MACRO DIVERSITY COMBINING SCHEMES FOR MULTICAST

TRANSMISSION IN HIGH-SPEED CELLULAR NETWORKS

Neila El Heni and Xavier Lagrange

IT/TELECOM Bretagne, campus de Rennes, BP 35510, France

Keywords:

Chase combining, clustering, multicast transmission, maximum ratio combining, selective combining.

Abstract:

In this paper, we study the transmission of data destined for several users on the radio interface using the

multicast mode, an interesting alternative of the conventional unicast mode. In the multicast mode, a packet is

sent simultaneously to several terminals in the same cell. We consider different techniques of macro diversity,

namely Selective Combining (SC) and Maximal Ratio Combining (MRC).

We develop an analytical model that allows the computation of the mean bitrate for both multicast and unicast

schemes. We use a scheduler that allocates bandwidth to mobiles according to their instantaneous channel

quality. In this context, we propose an efﬁcient user clustering considering their average radio channel quality.

The study shows that macro diversity improves the transmission performance especially for pure multicast.

1 INTRODUCTION

Packet scheduling is the functionality that distributes

radio resources between users. Intensive research has

been conducted on the performance of unicast sched-

ulers in cellular networks (e.g. (Al-Manthari et al.,

2006), (Liu et al., 2003)). During a service ses-

sion, users may experience different channel condi-

tions from a Transmission Time Interval (TTI) to an-

other. The packet scheduler uses the reported channel

qualities and chooses at each TTI the user to serve

with the suitable modulation and coding scheme.

Multicast services have drawn a lot of attention re-

cently. MBMS (Multimedia Broadcast/Multicast Ser-

vice) is currently speciﬁed in the 3GPP recommen-

dation. However, the focus is on the access and core

network rather then on the radio interface. The con-

ventional way to manage multicast services on the lat-

ter interface is to duplicate transmissions to the differ-

ent User Equipments (UEs). This may however con-

siderably waste radio resource if several users in the

same cell are registered to the same service as only

one user is served during a TTI. In this paper, such

an approach is called multiple-unicast. An interesting

alternative is to really send a given packet to several

users at the same time. In order to avoid packet losses,

the multicast scheduler must adapt the transmission

bitrate to the mobile that has the lowest Signal to

Noise Ratio (SNR). It is noteworthy that other multi-

cast schedulers can be used such as Multicast Propor-

tional Fairness (MPF) and Inter-group Proportional

Fairness (IPF) (Won et al., 2007). However, packet

losses are frequent with these algorithms and result-

ing retransmissions may decrease the system perfor-

mance.

In a previous paper (El Heni and Lagrange,

2008b), we have studied multicast and multiple-

unicast for several users in the same cell. It was

shown that multicast outperforms multiple-unicast

only when the average SNR is above a given thresh-

old. The main reason is that multicast scheduling has

to consider the worst SNR of the group of users as op-

posed to multiple-unicast scheduler that can choose

at each TTI the user that has the best SNR. Users

with low SNR are generally on the cell border and

may generally receive several base stations (BSs). It

is then interesting to combine transmissions of neigh-

boring BSs to increase the overall received SNR. Note

that the multicast service is not restricted to one cell

but can be delivered over several cells. In this con-

text, the same data transport block (TB) is transmitted

by several BSs. A UE may decode data from these

BSs simultaneously. If at least one copy of the same

TB is correctly received, this block is then considered

successfully transmitted. By extending the TB level

to the signal level, we identify this scheme as Selec-

tive Combining (SC) where a user selects the block

with the maximum SNR. Alternatively, the receiver

may combine replicas of the same ﬂow proportion-

ally to their strength like in Chase Combining (CC)

121

El Heni N. and Lagrange X. (2008).

MACRO DIVERSITY COMBINING SCHEMES FOR MULTICAST TRANSMISSION IN HIGH-SPEED CELLULAR NETWORKS.

In Proceedings of the International Conference on Wireless Information Networks and Systems, pages 121-126

DOI: 10.5220/0002025801210126

 SciTePress

(cha, ). The CC is a scheme of hybrid ARQ protocol

that is used in High Speed Downlink Packet Access

(HSDPA). With CC protocol, if an initial transmis-

sion is received with some errors, the corrupted data

packet is stored at the terminal and retransmissions

of identical coded data packets occur till a successful

reception. Then, the decoder combines these multi-

ple copies weighted by the SNR prior to decoding.

This method provides diversity (time) gain. We pro-

pose to use the same principle but with copies of the

same data block sent by different BSs. Extending the

block level to the physical level amounts to the Max-

imal Ratio Combining (MRC) scheme where redun-

dant signals are also combined proportionally to their

strength. The resulting SNR is then the sum of the

all received SNRs (eur, ). Conventional MRC (at the

signal level) with MBMS has been studied in other

papers, e.g. (Soares and Correia, 2006).

Our objective is to quantify the throughput gain of

applying macro diversity combining schemes to mul-

ticast scheduling. Our multicast scheduler is called

the equal-bitrate scheduler; it allocates bandwidth

to mobiles according to their instantaneous channel

quality. The multicast scheduler is based on a new

clustering strategy. Clustering is the way to deﬁne

sub-groups of users, all of them subscribing to the

same service. The new clustering method combines

multicast and unicast schemes according to the user’s

average channel conditions. We have developed it for

a single cell case in (El Heni and Lagrange, 2008a)

but it will be explained here again for the sake of clar-

ity. This paper is organized as follows. In Section 2,

the system model and assumptions are given. In Sec-

tion 3, we deﬁne the new clustering strategy. Section

4 explains the proposed equal-bitrate scheduler and

expands the scheduler model with the use of SC and

MRC. Section 5 gives the simulation results. Conclu-

sions are drawn in Section 6.

2 MODEL DESCRIPTION

2.1 General Considerations

In a regular cellular network, each cell has 6 neigh-

boring cells. In a ﬁrst approach, a cell may be di-

vided in 6 sectors, each of which having one serving

base station and one neighboring one. We restrict our

study to one sector. Let BS1 be the serving base sta-

tion and BS2 the neighboring one. This case is easily

generalized to the whole cell if we consider that fad-

ing values in each sector are independent and then the

system is invariant by rotation. We consider N users

that are randomly distributed in the studied sector rep-

Figure 1: Macro diversity with 2 cells.

resented by the shaded area S

in Figure 1. Users are

listening to BS1 and BS2 separated by a distance D

1,2

Considering an hexagonal model

1,2

√

3R (1)

where R is the cell radius. Large-scale mobility as-

pects and time constraints are not considered. Let

s,i, j

be the SNR of signal received by UE i from BS

s within cluster j and γ

s,i, j

its average value. Due to

channel variations, γ

s,i, j

are identical and independent

distribution (iid) variables that change randomly from

one TTI to another. The SNR is assumed to be con-

stant during a TTI. Let γ

i j

be the instantaneous SNR

after macro diversity combining at user i, which is

member of cluster j. We denote G as the number of

clusters and S

the size of cluster j. We deﬁne β

i j

the largest TBS supported by UE i. Let g be the func-

tion that relates β

i, j

to the reported γ

i, j

of the served

user i, hence

i j

= g(γ

i, j

). (2)

It is easy to see that g is a strictly increasing function.

Let h be the associated inverse function: γ

i, j

= h(β

i, j

Finally, we deﬁne γ

as the selected SNR for cluster j

and R

the mean bitrate of cluster j. Indices i, j and s

may be sometimes omitted for simplicity.

We consider only one multicast group, i.e. all

users in the serving cell listen to the same service.

Scheduling multiple services amounts to managing

priority between these services according to their QoS

requirements. These issues have been extensively de-

veloped in literature (Lundevall et al., 2004), (Kazmi

and Wiberg, 2003) and are out of the scope of our

study.

2.2 Propagation Model

The average SNR received by a UE may be computed

by using a conventional propagation model. The

model is explained via one BS. Let P

be the trans-

mit power to user i. The received power, denoted as

, is then given by

= P

(3)

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122

where h

is the path gain including shadowing, dis-

tance loss and antenna gain between user i and the

BS and χ

is the fast fading between user i and the

BS. Variable χ

is a random variable which represents

Rayleigh fast fading. It therefore has an exponential

distribution. The signal to interference ratio received

by user i is

α(P

max

−P

+ I

ext

(4)

where P

max

is the total transmit power of the cell, α is

the orthogonality factor and I

ext

represents the inter-

cell interference. The average SNR of user i located

at a distance d from the BS is given by

(d) =

sup

exp

−I

ext

−α(P

max

−P

dx (5)

where β is the pathloss exponent, A

is the distance-

loss at 1 m (with a BS antenna height of 30 m, a UE

antenna height of 1.5 m and a carrier frequency of

1950 MHz) and γ

sup

is deﬁned by

sup

α(P

max

−P

)

. (6)

3 PROPOSED CLUSTERING

STRATEGY

Clustering is the way to deﬁne sub-groups of users,

all of them subscribing to the same service. We pro-

pose a new clustering method called mixed cluster-

ing; it combines multicast and unicast schemes ac-

cording to the user’s average channel conditions. We

have seen in (El Heni and Lagrange, 2008b) that mul-

ticast outperforms multiple-unicast only for high av-

erage SNRs (above around 3.7 dB). Our clustering

scheme is then deduced as illustrated in Figure 2:

• An average SNR threshold is ﬁxed so that the sys-

tem can differentiate users. The average SNR is

declared as “low” if it is below a threshold value

denoted as γ

thres

. Let N

low

be the number of users

having a low average SNR.

• Users with low average SNRs have to be sepa-

rated from each other. In fact, if the cluster size

increases for low SNR values, the instantaneous

bitrate capacity within the cluster becomes lower

as the multicast strategy is conservative. Our so-

lution is to serve these users according to a unicast

scheme.

• Users with high average SNRs should follow a

multicast scheme. They are grouped in the same

Figure 2: Proposed clustering strategy.

cluster which contains N −N

low

users. Conse-

quently, the resulting number of clusters G is

equal to N

low

+ 1. Of course, if all users have low

average channel quality, G is equal to N

low

4 MULTICAST SCHEDULING

WITH SC AND MRC

4.1 Proposed Multicast Scheduler

In this study, we propose a scheduling scheme called

the equal-bitrate scheduler. It aims at increasing fair-

ness among multicast clusters while offering good

system throughput. Equal-bitrate scheduling is per-

formed in two steps. First, the scheduler determines

the convenient transmission bitrate for each cluster.

The intra-cluster bitrate allocation strategy is conser-

vative. We have then

= min

i=1..S

i, j

(t). (7)

We denote P

(x) as the cumulative distribution func-

tion (CDF) of a random variable X. Similarly, p

(x)

denotes the probability distribution function (PDF) of

X. Hence, the CDF of γ

is equal to

(x) = 1 −

∏

i=1



1 −P

i, j

(x)



. (8)

Once the bitrate of each cluster is determined, the

scheduler chooses the cluster to serve. In order to

maximize the global throughput, a natural solution is

to serve the cluster having the highest bitrate capac-

ity. However, the scheduling must guarantee fairness

between clusters. This may be achieved by realizing

MACRO DIVERSITY COMBINING SCHEMES FOR MULTICAST TRANSMISSION IN HIGH-SPEED CELLULAR

NETWORKS

123

the same average bitrate for all the clusters. For this

purpose, we deﬁne fairness factors M

j=1..G

such that

the scheduler serves the cluster having a higher bi-

trate capacity with a lower probability, i.e. time is not

uniformly shared between clusters. At instant t, clus-

ter j is served if the product of its instantaneous SNR

and its corresponding fairness factor M

is the highest

among all the clusters; hence, if and only if

= max

l=1..G

(γ

). (9)

It can be established that the mean bitrate used to

serve cluster j is

T TI

∞

(x)g(x)

∏

l=1,l6= j

(

)

(10)

where D

T T I

is the TTI duration. Equation (10) gives

a general formula for the average bitrate per cluster

j once the clusters are made. Note that this formula

depends on {M

}. The value of {M

}

j=1..G

is ﬁxed

so that ∀j = 2..G, R

= R

; with M

=1. The value of

G is determined by the clustering scheme detailed in

Section 3.

In the context of multiple-unicast, N single-user

clusters are considered. The individual mean bitrate

is derived from (10) for G = N (S

= 1 ∀j = 1..G).

T T I

∞

(x)g(x)

∏

l=1,l6= j

(

)

dx.

(11)

In the framework of pure multicast, the average bitrate

denoted as R

mcast

is derived from (10) for G=1. After

a few computation, we obtain

mcast

T T I

∞

∏

i=1

[1 −P

(h(x))]

dx. (12)

4.2 SC with Multicast Scheduling

According to selective combining, a user selects the

data bloc yielding the highest SNR. We have then

i, j

= max

s=1..S

(γ

s,i, j

) (13)

where S is the number of BSs received by a user (in

the framework of this study S = 2). The CDF of γ

i, j

is given by

i, j

(x) =

∏

s=1

s,i, j

(x). (14)

Combining equations (8), (10) and (14), we have the

average bitrate per cluster with SC and denoted as

j,SC

T T I

∞

(x)g(x)

∏

l=1,l6= j

(15)

[1 −

∏

i=1

(1 −

∏

s=1

s,i,l

(

))]]dx.

4.3 MRC with Multicast Scheduling

The case of MRC is more complex than SC. In fact, as

terminals combine the different transmissions propor-

tionally to their strength, the resulting SNR for user i

is given by (eur, )

i, j

∑

s=1..S

s,i, j

. (16)

The CDF of the SNR for user i is given by

i, j

(x) = Pr(

∑

s=1..S

s,i, j

≤ x ) (17)

When S=2, we deﬁne δ

i, j

as follows

i, j

= γ

2,i, j

−γ

1,i, j

. (18)

The CDF of γ

i, j

is given by

i, j

(x) =

−γ

2,i, j

exp(

−x

2,i, j

) + γ

1,i, j

exp(

−x

1,i, j

) + δ

i, j

(19)

Then, the average bitrate per cluster for MRC and de-

noted as R

j,MRC

can be easily deduced for S = 2 if

equations (8), (10) and (19) are combined.

j,MRC

T T I

∞

(x)g(x)

∏

l=1,l6= j

[1 −

∏

i=1

(20)

(1 −

−γ

2,i,l

exp(

−xM

2,i,l

) + γ

1,i,l

exp(

−xM

1,i,l

) + δ

i,l

)]dx.

4.4 Application to a Generic System

In (Knopp and Humblet, 1995), it was proposed a ref-

erence radio channel model based on an exponential

distribution for γ. Hence

(x) = 1 −exp(−x/γ) if x > 0. (21)

Supposing that each signal received by a UE follows

an exponential distribution for the SNR, equation (15)

is reformulated as follows

j,SC

T T I

∞

(x)g(x)

∏

l=1,l6= j

(22)

[1 −

∏

i=1

(1 −

∏

s=1

[1 −exp(−

s,i, j

)])]]dx.

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124

Table 1: Simulation parameters.

Frame period 2 (ms)

BS Transmission power 38 (dBm)

Intra-cell interference 30 (dBm)

Inter-cell interference -100 (dBm)

β 3.52

31.8 (dB)

W 5 (MHz)

In the case of pure multicast, equation (12) is rewrit-

ten for SC as follows

mcast,SC

T T I

∞

∏

i=1

(1 −

∏

s=1

[1 −exp

−h(x)

s,i

])dx.

(23)

as for multiple-unicast with SC, equation (11) is

rewritten as follows

j,SC

T T I

∞

(x)g(x)

∏

l=1,l6= j

∏

s=1

[1 − (24)

exp(

−xM

s,l

)]dx

Function g is given by Shannon formula (Shannon,

1948): g(γ

) = W D

T T I

log

(1 + γ

) where W is the

available bandwidth. Function h is then h(x) =

x/W D

T T I

−1.

In the context of MRC with pure multicast, equation

(12) is rewritten for S = 2 as follows

mcast,MRC

T T I

∞

∏

i=1

(1 − (25)

−γ

2,i, j

exp(

−h(x)

2,i, j

) + γ

1,i, j

exp(

−h(x)

1,i, j

) + δ

i, j

)dx.

As for MRC with multiple-unicast, we combine equa-

tions (11) and (19) as follow

j,MRC

T T I

∞

(x)g(x)

∏

l=1,l6= j

(26)

−γ

2,l

exp(

−xM

2,l

) + γ

1,l

exp(

−xM

1,l

) + δ

i, j

]dx.

5 EVALUATION RESULTS

In this section , we evaluate the gain of macro di-

versity techniques for different clustering schemes,

namely mutliple-unicast, pure multicast and mixed

clustering. Simulation parameters are listed in Table

1. We perform 120 iterations with different user dis-

tributions. Only one multicast service is considered.

We evaluate results for 5 and 10 randomly distributed

users located in cell 1 and listening to BS1 and BS2

(S=2). As we restrict ourselves to one service and one

cell, these numbers remain reasonable. In the case of

mixed multicasting, we ﬁx γ

thres

to 3.7 dB as found

in (El Heni and Lagrange, 2008b). Results of the av-

erage bitrate performance for SC with the 95% con-

ﬁdence intervals are depicted in Table 2. We see that

macro diversity using SC improves the system perfor-

mance. Gains for pure multicasting are of 20% and

18% for 5 and 10 UEs, respectively. In fact, the per-

formance of this scheme depends only on the lowest

SNR value; as the SC technique increases the chan-

nel quality particularily for users at the cell border

(i.e. having the lowest SNR), it has a direct impact

on the pure multicast scheduler. In the case of mixed

clustering, gains are of 8.5% and 6.5% for 5 and 10

UEs, respectively. With multiple-unicast, the gain is

of 7% and 5% for 5 and 10 UEs, respectively. Gains

of macro diversity with multiple-unicast and mixed

clustering are lower than those obtained for pure mul-

ticast. In fact, users with the lowest SNRs are served

in a unicast scheme and increasing their average chan-

nel quality allows a better bitrate capacity for these

users, the impact on the global system is less visible.

SC allows users with higher SNRs to be served more

frequently as the deviation between the lowest and the

highest average SNR is cut off. Results for Maximum

Ratio Combining are depicted in Table 3. Achieved

gains are higher than those achieved with MRC. Gains

for pure multicasting are of 31% and 28% for 5 and

10 UEs, respectively. In the case of multiple-unicast,

gains are of 12% and 9% for 5 and 10 UEs, respec-

tively. As for mixed clustering, gains are of 15.5%

and 14% for 5 and 10 UEs, respectively. It is note-

worthy that when N increases, user location tend to

concentrate in the middle of the cell where the signal

level is quite high. This is the reason for the decrease

of macro diversity gain.

6 CONCLUSIONS

In this study, we consider macro diversity in the

framework of multicast scheduling over high-speed

networks. We have developed an analytical model

for the mean bitrate calculations in order to evaluate

the resulting scheduling performance. To ensure an

optimal usage of our scheduler, we have used a clus-

tering strategy that classiﬁes terminals according to

their average channel quality. We have shown that

macro diversity using selective combining and max-

imum ratio combining improves the system perfor-

mance. The study shows that the macro diversity gain

MACRO DIVERSITY COMBINING SCHEMES FOR MULTICAST TRANSMISSION IN HIGH-SPEED CELLULAR

NETWORKS

125

Table 2: Throughput (bps) with conﬁdence intervals for different clustering strategies with/without SC.

Strategy N without SC with SC SC Gain

Pure multicast

5 UEs 4.28 10

±3.8% 5.14 10

±4% 20%

10 UEs 3.33 10

±4% 3.92 10

±5% 18%

Multiple-unicast

5 UEs 3.47 10

±3% 3.71 10

±2.3% 7%

10 UEs 2.45 10

±3.5% 2.57 10

±2% 5%

Mixed strategy

5 UEs 5.07 10

±2.9% 5.49 10

±2.8% 8.5%

10 UEs 4.19 10

±3.4% 4.45 10

±2.9% 6.5%

Table 3: Throughput (bps) with conﬁdence intervals for different clustering strategies with/without MRC.

Strategy N without MRC with MRC MRC Gain

Pure multicast

5 UEs 4.28 10

±3.8% 5.60 10

±4% 31%

10 UEs 3.33 10

±4% 4.31 10

±2.8% 28%

Multiple-unicast

5 UEs 3.47 10

±3% 3.82 10

±3.4% 12%

10 UEs 2.45 10

±3.5% 2.67 10

±3.3% 9%

Mixed strategy

5 UEs 5.07 10

±2.9% 5.85 10

±2.6% 15.5%

10 UEs 4.19 10

±3.4% 4.78 10

±3% 14%

is the highest for the pure multicast scheme. Consid-

ering multiple-unicast and mixed clustering, we ob-

tain equivalent results.

To exploit efﬁciently the advantages of macro di-

versity, some optimizations have to be considered in

relation with the feedback procedure and retransmis-

sion management. This could be considered in a fu-

ture work.

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