CHAPTER 5

RESOURCE ALLOCATION IN TWO-TIER NETWORKS USING FRACTIONAL FREQUENCY REUSE

5.1 INTRODUCTION

In OFDMA-based two-tier networks such as the macrocell–femtocell networks, co-tier/cross-tier and UL/DL interferences occur only when the aggressor (or the source of interference) and the victim use the same sub-channel. Therefore, it is essential to adopt an effective and robust interference management scheme that would mitigate the co-tier interference and reduce the CTI considerably in order to enhance the throughput of the overall network. As has been discussed in Chapter 2, different techniques such as cooperation among Macro evolved Node B (MeNB) and HeNBs and collaborative frequency scheduling [1], formation of groups of HeNBs and exchange of information (such as path-loss, geographical location, etc.) among neighboring HeNBs [2], power control approach [3, 4], and intelligent spectrum access [5] have been considered in the recent literature to reduce co-tier interference and CTI. However, in this chapter, we concentrate on an interference avoidance technique known as the FFR method (also advocated by Femtoforum in [6]1), which requires minimal cooperation among BSs, has a less complex operational mechanism, and is well-suited for OFDMA-based LTE-Advanced systems.

The basic mechanism of FFR corresponds to partitioning the macrocell service area into spatial regions and each sub-region is assigned with different frequency sub-bands. Therefore, the cell edge-zone MUEs do not interfere with the center-zone MUEs, and with an efficient channel allocation method, the cell edge-zone MUEs may not interfere with neighboring cell edge-zone MUEs. As a result, the cell edge-zone MUEs receive an acceptable signal quality which subsequently reduces the outage probability and increases the network capacity. Note that this type of FFR scheme, when operating on a relatively large time-scale, is referred to as a static FFR scheme. In contrast, dynamic FFR schemes [7] can operate on short time scales and can be optimized for system utility with varying network dynamics. However, they are more complex and less scalable compared to the static schemes.

In this chapter, for OFDMA-based two-tier macrocell–femtocell networks, we evaluate three different static FFR schemes originally proposed for homogeneous networks, namely, strict FFR, soft FFR, and sectored-FFR (in particular, FFR-3) schemes. Also, a new static FFR scheme is proposed in this chapter, which is referred to as the optimal static FFR (OSFFR) scheme. We provide a broad comparison among all these different FFR schemes based on performance metrics such as outage probability, average network sum-rate, and spectral efficiency in two-tier macrocell–femtocell networks.

5.2 DIFFERENT FFR SCHEMES

5.2.1 Strict FFR Scheme

The basic mechanism here is to apply frequency reuse factor (FRF) of one to the center-zone MUEs and FRF of N to the edge-zone MUEs. The available frequency band is partitioned in such a way that, in a cluster of N cells, the center-zone MUEs in each macrocell are allocated with a common sub-band of frequencies while the rest of the frequencies are equally partitioned into sub-bands according to the FRF of the edge-zone and assigned separately to each cell edge-zone of the cluster. Therefore, a total number of (N+1) sub-bands are required. Figure 5.1(a)(i) illustrates a cellular network with strict FFR deployment. Figure 5.1(a)(ii) illustrates a strict FFR deployment scenario with FRF of N=3 to edge-zone MUEs. In Figure 5.1(a)(iii), the vertical bar represents the labeling of different sub-bands that are used by both MeNB(s) and HeNBs in the cluster of cell(s) in Figure 5.1(a)(ii).

In this scheme, the cell-edge MUEs in a macrocell (e.g., macrocell 1) are not interfered by any other MeNB in tier-1. This significantly reduces the inter-cell co-tier interference. Also, since the cell center-zone and edge-zone MUEs use different sub-bands, intra-cell co-tier interference for the MUEs is mitigated. To reduce intra-cell CTI, an HeNB located in the center-zone needs to choose a sub-channel from a sub-band that is assigned to the MUEs in the edge-zone. With N = 3, since only two sub-bands are allocated per cell in a cluster, the HeNB situated in the cell edge-zone has to select a sub-channel from the same sub-band as used by the MUEs in the center-zone (Figure 5.1(a)(ii)). For such an allocation, the CTI would be significant especially near the transition areas of center-zone and edge-zone in a macrocell. Under this frequency allocation scenario, the HeNBs are constantly interfered by the omnidirectional transmission from the MUEs on the same sub-channel even though the MUEs and the HeNBs use different sub-bands in both center-zone and edge-zone. Also, the co-tier interference between HeNBs may become severe especially in the edge-zone since all the neighboring cell edge-zone HeNBs use limited number of sub-channels from the same sub-band.

One of the important design parameters here is the radius of the center-zone of the macrocell. Using Monte-Carlo simulations, it was shown in [8] that, for uniformly distributed MUEs, if the cell center-zone radius (rcenter) is 0.65 times the macrocell radius (R), then the average network throughput is maximized. We consider the same channel allocation and center-zone radius for strict FFR in a two-tier macrocell-femtocell network where in each cell of a cluster of size N, the total sub-channels allocated to center-zone MUEs is given by [8]: , where Kband is the total number of available sub-channels in a macrocell. The total sub-channels allocated to the edge-zone MUEs is given by .

5.2.2 Soft FFR Scheme

The soft FFR scheme uses a cell-partitioning technique similar to that of the strict FFR scheme. However, the center-zone MUEs of any cell are allowed to use the sub-bands of cell edge-zone MUEs of the neighboring cells within the cluster. For a cluster of N cells, the total number of available sub-channels in a cell is divided into N sub-bands with one sub-band assigned to each edge-zone. Figure 5.1(b)(i) depicts a cellular network with soft FFR deployment. Figure 5.1(b)(ii) illustrates the deployment of a soft FFR scheme with FRF of 3 to the edge-zone MUEs. The entire frequency is divided into sub-bands A, B, and C, and assigned to the cell edge-zone MUEs of macrocell 1, macrocell 2, and macrocell 7, respectively. Now, the center-zone MUEs of macrocell 1 are allowed to use sub-band B and sub-band C, that is, the sub-bands of cell edge-zone MUEs of macrocell 2 and macrocell 7, respectively. Therefore, soft FFR is more bandwidth-efficient than strict FFR.

In this scheme, both center-zone and edge-zone MUEs will experience interference from the tier-1 macrocells (Figure 5.1(b)(i)). A power control factor () is therefore introduced for the edge-zone MUEs to reduce ICI. That is, if an MUE m is located in the center-zone, then the transmission power from the tagged MeNB is Pkm on sub-channel k and if the MUE is located in the edge-zone, then the transmission power is, (). The optimal number of sub-channels allocated to center-zone MUEs is the same as that of the strict FFR case [8] and the total number of sub-channels allocated to edge-zone MUEs is given by

(5.1)

One of the major advantages of soft FFR is that it has better spectrum efficiency in comparison with strict FFR. Similar to strict FFR, an HeNB located in the center-zone may select the sub-band that is used by the MUEs in the edge-zone, and if the HeNB is located in the edge-zone, it chooses the sub-bands that are used by the MUEs in the center-zone (Figure 5.1(b)(ii)). Now, the HeNBs in the edge-zone have more options to choose a sub-channel, and therefore, the co-tier interference would be reduced. However, the CTI would be significant for users near the boundary of the center-zone and the edge-zone.

5.2.3 Sectored FFR (FFR-3) Scheme

The macrocell coverage area is partitioned into center-zone and edge-zone including three sectors per each zone (Figure 5.1(c)(i)). The entire frequency band is divided into two parts—one part is solely assigned to the center-zone (e.g., sub-band A in Figure 5.1(c)(ii)) and the other part is partitioned into three sub-bands (e.g., sub-bands B, C, and D) and assigned to the three edge-zones. An HeNB chooses a sub-band which is not used in the macrocell sub-area. When the HeNB is located in the center-zone, it also excludes the sub-band that is used by the MUEs in the edge-zone of the current sector [9].

As an example, when an HeNB is in edge-zone X1, it would only use sub-band A, C, or D and exclude sub-band B since sub-band B is used by the MUEs in region X1. Similarly, when an HeNB is in center-zone C1, it would avoid sub-band A which is used by the MUEs in the center-zone. It would also avoid sub-band B which is used by the MUEs in edge-zone X1, because the received signal power in sub-band B would be relatively strong for that HeNB which may create severe CTI [9]. Therefore, the HeNB in center-zone C1 would use sub-band C or D (Figure 5.1(c)(ii)). In this way, the intra-cell CTI will be minimized significantly. Due to sectoring, the inter-cell CTI would be reduced. For example, when a user is in region X1 in macrocell 1, CTI will be mainly from macrocell 2 and macrocell 7 rather than from all the six MeNBs in tier-1 of the network (Figure 5.1(c)(i)). As a result, the overall network sum-rate increases in comparison with strict FFR and soft FFR schemes.

The performance of a sectored FFR scheme such as the FFR-3 scheme can be improved by optimizing the edge-zone FRF, the center-zone radius, and the allocation of frequency resources in center-zone and edge-zone MUEs such that the overall network throughput is maximized. Therefore, similar to [10], an optimization problem can be formulated with the objective of maximizing the total network throughput subject to the minimum data rate requirement of MUEs in presence of HeNBs. By solving this optimization problem, we observe that the optimal edge-zone FRF for which the total network throughput is maximized is 6. The resulting FFR scheme is referred to as the optimal static fractional frequency reuse (OSFFR) scheme.

5.3 OPTIMAL STATIC FRACTIONAL FREQUENCY REUSE (OSFFR): AN IMPROVED FFR-BASED SCHEME

We consider the DL of a two-tier OFDMA-based heterogeneous wireless network consisting of an MeNB overlaid with several HeNBs. In this network model, each UE usually communicates on a specific sub-channel corresponding to the BS from which it receives the strongest signal strength, while the signals received from other BSs on the same sub-channel are considered as interference signals. We assume that an open access policy in employed within HeNBs where an MUE can connect to a nearby HeNB if the MUE experiences severe CTI or can achieve a higher throughput. We assume that there is a circular region corresponding to each HeNB where MUEs inside that region would request to connect to that HeNB (Figure 5.2). We assume that each sub-channel is assigned to at most one FUE or MUE. We consider sub-channel allocation in the network according to sector-based FFR. We assume that each macrocell has a total number of K sub-channels which are divided into (N+1) non-overlapping frequency sub-bands. Each sub-band consists of several sub-channels.

5.3.1 System Model and Assumptions

In the OSFFR scheme, the macrocell coverage is partitioned into center-zone and edge-zone with six sectors in each zone2 (Figure 5.1(d)(i)). The center-zone MUEs (i.e., the UEs situated within the optimal center-zone radius of the cell) are allocated with sub-band A with the number of sub-channels in this sub-band obtained from the solution of an optimization problem (to be described in Section 5.3.3). The rest of the available sub-channels are divided into 6 sub-bands (B, C, D, E, F, and G) each of which is allocated to one of the edge-zone sectors. The allocation of different frequency sub-bands to the different areas in the cell is shown in Figure 5.1(d)(ii). Thus, in the OSFFR, FRF of one is applied in the center-zone, while FRF of six is applied to the edge-zone MUEs.

Let and be the total number of sub-channels allocated for MUEs and FUEs in the center-zone, respectively. Let K(e)m and K(e)f be the total number of sub-channels allocated for MUEs and FUEs in the edge-zone, respectively. The sub-channel allocation in each zone is done based on optimal values of the system design parameters (e.g., optimal FRF, center-zone radius, and proportion of total number of sub-channels allocated to center-zone/edge-zone). The information about the spatial allocation of sub-channels for the MUEs can then be broadcast so that each femtocell knows which sub-channels it can use. We consider that each UE is allocated one sub-channel to satisfy the minimum rate requirement.3

5.3.2 Channel Allocation

The sub-channel allocation for sector-based FFR is illustrated in Figure 5.3. For such sub-channel allocation an HeNB executes Algorithm 5.1 to select the usable sub-channels in a distributed manner. In sector-based FFR, the available frequency band is divided into N+1 sub-bands. Let J be the set of all available frequency sub-bands in

Algorithm 5.1 OPERATIONAL ALGORITHM FOR SUB-CHANNEL ALLOCATION IN HENB

an MeNB. For example, in ffr-3 (Figure 5.3(a)(iii)), , and in ffr-6 (Figure 5.3(b)(iii)), .4 Let JU be the set of usable frequency sub-bands for the HeNB f (f Fm) which is set to J in the initialization phase of the HeNB. When HeNB f is turned on, it senses and collects the neighboring macrocell pilots signals. Hence it obtains the received signal strength indication (RSSI) [9] value (Rj, ) associated to each frequency sub-band from the pilot signals. Let T denote the set of RSSI values for all available frequency sub-bands in the macrocell, and denote the highest RSSI value. If the RSSI value of sub-band A is the highest (i.e., ), then HeNB f is located in the center-zone. In this case, HeNB f forms , a set of sub-bands (including sub-band A) whose RSSI values are comparatively higher than those of other sub-bands. Now, is excluded from JU, the set of usable frequency sub-bands for HeNB f located in any of the center-zones C1–CN. However, if the RSSI value of sub-band A is not the strongest, then HeNB f is located in one of the edge-zones X1–XN. Then, the set would consist of only one frequency sub-band that has the strongest RSSI value (i.e., the frequency sub-band which is used by the macrocell in the edge-zone of the current sector). Thus, is excluded from JU, the set of usable frequency sub-bands for HeNB f located in any of the edge-zones.

As an example, let us consider that an HeNB f is located in C1 center-zone. Now, for both FFR-3 (Figure 5.3(a)(ii)) and FFR-6 (Figure 5.3(b)(ii)) schemes, the HeNB f will exclude sub-bands used by the MUEs in center-zone and edge-zone of the current sector since the RSSI values for these sub-bands will be high. However, due to reduced center-zone sub-area for FFR-6, the HeNB will also exclude two more sub-bands that are used by the MUEs in the edge-zone just adjacent to the current sector. Hence, the set for FFR-3 would be: = {A, B}, and for FFR-6 it would be: = {A, B, G, F}. Now, the HeNB f would exclude from JU. Therefore, the set of usable frequency sub-bands for HeNB f located in center-zone C1 would be: JU = {C, D} and JU = {C, D, E} for FFR-3 and FFR-6, respectively. In an HeNB, we consider uniform transmission power on the sub-channels allocated to FUEs.

Note that, in Figure 5.1(d)(i), any MUE in the edge-zone would experience ICI mainly from one macrocell in tier-1. In other words, any MUE x located in edge-zone X1 of macrocell 1, which is allocated a sub-channel from sub-band G, will experience interference from only macrocell 4 if any MUE located in edge-zone X1 in this cell is using the same sub-channel. This reduces the ICI among MUEs substantially. In addition, since the center-zone MUEs do not share the spectrum with edge-zone MUEs, the intra-cell interference is mitigated. Furthermore, the entire macrocell adopts an FRF of 1. Under such deployment, when an HeNB is turned on, it senses the neighboring macrocell signals, executes Algorithm 5.1 in a distributed manner and chooses sub-bands which are not used in the macrocell sub-area. Similar to [9], when the HeNB is located in the center-zone, it excludes the sub-band used in the center-zone and the sub-band which is used by macrocell in the edge-zone of current sector (Figure 5.1(d)(ii)). The HeNB additionally excludes two sub-bands which are used by macrocell in the edge-zones just adjacent to the current sector. Note that a low complexity and low cost implementation of HeNBs for such autonomous operation will be an important issue for successful deployment of this scheme.

As an example, when the HeNB is in edge-zone X1, it would use sub-band A, B, C, D, E, or F and exclude sub-band G since the sub-band G is used by the macrocell in region X1. Now, when the HeNB is located in center-zone C1, it would avoid sub-band A which is used by the macrocell in the center-zone. It would avoid sub-band G which is used by the macrocell in edge-zone X1, because the received signal power in sub-band G would be strong for that HeNB. In addition, it would exclude sub-band B and F (two sub-bands used by the macrocell in the edge-zones of the adjacent sectors of the current sector for that HeNB) since the received signal power of sub-band B and F would be relatively strong for that HeNB. Therefore, the HeNB located in center-zone C1 would use sub-band C, D, or E.

For the proposed scheme, with a reduced macrocell sub-area, an HeNB has more sub-bands to select from. Therefore, the co-tier interference is reduced significantly in comparison with the FFR-3 scheme. Also, the intra-cell CTI to an FUE may only result from the MUE in the same sector in the center-zone or near the transition regions of the edge-zones of the neighboring sectors within a cell. The inter-cell CTI would be only from one neighboring MeNB. For example, an FUE in region X1 will experience CTI mainly from the corresponding sector of macrocell 7 (Figure 5.1(d)(i)). In addition, an HeNB in the edge-zone would have six sub-bands to select from. This reduces the probability of intra-cell co-tier interference in comparison to other FFR schemes.

In the next section, we will discuss how to optimize the spatial channel allocation parameters for the proposed scheme.

5.3.3 Optimization of Spatial-Channel Allocation Parameters

The objective is to maximize the total network throughput of two-tier femtocell network, subject to minimum rate requirement for the UEs. The optimization parameters of sector-based FFR are as follows: (i) Percentage of the overall frequency spectrum of the system that should be attributed to center-zone and edge-zone of macrocell service area; (ii) the dimension of the center-zone and edge-zone, that is, the center-zone radius with respect to to the macrocell radius; and (iii) the FRF of the macrocell edge-zone.

The formulation of the optimization problem is presented as follows (see Table 5.1 for the notations used):

Table 5.1 Summary of key notations

Notation	Definition
M, F	Set of all MeNBs/HeNBs
m, f	Serving MeNB/HeNB, m M and f F
	Set of MeNBs except the serving MeNB,
	Set of neighboring HeNBs except the serving HeNB,
,	Neighboring MeNB/HeNB, and
Fm	Set of all HeNBs in macrocell m
Xm, Yf	Set of macro UEs (MUEs)/femto UEs (FUEs) associated with MeNB(m)/HeNB(f)
xm, yf	MUE/FUE served by MeNB(m)/HeNB(f),
	xm Xm and yf Yf
K	Set of all sub-channels allocated in a macrocell,
k(s)	A sub-channel under consideration, k(s) K
,	Transmission power from MeNB(m)/HeNB(f) on sub-channel k(s)
,	Path-loss associated with sub-channel k(s) between MUE/FUE and MeNB/HeNB
,	Path-loss associated with sub-channel k(s) between MUE/FUE and HeNB/MeNB
,	Exponentially distributed channel power gain of unit mean associated with sub-channel k(s) between MUE/FUE and MeNB/HeNB
,	Exponentially distributed channel power gain of unit mean associated with sub-channel k(s) between MUE/FUE and HeNB/MeNB
,	SINR at MUE xm/FUE yf on sub-channel k(s)
	Minimum required rate for MUE xm
	Minimum required rate for FUE yf
	Indicator function and set to 1 if a sub-channel k(s) is assigned to a UE, otherwise it is set to 0
Pn	White noise power spectral density
ΔB	Bandwidth of a sub-channel
N	FFR frequency reuse factor of the edge-zone of MeNB (FRF Set, , )
	Macrocell radius resolution (e.g., )
K(c)m, K(e)m	Set of sub-channels allocated in a macrocell (m) center-zone and edge-zone, respectively

(5.2)

(5.3)

(5.4)

(5.5)

(5.6)

(5.7)

(5.8)

The above optimization problem is a Mixed Integer Non-Linear Optimization Problem which may be solved based on the approaches presented in [9]. However, these approaches, for example, time sharing for sub-channel allocation are not suitable for modeling admission control of UEs (as will be discussed in details in Chapter 6). Hence, we use Monte Carlo simulations to obtain the best configuration (which we refer to as the optimal solution) for the design parameters of sector-based FFR.5

In general, the signal-to-interference-plus-noise-ratio (SINR) for DL transmission to MUE xm from MeNB m on sub-channel k(s) is given by6

(5.9)

where is the transmission power from MeNB m on sub-channel k(s). is the exponentially distributed channel fading power gain associated with sub-channel k(s). is the path-loss associated with sub-channel k(s) between MUE xm and MeNB m which is given as , where PLoutdoor=28+35log10(d) dB [10], where d is the Euclidean distance between a BS and a UE in meters. However, is affected by both indoor and outdoor path-loss. In this case, d would be the Euclidean distance between an HeNB f and the edge of the indoor wall in the direction of MUE xm. This path-loss corresponds to indoor path-loss. After the wall, the path-loss will be based on the outdoor path-loss model. The indoor path-loss is modeled as follows [9]:

(5.10)

In (5.12), is the set of interfering MeNBs, which depends on the location of the MUEs and the specific sector-based FFR scheme deployed in the network.7 F is the set of interfering HeNBs adjacent to the MUE xm. Here, the adjacent HeNBs are defined as those HeNBs which are inside a circular area of radius 2rf centred at the location of MUE xm. Here, rf is the transmission radius of an HeNB in meters. Pn represents noise power spectral density and represents bandwidth of a sub-channel. The practical capacity for an MUE xm on sub-channel k(s) is then given by [10]: , where α is a constant defined by [9]. Here, BER represents the target BER (e.g., 10−6) [9].

For an FUE yf communicating with the HeNB f on sub-channel k(s), the DL SINR is given by

(5.11)

where is the set of all interfering (or adjacent) HeNBs and M is the set of interfering MeNBs. Here, represents indoor channel gain for distance d between the FUE and its serving HeNB. On the other hand, corresponds to both indoor and outdoor channel gain. Since the interfering signal is coming from the MeNB, we include the channel fading power gain in the denominator. For co-tier interference at HeNB, we only assume indoor channel gain since the transmission radius of the HeNB is relatively small. Again, note that the interfering HeNBs are defined as those HeNBs which are within a circular area of radius 2rf (e.g., rf = 30 m) centred at FUE yf. The practical capacity for an FUE yf is given as .

For each sector-based FFR (i.e., FFR-3 and FFR-6), we obtain the best configuration consisting of the number of sub-channels allocated in the center-zone and edge-zone as well as the center-zone radius with respect to the macrocell radius. In this optimization problem, we assume that the MUEs and HeNBs are uniformly distributed in the macrocell service area. We assume one active FUE per HeNB. The algorithm corresponding to the solution methodology of the optimization problem for channel allocation and interference avoidance is presented in Algorithm 5.2. We use Monte-Carlo simulations to obtain the best configuration. We consider 1000 spatial realizations of network topology to obtain the design parameters for sector-based FFR. First, for each realization, we execute Algorithm 5.2 1000 times (capturing the channel variation) to obtain the best configuration for this particular spatial realization. This process is performed 1000 times, that is, by changing the network topology (capturing the spatial distribution of the MUEs, HeNBs, and FUEs) to obtain the best configuration for the proposed framework. The main steps for solving the optimization problem can be stated as follows:

• For each FFR and center-zone radius, we first classify the macro users as center-zone MUEs and edge-zone MUEs. Then, we divide the available frequency band into center-zone and edge-zone sub-band for center-zone and edge-zone MUEs, respectively. The number of sub-channels in center-zone and edge-zone sub-band are K(c)m and K(e)m, respectively. However, K(e)m is equally partitioned according to FRF of the edge-zone and allocated to the MUEs of the edge-zone sectors.
• Under the sub-channel allocation for MUEs, the HeNBs execute Algorithm 5.1 (and as illustrated in Figure 5.3) to allocate sub-channels for FUEs.
• We calculate the maximum achievable capacity for each UE while satisfying its minimum rate and obtain the total throughput of the cell. Then, we obtain the optimal sub-channel allocation in center-zone and edge-zone that maximizes total throughput of the cell for each proportional center-zone radius (with respect to macrocell radius) and FFR scheme. Finally, we can obtain the best configuration consisting of optimal cell edge-zone FRF, percentage of the overall frequency spectrum allocated cell center-zone and edge-zone, and the radius of the cell center-zone radius with respect to the macrocell radius.

Algorithm 5.2   ALGORITHM FOR CHANNEL ALLOCATION AND INTERFERENCE COORDINATION

5.4 PERFORMANCE EVALUATION

5.4.1 Performance Metrics

We evaluate the performances of the different static FFR schemes in a two-tier macrocell–femtocell networking scenario by simulations (in MATLAB R2010a) in terms of outage probability, network throughput (or network sum-rate), and spectral efficiency.

Signal-to-interference-plus-noise-ratio (SINR): For DL transmission to MUE xm from MeNB m on sub-channel k, is given by

where Pkm is the transmission power from MeNB m on sub-channel k, is the exponentially distributed channel fading power gain associated with sub-channel k, and is the path-loss associated with sub-channel k between MUE xm and MeNB m which is given as . This path-loss corresponds to outdoor path-loss and is modeled as PLoutdoor=28+35log10(d) dB, where d is the Euclidean distance between a BS and a user in meters. However, is affected by both indoor and outdoor path-loss. In this case, d would be the Euclidean distance between an HeNB f and the edge of the indoor wall in the direction of MUE xm. After the wall, the path-loss will be based on an outdoor path-loss model.

Outage probability: We define the outage probability as the probability that a UE’s instantaneous SINR on a given sub-channel k falls below the SINR threshold γ and given as .

Sum-rate for FUEs in a macrocell: The maximum achievable capacity for an FUE yf is given as .

Average network sum-rate: The average network sum-rate, Cavg is

(5.12)

where, in general, = 1 when a sub-channel k is assigned to a UE. Otherwise, it is set to 0.

Spectral efficiency: We define the spectral efficiency (bits/s/Hz) in terms of average bits per second successfully received by a UE per unit spectrum. The spectral efficiency of transmission to MUE xm on sub-channel k is given as and that for FUE yf is given as . The average network spectral efficiency, S is thus given by

(5.13)

5.4.2 Simulation Parameters

The simulation parameters are shown in Table 5.2. The network is composed of 7 macrocells, and the HeNBs (i.e., femtocells) are randomly deployed over the macrocells. The number of HeNBs is varied up to 40 in one macrocell coverage area. We assume that the HeNBs operate in closed access mode (i.e., only registered FUEs will be able to access the HeNBs). The MUEs are uniformly distributed in the network. The MUEs and FUEs are randomly allocated with available sub-channels from the designated frequency bands corresponding to each sub-area for each scheme. We assume a “snap-shot” model, where all the network parameters (in Table 5.2) remain constant during a simulation run.

Table 5.2 Simulation parameters

Parameter	Value
Network size	1-tier (7 macrocells)
Radius of a macro cell	280 m
Radius of a femtocell	30 m
SNR at an MUE	10 dB
HeNB transmission power	20 mW
Number of MUEs in a macrocell	50
Maximum number of FUEs per femtocell	1
Channel bandwidth	10 MHz
Number of sub-channels	50
Sub-carrier spacing	15 kHz
White noise power spectral density	–174 dBm/Hz
Power control factor,	4

5.4.3 Simulation Results

Figure 5.4 shows variations in the network throughput with the fraction of the center-zone radius (with respect to the macrocell radius) for various cell edge-zone FRF. For each cell edge-zone FRF and fraction of the center-zone radius, the optimal number of sub-channels for center-zone MUEs is obtained by enumeration for which the network throughput is maximized.

For the OSFFR scheme, the total network throughput (or spectral efficiency (b/s/Hz) of the network) is maximized if center-zone radius is 54% of the total macrocell radius (Figure 5.4) and 36% of the total frequency resources are allocated for the center-zone MUEs (i.e., sub-band A). For FFR-3, the optimal center-zone radius is 61% of the macrocell radius and the optimal frequency resources for the center-zone MUEs is 48% of the whole frequency band. Table 5.3 shows the design parameters obtained for different sector-based FFR schemes as the minimum rate requirements and link-level transmission power vary within the network. The optimal values for the OSFFR and FFR-3 are used to obtain the performance evaluation results given below.

Table 5.3 Design parameters for sector-based FFR schemes

Figure 5.5(a) shows the variations in outage probability with SINR threshold for different FFR schemes (without HeNBs and with 40 HeNBs per macrocell to demonstrate how the outage probability deteriorates in presence of large number of HeNBs). Note that the strict FFR scheme exhibits slightly better outage performance when the SINR targets are low. This is due to the fact that, in strict FFR, the edge-zone MUEs of the center MeNB (i.e., the MeNB under observation) are not interfered by any other MeNBs of the first tier of the network. When the SINR threshold increases (e.g., >11.5 dB), the outage probability of strict FFR scheme (in presence of HeNBs) becomes higher than that of the proposed scheme and reaches close to that of the soft FFR scheme.

For the proposed scheme, ICI to the edge-zone MUEs is caused by only 1 MeNB, whereas for FFR-3 and soft FFR schemes, ICI is caused by 2 and 6 MeNBs, respectively. As a result, the outage probability is higher for these two FFR schemes. In comparison with the other FFR schemes, in the proposed scheme, the usable sub-bands for femtocells are increased in edge-zone and center-zone of a cell. As a result, the probability that two neighboring HeNBs would use the same sub-band and the same sub-channel is far more reduced as compared to the other FFR techniques. Therefore, the inter-HeNB interference is significantly reduced. Also, with the proposed scheme, due to the increased number of sub-bands for HeNBs in both center-zone and edge-zone, the number of sub-channels for FUEs per unit area increases. This results in a smaller probability of causing CTI with the MUEs in comparison with the other FFR schemes. As a result, the outage probability is comparatively low for the MUEs.

Figure 5.5(b) shows the variations in average network sum-rate as the number of HeNBs varies within the cell. We observe that the average network sum-rate for the proposed scheme is higher than that for each of the other FFR schemes. Again, this is due to reduced co-tier interference and CTI and hence higher SINR offered by the proposed scheme. Also, with the proposed scheme, the usable number of sub-channels per unit area increases when compared with the other FFR schemes, and consequently the spectral efficiency increases. Figure 5.6 shows variations in the spectral efficiency of the network as the number of HeNB varies. Note that, for the proposed scheme, with only 25 HeNBs per macrocell service area, the target spectral efficiency for LTE-A systems (i.e., 30 b/s/Hz [11]) is well satisfied. Also, from Figure 5.6, we observe that, for the edge-zone UEs, the average gains in spectral efficiency for the proposed scheme are 27%, 41%, and 49%, when compared with FFR-3, strict FFR, and soft FFR schemes, respectively. With the proposed scheme, for the UEs both in center-zone and edge-zone, the average gains in spectral efficiency are 23%, 43%, and 51%, when compared with FFR-3, strict FFR, and soft FFR schemes, respectively.

5.5 SUMMARY AND FUTURE RESEARCH DIRECTIONS

FFR is a simple and effective mechanism for interference management in OFDMA-based multi-tier networks. We have presented a broad comparison among four different FFR schemes, namely, strict FFR, soft FFR, FFR-3, and optimal static FFR (OSFFR) schemes, for two-tier networks. Simulation results have shown that the proposed OSFFR scheme offers a superior performance compared with the three other state-of-the-art FFR schemes. The FFR schemes described here correspond to partitioning and allocation of spectrum into different spatial regions of the macrocell service area in a static manner. Such static allocations may not be optimal under dynamic traffic load variation (e.g., due to the mobility of the UEs) and may increase the blocking probability. Note that an open access mode can reduce this blocking probability resulting from static resource partitioning. Optimal FFR schemes in the presence of mass deployment of HeNBs that satisfy the data rates for UEs as well the target blocking probabilities need to be developed. In this context, self-organizing and autonomous FFR frameworks will be desirable from the scalability point of view. In addition, dynamic power control methods can be developed to use in conjunction with FFR schemes to improve the capacity of multi-tier cellular networks. Such hybrid schemes based on resource partitioning through FFR as well as power control are currently being considered for LTE-Advanced systems.

REFERENCES

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1. Femtoforum has been renamed as Small Cell Forum: http://www.smallcellforum.org/.

2. Note that the future generation cellular systems (e.g., 4G and 5G systems) may introduce 6-sector cell operation to mitigate ICI.

3. Note that each sub-channel consists of several sub-carriers (i.e., 12) which may be increased to satisfy the minimum rate requirement.

4. Note that the sub-band notations are only used for symbolic purpose. Each sub-band consists of several sub-channels. However, the number of sub-channels available in each sub-band is obtained from the solution of an optimization problem.

5. Note that, based on the system requirements and configuration, the design parameters can be obtained off-line and stored in a look-up table.

6. Here xm=xc and xm=xe, if the MUE is located in center-zone and edge-zone, respectively.

7. For example, in a 1-tier MeNB network model, if the MUE is located at the center-zone, then for both the FFR-3 and FFR-6 schemes, the interfering MeNBs will be MeNB2–MeNB7 (Figure 5.3). On the other hand, if the MUE is located in edge-zone then the set would consist two MeNBs and one MeNB for FFR-3 and FFR-6, respectively. For example, in FFR-6 based scheme (Figure 5.3(b)), if MUE is positioned at X1 edge-zone, then the only interfering MeNB will be MeNB4.