1. 1
Channel Quality Measurement for Multicast Sessions
Kunniyur S Srisankar
Motorola India, Bangalore Email: srisankar@motorola.com
Saraswathi Venkataraman
BITS, Pilani Email: f2002047@bits-pilani.ac.in
Abstract— This paper describes scheduling algorithms to determine the
channel quality of the multicast sessions. The throughput of the multicast
and unicast sessions when each of these algorithms are employed, are
compared and evaluated. The simulations show how one of the algorithms
maximizes the throughput and yet ensures fair allocation of resources
between unicast and multicast sessions.
Index Terms— Multicast, Unicast, and Throughput
I. INTRODUCTION
Wireless medium is inherent broadcast in nature i.e., all nodes in
the transmission range of the transmitter can receive the packet
simultaneously. Such a characteristic enables services that require
the same stream of packet to be transmitted to several users at
the same time. Multicast services are services that are provided to
a subset of subscribers at the same time. A typical example of a
multicast service over a cellular network would be game statistics
that are beamed to all users subscribed to that service during a
football match. In such cases, transmitting the same statistics to the
subscribed users one by one is a waste of air resources. Many of the
current day wireless applications need to one to many (multicast)
communications e.g., conference meetings, wireless gaming etc. As
a result, the 3G standards (3GPP and 3GPP2) have recognized the
potential of multicast services and have taken steps to include them
in the specifications. Most of the research in wireless multicast
has been directed towards the development of end-to-end recovery
and routing mechanisms in wireless ad-hoc networks. However not
much attention has been paid to the MAC layer aspects like channel
condition determination of multicast sessions in cellular networks
(see [1,2,3,4] to name a few). In this paper we attempt to fill this
void. Similarly, most of the attention in wireless scheduling has been
directed towards providing delay guarantees for unicast users under
varying channel conditions (see [5,6,7,8,9,10,11] to name a few).
Current standards like HRPD-A emphasize on maximally utilizing
the air resources by transmitting data to users in the downlink that
have the best channel conditions (called opportunistic scheduling)
[10,11]. It is shown that such a channel aware scheduler dramatically
improves the throughput of the system. However such specifications
are defined for unicast sessions and do not include the possibility of
multicast sessions.
In any channel-aware scheduling algorithm, the channel condition
of the user is mapped into a scalar quantity (for example, frame
error rate, data transmission rate fora target frame error rate etc.) A
commonly used indicator of the channel quality of a particular user
is the maximum data rate that can be transmitted with a target error
rate to that user. However, in a multicast session there are multiple
users with different channel conditions. As a result, it is not clear
how one can compare the channel conditions of a multicast session
with a unicast session or even compare the channel conditions of
different multicast sessions. The problems that we wish to tackle in
this paper are:
• How to evaluate the channel condition of a multicast session?
• What is an appropriate mapping from the vector of channel
conditions to a scalar quantity that can be equitably compared
to unicast users?
We believe that the work will allow us to compare the channel
conditions of multicast sessions and unicast sessions and allow us to
fairly schedule them by utilizing the scheduling algorithms currently
proposed in the literature and standards.
II. SYSTEM MODEL
Consider a multicast session with N users in the session. Each user
provides fast feedback about the downlink channel condition using
the Date Rate Control (DRC) bits. Each user’s channel conditions
can be categorized by the packet size and the frame error rate. This
information is available from the DRC message sent by the user.
Let Pj(Tm, k) denote the block error rate of user j at time slot k
when a packet size is transmitted. Note that Pj(Tm, k) itself can be
random variable with a cumulative distribution function given by:
G(x) = P(P ≤ x). The effective throughput for user j in slot k is
given by: 1 − Pj(Tm, k)Tm
Let C(k) denote the channel condition of the multicast session
at time slot k. In a normal unicast session, a sessions channel
condition is directly determined from the DRC message. However,
in a multi-cast session, each user might potentially have varying
channel conditions and it might be hard to quantify the channel
condition. To characterize the channel conditions, we compare
two naive algorithms with the proposed algorithm. The two nave
algorithms are presented below:
A. Algorithm I :
Take the channel condition of the multicast session as the best
channel condition among all users. That is:
C(k) = argmaxj[maxT m(1 − Pj(Tm, k))Tm] (1)
The idea behind this approach is that the channel condition of
the multicast session is determined by the effective throughput of
the user with the best channel condition. A disadvantage of this
approach is that a multicast session will get many more opportunities
to transmit while not being successful to many of its subscribers.
This will lead to smaller throughputs for the entire cell (or sector).
This will also bias the system towards multicast sessions leading to
an unfair resource allocation policy.
B. Algorithm II:
Take the channel condition of the multicast session as the worst
channel condition among all users. That is:
C(k) = argminj[maxTm (1 − Pj(Tm, k))Tm] (2)

2. 2
In this case, the channel condition for the multicast session is taken
as the effective throughput of the user that has the worst channel.
In this approach, the rate of the multicast session in any slot is
determined by the worst channel condition among all the users in
that slot. As a result, a user with the worst channel dictates the rate
of the multicast session. Hence, users might have a bad experience
and instead opt for a unicast session that leads to wastage of valuable
air resources.
III. THE PROPOSED ALGORITHM
While algorithms I and II are nave proposals that opt for either the
worst or the best channel condition as the channel quality indicator,
we now propose a new channel determination policy that will enable
us to schedule multicast users fairly along with unicast sessions.
The base-station determines the channel condition of the multicast
session as follows:
C(k) =
1
N
maxTm
NX
j=1
(1 − Pj(Tm, k))Tm (3)
The maximum is taken over all packet sizes to give the maximum
effective throughput for all users. We then scale the value by the
number of users to get the average effective throughput per user.
This scaling is necessary to remove any bias against sessions with a
large number of users. The idea behind such a definition is that the
channel capacity is determined by the maximum average effective
throughput that is possible with the given users’ channel conditions.
Note that such a definition can also be extended to the case when
the frame error rate is a random variable with distribution given by
G(x),where
Gj,m(x) = 1 − Prob(Pj(Tm, k) ≤ x)
Let gj,m(x) = Gj,m(x)
In such a case the channel condition of the multicast user is given
as:
C(k) =
1
N
maxTm
NX
j=1
Tm
Z
gj,m(x)xdx =
1
N
maxTm E[Pj(Tm, k)]
(4)
where E[x] stands for the expectation of the random variable x.
In this paper, we wish to evaluate the proposed channel condition
determination algorithm in (3) with other two algorithms (1) and (2)
using various scheduling schemes. In particular we plan to compare
the above three channel-condition determination algorithms in terms
of:
• Fairness among multicast flows with different subscription levels
• Fairness between multicast and unicast flows
IV. SIMULATION RESULTS AND DISCUSSION
We examine the effective throughput in a wireless network with
several unicast and multicast sessions. We evaluate the performance
of each of the algorithms under various conditions. The simulation
results substantiate that the proposed algorithm attains significantly
higher output than the other algorithms.
A. Simulation Model
We assume that the channel conditions are equally probable and
randomly generate channel conditions for all users. Time is slotted
and we assume that each packet can be transmitted in a single slot.
We assume that the user can send packet sizes of 128 bits, 256 bits,
512 bits and 1024 bits in a slot respectively. We also assume that
the corresponding error rate for a given packet size (P1, P2, P3, P4)
and channel condition (D1, D2, D3, D4) is given.
chnlcndtn/pktsize D1 D2 D3 D4
P1(128 bits) 0.02 0.01 0.008 0.005
P2(256 bits) 0.12 0.02 0.01 0.008
P3(512 bits) 0.22 0.12 0.02 0.008
P4(1024 bits) 0.30 0.20 0.12 0.02
We measure the throughput of a receiver as the number of packets
received successively per unit time. We first simulate a network
with m unicast users and a single multicast session with u users.
The effective throughput is found by averaging the throughput
calculated over 20 iterations. This run is repeated every time the
number of users is increased. Depending on the algorithm used, the
slots are allocated either to the multicast or the unicast session. We
simulate three scenarios here. In the first scenario, the number of
multicast users in a single session is increased while the number of
unicast users is kept constant. In the second scenario, we compare
the throughputs of two multicast sessions comprising of 5 and 25
users. In the third, the number of unicast users is increased while
the number of multicast users is kept constant.
B. Discussion
1) Scenario 1: In this scenario, the number of users in a multicast
session is increased from 2 to 40 users while the number of
unicast users is fixed at 5. We calculate the throughputs achieved
and the percentage of slots allocated to the multicast and unicast
sessions for all the three algorithms. Algorithm I assumes the
best channel condition among all multicast users as representative
of the session and compares it with the best channel condition
among all unicast users. As a result, more slots are allotted to the
multicast session when the number of multicast users is increased
(Figure 1). Algorithm II assumes the worst channel condition among
all multicast users as representative of the multicast session and
compares it with the channel condition of the unicast users. Here
again, since the number is more, the probability of at least one bad
channel condition occurring among all multicast users is more in the
case of multicast and hence Algorithm II allocates more slots to the
unicast session (Figure 2). When the proposed algorithm is used,
it is observed that, although the fraction of slots that are allocated
to the multicast session is lesser than that of the other algorithms,
the effective throughput is more (Figure 3,4). Hence, there is fair
allocation of resources for both the unicast and multicast session
when the proposed algorithm is employed.
2) Scenario 2: Here, the throughputs of two multicast sessions are
compared. It is run over 20 iterations and the throughput obtained
in each run is plotted. It is observed that the throughput of the
multicast session II (25 users) is more when the proposed algorithm
and Algorithm I is employed. Algorithm I allocates more slots to the
multicast session of 25 users because there is a higher probability

3. 3
of the best channel condition occurring in multicast session II.
Similarly, Algorithm II allots more slots to the multicast session of
5 users. The proposed algorithm allocates resources fairly between
both the sessions. (Figures 5-8)
3) Scenario 3: Here, the number of unicast users is increased,
while the number of multicast users in the sessions is kept constant
at 5 . Algorithm I allocates more slots to the unicast users, as there is
less probability for one of the users in the multicast session to have
the best channel condition. Hence, as the number of unicast users
increase, Algorithm I allocates more slots to the unicast session.
This is evident from Figure 9 .The effective throughput of the
multicast session, obtained by employing the proposed algorithm,
is first very high, as there are few unicast users. However, as the
number of unicast users increase, the effective throughput of the
multicast session decreases. In the case of unicast, the throughput
that is obtained is more than that of multicast when the number of
users is increased.
0 5 10 15 20 25 30 35 40
0
10
20
30
40
50
60
70
80
90
100
The number of multicast users
Thepercentageofslotsofthemulticastusers
Best channel
Worst channel
Proposed
Fig. 1. The percentage of slots allotted to the multicast session in Scenario
1
0 5 10 15 20 25 30 35 40
0
10
20
30
40
50
60
70
80
90
100
The number of multicast users
Thepercentageofslotsoftheunicastusers
Best channel
Worst channel
Proposed
Fig. 2. The percentage of slots allotted to the unicast session as in Scenario
1
V. CONCLUSION
Channel quality measurement in multicast sessions presents
challenges that are not encountered in unicast session because there
are multiple users with different channel conditions. The objective
0 5 10 15 20 25 30 35 40
0
100
200
300
400
500
600
700
800
900
1000
THe number of multicast users
TheEffectivethroughputofthemulticastusers
Best channel
Worst channel
Proposed
Fig. 3. The effective throughput of the multicast session as the number of
multicast users are increased as in Scenario 1
0 5 10 15 20 25 30 35 40
0
200
400
600
800
1000
1200
THe number of multicast users
TheEffectivethroughputoftheunicastusers
Best channel
Worst channel
Proposed
Fig. 4. The effective throughput of the unicast users as the number of
multicast users are increased as in Scenario 1
therefore is to find out a means by which one can compare the
channel conditions of multicast and unicast sessions and schedule the
packets accordingly. The proposed algorithm attains high throughput
and at the same time ensures fair and efficient allocation of resources
between the multicast and unicast sessions
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4. 4
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The number of iterations
TheeffectivethroughputofmulticastsessionI
Best channel
Worst channel
Proposed
Fig. 5. The effective throughput of the first multicast session where there
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The number of iterations
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0 2 4 6 8 10 12 14 16 18 20
0
10
20
30
40
50
60
70
The number of multicast users
ThenumberofslotsallocatedtomulticastSessionI
Best channel
Worst channel
Proposed
Fig. 7. The percentage of slots allotted to the first multicast session of 5
users as in Scenario 2
0 2 4 6 8 10 12 14 16 18 20
0
10
20
30
40
50
60
70
The number of multicast users
ThenumberofslotsallocatedtomulticastsessionII
Best channel
Worst channel
Proposed
Fig. 8. The percentage of slots allotted to the second multicast session of
25 users as in Scenario 2
0 5 10 15 20 25 30 35 40
0
10
20
30
40
50
60
70
80
90
100
The number of unicast users
Thepercentageofslotsoftheunicastusers
Best channel
Worst channel
Proposed
Fig. 9. The percentage of slots allotted to the unicast users as the number
of unicast members are increased as in Scenario 3

5. 5
0 5 10 15 20 25 30 35 40
0
10
20
30
40
50
60
70
80
The number of unicast users
Thepercentageofslotsofthemulticastusers
Best channel
Worst channel
Proposed
Fig. 10. The percentage of slots allotted to the multicast users as the number
of unicast numbers are increased as in Scenario 3
0 5 10 15 20 25 30 35 40
0
100
200
300
400
500
600
700
800
900
1000
THe number of unicast users
TheEffectivethroughputofthemulticastusers
Best channel
Worst channel
Proposed
Fig. 11. : The effective throughput of the multicast users as the number of
unicast users are increased as in Scenario 3
0 5 10 15 20 25 30 35 40
0
200
400
600
800
1000
1200
THe number of unicast users
TheEffectivethroughputoftheunicastusers
Best channel
Worst channel
Proposed
Fig. 12. : The effective throughput of the unicast users as the number of
unicast users are increased as in Scenario 3