A Hybrid Mode User-Location-Aware Network

MIMO with Limited Feedback for Cellular

DownlinkMohsen Eslami1, Witold A. Krzymien1, and Mazin Al-Shalash2

1 University of Alberta / TRLabs, Edmonton, Alberta, Canada2 Huawei Technologies, Plano, TX, USA

Abstract—MIMO downlink with base station coordination ina cellular network is considered. In centralized coordinatedtransmission from a cluster of base stations, the channel stateinformation (CSI) of users needs to be sent to a central processorfor precoding and resource allocation. Real time CSI feedbackfrom the users to their home base station and from the basestations to the central processor is a serious challenge from apractical point of view. A hybrid mode transmission schemewith reduced feedback requirement exploiting user locationinformation and cell sectorization is proposed, in which someusers are served using single-cell multiuser MIMO (MU-MIMO)approach and some using the network MIMO approach. Using avirtual MIMO downlink channel model the feedback requirement,complexity of user scheduling and precoding/power allocationwith most multiuser MIMO precoding techniques is substantiallyreduced compared to the corresponding case using full CSI.Dirty paper coding (DPC) and zero forcing beamforming (ZFBF)precoding techniques are used to demonstrate the performanceof the hybrid mode network MIMO technique.

I. INTRODUCTION

While network multiple-input multiple-output (MIMO)

[1-2], also known as coordinated multipoint transmis-

sion/reception (CoMP), has a potential to be the effective

way of reducing inter-cell interference in cellular networks,

it suffers from some limitations in practice. One limitation is

the large amount of channel state information (CSI) feedback

required. Indeed, the per-cell amount of required CSI at

transmitter (CSIT) in network MIMO is much greater than

that for single-cell multiuser MIMO (MU-MIMO). Most of

the existing network MIMO techniques rely on the availability

of full CSI of all user terminals at the central processing

unit, which presents a big challenge in implementing network

MIMO. As a result, network MIMO techniques with reduced

CSI requirement are of great interest. To the best of our

knowledge the problem of reducing feedback overhead in

network MIMO transmission has not been well addressed

in the literature. [3-4] are examples of very few related

contributions available.

In this work, a network MIMO scheme is proposed, which

takes advantage of user location information to reduce CSI

feedback overhead for downlink coordinated transmission. In

the proposed hybrid mode scheme, users located at cell edges

are served by several coordinated base stations, while users

closer to the cell center are served only by their MU-MIMO

home base station. The CSI feedback is reduced using a two

stage feedback, where in the first stage users send back a single

real value and in the second stage only a subset of users send

back additional CSI information. The proposed scheme takes

advantage of cell sectorization to additionally reduce inter-cell

interference and limit the number of users that are seriously

affected by interference.

II. SYSTEM MODEL

Downlink of a sectorized cellular network is considered, in

which the base station is equipped with Nt antennas/sector

and each cell is divided into S sectors. It is assumed there are

K users in each cell, each equipped with Nr antennas. The

Nr by Nt complex channel matrix between antennas of the

sth sector of the bth base station (1 ≤ s(b) ≤ S, 1 ≤ b ≤ B)

and the kth user (1 ≤ k ≤ K) is denoted by Hk,s(b) . We

consider a B = 19 cell layout, which encompasses two tiers

of cells around the center cell. For the kth user assigned to

sector s(b), the received signal is

rk =Hk,s(b)xs(b) +∑

s(b),s6=s

Hk,s(b)xs(b)

+∑

s(b),b6=b

Hk,s(b)xs(b) + nk,

(1)

where the first term contains the intended signal for user

k, the second term is inter-sector interference caused by

other sectors of the same cell and the third term is inter-

cell interference from sectors of neighboring cells. xs(b) is

an Nt dimensional transmitted signal (after precoding) from

sector s of the bth base station and trace(

E[xs(b)xHs(b) ]

)

≤ P ,

where the superscript H denotes the Hermitian transpose. The

Nr dimensional vector nk ∼ CN (0, INr) is additive zero

mean complex white Gaussian noise with identity covariance

matrix. In case of cluster coordination a sum power constraint

is assumed.

A. Channel Model

The channel is modeled according to [5]

Hk,s(b) = Hw

√

(

dk,b

d0

)−β

A(θk, s(b))ρk,bΓ0, (2)

where dk,b is the distance between the bth base station and

the kth user, d0 is a fixed reference distance, β = 3.5 is

978-1-61284-887-7/11/$26.00 ©2011 IEEE

the path loss exponent, A(θk, s(b)) is the antenna gain as a

function of the angle of departure θk to user k from the antenna

array in sector s of BS b, ρk,b is the lognormal shadowing

between the bth base station and the kth user with σρ = 8dB standard deviation. Γ0 is the reference signal to noise ratio

(SNR) defined as the SNR measured at the reference distance

d0 = 1 km, assuming a single user transmission from the

cell center at full power and accounting only for the distance-

dependent path loss. We assume Γ0 = 20 dB.

B. Virtual MIMO Downlink Channel

Using singular value decomposition user k can decompose

its channel, Hk,s(b) = Uk,s(b)Σk,s(b)VHk,s(b) , where the size

Nr × Nt diagonal matrix Σk,s(b) has entries of decreasing

magnitude. Let σk,s(b) = max σ(Hk,s(b) ) be the maximum

singular value of Hk,s(b) . Let’s assume that the transmitter

sends only one stream to each user (this is a suboptimal

approach [6]) and user k uses UHk,s(b) as its receiver processing

matrix. Then the received signal on the strongest singular value

will be

rk = uHk,s(b)rk = σk,s(b)v

Hk,s(b)xs(b) + Ik + u

Hk,s(b)nk

= hk,s(b)xs(b) + Ik + nk

(3)

where uk,s(b) and vk,s(b) denote the first column of Uk,s(b) and

Vk,s(b) , respectively. The term Ik denotes the post-processing

interference, which can be easily determined using (1). In

(3), hk,s(b) = σk,s(b)vHk,s(b) is called the effective channel of

user k [6]. By integrating the receive beamformer into the

channels, the original MIMO downlink channel becomes a

virtual MIMO downlink channel, in which user k has one

antenna whose effective channel is hk,s(b) . Therefore, σk,s(b)

and vHk,s(b) specify the gain and the direction of the effective

channel at user k, respectively.

III. PROPOSED SCHEME: USER-LOCATION-AWARE

HYBRID COMP WITH LIMITED FEEDBACK

In order to devise a network MIMO scheme, which effec-

tively reduces inter-cell interference and also meets practical

limitations on CSI feedback, the following points need to be

considered:

1) Coordinated transmission is practically feasible within a

limited number of base stations.

2) Network MIMO can accommodate sectorization to re-

duce inter-cell interference.

3) Network MIMO can be implemented by coordinated

transmission from antennas of a number of sectors of

a cluster, where each sector belongs to a different cell.

4) In a cellular network, cell-edge users are much more

vulnerable to intercell interference. Therefore, in any

network MIMO technique priority should be given to

cell-edge users.

5) Location of users in a cell may be available at the

home base station of that cell for emergency or security

reasons. It might also be available at user terminals.

Using location information of each user, cell edge users can

be identified and be given priority in the coordinated trans-

mission. In fact, as we will show later by carefully deciding

on the number of sectors and grouping them to form a cluster,

CSI of cell edge users is most important for network MIMO

transmission. Fig. 1 shows how by considering S = 3 or

S = 6 sectors/cell and coordinating transmission among three

sectors, the whole area is covered while inter-cell interference

is substantially reduced. Larger values for S are also possible.

However, due to practical constraints and complexity they will

not be considered in this work.

The center area of the three adjacent sectors is the cell edge

area, in which users are served using network MIMO. The

distance of the users located in this area from their home base

station is greater than Rth and due to the geometry of cell

layout Rth ≤√

32 Rc, where Rc denotes the edge length of

each hexagonal cell. Users located in the remaining area of

each sector (the yellow area closer to each base station) are

served by single MU-MIMO home base station.

1) Proposed scheme: The proposed coordinated transmis-

sion scheme is as follows:

• Each user located in the center area of a cluster, for which

the distance to their home base station is greater than Rth

estimates the aggregate channel of its three closest BSs,

i.e.,

Hk =[

Hk,s(b1) ,Hk,s(b2) ,Hk,s(b3)

]

Nr×3Nt

, (4)

where s(b1), s(b2) and s(b3) are three sectors of the

cluster considered. Then, each user performs SVD on the

aggregate channel Hk and finds its gain, σk (see Section

II-B),

Hk = UkΣkVHk (5)

Then, considering the largest singular value and (3), for

user k we have

rk = uHk rk = σkv

Hk x + Ik + u

Hk nk

= hkx + Ik + nk

(6)

where σk and vHk become the gain and the direction of

the effective channel at user k, respectively. Next, the

user sends back its channel gain to its home BS.

• A user located within a radius Rth of its home BS only

estimates its home BS’s channel, i.e., if it is in sector

sbi , i ∈ {1, 2, 3}, it only estimates Hk,s(bi) . Then, the

user finds the gain of its equivalent channel, σk,s(bi) , and

sends it back to its home BS.

• The channel gains fed back by all users of a cluster

are sent to the central processing unit (CPU) for user

scheduling.

• The CPU selects L ≤ K users in total from the two sets

of users (set of users in the cell edge area of a cluster

and set of users close to a BS) with the largest channel

gain, forms the set SL, and asks those users to send back

their channel direction vector, i.e., vHk or v

Hk,S(bi) . Note

that QoS requirement of users can be applied here by

forcing the algorithm to select a specific number of users

from each set or comparing the weighted channel gains

of users.

• The CPU selects 3Nt users to be served using maximum

sum-rate (Max SRate) criterion, as follows:

1) Let π(1) = arg maxk∈SLσk,s(bi) as the first selected

user and delete its index from the set SL to form

a new set denoted by SL−1. Set Θ = vπ(1) and

l = 2.

2) Let

π(l) = arg maxk∈SL−l+1

(

1 − vHk Θl−1Θ

Hl−1vk

)

σ2k.

(7)

Delete user π(l) from the set SL−l+1 to form a new

candidate set SL−l and calculate vπ(l) = vπ(l) −Θl−1Θ

Hl−1vπ(l). Update Θl = [Θl−1

1‖vπ(l)‖ vπ(l)].

3) Set l = l + 1. If l ≤ 3Nt, go back to step 2;

Otherwise terminate.

Then considering the virtual MIMO channel of Section

II-B, the system model for the selected users can be

written according to

r = DTH

xs + I + n (8)

where r contains the received signals of the 3Nt se-

lected users (rks), the matrix D is a diagonal matrix

containing the 3Nt singular values of selected users’

channels, T =[

vπ(1) . . . vπ(3Nt)

]

3Nt×3Nt

con-

tains the direction vectors of selected users’ equivalent

channels, and xs contains the symbols transmitted on

the strongest eigenmode of selected users. For users that

are served by network MIMO, vπ(k) = vπ(k) (see (4)-

(6)), and for users served by single-cell MU-MIMO,

vπ(k) = [vHπ(k),sbi

01×2Nt]H .

• The CPU applies DPC or zero-forcing beamforming

(ZFBF) (the virtual MIMO channel of each user is a

MISO channel) to the equivalent size 3Nt × 1 channel

vectors of the selected users.

2) Determining the L value: A heuristic approach is to set

L = 9N2t , as we know this is the maximum number of users

that DPC serves [7]. Another approach would be to set L to be

the expected number of users having a largest singular value

greater than average.

3) CSI feedback reduction: Here we consider the users in

an entire cell and compare the amount of feedback required

be to send back by all users in two cases:

• Full CSI:

There are K users in each cell and each users needs to

feedback an Nr by 3Nt complex-valued channel matrix,

which adds up to Nf = 6KNrNt real values.

• Proposed scheme:

At the first stage of the proposed scheme the users send

back a single real value. Then, L users are asked to send

back the gains of their virtual channels, which for users

within the radius Rth is a size 1 × Nt vector and for

users farther than Rth it is a 1 × 3Nt vector of complex

values. For simplicity, let’s assume the number of selected

users is equally divided between the cell edge and the cell

center areas. Then

Nf ≈L

2(6NrNt + 2NrNt) + K = 4LNrNt + K. (9)

This means that for small to moderate values of K , the

feedback is reduced by a factor of ≈ 2L3K

, and for large

values of K it is reduced by a factor of ≈ 16NrNt

.

IV. SIMULATION RESULTS

In this section, we compare the cumulative distribution

function (CDF) of the sum rate for the network MIMO

transmission strategy proposed in Section III.A for cellular

downlink with full and partial CSI. For partial CSI, we

compare the proposed scheme with the scheme of [8], in which

users close to their home BS send back full CSI and users on

the cell-edge area send back partial CSI.

A. Simulation setup

K users are uniformly dropped in the center cell area of a

B = 19-cell network. Each base station is equipped with 24antennas in total and S = 6 sectors per cell are considered,

which results in each sector having Nt = 4 transmit antennas.

Each user has Nr = 2 receive antennas. In each simulation,

users are dropped in the center cell 500 times, and for each

drop of users the simulation is run for 1000 time slots (each

time slot is equal to the coherence time of the channel). L =20 has been considered in the proposed scheme (see Section

III-1).

B. Results

Figure 2 shows the CDF of sum rate for different schemes

for the cellular network described above. For DPC the through-

put loss of the proposed scheme due to around 60 % reduction

in CSI is relatively significant. However, with ZFBF and the

proposed scheme (60 % reduction in CSI compared t the full

CSI case), it is only around 1 b/s/Hz less than that of location

aware network MIMO technique with 50 % reduction in CSI,

which has been proposed in [8]. Same comparison has been

made in Figure 3 for K = 100 users. By comparing the results

shown in Figures 2 and 3, it appears that the increase in the

number of users does not improve the performance of the

proposed scheme. That is due to the fact that L is the same

in both cases, which means that the number of eigenvectors

used to search through by MaxSRate algorithm (Section III-1)

is the same in both cases. In other words, to enhance the

performance of the proposed scheme as K increases, L needs

to be increased.

V. CONCLUSIONS

Using user location information and cell sectorization, a

hybrid mode transmission scheme with reduced feedback

requirement has been proposed, which serves users by em-

ploying either single-cell multiuser MIMO (MU-MIMO) or

network MIMO depending on each user’s location. A virtual

MIMO downlink channel model has been introduced followed

by a two-stage feedback scheme, which together reduce the

feedback requirement and complexity of user scheduling and

precoding/power allocation under most multiuser MIMO pre-

coding techniques. The results show that for the throughput to

increase, the number of feedback terms must increase with the

number of users. In addition, orthogonality of the equivalent

vector channels of the selected users plays an important role

Fig. 1. A cellular layout with S = 3 and S = 6 sectors/cell. Regions,in which users send back full or partial CSI are shown as white or yellow,respectively.

in increasing the sum rate, especially for ZFBF. Hence, the

issue of finding improved methods to more effectively find

users with orthogonal (or close to orthogonal) equivalent

vector channels while keeping the feedback level same as the

proposed scheme needs to be further investigated.

ACKNOWLEDGEMENT

Funding for this work has been provided by TRLabs, Rohit SharmaProfessorship, Huawei Technologies and the Natural Sciences andEngineering Research Council (NSERC) of Canada. The benefits tothis work of the interaction with our colleagues within the EC FP7WHERE2 project are also acknowledged.

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0 20 40 60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum rate [b/s/Hz per cell]

CD

F o

f s

um

ra

te

DPCZF

Proposedscheme with ZFBF

Fig. 2. CDF of the sum rate [b/s/Hz per cell] for S = 6 sectors per cell,Nt = 4 antennas per sector, Nr = 2 antennas per user, and K = 60 usersper cell. The results are for DPC, BD and proposed ZFBF schemes with: 1)Full CSIT from all users (dotted-line); 2) Full CSIT from cell edge users andpartial CSIT from cell center users (dashed lines, see [8]); 3) Proposed hybridmode transmission scheme with reduced CSI feedback (solid lines).

0 20 40 60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum rate [b/s/Hz per cell]

CD

F o

f su

m r

ate

DPC

ZF

ProposedschemewithZFBF

Fig. 3. CDF of the sum rate [b/s/Hz per cell] for S = 6 sectors per cell,Nt = 4 antennas per sector, Nr = 2 antennas per user, and K = 100 usersper cell. The results are for DPC, BD and proposed ZFBF schemes with: 1)Full CSIT from all users (dotted-line); 2) Full CSIT from cell edge users andpartial CSIT from cell center users (dashed lines, see [8]); 3) Proposed hybridmode transmission scheme with reduced CSI feedback (solid lines).