (m). (6)

Step 6 : Increment iteration index n, and go back to Step

2 until certain stopping criteria is satisfied. For

example, ∆(n)j is very close to 1 for every CS CoMP

cluster j ∈ J .

Step 7 : The power back-off factor for the CS CoMP cluster

j is computed as δj =∏nf−1

l=0 ∆(l)j , where nf is the

final value of the iteration index.

In the following, we study the convergence properties of the

iterative sum-min algorithm.

Lemma 1. For each antenna m ∈ Γ , the sequence of power

margins {∆(n)(m)}n≥1 generated by the sum-min algorithm

satisfies ∆(n)(m) ≥ 1 and ∆(n+1)(m) ≤ ∆(n)(m) for all

n ≥ 1.

Proof: For n ≥ 1, it follows from (4) that for all m ∈ Γ,

∆(n)(m) = P t(m)∑j:B(m)∈C j

π(n)j (m)

=P t(m)

∑j:B(m)∈C j

min

m′:B(m′)∈C j∆(n−1)(m′)

π(n−1)j (m)

≥P t(m)

∆(n−1)(m)∑

j:B(m)∈C jπ(n−1)j (m)

= 1,

where the second equality follows from (5) and (6), and the

last equality follows from the definition of ∆(n−1)(m). Now,

again from (4), we have

∆(n+1)(m)

∆(n)(m)=

∑j:B(m)∈C j

π(n)j (m)∑

j:B(m)∈C jπ(n+1)j (m)

=

∑j:B(m)∈C j

π(n)j (m)

∑j:B(m)∈C j

min

m′:B(m′)∈C j∆(n)(m′)

π(n)j (m)

≤

∑j:B(m)∈C j

π(n)j (m)∑

j:B(m)∈C j1 · π

(n)j (m)

= 1,

where the inequality follows from ∆(n)(m) ≥ 1 for all m ∈Γ. Hence, the sequence {∆(n)(m)}n≥1 is monotonically non-

increasing.

Lemma 2. For each CS CoMP cluster j ∈ J , the sequence

of minimum power margins {∆(n)j }n≥1 generated by the

sum-min algorithm satisfies ∆(n)j ≥ 1 for all n ≥ 1 and

limn→∞

∆(n)j = 1.

Proof: ∆(n)j ≥ 1 for all n ≥ 1 is obvious from Lemma 1

and (5). It also follows immediately from Lemma 1 and (5) that

the sequence {∆(n)j }n≥1 is a monotonically non-increasing



sequence for all j ∈ J . Therefore, the sequence {∆(n)j }n≥1

has a limit, denoted by cj , which is no less than one. Now

suppose cj > 1, then from (6), we have that for some m ∈ Γ,

π(n)j (m) ≥ (cj)n−1 π

(1)j (m) → ∞ as n → ∞, which is a

contradiction since

π(n)j (m) ≤

j:B(m)∈C j

π(n)j (m) =

P t(m)

∆(n)(m)≤ P t(m) < ∞

for all n ≥ 1, where the equality above follows from (4).

From these lemmas, one can conclude that after only one

iteration, the resulting power back-off factors {δj}j∈J is

guaranteed to satisfy the power constraints of all antennas in

the network (since ∆(1)(m) ≥ 1 for all m ∈ Γ). Moreover, the

algorithm is guaranteed to converge, and additional iterations

after the first iteration yield higher values of {δj}j∈J so that

the power of each antenna can be more fully utilized.

V. NUMERICAL RESULTS

In this section, we present system simulation results of

an OFDM cellular communication system employing CoMP

transmission in the downlink using the cluster-wise centralizedand the distributed architectures described above. The system

configuration follows to large extent the 3GPP Long Term

Evolution (LTE) standard [9]. For the distributed case, a

total of 57 hexagonal cells or sectors served by 19 sites

are simulated, as depicted in the Fig. 4. The coordination

sets of those CS CoMP clusters near the edge of the layout

are wrapped around, forming a total of 57 overlapping CS

CoMP clusters, each centered at one cell. For the cluster-wise

centralized case, each CoMP cluster is formed by grouping 9

neighboring cells (or sectors) served by 3 sites with sectorized

antennas, as depicted in Fig. 5. A total of 7 CoMP clusters

(i.e. 63 cells) are simulated in this layout. For both layouts,

radio signals are wrapped around from one end of the layoutto another end. Moreover, each cell is assumed to serve one

scheduled user in each time frame and frequency subcarrier.

All cells are also assumed to be synchronized in time, and

the cyclic prefix is assumed to be sufficiently long for the

propagation delays of each (CS) CoMP cluster. Each user is

assumed to have 2 receive antennas and to move at a speed

of 3 km per hour. Other system simulation parameters are

summarized in Table I.

Fig. 6 compares the performance of the cluster-wise cen-

tralized and the distributed CoMP architectures, in terms of

system throughput (sum data rates of all users) versus data

throughput of the 5-percentile users, which is indicative of

the data throughput of users located near cell edges. Thecurves labeled by ‘Cn’ and ’Dn’ are for the centralized and

the distributed architecture, respectively, where ‘n’ denotes the

number of cells per (CS) CoMP cluster. For example, the

curve labeled “D1” represents the performance for the case

when the coordination set of each CS CoMP cluster only

contains the serving BS. The notation ‘C=k’ means the BSs

of ‘k’ tiers of neighboring cells or sectors are connected to

form the coordination set, while the notation ‘I=m’ means ‘m’

additional tiers of neighboring cells or sectors are in the region

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Fig. 4. Cell Layout with Sectorized antennas for Distributed CoMPArchitecture (red dots denote site locations)

of interference avoidance. The multi-user TxWF precoder is

used for both cluster-wise centralized and distributed cases.

For comparison, the green curve represents the performanceof a non-CoMP system using the fixed codebook of precoding

matrices as defined in LTE [9].

As shown in Fig. 6, the distributed architecture yields

substantially better performance, in both the cell-edge user

data rate and the total system data throughput, over the cluster-

wise centralized architecture with a smaller number of cells per

CoMP cluster. Moreover, enlarging the region of interference

avoidance beyond the cells covered by the coordination set

can give significant additional gain, at the expense of more

CSI measurements and/or feedback for the network. Note that

at high load, the gain in system throughput attained by the

distributed architecture with a large RoI diminishes slightly,

due to the limitation in the transmit dimension of the precoder

and the increased number of users in RoI.

Fig. 7 shows the distributions of user data rates at an

averaged load of half a user per cell. As shown, compared

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Fig. 5. Cell Layout with Sectorized antennas for Centralized CoMPArchitecture with 9 Cells Per CoMP cluster (red dots denote site locations)



0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

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2

2.5

3Dist−DL 7 Cells per CS−CoMP Cluster with 4x2 TxWF − Ideal CSI−Tx

System Throughput [bps/Hz/sector]

C e l l − e d g e ( 5 p c t )

b i t r a t e [ b p s / H z ]

Non−CoMP

C9−TxWF

D1−TxWF (C=0,I=1)D7−TxWF (C=1,I=0)

D7−TxWF (C=1,I=1)

Fig. 6. Performance Comparison of Centralized vs. Distributed CoMP

to the centralized architecture, the distributed architecture is

capable of supporting substantially higher data rates for allusers with a smaller number of cells per CoMP cluster.

V I . CONCLUSIONS

In this paper, we studied the system performance of linear

multi-user precoding under a distributed architecture for CoMP

transmission in a cellular network. We propose a simple

method for computing the precoding matrices in a distributed

manner by separating them into a tentative part, which is com-

puted independently by different cell-specific CoMP clusters,

and a scaling part for power back-off, which is negotiable

across CoMP clusters. The tentative precoding matrices are

computed in such a way that maximizes the desired user data

rates in the serving cell while minimizing the interferenceto other users in the surrounding region. A simple sum-min

Modulation QPSK, 16QAM, 64 QAM

Coding Practical Turbo Codes

Link Adaptation Ideal (i.e. based on perfect chan-nel quality measurements)

Channel Model 3GPP SCM [10]

Scattering Envi ronment Suburban-macro [9]

Base Antennas 120-degree antenna (with nodown tilt)

Bandwidth 5 [MHz]

Frequency Reuse 1/1

Inter-site distance 500[m]

user Receiver Ideal MMSE-SIC

Data Traffic Model Full buffer

Scheduling Round Robin

Tx Power per antenna 5 [Watts]Antennas Base: 4 ; UT: 2

Sectors per CoMP cluster Cluster-wise centralized: 9 sec-tors (fixed)Distributed: 1 or 7 sectors (cell-specific)

Number of CoMP clusters Cluster-wise centralized: 7Distributed: 57 (cell-specific,with wrap-around)

Precoding Schemes TxWF = Transmit Wiene r Filter

TABLE ISYSTEM SIMULATION PARAMETERS

algorithm was introduced for computing the power back-off

factors in a distributed manner, and its convergence properties

were analyzed. Through system simulations with practical

channel models, we found that the distributed architecture

with the proposed distributed method of computing multi-

user linear precoders can lead to substantially better system

performance than the cluster-wise centralized architecture.

ACKNOWLEDGMENT

This work was partly supported by the Sixth

Framework Programme via the COOPCOM project

(http://www.coopcom.eu.org). The author would like to

thank Kambiz C. Zangi, George Jongren, and Magnus A.

Olsson for valuable comments and suggestions.

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0 1 2 3 4 5 6 7 8 90

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1Dist−DL 7 Cells per CS−CoMP Cluster with 4x2 TxWF − Ideal CSI−Tx; (load = 0.5)

P r ( U s e r D a

t a R a t e < =

a b s c i s s a )

Data Rate [bps/Hz]

Non−CoMP

C9−TxWF

D1−TxWF (C=0,I=1)

D7−TxWF (C=1,I=0)

D7−TxWF (C=1,I=1)

Fig. 7. User Data Rate Distributions of Centralized and Distributed CoMPat Medium Load (averaged 1/2 user per cell)

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