[ieee 2007 ieee 18th international symposium on personal, indoor and mobile radio communications -...

The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’07)

COORDINATING BASE STATIONS FOR GREATER UPLINK SPECTRAL

EFFICIENCY IN A CELLULAR NETWORK

Sivarama Venkatesan

Bell Laboratories, Alcatel-Lucent

Holmdel, New Jersey, U.S.A.

ABSTRACT

We propose an ambitious approach towards lifting the limits

imposed by cochannel interference on the uplink spectral ef-

ficiency of a cellular network, viz., coordinating several base

stations in the reception of users within their coverage area,

and suppressing interference between users by means of coher-

ent linear beamforming across the base stations. We evaluate

by simulation the potential gain in spectral efficiency from such

coordination, when there is 1 user per base station antenna in

the network, and all users (but for a small fraction in outage)

must be served at a constant and common data rate. We high-

light the dependence of the spectral efficiency gain on the num-

ber of rings of neighbors with which each base station is coor-

dinated, as well as the underlying signal-to-noise ratio (SNR)

distribution in the network. Results from this study point to

the possibility of doubling the uplink spectral efficiency with

1-ring coordination and nearly quadrupling it with 4-ring coor-

dination, under high-SNR conditions.

I INTRODUCTION

The spectral efficiency achievable on the uplink of today’s cel-

lular networks is fundamentally limited by the interference be-

tween users sharing the same channel. Increasing the transmit-

ter power available to each user does not increase the spectral

efficiency of the network appreciably beyond a point, because

the signal-to-interference-plus-noise ratio (SINR) on each link

begins to saturate. Within the SINR limits imposed by cochan-

nel interference, link performance is already close to optimal,

thanks to the use of sophisticated error correcting codes, adap-

tive modulation, incremental redundancy, etc. While the SINR

distribution can be improved by imposing a frequency reuse

pattern on the network, the resulting spectral efficiency is typ-

ically even lower, due to the incurred loss in bandwidth within

each sector.

Therefore, novel strategies for mitigating cochannel inter-

ference are likely to be crucial in meeting the uplink spectral

efficiency requirements of future-generation cellular networks.

In this paper, we propose one such strategy, viz., coordinat-ing several base stations in the reception of users within theircoverage area. We suppose that the network has several “coor-

dination clusters”, each consisting of a base station and one or

more rings of its neighbors, and that the antennas of all the base

stations in each cluster can act as a single coherent antenna ar-

ray. Each user in the network is received at one such cluster.

We show that the interference affecting each user can then be

suppressed quite effectively by means of coherent linear beam-

forming at the antennas of all the base stations in its assigned

cluster, thereby greatly increasing the attainable spectral effi-

ciency.

For research on downlink interference mitigation by means

of coherently coordinated transmission from multiple base sta-

tions, see [1–3]. One distinguishing feature of our work is that

we highlight the dependence of the spectral efficiency gain on

the number of rings of neighbors with which each base station

is coordinated. By contrast, in [1–3], an “all or nothing” model

is assumed for coordination, i.e., either there is no coordination

between base stations, or all the base stations in the network are

coordinated. In practice, it would obviously be helpful to know

how far coordination must extend in order to realize a desired

spectral efficiency gain (intuitively, we do not expect coordina-

tion with faraway base stations to be very beneficial).

Another distinguishing feature is that we quantify the coor-

dination gain in terms of the underlying signal-to-noise ratio

(SNR) distribution in the network, the latter being determined

by the transmitter power available to each user, bandwidth of

operation, propagation characteristics of the environment, an-

tenna gains, amplifier noise figures, etc. Some thought shows

that cochannel interference mitigation should have a greater

impact on spectral efficiency in a higher-SNR environment,

since the level of cochannel interference relative to receiver

noise is then higher.

To estimate the potential spectral efficiency gain from up-

link coordination of base stations, we assume that the network

is populated with 1 user per base station antenna (i.e., 1 user

per spatial dimension), and that all these users, but for a small

fraction consigned to outage due to unfavorable channel condi-

tions, must be served at a common data rate. Using results on

power control from [4–6], we develop algorithms for identify-

ing the subset of users that must be declared in outage, as well

as the powers at which the remaining users must transmit and

the coordination clusters at which they must be received. We

then determine (by simulation) the largest common data rate

that is consistent with the desired user outage probability, for

coordination clusters of different sizes.

As is arguably appropriate in a preliminary investigation of

this nature, we make several idealizing assumptions and gloss

over several practical difficulties, in order to get a sense of the

potential payoff without getting bogged down in details. For

example, we ignore channel estimation issues by assuming the

availability of perfect channel state information wherever nec-

essary. We also do not dwell on the bandwidth, latency, and

synchronization requirements on the backhaul network con-

necting the base stations in each cluster, in order for them to

process their received signals jointly and coherently. We rele-

gate the examination of all such issues to future work.

The rest of the paper is organized as follows. We describe the

1-4244-1144-0/07/$25.00 c©2007 IEEE


D

s

Figure 1: Sector orientation

cellular network model assumed in this study in Sec. II, and the

simulation methodology used to evaluate the coordination gain

in Sec. III. The results from the simulations are in Sec. IV, and

the conclusions in Sec. V.

II NETWORK MODEL

We focus our study on an idealized cellular network of 127

regular hexagonal cells (center cell plus 6 rings of neighbors),

with a base station at the center of each cell. We assume that

the network is wrapped around at its edges, so that every cell

can effectively be regarded as the center cell of the network.

Each cell has 3 sectors, with main lobe directions as indi-

cated by the arrows in Figure 1. There are N receiving anten-

nas per sector, each having an idealized antenna beam pattern

given by

A(θ) = min

{12

(θ

Θ

)2

, Am

}, −π ≤ θ < π. (1)

Here, A(θ) represents the beam attenuation in dB along a di-

rection making an angle of θ radians with the main lobe di-

rection. The parameters Θ and Am are respectively the 3-dB

beamwidth (in radians) and the maximum beam attenuation (in

dB). We set Θ = 7π/18 and Am = 20.

A Channel model

In the interest of simplicity, we assume that all user-to-sector

links in the network are flat-fading and time-invariant, and that

there is perfect symbol synchronization between all users at

each sector. Further, we assume that each user in the network

has a single omnidirectional transmitting antenna. Accord-

ingly, we model the complex baseband signal vector ys(t) ∈C

N received at the N antennas of sector s during symbol pe-

riod t as

ys(t) =U∑

u=1

hs,uxu(t) + zs(t). (2)

Here, U is the total number of users in the network; xu(t) ∈ C

is the complex baseband signal transmitted by user u during

symbol period t; hs,u ∈ CN is the vector representing the

channel from user u to sector s; and zs(t) ∈ CN is a circularly

symmetric complex Gaussian vector representing additive re-

ceiver noise, with E [zs(t)] = 0 and E [zs(t)z∗s(t)] = I. We

subject each user to a transmitted power constraint of 1, i.e.,

E |xu(t)|2 ≤ 1.

Each channel vector hs,u has a position-dependent power

loss component, a lognormal shadow fading component, and a

complex Gaussian multipath fading component. Specifically,

hs,u =√

η

(ds,u/D)α 10A(θs,u)/1010γs,u/10gs,u. (3)

In (3), ds,u is the distance between user u and sector s, and

D is half the distance between neighboring base stations (see

Figure 1); α is the path loss exponent, taken to be 3.8; θs,u ∈[−π, π) is the angle in radians that the position vector of user urelative to sector s makes with the main lobe direction of sec-

tor s; A(·) is the sector antenna beam pattern, as in (1); γs,u is

a real Gaussian random variable of mean 0 and standard devi-

ation 8, representing the effects of large-scale shadow fading;

and gs,u is an N -dimensional circularly symmetric complex

Gaussian vector of mean 0 and covariance I, representing the

effects of small-scale multipath fading.

For each user u, we assume that the shadow fading ran-

dom variables γs,u corresponding to different sectors s are in

fact jointly Gaussian, with 100% correlation between sectors

of the same cell and 50% correlation between sectors of differ-

ent cells. But for these constraints, the random variables γs,u,

gs,u, and zs(t) in (2) and (3) for different s, u, and t are all

statistically independent.

Under all the above assumptions, we can interpret the param-

eter η in (3) as the average SNR at sector s of a user u located

at half the distance to the neighboring base station along the

main lobe direction (for the sector s in Figure 1, this location is

indicated by a cross), when the shadow fading random variable

γs,u is at its mean value of 0 (or, equivalently, when there is no

shadow fading). The SNR distribution over the network is then

determined by η and the path loss exponent α (equal to 3.8).

Note that the value of D is immaterial (i.e., we have scale in-

variance). We will henceforth refer to η simply as the referenceSNR at the cell edge.

As η is increased from a very small value to a very large

value, the network goes from being limited primarily by re-

ceiver noise to being limited primarily by interference between

users. We can therefore expect the mitigation of interference

through coordinated reception at multiple base stations to be

more beneficial at higher η values. In the simulations, we will

determine the coordination gain as a function of η, varying the

latter over a wide range of values.

B Coordination clusters

We define a coordination cluster to be a subset of base stations

that jointly and coherently process the received signals at the

antennas of all their sectors. We suppose that the network has a

predefined set of coordination clusters, and that each user can

be assigned to any one of these clusters. Further, we assume

that each cluster uses a linear minimum-mean-squared-error

(MMSE) beamforming receiver to detect each user assigned

to it, in the presence of interference from all other users in the

network (we do not consider receivers based on interference

cancellation).

To highlight the dependence of the spectral efficiency gain

on the number of rings of neighbors with which each base sta-


(a) r = 0 (b) r = 1

(c) r = 2 (d) r = 4

Figure 2: r-ring coordination clusters

tion is coordinated, we will be interested in coordination clus-

ters having a specific structure. For any integer r ≥ 0, we de-

fine an r-ring coordination cluster to consist of any base station

and the first r rings of its neighboring base stations (accounting

for wraparound), and Cr to be the set of all r-ring coordination

clusters in the network. Figure 2 illustrates 0-ring, 1-ring, 2-

ring, and 4-ring coordination clusters.

Note that each base station is at the center of a unique cluster

in Cr. As a result, all cells are equally favored from the point

of view of coordination (this spatial homogeneity is the reason

we consider overlapping clusters, instead of disjoint ones). The

total number of base stations in each coordination cluster in

Cr is 3r2 + 3r + 1. The latter is also the number of clusters

in Cr to which any given base station in the network belongs.

To ensure that coordination is truly limited to the first r rings

of neighbors, we will disallow any exchange of information

between clusters in Cr through base stations that they may have

in common.

With C0 as the set of coordination clusters in the network,

there is in fact no coordination between base stations. This

case will serve as the benchmark in estimating the spectral effi-

ciency gain achievable with sets of larger coordination clusters.

Specifically, we will compare C1, C2, and C4 with C0.

With some abuse of notation, we will denote by hC,u ∈C

3N |C| the channel from user u to the antennas of all the base

stations in the coordination cluster C (here |C| denotes the

number of base stations in C). Then, with user u transmit-

ting power pu, the SINR attained by user u at cluster C is

h∗C,u

(I +

∑v �=u pvhC,vh∗

C,v

)−1

hC,u pu. Note that this ex-

pression assumes perfect knowledge at cluster C of the chan-

nel vector hC,u and the composite interference covariance∑v �=u pvhC,vh∗

C,v .

III SIMULATION METHODOLOGY

The objective of the simulations is to compare the spectral ef-

ficiencies achievable with the coordination cluster sets C0, C1,

C2, and C4 (as defined above), when all users in the network tar-

get a constant and common data rate. For meaningful results,

we must allow a small fraction of the users to be in outage

due to unfavorable channel conditions. We take this allowed

user outage probability to be 10%. For each set of coordination

clusters Cr, we determine the user outage probability for a few

target rates, and then interpolate between those rates to obtain

the rate that results in 10% user outage.

Given a target rate per user of R bits/sym, we determine the

resulting user outage probability from several independent tri-

als, in each of which we do the following:

1. Populate the network with users.

2. Determine how many of the above users must be declared

in outage, so that the remaining users can all attain the

target rate of R bits/sym.

We obtain the user outage probability by summing the number

of users in outage across trials, and dividing by the total number

of users in those trials.

A Populating the network with users

We assume that the network is loaded randomly and uniformly

with N users per sector, N being the number of receiving an-

tennas in each sector. In other words, we allow only 1 user

per sector antenna. The justification for this assumption is that

a larger pool of users can be split between orthogonal dimen-

sions, e.g., time slots or frequency bands, so that there are only

N users per sector in each dimension (note that we would have

to assume such dimensions to be orthogonal over the entire net-

work, and not just within each sector).

We choose the N users associated with sector s to have

higher average path gain to sector s than to any other sector,

while ensuring that users are equally likely to be situated at all

locations in the network. The average path gain from user u to

sector s is the quantity under the square root sign on the RHS

of (3).

B Determining users in outage

Suppose that the set of coordination clusters in the network is

Cr for some r ≥ 0. Let the target rate for each user in the

network be R bits/sym. Since there are 3N users per cell, the

offered load to the network is then 3NR bits/sym/cell. We will

assume Gaussian signaling and ideal coding, so that the target

rate of R bits/sym translates to a target SINR of ρ � 2R−1 for

each user.

1) Case 1: No users in outage

To begin with, suppose that the target SINR ρ is small enough

for all the users to achieve it, given the power constraint on

each user and the interference between users. This means that

there exists a feasible setting of each user’s transmitted power,

and an assignment of users to coordination clusters, such that

each user attains an SINR of ρ or higher at its assigned clus-

ter, with an SINR-maximizing linear MMSE receiver. In this

situation, we can use the following iterative algorithm from [4]

(also see [5,6]) to determine the transmitted powers and cluster

assignments for all the users:

1. Initialize all user powers to 0: p(0)u = 0 for all u.


2. Given user powers {p(n)u }, assign user u to the cluster

C(n)u where it would attain the highest SINR:

C(n)u = arg max

C∈Cr

h∗C,uQ

(n)C,uhC,u, (4)

Q(n)C,u �

I +

∑v �=u

p(n)v hC,vh∗

C,v

−1

. (5)

Let p(n+1)u be the power required by user u to attain the

target SINR of ρ at the cluster C(n)u , assuming every other

user v continues to transmit at the current power level:

p(n+1)u = ρ

(h∗

C(n)u ,u

Q(n)

C(n)u ,u

hC

(n)u ,u

)−1

. (6)

3. Iterate until convergence.

In [4], the above iteration is shown to converge to transmitted

powers {p̃u} that are optimal in the following strong sense: if

it is possible for every user to attain the target SINR of ρ with

transmitted powers {pu}, then pu ≥ p̃u for every u. In other

words, the iteration minimizes the power transmitted by everyuser, subject to the target SINR of ρ being achieved by all users.

2) Case 2: Some users in outage

In general, however, it might be impossible for all the users to

achieve the target SINR simultaneously. We must then settle

for serving only a subset of the users, declaring the rest to be

in outage. In principle, we could determine the largest support-

able subset of users by sequentially examining all subsets of

users in decreasing order of size, but this approach is practical

only when the number of users is small.

Instead, we will modify the iterative algorithm of [4] slightly

to obtain a suboptimal but computationally efficient algorithm

for determining which subset of users should be served. Af-

ter each iteration, the modified algorithm declares users whose

updated powers exceed the power constraint of 1 to be in out-

age, and eliminates them from consideration in future itera-

tions. This progressive elimination of users eventually results

in a subset of users that can all simultaneously achieve the tar-

get SINR ρ. For this subset of users, the algorithm then finds

the optimal transmitted powers and cluster assignments. How-

ever the user subset itself need not be the largest possible; es-

sentially, this is because we do not allow a user consigned to

outage in some iteration to be resurrected in a future iteration.

For completeness, we describe the modified algorithm below:

1. Start with no user in outage, and all user powers initialized

to zero: p(0)u = 0 for all u.

2. Given user powers {p(n)u }, assign each user u not in out-

age to the cluster C(n)u in (4), and update its power to the

value p(n+1)u in (6) (with Q(n)

C,u given by (5)).

3. Declare users u with p(n+1)u > 1 to be in outage, and reset

their powers to zero in all future iterations.

4. Iterate until convergence.

6 12 18 24 301

3

5

79

11

1315

No coordination

Reference SNR at cell edge (dB)

Spec

tral e

ffic

ienc

y (b

its/s

ym/c

ell)

1 antenna/sector, 1 user/sector

2 antennas/sector, 2 users/sector


Figure 3: Spectral efficiency without coordination

IV SIMULATION RESULTS

For the simulation results, we consider 3 different values of

N , the number of antennas per sector as well as the number of

users per sector, viz., N = 1, 2, 4.

Figure 3 shows the network spectral efficiency for each value

of N as a function of the cell-edge reference SNR η in (3), with

C0 as the set of coordination clusters, i.e., with no coordination

between base stations. The spectral efficiency is defined as the

offered load to the network (in bits/sym/cell) that results in 10%

user outage.

For each value of N , when η is small, receiver noise domi-

nates interference from other users, and therefore the spectral

efficiency increases appreciably with η. However, at high val-

ues of η, the spectral efficiency begins to saturate as the net-

work becomes limited by interference between users, rather

than receiver noise. It is this limit that we are attempting to

overcome through the coordination of base stations.

Figures 4, 5, and 6 illustrate the spectral efficiency gain

achievable with different coordination cluster sizes, for N = 1,

N = 2, and N = 4, respectively. Specifically, each figure

shows the ratio of the spectral efficiency achievable with C1(1-ring coordination), C2 (2-ring coordination), and C4 (4-ring

coordination) to that achievable with C0 (no coordination), for

a different value of N . Note that:

1. The coordination gain increases with the reference SNR

η in each case, because interference mitigation becomes

more helpful as the level of interference between users

goes up relative to receiver noise.

2. At the low end of the η range, most of the spectral effi-

ciency gain comes just from 1-ring coordination. This is

because most of the interferers that are significant rela-

tive to receiver noise are within range of the first ring of

surrounding base stations. However, as η is increased, in-

terferers that are further away start to become significant

relative to receiver noise, and therefore it pays to increase

the coordination cluster size correspondingly.

3. The coordination gain values are not very sensitive to N ,

the number of antennas per sector as well as the number


6 12 18 24 301.5

2

2.5

3

3.5

41 antenna/sector, 1 user/sector


Coo

rdin

atio

n ga

in

1−ring coord.

2−ring coord.

4−ring coord.

Figure 4: Coordination gain: 1 antenna/sector, 1 user/sector

6 12 18 24 301.5

2

2.5

3

3.5



Coo

rdin

atio

n ga

in

1−ring coord.

2−ring coord.

4−ring coord.

Figure 5: Coordination gain: 2 antennas/sector, 2 users/sector

of users per sector, suggesting that it is the ratio of users

to sector antennas (1 in all our results) that matters.

The results from the simulations indicate that, in a high-SNR

environment, the uplink spectral efficiency can potentially be

doubled with 1-ring coordination, and nearly quadrupled with

4-ring coordination. When the user-to-sector-antenna ratio is

smaller than 1, the coordination gain will be somewhat lower

since, even without coordination, each base station can then

use the surplus spatial dimensions to suppress a larger portion

of the interference affecting each user it serves. The coordi-

nation gain with a user-to-sector-antenna ratio larger than 1

will also be lower, because the composite interference affect-

ing each user at any coordination cluster will then tend towards

being spatially white, making linear MMSE beamforming less

effective at interference suppression.

V CONCLUSIONS

In this paper, we have proposed and investigated a novel strat-

egy for alleviating the cochannel interference problem on the

uplink of today’s cellular networks, viz., coordinating several

base stations in the reception of user signals, and suppressing

interference between users by means of coherent linear beam-

forming across the base stations. We have quantified the poten-

tial gain in uplink spectral efficiency from such coordination,

albeit with several idealizations and simplifications. Our results

6 12 18 24 301.5

2

2.5

3

3.5



Coo

rdin

atio

n ga

in

1−ring coord.

2−ring coord.

4−ring coord.

Figure 6: Coordination gain: 4 antennas/sector, 4 users/sector

suggest a potential doubling in spectral efficiency when every

base station is coordinated with its first ring of neighbors, and

a near quadrupling when every base station is coordinated with

its first four rings of neighbors (under high-SNR conditions).

However several issues will need to be addressed before such

large spectral efficiency gains can be realized in practice. For

example, techniques must be developed to estimate the channel

from a user to a faraway base station without excessive over-

head for training signals, especially in a highly mobile environ-

ment (data-aided channel estimation methods could be investi-

gated for this purpose). Also, a high-bandwidth, low-latency

backhaul network will be required for several base stations to

jointly process their received signals in a timely manner (coher-

ent processing also requires a high degree of synchronization

between the base stations). The costs associated with such a

network must be considered in relation to the savings from the

greater efficiency in the use of scarce spectrum. More gener-

ally, base station coordination must be compared in economic

terms with alternative approaches to increasing uplink spectral

efficiency.

The above notes of caution notwithstanding, base station co-

ordination appears to be a promising approach towards meeting

the uplink spectral efficiency needs of future cellular networks,

deserving of further research on several fronts.

REFERENCES

[1] K. Karakayali and G. J. Foschini and R. A. Valenzuela and R. D. Yates,

“On the maximum common rate achievable in a coordinated network”,

Proc. IEEE ICC, pp. 4333-4338, 2006.

[2] G. J. Foschini and K. Karakayali and R. A. Valenzuela, “Coordinating

multiple antenna cellular networks to achieve enormous spectral effi-

ciency”, IEE Proc. Commun., vol. 153, pp. 548-555, Aug. 2006.

[3] K. Karakayali and G. J. Foschini and R. A. Valenzuela, “Network co-

ordination for spectrally efficient communications in cellular systems”,

IEEE Wireless Commun. Mag., pp. 56-61, Aug. 2006.

[4] F. Rashid-Farrokhi and L. Tassiulas and K. J. R. Liu, “Joint optimal

power control and beamforming in wireless networks using antenna ar-

rays”, IEEE Trans. Commun., vol. 46, pp. 1313-1324, Oct. 1998.

[5] S. Hanly, “An algorithm for combined cell-site selection and power con-

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