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Abstract—Multicasting is emerging as an enabling technology
for multimedia transmissions over wireless networks to support
several groups of users with flexible quality of service (QoS)
requirements. Although multicast has huge potential to push the
limits of next generation communication systems; it is however
one of the most challenging issues currently being addressed. In
this survey, we explain multicast group formation and various
forms of group rate determination approaches. We also provide
a systematic review of recent channel-aware multicast scheduling and resource allocation (MSRA) techniques proposed for
downlink multicast services in OFDMA based systems. We study
these enabling algorithms, evaluate their core characteristics,
limitations and classify them using multidimensional matrix. We
cohesively review the algorithms in terms of their throughput
maximization, fairness considerations, performance complexities,
multi-antenna support, optimality and simplifying assumptions.
We discuss existing standards employing multicasting and further
highlight some potential research opportunities in multicast
systems.
Index Terms—multicasting, resource allocation, multicast survey, scheduling, OFDMA, subcarrier allocation, power allocation,
resource optimization, quality of service, multicast standards.
I. INTRODUCTION
OVERWHELMING demands for high data rates and the need to support large number of users with flexible
quality of service (QoS) requirements has led to an explosive surge in mobile and wireless communication systems
development in recent years. These demands and requirements are anticipated to be more intense in the future as
more military applications and commercial services become
more prevalent. Of particular interest are certain applications
which require transmission to selected groups of users that
naturally lend themselves towards multicasting. For instance,
geographic information updates such as traffic reports, local
news, weather forecast, stock prices and location-based adverts. Multimedia entertainments such as IPTV, mobile TV,
video conferencing, and other multimedia services, which
currently account for one-third of mobile internet market,
are some of the disruptive innovations that can be deployed
using multicast technology [1]–[7]. Since there is no substitute
Manuscript submitted 10 May 2011; revised 05 August 2011 and 11
January 2012. This work was supported by the World-Class University Program through the National Research Foundation of Korea (R31-10026), and
Grant K20901000004-09E0100-00410 funded by the Ministry of Education,
Science, and Technology (MEST).
The authors are with the School of Information and Communication, Department of Nanobio Materials and Electronics, Gwangju Institute
of Science and Technology, GIST, Gwangju, 500-712, South Korea (email:[email protected]; [email protected]; [email protected])
Digital Object Identifier 10.1109/SURV.2012.013012.00074
Fig. 1. Multicast system where multiple users requesting same service share
allocated system resources. The users may not be in the same location.
for intelligent deployment and utilization of finite resources,
hence, when multiple users within the same or adjacent cell
require same content, multicasting allows such users to form
groups and share allocated resources as illustrated in Fig. 1.
The idea further maximizes spectral efficiency and minimizes
transmission power consumption at the base station while also
maximally utilizing the limited system resources [4]. This is
in contrast to unicast transmissions where users cannot share
resources and as many transmissions as number of users are
required for full cell coverage.
Meanwhile, next generation communication systems must
address challenges of multimedia broadcast due to wide variations of the wireless channel, high mobility of users and
limited system resources. To resolve these challenges, combinations of multicasting together with orthogonal frequency
division multiple access (OFDMA), multiple-input-multipleoutput (MIMO) antenna scheme, scheduling, and dynamic radio resource allocation (DRA) have been particularly identified
as spectrum efficient techniques to maximize spectral utilization, minimize transmission power consumption at the base
station (BS) and provide better quality of experience (QoE)
for users within the network. These technologies have been
widely adopted as multimedia broadcast multicast services
(MBMS) in few cellular standards such as IEEE802.16 (Fixed
and Mobile WiMAX) and the 3GPP Long Term Evolution
(LTE) to accommodate high speed mobility as well as support
high rates for nomadic and mobile users [8].
The main idea of OFDMA is the distribution of the narrowband subcarriers among users depending on their channel
Fig. 2. Various aspects of channel-aware multicast scheduling and resource allocation (MSRA) as discussed in this paper.
characteristics [9], whereas, MIMO uses multiple antenna at
both the transmitter and receiver to enable increased spectral efficiency for a given total transmit power by properly
multiplexing parallel channels and taking advantage of antenna diversities. Similarly, scheduling and dynamic resource
allocation establish management protocols to ensure fair and
efficient exploitation of system resources. The transmission
strength of OFDMA together with advanced antenna capabilities of MIMO allow more users to be packed into available
resources in frequency and spatial domains. Combination of
MIMO-OFDMA unique features has been reported to result
in enhanced system total capacity [10].
Multicast scheduling and resource allocation (MSRA) is
based on two types of multicast transmissions: Single-rate and
multi-rate transmissions. In single-rate, the BS transmits to
all users in each multicast group at the same rate irrespective
of their non-uniform achievable capacities whereas in multirate, the BS transmits to each user in each multicast group
at different rates based on what each user can handle. Until
recently, single-rate scheme has been quite popular and widely
accepted due to its implementation simplicity and low complexity. Multi-rate, on the other hand, has been receiving more
attention lately because of necessity to achieve user throughput
differentiation such that improved system spectral efficiency
is attained.
MSRA is still confronted with various technical challenges.
For example, in single-rate transmission, multicast services
must be transmitted at a rate low enough for the least (worst
or minimum) user to decode and high enough to maximally
utilize system resources. Hence, the major problem is determining the most efficient single rate to transmit to each group
without being insensitive to users with bad channel quality
or unfair to users with high throughput potentials. Invariably,
single-rate multicasting translates to trade-off between the
transmission rate and system coverage.
In multi-rate transmission however, the problem is how to
reduce the computational complexities, coding, and synchronization difficulties associated with transmission to multiple
subgroups or individual group members. Based on these two
types of multicast group rate determinations, scheduling, resource allocation and optimization can then be performed such
that spectral efficiency is achieved, various network resources
are optimally utilized without performance degradation and
users’ QoS requirements are satisfied given that they experience different channel fading dynamics.
While a huge plethora of literature exists on scheduling
and dynamic resource allocation (DRA) in unicast multiuser
OFDM systems as surveyed in [11], [12], works on multicast
scheduling and resource allocation (MSRA) are just beginning
to emerge in broadband wireless systems. Authors of [13] and
[6] examined single-rate multiple multicast groups within a
single cell while [14] and [15] investigated multiple multicasts
with multi-rate transmissions. All these algorithms consider
different performance metrics and constraints. Of particular
challenge is the resulting optimization problem of multiple
antenna complexities at both the BS and individual users.
Specifically, [5] and [16] are among the few works investigating MIMO techniques in multicast. Hence, MSRA in wireless
networks is currently a research area with many open issues.
A major goal of this survey article is to present a concise
and insightful view of the current knowledge in several aspects
of channel-aware MSRA algorithms and then provide succinct
classifications of these algorithms as illustrated in Fig. 2.
We start by introducing MSRA fundamentals and various
group formation concepts in Section II. We discuss challenges
associated with MSRA in Section III while in Section IV,
we explain approaches in MSRA to address optimality and
complexities. Main ideas, features and limitations of enabling
algorithms and their various forms are studied in Section V.
Multicasting features of some modern wireless standards are
explained in Section VI. Finally, Section VII provides insight
to some potential research opportunities and our conclusions
are presented in Section VIII. Although, we do not claim
absolute completeness of resource allocation algorithms in this
study - because this would probably result in an heterogeneous
list of scientific contributions - but extensive analysis has been
provided.
II. MULTIMEDIA MULTICAST FUNDAMENTALS
In this section, we provide insight into various multicast
group formation strategies proposed in the literature for singlerate and multi-rate multicast group transmission schemes. We
also address potential anomaly behavior in multicast groups.
LCG Users at the cell edge with bad channel dynamics.
·
Multicast group compose of several users with
varying channel quality index and distance from BS.
Fig. 3. Multicast group formation using single transmission rate. The singlerate can be fixed rate, average group throughput or rate of least capable user
in the group.
A. Single-Rate Multicast Transmissions & Group Formation
Single rate transmission requires no special group formation
except to determine a compromising transmission rate suitable
for all users in the group as in Fig.3. To permit researchers to
design and propose practical MSRA algorithms, three simple
schemes have been adopted widely in the literature. First is
a pre-defined fixed default rate [17], [18]. Second is adaptive
selection and transmission at worst user’s rate (i.e. user with
least channel gain) [19] and finally, dynamic transmission
using group average throughput [20]. In what follows, we
discuss these schemes and their variants.
1) Pre-defined Fixed Rates: It has been argued that using
a pre-defined fixed default group transmission rates for all
multicast group is sufficient. In fact, existing communication
systems such as CDMA2000 1xEV-DO networks use fixed
data rate of 204.8Kbps for multicast transmission and equal
resources are assigned to all users in cyclic round-robin
fashion irrespective of their channel characteristics [17], [18].
This means, there is no priority consideration and system resources are evenly distributed. This easy approach is especially
designed to favorably satisfy cell edge users who are expected
to have low channel gains due to their bad channel quality
resulting from their farthest distance from central BS.
However, in the likely event that we assume the fixed rate
is always equal to the instantaneous achievable rates of the
minimum users at the cell edge, then, using pre-defined fixed
rate results in max-min fairness (see Section III-C2) since the
resulting minimum user is given resource allocation priority
to realize its maximum achievable rate. This rate is the worst
rate because it assumes that there is always a user at the edge
of the cell regardless whether such a user is actually present or
not. Although, fixed rate approach is simple to implement with
low complexity and also guarantees reliable multicast to users
at cell edge; it is however undesirable since it puts severe restriction on achievable system throughput when users’ channel
differentiation is considered especially for those users close
to the base station with good channel quality. Additionally,
this scheme does not offer any utility maximization, hence,
it is unresponsive towards intra-group and inter-group user
fairness. Intra-group refers to the interaction and coexistence
of multiple users within a single multicast group whereas
inter-group refers to such competitive coexistence in multiple
multicast where numerous groups compete among themselves
for system resources.
2) Least Channel Gain (LCG) User Rate: A system is
only as strong as its weakest link. So also is a single-rate
multicast system based on LCG user. This scheme adaptively
sets the group transmission rates to suit the user with the worst
(minimum) channel quality [5]–[7], [19].While LCG scheme
has spurred other approaches, the scheme itself is highly
conservative and spectrally inefficient since users within the
group (close to the BS) experiencing good channel gains are
severely hindered from utilizing link adaptation to exploit their
good channel gain. Besides, as the group size increases, the
data capacity of the group becomes limited, because more
users now share resources assigned to the group based on LCG
user, consequently, capacity benefits of the multicast system
diminishes as the number of users increases [21]. It is obvious
that LCG scheme is a pessimistic special case of pre-defined
fixed rates discussed in Section II-A1.
3) Average (AVG) Group Throughput: Another way to improve system capacity and exploit multiuser channel dynamics
is to enable the BS transmits to each multicast group based on
long-term moving average throughput of the group [13], [20],
[22]. Group averaging technique has various forms. For instance, [22] orders users’ instantaneous achievable throughput
and selects the median throughput that can support half (50%)
of all group member while in [20] and [13], authors develop
models that allow the BS to select appropriate single data
transmission rate based on the exponential moving average
received throughput of each user inside the cell. Another
important but yet rarely researched area is physical layer
multicasting using multiple antenna where users’ average
signal-to-noise ratios (SNR) is used to determine the group’s
single transmission rate [23]–[25].
In [24], authors show that capacity maximization based on
SNR averaging provides higher capacity than LCG scheme
and further justifies that under certain scenarios, when users
are mobile, SNR averaging corresponds to the LCG scheme.
However, studies by Sun et al. [23] differ from [24] by
showing that not only does the LCG scheme offer practical
implementation benefits, but also satisfies the QoS of each
user. Interestingly, results of [23] is only valid provided the
optimized LCG SNR meets the threshold required for successful reception. Fundamentally, concept of group throughput
or group SNR averaging premise on guaranteeing reliable
transmission and successful decoding to half the user in
the system. This overtly optimistic scheme invariably means
certain packet loss is inevitable, especially for users far from
the central BS who cannot cope with the high average group
rates.
B. Multi-Rate Multicast Transmissions & Group Formation
Multi-rate multicast transmission emerges to address the
sub-optimality that exists in single-rate transmission considering the intrinsic heterogeneous channel characteristics
of wireless networks. This diversity, if not well addressed
A. Suboptimal Strict Throughput Single-Rate Algorithms
Suboptimal algorithms for multicast-based resource allocation in existing literature can be differentiated based on two
basic properties: The reduction assumptions towards simplifying the complexity of the problems, and the isolation methods
used to divide the problems into independent steps such that
each step has polynomial complexity. For the first, subcarriers
are assigned to each group with objective of maximizing total
system capacity. This step assumes that total system transmit
power is evenly distributed over all subcarriers. In the second,
transmit power is optimally allocated to each preselected
subcarrier using Lagrange multiplier method or the KarushKuhn-Tucker (KKT) conditions [63] - which interestingly, is
similar to the conventional waterfilling rule - to enforce group
rate proportionality.
These two steps are usually adopted, however, the difference
is the techniques used to assign subcarriers, which we shall
discuss in detail. For instance, [7], shows that if equal power is
applied to selective subcarriers with good channel gains, total
throughput of zero pathloss difference of suboptimal heuristic
scheme approximates the performance of the optimal scheme
even with flat transmit power spectral density (PSD). This simple approach is an example of strict throughput maximization
which reduces computation complexity mainly to subcarrier
allocation and eliminates need for power allocation. When
we consider multiple multicast services, complexity increases
because we need to determine which group receives the best
subcarrier in each iteration. This subcarrier allocation decision
is determined by the system objectives possibly formulated in
terms of strict throughput maximization or fairness of access
to network resources.
This case was further studied in [19] where subcarrier n is
allocated to group g having potential maximum data rate as
given in eqn. (8). This is equivalent to assigning subcarrier
n to group g with maximum SNR or highest channel gain
noting that each group rate is based on worst channel user.
Similar works for single multicast MIMO using spatial multiplexing and multi-multicast MIMO using weighting precoding
are done in [5] and [16] respectively. These works further
define two additional approximations for eqn. (8), which are
functions of the eigenvalues of the channel matrix for the low
and high SNR regions where the SNR is close to zero and
>> average SNR respectively.
max
g∈G
(Rg,n)=|Kg| log2 1 + N1 g,nPT otal (8)
The significance of these approximations is the reduction in
computation complexity of the algorithm in the SNR extremes.
In contrast to LCG user where performance degrades as the
number of users increase, these schemes achieve higher system
capacities even at the low SNR region since groups with better
channel condition always have resources. Results in [5] also
show that as the channel power gap increases larger gains is
achievable.
As with all STM objective functions, fair access to system resources between groups with diverse carrier-to-noise
ratio (CNR) is not considered. If the link difference among
multicast group is large, group with high CNR will dominate
the resource for a large amount of time, leaving groups with
low link quality to starve. For example, schemes in [5] can
potentially shut out groups with poor channel gain or fewer
numbers of users since it is based on maximum aggregate
data rate which increases as users per group and channel
gain increase. Tables II shows summary of suboptimal strict
throughput single-rate algorithms.
B. Suboptimal Max-Min Fair Single-Rate Algorithms
One possible way to prevent greedy resource utilization
by HCG groups and maintain balance between throughput
maximization and fairness is to impose minimum number of
subcarrier to allocate to each group. Ngo et al. [7] shows
that by adding one more constraint as shown in eqn. (9)
to constraints in (5)-(7), certain level of flexibility and fair
resource access can be assured.
N n
=1
δ
g,n ≥ αg|G g=1 , (9)
where 0 ≤ αg ≤ N, G g=1 αg ≤ N, and αg is the minimum
number of subcarrier to assign to each group.
Interestingly, the total capacity result of the suboptimal
fair scheme approximates performance of the suboptimal
strict throughput even at 2.5dB pathloss difference. However,
determination of the optimal choice of αg is not trivial because
if α
g → 0, problem becomes strict throughput whereas, the
problem becomes strict fairness if αg → MG .
A compensation approach was proposed in [6], [26] where
fairness is enforced by compensating each group for low rate
- relative to the target rate required by the group - by moving
them to better subcarrier with higher CNR. That is, in the
next transmission of each multicast group, subcarrier having
maximum channel gain (best subcarrier) is assigned to the
group with least data rate in the previous transmission. In
addition to showing intergroup relationship that may exist in a
cell, this approach ensures that no group dominates the system
resources and low rate groups do not experience outright
resource starvation.
1) Max-Min Fair & QoS Considerations: Besides throughput and fairness system objectives, it is equally important
to provide satisfying quality of service to users because bad
QoS affects users’ level of satisfaction and defeats the system
purpose. One way to achieve this is to ensure that achievable
rates for each single-rate multicast group satisfy the minimum
rate requirements of contents served. In [56], the following
constraint is added to constraints (5)-(7):
R
g,n ≥ Rg,n min 1 ≤ n ≤ N, (10)
where Rmin
g,n is the least data rate requirement to satisfy users’
QoS requirements. Resulting optimization solution guarantees
acceptable service quality if LCG users experience good
channel quality but it invariably results in absolute resource
starvation for all group members once the minimum user in
the group cannot satisfy own rate requirements. Hence, in low
SNR regime where LCG user’s data rate is less than QoS
requirement, system performance degradation may result.
To satisfy the QoS requirements of users in a multicast
group, [15], [65] applied IDT and redefined the base stream
as the minimum rate all users must receive to satisfy QoS
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Abstract—Multicasting is emerging as an enabling technology
for multimedia transmissions over wireless networks to support
several groups of users with flexible quality of service (QoS)
requirements. Although multicast has huge potential to push the
limits of next generation communication systems; it is however
one of the most challenging issues currently being addressed. In
this survey, we explain multicast group formation and various
forms of group rate determination approaches. We also provide
a systematic review of recent channel-aware multicast scheduling and resource allocation (MSRA) techniques proposed for
downlink multicast services in OFDMA based systems. We study
these enabling algorithms, evaluate their core characteristics,
limitations and classify them using multidimensional matrix. We
cohesively review the algorithms in terms of their throughput
maximization, fairness considerations, performance complexities,
multi-antenna support, optimality and simplifying assumptions.
We discuss existing standards employing multicasting and further
highlight some potential research opportunities in multicast
systems.
Index Terms—multicasting, resource allocation, multicast survey, scheduling, OFDMA, subcarrier allocation, power allocation,
resource optimization, quality of service, multicast standards.
I. INTRODUCTION
OVERWHELMING demands for high data rates and the need to support large number of users with flexible
quality of service (QoS) requirements has led to an explosive surge in mobile and wireless communication systems
development in recent years. These demands and requirements are anticipated to be more intense in the future as
more military applications and commercial services become
more prevalent. Of particular interest are certain applications
which require transmission to selected groups of users that
naturally lend themselves towards multicasting. For instance,
geographic information updates such as traffic reports, local
news, weather forecast, stock prices and location-based adverts. Multimedia entertainments such as IPTV, mobile TV,
video conferencing, and other multimedia services, which
currently account for one-third of mobile internet market,
are some of the disruptive innovations that can be deployed
using multicast technology [1]–[7]. Since there is no substitute
Manuscript submitted 10 May 2011; revised 05 August 2011 and 11
January 2012. This work was supported by the World-Class University Program through the National Research Foundation of Korea (R31-10026), and
Grant K20901000004-09E0100-00410 funded by the Ministry of Education,
Science, and Technology (MEST).
The authors are with the School of Information and Communication, Department of Nanobio Materials and Electronics, Gwangju Institute
of Science and Technology, GIST, Gwangju, 500-712, South Korea (email:[email protected]; [email protected]; [email protected])
Digital Object Identifier 10.1109/SURV.2012.013012.00074
Fig. 1. Multicast system where multiple users requesting same service share
allocated system resources. The users may not be in the same location.
for intelligent deployment and utilization of finite resources,
hence, when multiple users within the same or adjacent cell
require same content, multicasting allows such users to form
groups and share allocated resources as illustrated in Fig. 1.
The idea further maximizes spectral efficiency and minimizes
transmission power consumption at the base station while also
maximally utilizing the limited system resources [4]. This is
in contrast to unicast transmissions where users cannot share
resources and as many transmissions as number of users are
required for full cell coverage.
Meanwhile, next generation communication systems must
address challenges of multimedia broadcast due to wide variations of the wireless channel, high mobility of users and
limited system resources. To resolve these challenges, combinations of multicasting together with orthogonal frequency
division multiple access (OFDMA), multiple-input-multipleoutput (MIMO) antenna scheme, scheduling, and dynamic radio resource allocation (DRA) have been particularly identified
as spectrum efficient techniques to maximize spectral utilization, minimize transmission power consumption at the base
station (BS) and provide better quality of experience (QoE)
for users within the network. These technologies have been
widely adopted as multimedia broadcast multicast services
(MBMS) in few cellular standards such as IEEE802.16 (Fixed
and Mobile WiMAX) and the 3GPP Long Term Evolution
(LTE) to accommodate high speed mobility as well as support
high rates for nomadic and mobile users [8].
The main idea of OFDMA is the distribution of the narrowband subcarriers among users depending on their channel
Fig. 2. Various aspects of channel-aware multicast scheduling and resource allocation (MSRA) as discussed in this paper.
characteristics [9], whereas, MIMO uses multiple antenna at
both the transmitter and receiver to enable increased spectral efficiency for a given total transmit power by properly
multiplexing parallel channels and taking advantage of antenna diversities. Similarly, scheduling and dynamic resource
allocation establish management protocols to ensure fair and
efficient exploitation of system resources. The transmission
strength of OFDMA together with advanced antenna capabilities of MIMO allow more users to be packed into available
resources in frequency and spatial domains. Combination of
MIMO-OFDMA unique features has been reported to result
in enhanced system total capacity [10].
Multicast scheduling and resource allocation (MSRA) is
based on two types of multicast transmissions: Single-rate and
multi-rate transmissions. In single-rate, the BS transmits to
all users in each multicast group at the same rate irrespective
of their non-uniform achievable capacities whereas in multirate, the BS transmits to each user in each multicast group
at different rates based on what each user can handle. Until
recently, single-rate scheme has been quite popular and widely
accepted due to its implementation simplicity and low complexity. Multi-rate, on the other hand, has been receiving more
attention lately because of necessity to achieve user throughput
differentiation such that improved system spectral efficiency
is attained.
MSRA is still confronted with various technical challenges.
For example, in single-rate transmission, multicast services
must be transmitted at a rate low enough for the least (worst
or minimum) user to decode and high enough to maximally
utilize system resources. Hence, the major problem is determining the most efficient single rate to transmit to each group
without being insensitive to users with bad channel quality
or unfair to users with high throughput potentials. Invariably,
single-rate multicasting translates to trade-off between the
transmission rate and system coverage.
In multi-rate transmission however, the problem is how to
reduce the computational complexities, coding, and synchronization difficulties associated with transmission to multiple
subgroups or individual group members. Based on these two
types of multicast group rate determinations, scheduling, resource allocation and optimization can then be performed such
that spectral efficiency is achieved, various network resources
are optimally utilized without performance degradation and
users’ QoS requirements are satisfied given that they experience different channel fading dynamics.
While a huge plethora of literature exists on scheduling
and dynamic resource allocation (DRA) in unicast multiuser
OFDM systems as surveyed in [11], [12], works on multicast
scheduling and resource allocation (MSRA) are just beginning
to emerge in broadband wireless systems. Authors of [13] and
[6] examined single-rate multiple multicast groups within a
single cell while [14] and [15] investigated multiple multicasts
with multi-rate transmissions. All these algorithms consider
different performance metrics and constraints. Of particular
challenge is the resulting optimization problem of multiple
antenna complexities at both the BS and individual users.
Specifically, [5] and [16] are among the few works investigating MIMO techniques in multicast. Hence, MSRA in wireless
networks is currently a research area with many open issues.
A major goal of this survey article is to present a concise
and insightful view of the current knowledge in several aspects
of channel-aware MSRA algorithms and then provide succinct
classifications of these algorithms as illustrated in Fig. 2.
We start by introducing MSRA fundamentals and various
group formation concepts in Section II. We discuss challenges
associated with MSRA in Section III while in Section IV,
we explain approaches in MSRA to address optimality and
complexities. Main ideas, features and limitations of enabling
algorithms and their various forms are studied in Section V.
Multicasting features of some modern wireless standards are
explained in Section VI. Finally, Section VII provides insight
to some potential research opportunities and our conclusions
are presented in Section VIII. Although, we do not claim
absolute completeness of resource allocation algorithms in this
study - because this would probably result in an heterogeneous
list of scientific contributions - but extensive analysis has been
provided.
II. MULTIMEDIA MULTICAST FUNDAMENTALS
In this section, we provide insight into various multicast
group formation strategies proposed in the literature for singlerate and multi-rate multicast group transmission schemes. We
also address potential anomaly behavior in multicast groups.
LCG Users at the cell edge with bad channel dynamics.
·
Multicast group compose of several users with
varying channel quality index and distance from BS.
Fig. 3. Multicast group formation using single transmission rate. The singlerate can be fixed rate, average group throughput or rate of least capable user
in the group.
A. Single-Rate Multicast Transmissions & Group Formation
Single rate transmission requires no special group formation
except to determine a compromising transmission rate suitable
for all users in the group as in Fig.3. To permit researchers to
design and propose practical MSRA algorithms, three simple
schemes have been adopted widely in the literature. First is
a pre-defined fixed default rate [17], [18]. Second is adaptive
selection and transmission at worst user’s rate (i.e. user with
least channel gain) [19] and finally, dynamic transmission
using group average throughput [20]. In what follows, we
discuss these schemes and their variants.
1) Pre-defined Fixed Rates: It has been argued that using
a pre-defined fixed default group transmission rates for all
multicast group is sufficient. In fact, existing communication
systems such as CDMA2000 1xEV-DO networks use fixed
data rate of 204.8Kbps for multicast transmission and equal
resources are assigned to all users in cyclic round-robin
fashion irrespective of their channel characteristics [17], [18].
This means, there is no priority consideration and system resources are evenly distributed. This easy approach is especially
designed to favorably satisfy cell edge users who are expected
to have low channel gains due to their bad channel quality
resulting from their farthest distance from central BS.
However, in the likely event that we assume the fixed rate
is always equal to the instantaneous achievable rates of the
minimum users at the cell edge, then, using pre-defined fixed
rate results in max-min fairness (see Section III-C2) since the
resulting minimum user is given resource allocation priority
to realize its maximum achievable rate. This rate is the worst
rate because it assumes that there is always a user at the edge
of the cell regardless whether such a user is actually present or
not. Although, fixed rate approach is simple to implement with
low complexity and also guarantees reliable multicast to users
at cell edge; it is however undesirable since it puts severe restriction on achievable system throughput when users’ channel
differentiation is considered especially for those users close
to the base station with good channel quality. Additionally,
this scheme does not offer any utility maximization, hence,
it is unresponsive towards intra-group and inter-group user
fairness. Intra-group refers to the interaction and coexistence
of multiple users within a single multicast group whereas
inter-group refers to such competitive coexistence in multiple
multicast where numerous groups compete among themselves
for system resources.
2) Least Channel Gain (LCG) User Rate: A system is
only as strong as its weakest link. So also is a single-rate
multicast system based on LCG user. This scheme adaptively
sets the group transmission rates to suit the user with the worst
(minimum) channel quality [5]–[7], [19].While LCG scheme
has spurred other approaches, the scheme itself is highly
conservative and spectrally inefficient since users within the
group (close to the BS) experiencing good channel gains are
severely hindered from utilizing link adaptation to exploit their
good channel gain. Besides, as the group size increases, the
data capacity of the group becomes limited, because more
users now share resources assigned to the group based on LCG
user, consequently, capacity benefits of the multicast system
diminishes as the number of users increases [21]. It is obvious
that LCG scheme is a pessimistic special case of pre-defined
fixed rates discussed in Section II-A1.
3) Average (AVG) Group Throughput: Another way to improve system capacity and exploit multiuser channel dynamics
is to enable the BS transmits to each multicast group based on
long-term moving average throughput of the group [13], [20],
[22]. Group averaging technique has various forms. For instance, [22] orders users’ instantaneous achievable throughput
and selects the median throughput that can support half (50%)
of all group member while in [20] and [13], authors develop
models that allow the BS to select appropriate single data
transmission rate based on the exponential moving average
received throughput of each user inside the cell. Another
important but yet rarely researched area is physical layer
multicasting using multiple antenna where users’ average
signal-to-noise ratios (SNR) is used to determine the group’s
single transmission rate [23]–[25].
In [24], authors show that capacity maximization based on
SNR averaging provides higher capacity than LCG scheme
and further justifies that under certain scenarios, when users
are mobile, SNR averaging corresponds to the LCG scheme.
However, studies by Sun et al. [23] differ from [24] by
showing that not only does the LCG scheme offer practical
implementation benefits, but also satisfies the QoS of each
user. Interestingly, results of [23] is only valid provided the
optimized LCG SNR meets the threshold required for successful reception. Fundamentally, concept of group throughput
or group SNR averaging premise on guaranteeing reliable
transmission and successful decoding to half the user in
the system. This overtly optimistic scheme invariably means
certain packet loss is inevitable, especially for users far from
the central BS who cannot cope with the high average group
rates.
B. Multi-Rate Multicast Transmissions & Group Formation
Multi-rate multicast transmission emerges to address the
sub-optimality that exists in single-rate transmission considering the intrinsic heterogeneous channel characteristics
of wireless networks. This diversity, if not well addressed
A. Suboptimal Strict Throughput Single-Rate Algorithms
Suboptimal algorithms for multicast-based resource allocation in existing literature can be differentiated based on two
basic properties: The reduction assumptions towards simplifying the complexity of the problems, and the isolation methods
used to divide the problems into independent steps such that
each step has polynomial complexity. For the first, subcarriers
are assigned to each group with objective of maximizing total
system capacity. This step assumes that total system transmit
power is evenly distributed over all subcarriers. In the second,
transmit power is optimally allocated to each preselected
subcarrier using Lagrange multiplier method or the KarushKuhn-Tucker (KKT) conditions [63] - which interestingly, is
similar to the conventional waterfilling rule - to enforce group
rate proportionality.
These two steps are usually adopted, however, the difference
is the techniques used to assign subcarriers, which we shall
discuss in detail. For instance, [7], shows that if equal power is
applied to selective subcarriers with good channel gains, total
throughput of zero pathloss difference of suboptimal heuristic
scheme approximates the performance of the optimal scheme
even with flat transmit power spectral density (PSD). This simple approach is an example of strict throughput maximization
which reduces computation complexity mainly to subcarrier
allocation and eliminates need for power allocation. When
we consider multiple multicast services, complexity increases
because we need to determine which group receives the best
subcarrier in each iteration. This subcarrier allocation decision
is determined by the system objectives possibly formulated in
terms of strict throughput maximization or fairness of access
to network resources.
This case was further studied in [19] where subcarrier n is
allocated to group g having potential maximum data rate as
given in eqn. (8). This is equivalent to assigning subcarrier
n to group g with maximum SNR or highest channel gain
noting that each group rate is based on worst channel user.
Similar works for single multicast MIMO using spatial multiplexing and multi-multicast MIMO using weighting precoding
are done in [5] and [16] respectively. These works further
define two additional approximations for eqn. (8), which are
functions of the eigenvalues of the channel matrix for the low
and high SNR regions where the SNR is close to zero and
>> average SNR respectively.
max
g∈G
(Rg,n)=|Kg| log2 1 + N1 g,nPT otal (8)
The significance of these approximations is the reduction in
computation complexity of the algorithm in the SNR extremes.
In contrast to LCG user where performance degrades as the
number of users increase, these schemes achieve higher system
capacities even at the low SNR region since groups with better
channel condition always have resources. Results in [5] also
show that as the channel power gap increases larger gains is
achievable.
As with all STM objective functions, fair access to system resources between groups with diverse carrier-to-noise
ratio (CNR) is not considered. If the link difference among
multicast group is large, group with high CNR will dominate
the resource for a large amount of time, leaving groups with
low link quality to starve. For example, schemes in [5] can
potentially shut out groups with poor channel gain or fewer
numbers of users since it is based on maximum aggregate
data rate which increases as users per group and channel
gain increase. Tables II shows summary of suboptimal strict
throughput single-rate algorithms.
B. Suboptimal Max-Min Fair Single-Rate Algorithms
One possible way to prevent greedy resource utilization
by HCG groups and maintain balance between throughput
maximization and fairness is to impose minimum number of
subcarrier to allocate to each group. Ngo et al. [7] shows
that by adding one more constraint as shown in eqn. (9)
to constraints in (5)-(7), certain level of flexibility and fair
resource access can be assured.
N n
=1
δ
g,n ≥ αg|G g=1 , (9)
where 0 ≤ αg ≤ N, G g=1 αg ≤ N, and αg is the minimum
number of subcarrier to assign to each group.
Interestingly, the total capacity result of the suboptimal
fair scheme approximates performance of the suboptimal
strict throughput even at 2.5dB pathloss difference. However,
determination of the optimal choice of αg is not trivial because
if α
g → 0, problem becomes strict throughput whereas, the
problem becomes strict fairness if αg → MG .
A compensation approach was proposed in [6], [26] where
fairness is enforced by compensating each group for low rate
- relative to the target rate required by the group - by moving
them to better subcarrier with higher CNR. That is, in the
next transmission of each multicast group, subcarrier having
maximum channel gain (best subcarrier) is assigned to the
group with least data rate in the previous transmission. In
addition to showing intergroup relationship that may exist in a
cell, this approach ensures that no group dominates the system
resources and low rate groups do not experience outright
resource starvation.
1) Max-Min Fair & QoS Considerations: Besides throughput and fairness system objectives, it is equally important
to provide satisfying quality of service to users because bad
QoS affects users’ level of satisfaction and defeats the system
purpose. One way to achieve this is to ensure that achievable
rates for each single-rate multicast group satisfy the minimum
rate requirements of contents served. In [56], the following
constraint is added to constraints (5)-(7):
R
g,n ≥ Rg,n min 1 ≤ n ≤ N, (10)
where Rmin
g,n is the least data rate requirement to satisfy users’
QoS requirements. Resulting optimization solution guarantees
acceptable service quality if LCG users experience good
channel quality but it invariably results in absolute resource
starvation for all group members once the minimum user in
the group cannot satisfy own rate requirements. Hence, in low
SNR regime where LCG user’s data rate is less than QoS
requirement, system performance degradation may result.
To satisfy the QoS requirements of users in a multicast
group, [15], [65] applied IDT and redefined the base stream
as the minimum rate all users must receive to satisfy QoS
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