Joint Scheduling and Resource Allocation with Fairness Based on the

Signal-to-Leakage-plus-Noise Ratio in the Downlink of CoMP Systems1

Rana A. Abdelaal2, Khaled Elsayed and Mahmoud H. Ismail

rabdelaal@ieee.org, khaled@ieee.org, mhismail@ieee.org

Department of Electronics and Communications Engineering, Cairo University

Giza, Egypt, 12613

Phone: +202 3567 8839, Fax: +202 3572 3486

Abstract

Recent research has shown that Coordinated Multi Point (CoMP) transmission can provide significant

gains in terms of the overall cell capacity and cell-edge user throughput [1]. The main purpose of this

paper is to enhance the overall cell throughput, the cell-edge user’s throughput, and the fairness among

user equipment terminals (UEs) in LTE-Advanced (LTE-A) systems using CoMP. Towards that end, we

propose two novel Resource Allocation (RA) strategies based on the Signal-to-Leakage-plus-Noise-Ratio

(SLNR) for the downlink of CoMP transmission in LTE-A systems. The proposed RA strategies select

the UEs that can efficiently share the same resource block (RB) without degrading the overall throughput

by using the SLNR metric. Moreover, a fairness algorithm is proposed to achieve certain level of fairness

among the UEs and to improve the cell-edge UEs throughput. In addition, we compare the proposed

strategies to the RA based on the more common Signal-to-Interference-plus-Noise-Ratio (SINR) strategy.

The SLNR-based RA is shown to provide significant gains in throughput reaching up to 80% in the

overall system and is shown to have even less complexity than the typical SINR-based RA. Moreover, by

evaluating the proposed strategies in terms of the average cell throughput, cell-edge user throughput, and

fairness among UEs, simulations show that the proposed strategies present superior performance

compared to the more common SINR strategy. With such advantages as enhanced throughput and lower

complexity, the proposed schemes are suitable for application in practical cellular systems.

Keywords: Coordination; coordinated multi point transmission; cellular networks; LTE; interference

mitigation; Resource Allocation; fairness.

1. Introduction

Recent advances in wireless communications such as the use of multiple-input-multiple-output (MIMO)

systems and orthogonal frequency division multiplexing (OFDM) have managed to reduce the detrimental

effect of fading in wireless communication systems. Consequently, the capacity of modern wireless

cellular networks is now mainly restricted by inter-cell interference (ICI). Typically, in cellular systems, a

geographical region is divided into cells, which handle ICI through the use of pre-defined frequency reuse

patterns [2]. Although these frequency reuse schemes result in an inefficient use of the available

1 This work is part of the 4G++ research project supported by the National Telecom Regulatory Authority (NTRA)

of Egypt.

2 Rana A. Abdelaal is the corresponding author.

bandwidth, they guarantee that near cell-edge users belonging to adjacent cells do not share similar

frequencies and thus, have limited ICI. Recently, as bandwidth progressively becomes a more scarce

resource, future cellular networks shift gradually closer to the maximal frequency reuse of unity [3].

Consequently, efficient resource allocation (RA) will play an essential role in future networks in order to

guarantee that the interference level does not excessively increase.

One of the key enabling technologies that is proposed to be used in the next generation cellular system

known as LTE-Advanced (LTE-A) in order to overcome the problem of excessive ICI due to the unity

frequency reuse is coordinated multi-point (CoMP) transmission. CoMP targets increasing the average

cell and cell-edge user throughput, through limiting the ICI. There have been several previous studies in

the literature, which show that CoMP could provide significant gains in terms of achievable throughput

resulting in meeting the requirements of IMT-Advanced for next generation wireless systems [4]. These

works will be briefly covered in the following subsection.

1.1. Prior Work on CoMP

The basic idea of CoMP is to eliminate ICI through cooperation between a number of base stations (BSs)

or enhanced Node-Bs (eNBs), across several cells or sectors, under the command of a central entity that

turns interference into a useful signal. As an alternative CoMP architecture, cooperation can be achieved

inside a specific cell, where the cell can consist of several remote radio equipment (RREs), which can be

connected to a central BS or eNB (like in Fig. 1, for example). The main objectives of CoMP are to

mitigate the interference; provide high spectral efficiency over the entire cell area; and increase the

overall throughput, especially the cell-edge throughput [5]. This is made possible through the exchange of

data, control information as well as channel state information (CSI). This exchange of information occurs

over the interface connecting the central BS and the RREs (or the multiple BSs), which can be

implemented through the use of optical fibers or via dedicated radio thus making high-speed transfer of

signals possible. Full coordinated transmission is achieved among the RREs (or the BSs) through unified

radio resource management (RRM) at the central BS/eNB (or the central entity) [4]. Although CoMP

naturally increases the system complexity, it provides significant capacity and coverage benefits, making

it worth considering for constructing high capacity cellular systems [6].

The coordination in CoMP can be simple as in the techniques that focus on interference avoidance or

more complex as in the case where the same data is transmitted from multiple transmission sites. Based

on that, two approaches for CoMP are often considered. The first approach is coordinated scheduling

(CS) and the second approach is joint processing (JP), respectively. The main difference between both

approaches is the level of coordination between the transmission points. It has been previously shown that

optimizing RA for both CoMP approaches can provide high gains in terms of total throughput and

capacity enhancement.

eNB

RRE RRE

RRERRE

RRE RRE

Figure 1: Example of the proposed cell model

In CS CoMP approach, the transmission to a single scheduled UE is performed by a unique transmission

point (each UE receives the data from its serving cell only). However, the scheduling, including any

transmission weights, is dynamically coordinated between several transmission points in order to control

and/or reduce the unnecessary interference between different transmissions. In principle, the best serving

set of UEs will be selected so that the transmitter beams are constructed to reduce the interference on

other UEs, while increasing the served UE’s signal strength. Hence, the cell-edge user throughput can be

improved due to the increase in the received Signal-to-Interference-plus-Noise-Ratio (SINR). CS

approach has been studied extensively in [7-8], and it has been shown that it can achieve relatively good

performance in terms of throughput and spectral efficiency.

On the other hand, in JP CoMP approach, the data is simultaneously transmitted from multiple

transmission points to each UE. In other words, multiple transmission points are allowed to transmit the

same data to a single UE simultaneously over the same resource block (RB). In the context of LTE-A, an

RB is a collection of subcarriers that are handled together as an allocation unit available for data

transmission. When an RB is allocated to a certain UE, this means a definite frequency channel is

assigned to this UE [8]. Thus, in JP, the multi-point transmitters will behave like a single transmitter with

antennas that are geographically separated. This scheme has the potential for higher performance,

compared to coordination only in the scheduling, but comes at the expense of more stringent requirement

on the backhaul communication between the coordinating transmission points in order to share the data to

be transmitted. A JP scheme has been proposed in [8] and it has been shown that this scheme can bring

significant gains to both the average cell throughput and the cell-edge user throughput. The authors of [9]

focus on the availability of the CSI that allow BSs to coordinate. They show that although CoMP might

require a relatively moderate amount of backhaul communication, it can be quite powerful in terms of

capacity enhancement.

1.2. Review of Resource Allocation Schemes for CoMP

Lots of works in the literature have proposed various RA algorithms in conjunction with either CS-CoMP

or JP-CoMP. For example, in [10], an RA model based on the graph coloring problem has been studied

for the downlink of a JP system with carrier aggregation. It has been shown that their RA model can

efficiently be used in the downlink of JP system. This is because it can mitigate interference, which

maximizes the performance of both the network and individual UEs. Likewise, the authors in [11]

consider an RA algorithm for CS system. They focus on the overall network capacity as a measure of

system performance. It has been shown that optimizing the RA problem promises significant gains in

network capacity and system throughput. In [12], the authors discuss the RA problem in case of

coordination across BSs equipped with multiple antennas. An iterative based RA algorithm is presented.

It has been shown that the proposed algorithm is efficient and can provide appreciable performance

improvement. In [13], an RA technique was proposed for the downlink of a CS system. Although the

simulation results presented show high gains in terms of throughput, the discussed RA technique has two

main drawbacks. First, it calculates the SINR for all UEs over all the available RBs in order to allocate

the RB, which provides the highest SINR value to each UE. This allocation process is not practical as it

requires extensive computations and signaling of channel states and leads to excessive delays. The second

drawback is that the proposed allocation method does not maintain fairness among UEs. For example, if a

certain UE has a good channel (relatively good SINR), there is nothing in the algorithm proposed in [13]

that prevents allocating most of the available RBs to such a UE. In that case, the other UEs may not get

the chance to be served.

The authors in [14] proposed a JP scheduling algorithm where the BSs are grouped into a static cluster. It

has been assumed that each UE is served by all the BSs within the same cluster. The cell model proposed

is a centralized model, where there is a central scheduler available in each cluster that has the knowledge

of the CSI of all UEs being served by the same cluster. In addition, it is responsible for managing all the

resources of the cluster. Once the central scheduler has allocated the resources to the scheduled UEs, the

information of the RA is distributed to the rest of the BSs. The model proposed in [14] has two main

drawbacks. First, the scheduling information is assumed to be sent from the central scheduler to the rest

of the BSs over the X2 interface. Since large amount of data needs to be sent, intolerable delays could

occur and large-bandwidth connections are needed. The second drawback is that only the central

scheduler is responsible for allocating resources, so scheduling is done by only one BS, not jointly. This

scheduling is not necessarily efficient for the rest of BSs belonging to the same cluster.

Also, in [15], an implementation of a JP system has been tested using real-world channels and it has been

shown that JP can indeed improve the total throughput in real-world implementations. In addition, in [16],

a RA algorithm that allows RB sharing among UEs is proposed for the CoMP scheme. The algorithm

selects a group of UEs to share each available RB. The UEs with high SINR values over a certain RB are

grouped and served over this RB. The main disadvantage of this algorithm is that the group of the UEs

sharing the same RB will interfere on each other thus limiting the achieved throughput.

In [17], the authors present RA schemes to enhance the performance of CoMP systems. Their proposed

schemes provide a trade-off between system throughput and energy saving. Also an algorithm to enhance

fairness among UEs by reducing the UE starvation that may result due to allocating resources to the best

UEs is also presented. Simulation results are presented to confirm the performance in terms of system

throughput and fairness to UEs. Also in [18], RA algorithm for JP CoMP is proposed with the aim of

scheduling UEs to maximize the system throughput. The proposed algorithm consists of proportional fair

scheduling and precoding algorithm that allows each UE to be scheduled either in a single-cell or multi-

cell mode. The logarithmic relationship between rate and SINR has been used in the problem formulation.

Thus, the proposed algorithm aims at maximizing the throughput through maximizing the SINR. The

optimal solution can be obtained using exhaustive search over all possible scheduling combinations.

However, as the number of UEs grows, this incurs significant search complexity so they have proposed a

heuristic solution since the optimal solution is difficult to obtain.

1.3. Contributions

Typically in the literature, and as can be seen from the literature survey provided above, CS and JP RA

schemes are based on the use of the SINR as the performance metric that needs to be maximized in order

to increase the overall cell throughput. However, the problem of maximizing the SINR for each UE is

known to be challenging and complicated due to its coupled nature and no closed-form solution is

available yet. Instead, our work at hand is based on the maximization of the Signal-to-Leakage-plus-

Noise-Ratio (SLNR) metric, which was first introduced within the context of MIMO systems in [19].

Leakage refers to the interference caused by the signal intended for a desired UE on the remaining UEs in

the cell. In [19], the SLNR metric has been used for designing precoders with the aim of comparing with

zero forcing precoding in terms of complexity and the conditions on the number of transmit and receive

antennas. However, in this work, we use the SLNR metric with different perspective and different

objectives as will be shown later. It was shown in [19] that the use of SLNR as an objective metric

outperforms the conventional SINR. Furthermore, the leakage-based criterion leads to a decoupled

optimization problem and admits an analytical closed-form solution for the precoders design [20].

One important note is due here, although the relationship between the SLNR and the throughput is not

straightforward, it is very intuitive to conclude that by increasing the SLNR metric, the throughput will be

enhanced. As will be shown in the sequel, maximizing the SLNR is even significantly less complex than

maximizing the SINR metric of all UEs in a specific cell and leads to even better results in terms of the

achieved average cell throughput. Motivated by that, we propose two novel RA strategies for the

downlink of the CoMP system in LTE-A system, which select the UEs that can efficiently share the same

RB without degrading the overall throughput by using the SLNR metric. Thus, we do not need to

calculate all the SINR values for all UEs over all RBs as in [9-13]. Moreover, an algorithm is proposed to

achieve some degree of fairness among the UEs and to improve the cell-edge UEs throughput, a problem

that has not been tackled in [13]. The proposed model assumes coordination between RREs, thus high

speed links, such as optical fibers or dedicated radio links, can be used to connect RREs to the BS.

It is important to note that all of the prior works (with the exception of [11]) assume centralized

algorithms. Thus, even though they can achieve relatively good performance, they are too complicated to

be implemented in practice. In contrast, in this work, we assume a distributed RA algorithm. Thus, the

RA problem is solved jointly by all RREs belonging to the cell, instead of assigning resources only in a

central unit. Also, our proposed RA algorithm is more reliable since it does not depend on a single unit

only. Moreover, all of the RA algorithms in the prior work excluding [16] assume that only one UE is

allowed to use each RB. However, our proposed RA algorithm does allow a group of UEs to utilize the

same RB. Thus, it is expected that the proposed algorithm will provide better data rate. In addition, none

of the prior work discussed in the previous subsection considered fairness among UEs except for [17].

However, in this paper we take fairness among UEs into consideration as will be discussed in details in

Section 4.

It is worth mentioning, that the main concept behind the work done in [18], is the possibility of achieving

higher sum rate in some cases using single transmission point without coordination as compared to JP

CoMP. This basically happens under the assumption that there is no RB sharing. In that case, two

scenarios can happen for each RB: the cell can allocate the RB to one of its UE on a single cell mode, or

the cell can help a UE belonging to a neighbor cell by performing JP CoMP. Based on the channel that

each UE experience, a dynamic switch between non-CoMP (setup A) and CoMP (setup B) may possibly

lead to higher overall rate. However, in our proposed solution, RB sharing is allowed. Thus, a more

sophisticated setup can be achieved: setup C, where each cell can allocate the RB to more than one UE by

using JP CoMP. As will be discussed later, the group of UEs selected to share the RB, are the UEs that

interfere the least on each other. Thus, this new setup will definitely lead to higher throughout than setups

A and B. Essentially, dynamic switching between non-CoMP and CoMP does not apply to our work.

Please refer to Fig. 2 for explanation of setups A, B, and C.

In order to demonstrate the efficiency of the proposed algorithms, we present a comprehensive

comparison between four RA strategies; both proposed CS and JP schemes based on SLNR and both CS

and JP schemes based on SINR that has been addressed in [16]. By evaluating the proposed RA strategies

and fairness algorithm with different realistic propagation scenarios proposed in [21], we show significant

enhancements in terms of the cell throughput, the cell-edge user throughput, and fairness among UEs.

The remainder of this paper is organized as follows. Section 2 details the system model under

investigation. Section 3 provides the proposed resource allocation strategies. In Section 4, we discuss the

fairness algorithm and apply it to the proposed RA strategies. Section 5 discusses the simulation results,

both in terms of throughput enhancement and in terms of fairness. Finally, we draw the main conclusions

with suggestions for future research in Section 6.

2. System Model and Assumptions

In this section, we present certain important aspects of the CoMP LTE-A system design and the model

adopted to evaluate the performance of the proposed strategies is presented. We consider a cellular system

where each cell consists of one eNB, M RREs under its control, and serves K single-antenna UEs. An

example of such cell is shown in Fig. 1. There exists N RBs in the system and each of them may be

assigned to one or more UEs. We consider a 20 MHz bandwidth, consisting of 100 RBs, each RB consists

of 12 subcarriers with 15 kHz spacing, which are typical values for an LTE-A system. Channel coherence

bandwidth is assumed to be larger than the bandwidth of the RB leading to flat fading over each RB.

Uniform power allocation among RBs is considered and the overall transmit power available for each

RRE (P) is uniformly divided among the N RBs. So, the power allocated to each RB is simply Pn = P/N

(assuming all RBs are utilized by the RRE). Each RRE is assumed to have a single antenna and the UEs

are assumed to be uniformly distributed over the cell coverage area.

Figure 2: Setups A, B, and C

The classical solution for cooperating in CoMP is, as mentioned before, based on the SINR. The received

SINR at the nth RB of the kth UE is given by:

| |

∑ | |

(1)

where , is complex channel vector of the links between the kth UE and

all M RREs of the CoMP cell (as shown in Fig. 3), is the Additive White Gaussian Noise (AWGN)

power at the kth UE. is an weighting (precoding) vector that shapes the data transmitted from

the M RREs to the kth UE. The choice of the weighting vector depends on the used scheme (CS or JP) as

will be discussed in more details in Section 3.1.

Figure 3: System Model

In (1), a single RB is considered and its index (n) is dropped for simplicity of notation. As shown in (1),

the unknown variables that need to be optimized via coordination are the weighting vectors for all UEs

( in the numerator and the summation over in the denominator). Consequently, in order to select

that maximizes

for each UE, all the weighting vectors for the rest of the UEs must be taken into

account in the optimization problem. The optimal solution for such a problem is indeed NP-hard [22]. In

contrast, in this paper, the SLNR is considered as the performance metric. The SLNR (βk) at the kth UE

over the nth RB can be expressed as:

β

| |

∑ | |

(2)

As shown in (2), the numerator represents the signal intended for the kth UE and the first term in the

denominator represents the leakage caused by the signal intended for the kth UE on the remaining UEs.

The leakage concept is illustrated in Fig. 4. It can be noted that the summation in the denominator is over

instead of as in (1), which greatly reduces the computational complexity as will be shown later in

the sequel. It is thus considered more suitable for RA in practical cellular networks. The choice of the

weighting vectors { } as well as the scheduling of the UEs as proposed in this paper will be targeting

the maximization of the SLNR:

Maximize β

subject to ‖ ‖ .

(3)

The solution to this problem will be shown in the next section for both CS and JP schemes. Finally, the

achieved throughout for the kth user is given by:

∑

(4)

where is the rate achieved by the kth user over the nth RB and = zero if the kth user is not

allocated the nth RB. The overall cell throughput is thus obtained as:

∑ ∑

(5)

The achievable rate by the kth UE is directly proportional to its SINR by Shannon formula:

(6)

It is important to note that during the RA algorithm, the rate is computed according to (6). However,

while evaluating the system performance, the rate is computed differently since it depends on the

modulation and coding scheme (MCS) used. The MCS is selected according to the channel quality

indicator (CQI) that is available at the eNB through feedback. According to the LTE standard, a CQI table

of 15 entries is used, in which each CQI index refers to a specific channel coding rate and a modulation

order (QPSK, 16 QAM, and 64 QAM).

Figure 4: The leakage concept.

3. The Proposed Resource Allocation Strategies

In this section, the proposed RA strategy is discussed. The general aim of allocating resources in a CoMP

system is to maximize the throughput by reducing the interference effect, so our proposed strategy aims at

maximizing the throughput per RB, which directly leads to maximizing the overall throughput achieved

by the entire bandwidth. For each RB, a set of UEs will be selected to have their data

transmitted over the same RB. Scheduling decisions can be taken to dynamically determine which UEs

can simultaneously use the same RB.

3.1. Selection of the Weighting Vectors

In case of the CS scheme, the weighting vector determines which RRE should serve a specific UE. It is

assumed that all RREs have perfect knowledge about all channel parameters. Since, in CS, each UE is

served by only one RRE, then all the elements in are zeros except only one element will be equal to

unity, which corresponds to the serving RRE. The index of the serving RRE can be easily obtained by

solving the optimization problem in (3) through a simple exhaustive search procedure. On the other hand,

in the case of the JP scheme, the same data packet is sent to a specific UE from all RREs and thus is

not easily obtained as in the case of CS. This optimization problem has been solved in [19] in the context

of MIMO systems and the solution was found to be:

((| |

)

) , (7)

where is the identity matrix, is the eigenvector corresponding to the maximum eigenvalue

of the matrix computed in (7), and is a matrix given by:

[ ] , (8)

It is worth noting that since we assume equal power allocation, there is no need to include the power term

in designing the weighting vectors. Thus, the weighting vectors are normalized. It is also worth

mentioning that the scheduled UEs channel qualities is taken into consideration in the selection of the

weighting/precoding vectors through maximizing the SLNR. As shown in (2), the numerator of the SLNR

contains , which reflects the channel qualities of each UE. Selecting the maximum SLNR for each UE

will guarantee the selection of the best RRE(s) to serve each UE in the CS and JP CoMP schemes,

respectively. Secondly, the intended signal to each scheduled UE is accompanied by a

leakage/interference on other UEs. So, by considering the minimum leakage values from all the scheduled

UEs, we actually consider their channel qualities indirectly.

3.2. The Grouping Algorithm

The task of the grouping algorithm is to select the UEs that can efficiently share the same RB without

degrading the overall throughput. In other words, the UEs that leak the least on each other should be

assigned the same RB. In that way, the overall throughput will be enhanced and the available bandwidth

will be efficiently utilized. In both of the CoMP schemes proposed earlier, the grouping algorithm is the

same. The following steps will be repeated for every RB available. The set of UEs S is initialized to the

empty set and in both schemes will be populated via the following algorithm:

Algorithm 1: Grouping Algorithm based on Leakage

Initialization: (β )

{ } while stopping condition is not satisfied do

( )

End

The first step in the algorithm is the initialization; the UE with maximum SLNR will be chosen and set to

be the first item in the set : The UE with maximum SLNR is the one that has a relatively strong direct

channel and also has relatively low interference on other UEs. Hence, it is the UE that will leak the least

towards other UEs when sharing the RB with them. The initial element in will thus be chosen. Second,

the leakage value vector from all the elements in the set in the direction of the rest of UEs will be

computed. Leakage refers to the interference caused by the signals intended for the UEs belonging to on

the remaining UEs. The interference on UE due to the leakage from the UEs belonging to the set

can be calculated as follows:

∑ | |

(9)

where is calculated for all UEs that do not belong to the set , i. e., The UE with the

minimum amount of leakage will then be added to the set . Thus, the UE that will be affected the least

will share the RB with the UEs belonging to the set. Finally, the algorithm will continue grouping UEs till

a certain condition is satisfied. The stopping criteria are described in details in the next subsection.

3.3. The Stopping Criterion

Selecting the stopping criteria is a very important issue as it directly affects the overall achieved

throughput. We propose and investigate a number of stopping criteria as follows:

1. Marginal Utility: In this method a utility function is defined as the log function of the achieved

throughput [23], i. e.,

( ) (10)

and the following condition is checked so as to allow sharing the RB (to allow grouping):

,

(11)

where is the utility function of the UE that is currently being tested whether or not to be

added to the set, is the sum of the utility functions of the UEs that have been previously in

the group (excluding the newest UE) computed after adding the new UE and taking its

interference effect on the attainable throughputs, and is the sum of the utility functions of

the UEs in the set computed before adding the new UE. If (11) is satisfied then this UE (newest

UE) will be added, otherwise the grouping will be terminated. This approach is efficient and

provides high overall throughput gains but it does not take into consideration the case when the

throughput drops by adding a particular UE while it has not yet reached the maximum throughput

(global maximum to be reached) and so the algorithm might terminate early before reaching the

highest achievable throughput.

2. Marginal Utility with look-ahead: In this method, the same marginal utility condition in (11) is

used. However, if the condition is not fulfilled, we choose to go one level deeper into the test. In

particular, we construct a temporary set that includes the original set plus the ith UE, which is the

UE that may or may not be added to the set. Then the (i+1)th UE will be selected and the

marginal utility condition in (11) will be again checked for the temporary set with the (i+1)th UE.

If it is still not satisfied, the algorithm will terminate with the original set (not the temporary).

However, if the condition is fulfilled then the algorithm will terminate with a new set, which is

the union of the temporary set and the (i+1)th UE. This algorithm is described in more details in

Fig. 5. In general, this algorithm can include more than two stages of look-ahead; however, the

algorithm with two stages has presented high gains in terms of throughput as will be shown in

Section 5.

This stopping condition is efficient as it does not terminate once the throughput decreases as in

[16], neither does it terminate once the utility function-based condition is unfulfilled as the

marginal utility stopping condition does. Although this stopping condition is suboptimal, it is

practical and leads to high throughput gains as will be shown in Section 5.

3.4. Computational Complexity Comparison

As shown earlier, in the proposed RA strategies, the weighting vector is selected in order to maximize

(2). Maximizing the SLNR metric ( for the kth UE indeed requires less number of computations

compared to maximizing the SINR for the same UE. This is because maximizing the SLNR for each UE

is an independent process. In other words, maximizing the SLNR for a certain UE requires checking all

possible links only for this UE, and no need to check other UEs links. This is because SLNR measures the

amount of signal power indented for this UE versus the amount of leakage on other UEs due to that link.

Temp set = UE set + UE i

UE i+1

UE set UE i

o/p set = UE set + UE i

Not Satisfied

Marginal Utility condition

Satisfied

Marginal Utility condition

o/p set = Temp set + UE i+1Satisfied

o/p set = UE set

Not Satisfied

Figure 5: Marginal utility with look-ahead flow chart

In contrast, maximizing the SINR metric is much more complex process; as the SINR for each UE cannot

be optimized independently. This is because the interference at each UE is dependent on the other UEs

links. Thus, to optimize the SINR for a certain UE, an algorithm should try linking this UE with all

possible links. Also, for each possibility it should try linking other UEs with all possible links.

Consequently, the proposed strategies computational complexity is greatly reduced by considering the

SLNR as the main metric. For example, the complexity order of maximizing the SINR metric for each UE

assuming K UEs and M RREs and the CS strategy is as follows:

Number of computations in SINR-based RA

,

, otherwise.

(12)

This is because in order to maximize the SINR for a specific UE, two stages are needed. The first is to try

linking this specific UE to all RREs in the cell. The second is that while this specific UE is linked with

any RRE, all possible links between the rest of UEs and the rest of RREs should be checked. The number

of computations for the first stage is M in both cases mentioned in (12). However, the number of

computations for the second stage depends on both M and K. When , the second stage actually will

need the same number of computations for selecting RREs from the available RREs to

serve the UEs existing in the cell. Moreover, the order of selection should be taken into account.

Consequently, the number of computations for the second stage will be -permutations of

in case . When , the second stage will need the same number of computations for selecting

UEs from the available UEs to be served by the available RREs existing in the cell.

Moreover, the order of selection should be taken into account. Consequently, the number of computations

for the second stage will equal -permutations of ) in case . By multiplying the

number of computations of both stages and using the basic definition for permutations, (12) can be

obtained.

On the contrary, the complexity of maximizing the SLNR metric for each UE considering the same model

as above is simply of order M. In order to overcome the high computational complexity of maximizing

the SINR at each UE, some papers select the weighting vectors that are corresponding to the maximum

channel gain, such as in [16]. However, selecting the weighting vectors in that way does not take into

consideration the interference channels. In contrast, our proposed model maximizes the SLNR metric for

each UE, which checks the interference channels as well as the direct channel.

4. The Resource Allocation Algorithm with Fairness

The objective of the proposed fairness algorithm is to provide a certain level of fairness among UEs.

Since our proposed resource allocation strategies based on SLNR assure that each RB achieves relatively

high throughput, the overall throughput is optimized. In this section, our algorithm will be updated to

assure that the RBs are efficiently allocated to the UEs with fairness taken into account. Simulation

results have shown an improvement in the fairness among users as will be shown in the sequel.

Initially: Construct the fairness vector F that counts the number of RBs that has been assigned to

each UE in the cell, viz., [ ], where is the number of RBs allocated to the kth UE. In

addition, the weighting vectors are selected so as to maximize the SLNR (β as before. The

following algorithm will be executed:

Algorithm 2: Grouping Algorithm based on leakage and fairness

For n = 1 : N

(β )

= + 1

Normalize F and

While stopping condition is not satisfied

( )

F( ) = F( ) + 1

Normalize F and

End While

End For

The first step in the algorithm is adding the UE with the maximum β

to the set as discussed earlier.

Following that, the fairness vector F will be updated, such that

(13)

where is assumed to be the UE with the maximum β . The leakage vector from in the direction of the

rest of UEs will then be computed as discussed earlier in Section 3.1 and both the leakage and fairness

vectors will be normalized such that

and

(14)

where [ ], [ ] is the maximum element in the fairness vector

and is the maximum element in the leakage vector. The UE that is corresponding to the minimum

element in the vector [ ] will then be added to the set . By that step, the UE

that has been allocated relatively less number of RBs compared to other UEs and is affected with

relatively low leakage from the set is the one selected to join the set . This will guarantee some

fairness among UEs as it prevents allocating most of the available RBs to UEs with good channels.

Consequently, cell-edge users will get the chance to be served, unlike the RA algorithm in [13]. The

algorithm will then keep adding UEs till the stopping criterion is satisfied. The stopping criterion could be

any one of those discussed in details in Section 3.2. Since the fairness vector controls allocating resources

to UEs, the algorithm above should be repeated for all the available RBs. It worth noting that, the fairness

vector should not change until allocating all available RBs, because it is the only indicator on the number

of RBs allocated to each UE. By applying the fairness algorithm, both CS and JP schemes have provided

better fairness to the UEs as will be evident from the results shown in Section 5.

5. Simulation Results and Analysis

The RA strategies described in Sections 3 and 4 are now evaluated in this section through simulations. In

order to capture the impact of long term propagation effects on the system performance, several snapshots

are simulated and the results are averaged. To evaluate the performance of our proposed strategies, we

simulate a cellular system with the parameters shown in Table 1. In our simulations, we consider two

typical propagation scenarios; the typical urban macro-cell model and the bad urban macro-cell model,

which is same as the typical urban macro-cell scenario plus long delays. Both models are based on the

WINNER channel model [21]. It is worth noting that the number of UEs sharing the same RB | | is

restricted by the number of RREs in the cell in case of the CS scheme. That is due to the fact that, each

RRE cannot serve more than one UE over the same RB. However, there is no such limitation in case of

JP.

Table 1: Main Simulation Parameters

Parameter Value

Number of RREs per cell 6

Carrier Center Frequency (GHz) 2

Subcarrier spacing (KHz) 15

Number of RBs (N) 100

Number of subcarriers per RB 12

System bandwidth (MHz) 20

Propagation Scenarios Typical urban macro-cell and Bad urban macro-cell [21]

Number of antennas per UE One

Number of antennas per RRE One

Power distribution among RBs Uniform

UEs distribution among cell area Uniform

Scheduling algorithms CS, JP

Used modulation schemes QPSK, 16-QAM, 64-QAM

Number of UEs per set | | Less than or equal to 6 in case of CS and unlimited in case of JP

5.1. RA Strategies Without Applying The Fairness Algorithm

In order to assess the effectiveness of the proposed strategies, we compare them to the algorithms that

have been adopted for CoMP in [16]. This algorithm chooses the weighting vectors corresponding to the

highest channel gains and allocates the available RB to the UE with the highest SINR and continues

allocating the same RB to other UEs as long as the cell throughput increases. Otherwise, it finishes and

goes to the next RB.

Figs. 6 and 7 show the CS schemes with typical urban macro-cell model and bad urban macro-cell model,

respectively. The shown curves in each figure correspond to the proposed CS strategies based on SLNR

with look-ahead and with marginal utility as stopping criteria. The fourth curve corresponds to CS based

on the SINR criterion as outlined above. Both figures present the average throughput per RB, in Kbps, of

the simulated CS strategies as a function of the number of UEs per cell. As shown in both figures, the CS

strategy based on SLNR with marginal utility and look-ahead criterion exhibits an average throughput

gain of 61% as compared to that of the CS based on SINR strategy. Finally, the CS strategy based on

SLNR with marginal utility criterion presents an average throughput gain of 52% relative to the CS based

on SINR strategy. This confirms our intuition that the proposed RA strategies based on the SLNR metric

improve the overall throughput. These results show high throughput improvement, which is due to the use

of the SLNR-based criterion [19].

It is also worth noting that; throughput can be more enhanced as there are still gaps in the curves between

the rate we have reached and the available capacity in case of no interference considered. The rate

achieved in case of neglecting interference is calculated by allocating the same RB to the same UEs

selected using our proposed RA strategies.

Figs. 8 and 9 display the same results above but for the JP schemes. Again, the difference between both

figures is only in the propagation scenario used. From these figures, it is evident that, the JP strategy

based on SLNR with marginal utility and look-ahead criterion presents an average throughput gain of

24% as compared to the JP strategy based on SINR. Finally, the JP strategy based on SLNR with

marginal utility presents an average throughput gain of 7% relative to the JP based on SINR strategy. As

shown, the proposed RA strategies based on SLNR provide higher gains than that of the RA strategy

based on SINR. This is basically due to the accurate choice of the stopping criteria and also for the reason

that the weighting vectors are determined more accurately so as to maximize the SLNR metric for all

UEs.

As can be shown, the CS gains relative to the conventional scheme based on SINR are higher than that of

the JP gains. This is due to the system capacity limitations. It can be shown from both Figs. 6 and 7 that

the CS strategy based on SLNR approaches an average of 74.6% of the throughput achieved assuming no

interference. Also as shown in Figs. 8 and 9, the JP strategy based on SLNR approaches an average of

77.6% of the throughput achieved assuming no interference.

Figure 6: Throughput of the CS strategies in typical urban macro-cell scenario

20 22 24 26 28 30 32 34 36 38 4030

40

50

60

70

80

90

100

110

Number of users per cell

Th

rou

gh

pu

t p

er

RB

[K

bp

s]

CS based on SLNR and look ahead

CS based on SLNR and marginal utility

CS based on SINR

Throughput with no Interference

Figure 7: Throughput of the CS schemes in bad urban macro-cell scenario

Figure 8: Throughput of the JP strategies in typical urban macro-cell scenario

20 22 24 26 28 30 32 34 36 38 40

20

30

40

50

60

70

80

Number of users per cell

Th

rou

gh

pu

t p

er

RB

[K

bp

s]

CS based on SLNR and look ahead

CS based on SLNR and marginal utility

CS based on SINR

Throughput with no Interference

20 22 24 26 28 30 32 34 36 38 40

70

80

90

100

110

120

130

140

150

Number of users per cell

Th

rou

gh

pu

t p

er

RB

[K

bp

s]

JP based on SLNR and look ahead

JP based on SLNR and marginal utility

JP based on SINR

Throughput with no Interference

Figure 9: Throughput of the JP schemes in bad urban macro-cell scenario

It is interesting to observe that in the case of CS, the number of UEs sharing the same RB is restricted by

the number of RREs in the cell, as each RRE can serve only one UE over the same RB. However, in case

of JP, the number of UEs sharing the same RB is not related to the number of RREs, as all RREs are

serving each UE. Consequently, the JP RA scheme leads to higher throughput gains as compared to the

CS, which is evident from the results shown.

5.2. RA Strategies with the Fairness Algorithm

To evaluate the performance of the proposed fairness algorithm discussed in Section 4.1, we consider

three RA strategies. First, we consider our proposed CS based on the SLNR with the look-ahead stopping

criterion. Second, we consider our proposed JP based on SLNR with look-ahead stopping criterion. And

finally, we consider the conventional CS based on SINR for comparison purposes.

Since the main aim of the fairness algorithm is to maintain fairness among UEs specially the cell-edge

UEs, we opt to investigate the UEs throughput cumulative distribution function (CDF) before and after

applying the fairness algorithm. Figs. 10 and 11 display the user throughput CDF for different RA

strategies with/without applying the fairness algorithm. Each CDF plot is the result of 1000 different

channel realizations and for each channel realization, we assume 10 UEs per cell. So the data used for

drawing the CDF curve are 10,000 UEs throughput values. As shown in both figures, the proposed JP

scheme has the best CDF, and the proposed CS scheme has better CDF than the conventional CS based

on SINR.

From the CDF plots, we estimate the nominal cell-edge throughput which we define as the throughput

value which is less than the throughput achieved by 90% of the UEs belonging to the same cell. For

example, consider Fig. 10, which shows that the nominal cell-edge throughput for the proposed CS is 0.5

Mbps and the highest throughput achieved is around 1.2 Mbps. After applying the fairness algorithm, the

nominal cell-edge throughput is still the same 0.5 Mbps as shown in Fig. 11. However, the highest user

throughput is around 0.9 Mbps. So, we conclude from both figures that some of the UEs that are not cell-

20 22 24 26 28 30 32 34 36 38 4060

70

80

90

100

110

120

130

140

150

Number of users per cell

Th

rou

gh

pu

t p

er

RB

[K

bp

s]

JP based on SLNR and look ahead

JP based on SLNR and marginal utility

JP based on SINR

Throughput with no Interference

edge have lost some throughput, which directly means that some RBs have been saved. In order to make

sure that these RBs have been used by the cell-edge UEs, which indicates the achievability of a degree of

fairness, the entire user throughout distribution will be studied.

Considering the JP scheme, as shown in Fig. 10, before applying the fairness algorithm, the nominal cell-

edge throughput can be estimated as 0.75 Mbps and the highest throughput achieved is around 1.8 Mbps.

On the other hand, after applying the proposed fairness algorithm, the nominal cell-edge throughput is not

the same, it is 0.76 Mbps as shown in Fig. 11 whereas the highest user throughput is 1.3 Mbps. So, it is

clear that the cell-edge user throughput is enhanced. However, again the entire user throughout

distribution must be studied.

As shown in Figs. 12a and 12b, which show the probability distribution function of the throughput over

the cell for the CS scheme, most of the cell-edge users after fairness algorithm have a throughput higher

than 0.35 Mbps for the CS scheme. In contrast, most of the cell-edge users without fairness have a

throughput higher than 0.25 Mbps. This observation is valuable as it proves that the RBs saved by some

of the UEs have been allocated to cell-edge UEs, which improves the cell-edge throughput.

Figure 10: User Throughput Cumulative Distribution Curve without Fairness

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1

Throughput Per User (Mbps)

CD

F

CS based on SLNR

JP based on SLNR

Conventional scheme based on SINR

Figure 11: User Throughput Cumulative Distribution Curve with Fairness

(a)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.2

0.4

0.6

0.8

1

Throughput Per User (Mbps)

CD

F

CS based on SLNR

Conventional based on SINR

JP based on SLNR

0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

100

200

300

400

500

600

Throughput Per User (Mbps)

Nu

mb

er

of

Use

rs

(b)

Figure 12: User Throughput Distribution for CS: a) without Fairness; b) with Fairness.

Figs. 13a and 13b show the throughput distribution for the JP scheme. From the figures, it can be seen the

number of UEs that used to have high throughput has been reduced after applying the fairness algorithm.

For example, more than 600 UEs out of the 10,000 UEs have been able to achieve 1 Mbps throughput

without fairness as shown in Fig. 13a. However, only less than 350 UEs have been able to achieve 1

Mbps after applying the proposed fairness as shown in Fig.13b. Obviously, the difference in the

throughput has been given to the cell-edge UEs.

It is also important to study the achievable cell-edge throughput and the average cell throughput for each

channel realization separately. Figs 14 and 15 depict the cell-edge user throughput versus the average cell

throughput before/after applying the fairness algorithm.

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

100

200

300

400

500

600

700

Throughput Per User (Mbps)

Nu

mb

er

of

Use

rs

(a)

(b)

Figure 13: User Throughput Distribution for JP: a) without Fairness; b) with Fairness

As shown in Fig. 14, before applying the fairness algorithm, we can see that most probably the

achievable average cell user throughput for the CS scheme (areas with high intensity of points) ranges

from 0.5 till around 1 Mbps and the cell-edge user throughput ranges from 0.25 till around 0.5 Mbps. In

contrast, according to Fig. 15, after fairness, the most probable achievable average cell throughput ranges

from 0.5 till around 0.9 Mbps and the cell-edge user throughput ranges from 0.35 till around 0.5 Mbps

which emphasizes the fairness enhancement concluded from the CDF curves. In order to further prove

that the proposed fairness algorithm is effective, Jain's fairness index has been computed according to

(15) before and after applying the fairness algorithm.

∑

∑

(15)

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

100

200

300

400

500

600

700

Throughput Per User (Mbps)

Nu

mb

er

of

Use

rs

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

50

100

150

200

250

300

350

400

450

500

Throughput Per User (Mbps)

Nu

mb

er

of

Use

rs

where is the Jain’s fairness index, is the rate achieved by the kth UE, and K is the number of UEs.

Jain’s fairness index for the proposed CS without fairness was found to be 0.6083. On the contrary, it was

found to be 0.8706 after applying the fairness algorithm [24].

As shown in Fig. 14, before applying the fairness algorithm to the proposed JP, we can see that the most

probably achievable average cell throughput (areas with high intensity of points) ranges from 0.8 till

around 1.25 Mbps and the cell-edge user throughput ranges from 0.55 till around 0.75 Mbps. In contrast,

according to Fig. 15, after fairness the most probable achievable average cell user throughput ranges from

0.8 till around 0.95 Mbps and the cell-edge user throughput ranges from 0.68 till around 0.8 Mbps, which

again emphasizes the observations obtained from the CDF curves.

Moreover, the Jain’s fairness index was found to be 0.7146 and 0.8830 before and after applying the

fairness algorithm, respectively. In order to assure that our both proposed schemes provide a higher level

of fairness compared to the conventional system based on the SINR, again Jain’s fairness index has been

calculated for the conventional system as well. It was found to be around 0.865, which is less than that of

both proposed schemes with and without fairness. From Figs. 14 and 15, it is interesting to observe that

each point can show the fairness achieved. For example, in case of JP based on SLNR when the average

user throughput is 1.2 Mbps, the cell edge user can achieve only 0.75 Mbps without applying the fairness.

However, with the fairness the cell edge user can achieve about 0.98 Mbps for the same average user

throughput. That clearly indicates the fairness achieved.

It is worth noting that, power management is also an important factor in enhancing the performance of

LTE-A CoMP systems. Thus, optimized power allocation algorithms can be performed on top of our

proposed RA algorithm with the aim of further enhancing the achievable throughput. It has been shown in

[25] that non-uniform power allocation can further improve the system performance.

6. Conclusions and Work Extensions

In this paper, we proposed two novel RA strategies based on SLNR for CoMP systems. We showed that

the use of the SLNR criterion provides significant gains as compared to the more classical SINR one.

Moreover, we showed that the proposed strategies have a significantly less computational complexity.

Using simulations, different stopping criteria have been investigated and it has been shown that using the

marginal utility condition with look-ahead criterion achieves relatively high gains and is efficient. We

also showed that the proposed fairness algorithm can enhance the cell-edge throughput and assure that the

RBs are efficiently allocated to the UEs with fairness taken into account. Future work should consider the

impact of the non-uniform power allocation, where different UEs are being served using different powers.

Figure 14: Cell-edge User Throughput versus Average User Throughput without Fairness

Figure 15: Cell-edge User Throughput versus Average User Throughput with Fairness

0.2 0.4 0.6 0.8 1 1.2 1.4 1.60.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Average User Throughput (Mbps)

Cell

-ed

ge U

ser

Th

rou

gh

pu

t (M

bp

s)

CS based on SLNR

JP based on SLNR

Conventional based on SINR

0.2 0.4 0.6 0.8 1 1.2 1.4 1.60.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Average User Throughput (Mbps)

Ce

ll-e

dg

e U

se

r T

hro

ug

hp

ut

(Mb

ps)

CS based on SLNR

JP based on SLNR

Conventional based on SINR

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