 Research
 Open Access
Joint ABS and user grouping allocation for HetNet with picocell deployment in downlink
 WeiChen Pao^{1},
 JhihWei Lin^{2},
 YungFang Chen^{2}Email authorView ORCID ID profile and
 ChinLiang Wang^{3}
https://doi.org/10.1186/s1363801709459
© The Author(s). 2017
 Received: 7 October 2016
 Accepted: 13 September 2017
 Published: 2 October 2017
Abstract
In order to resolve the cochannel intercell interference problem in heterogeneous networks (HetNet), the feature of almost blank subframes (ABS) in the time domain of the enhanced intercell interference coordination (eICIC) is utilized. In this paper, an ABS configuration design is developed on downlink in HetNet and the associated resource allocation problem for maximizing the system performance with fairness among user equipments (UEs) is considered. Compared to conventional problems, the resource assignment problems include the configuration of ABS pattern and the resource allocation for macro UEs and pico UEs, which aims to maximize the downlink throughput and balance the traffic offloading in intrafrequency HetNet deployments. First, this paper introduces an ABS pattern design by using the channel condition, which is developed in terms of the time domain resource. Subframes are categorized as protected or normal subframes for reducing interference impact to pico UEs. Based on the configuration of the ABS pattern, we develop a grouping strategy to determine which pico UEs use either protected or normal subframes. Besides, the assignment of resource blocks with respect to the resource in the frequency domain is developed along with the fairness among UEs. The proposed joint allocation scheme takes the system throughput and the fairness into account, and has better performance than the existing schemes. Simulation results also reveal that the performance of the proposed joint allocation scheme approximates the optimal solution with the full search scheme.
Keywords
 Intercell interference coordination
 Almost blank subframe
 Heterogeneous network
 Proportional fairness
 Resource allocation
1 Introduction
Orthogonal frequency division multiple access (OFDMA) system has been chosen for the nextgeneration broadband wireless system standards [1] in order to satisfy the growing demands on the high data traffic in the mobile communication systems. The Third Generation Partnership Project (3GPP) Long Term Evolution (LTE) has been regarded as a promising mobile technology with increased system sum rates [2]. The LTEAdvanced (LTEA) is an evolution of LTE, which achieves International Mobile Telecommunications (IMT)Advanced requirements [3–5]. With more data traffic demand in the future, enhancing the system spectral efficiency by the deployment of traditional macro eNodeBs (eNBs) has high cost. Therefore, heterogeneous networks (HetNet) have been widely discussed in 3GPP LTEA standards [6, 7]. HetNet includes highpower macro eNBs and lowpower nodes, such as femto eNBs, pico eNBs, and relays [8–10].
In order to offload user equipments (UEs) from a macro eNB to a pico eNB more efficiently, cell range expansion (CRE) has been introduced in 3GPP LTEA [11]. In the CRE method, a bias value is introduced and added to reference signal received power (RSRP) of pico eNBs. A CRE region is introduced where the system pretends that UEs have better signal quality from the pico eNB. Therefore, the system may tend to offload UEs from the macro eNB to the pico eNB. More UEs may connect to pico eNBs for load balancing. The control of the bias and the related offloading is discussed in [12, 13]. However, the UE which is handed over from the macro eNB to the pico eNB with the CRE technique may suffer severe interference from the macro eNB since the received signal from pico eNB is still weak. A major problem in HetNet [14] is the crosstier intercell interference (ICI) because the lowpower nodes such as pico eNBs share the same frequency band with the macro eNBs. In order to improve the performance and reduce the crosstier interference, a major feature of enhanced intercell interference coordination (eICIC) [10, 15–18] is to coordinate intercell interference in time domain by implementing almost blank subframe (ABS). The method of timedomain multiplexing (TDM) using ABS [19, 20] is introduced to avoid heavy ICI on both data and control channels of the downlinks. When the ABS scheme is employed, subframes will be further configured as either normal subframes or protected subframes. For normal subframes, UEs served by macro eNBs (macro UEs) and served by pico eNBs (pico UEs) are all allowed to use these subframes. For protected subframes, only pico UEs are allowed to use those subframes. The designs of the CRE region and the ABS pattern can be developed to have gain and benefit for the whole system, such as traffic offloading and throughput.
Regarding the above discussion, we focus on the challenges for maximizing the system performance with fairness among UEs in HetNet which include the configuration design of the ABS pattern and the resource allocation for macro UEs and pico UEs in terms of the time domain resource, i.e., subframe configuration including protected subframe and normal subframe where the resource is located in the time domain, and the frequency domain resource, i.e., subcarrier allocation to multiple UEs where this resource is located in the frequency domain. Due to the design of the CRE region and ABS to protect Pico UEs, the resource allocation problem becomes more complicated. The ABS pattern needs to be configured and coordinated among eNBs for the purpose of the maximization of system capacity or throughput. Also, subcarriers should be properly assigned to macro UEs and Pico UEs. The associated configuration, i.e., a normal or a protected subframe of a particular subcarrier will determine the amount of the suffered interference. We also consider fairness among Pico UEs. Consequently, the proposed resource allocation scheme comprises the ABS configuration, the Pico UE grouping, and the subcarrier allocation.
First, this paper focuses on the design for the configuration of an ABS pattern. The problems of cell selection combined with ABS density are investigated in [21–23]. The channel state is usually assumed to be time invariant in the period of an ABS pattern [24, 25]. Thus, most of papers only discuss the ABS density without determining which subframes should be configured as protected subframes. The system performance, e.g., throughput, is affected by the ABS configuration since each subcarrier or each UE experiences different channel condition. In the view of the time domain, the ABS pattern design strategy is developed. We utilize the channel condition to design an evaluation function as an indicator which aims to maximize the sum rate of the system. The indicator can efficiently determine which subframes should be configured as protected subframes. Different from the previous work [22], the ABS pattern is dynamically adjusted, instead of fixed.
Second, this paper develops a pico UE grouping strategy based on an optimization technique to determine which pico UEs use protected subframes or normal subframes. Various schemes of pico UE grouping [24–27] have been investigated in the HetNet with CRE. The simplest way is that all pico UEs are assigned to use protected subframes [26], which means pico eNBs only work in protected subframes. This scheme may cause the reduced performance in pico eNBs due to the limited resources. In [27], some pico UEs which are handovered from a macro eNB to a pico eNB with the CRE technique are assigned to the protected UE set and others are assigned to the normal UE set. In [25], “brute force search” by employing integer programming is used to get the optimal solution for the problem of the timedomain resource partitioning for enhanced intercell interference coordination. However, this scheme has a high computational complexity. In order to reduce the computational complexity, one scheme [24] using Nash bargaining solution (NBS) is proposed to reduce the complexity, but the NBS scheme only finds a suboptimal solution in some sense. Therefore, it raises our motivation to develop a pico UE grouping scheme with a low computational complexity while approximating the optimal solution. We also develop a strategy for the pico UE grouping to determine which pico UEs use either the normal subframes or the protected subframes. Deviated from the tradition UE grouping methods [28–30], Pico UEs will be redistributed by using a fast adjustment in a group basis and a refinement mechanism on a perUE basis. Accompanied by the redistribution, the radio resource blocks in the frequency domain are allocated jointly per subframe.
Finally, in this paper, we propose joint allocation scheme to maximize the system performance while considering fairness among UEs by appending some processing procedures. A dynamic ABS pattern design is introduced. Based on the ABS pattern, UE grouping strategies including the fast adjustment and the refinement mechanism are introduced. Meanwhile, the radio resource allocation is executed as well. The proposed scheme outperforms the existing schemes [24, 27] and approaches the full search scheme [25] while the computational complexity is greatly reduced. The proposed algorithm is different from other works, such as (1) timedomain resource portioning [23, 24, 27] without user grouping or subcarrier allocation, (2) fair scheduling [31, 32] without ABS configuration and user grouping, or (3) user selection and resource allocation algorithm [33] without ABS configuration.
Our contributions and new ideas include (a) a joint allocation scheme is first developed in the time domain and the frequency domain, including the consideration of the proportional fairness among UEs; (b) a new evaluation function based on an optimization technique is proposed to determine the configuration of subframes, i.e., normal and protected subframes. A low complexity associated strategy is thus proposed; (c) another new evaluation function is derived for UE grouping, i.e., in either the normal or the protected UE set; (d) the proposed scheme outperforms the existing schemes [24, 27], and approaches the optimal solution with the full search scheme [25].
2 System model and problem formulation
The offloaded UEs in the CRE region may suffer from ICI of macro eNBs. In normal subframes, macro UEs and pico UEs are all allowed to use those subframes. In this paper, pico UEs will be further classified into two sets, a normal UE set Ω ^{(normal)} and a protected UE set Ω ^{(protected)}. UEs in the normal UE set use the normal subframes, and UEs in the protected UE set use the protected subframes. We also assume that the same ABS patterns are configured for all eNBs under consideration, which is the synchronous configuration of ABS pattern [34] as shown in Fig. 1. An ABS pattern means the pattern of the protected subframes in a frame. The channel state information is known to eNBs and the information of ABS configuration exchanges through X2 interface between all eNBs in LTE [19].
\( 1/{\overline{R}}_{k^{\prime}}^{\left(\mathrm{Macro}\right)}\left[i\right] \)and\( 1/{\overline{R}}_{k^{{\prime\prime}}}^{\left(\mathrm{Pico}\right)}\left[i\right] \)in Eq. (8) are the proportional fairness (PF) factors which are introduced to strike a balance between the system performance and the fairness among UEs [32]; i is the subframe index; Iis the number of subframes in one frame; J is the window size which is the number of the frames in a PF period; ε[i]and ε ^{∗}[i]are the binary indicators; ε[i] = 1 (ε ^{∗}[i] = 0) represents that the ith subframe belongs to the normal subframe; ε ^{∗}[i] = 1 (ε[i] = 0) represents that the ith subframe belongs to the protected subframe; \( {C}_{k^{{\prime\prime} }} \) and\( {C}_{k^{{\prime\prime}}}^{\ast } \) denote the indicators for the UE k ^{″} whether it is assigned to the normal UE set or the protected UE set. \( {C}_{k^{{\prime\prime} }}=1 \)(\( {C}_{k^{{\prime\prime}}}^{\ast }=0 \)) represents that the k ^{″}th pico UE is assigned to the normal UE set; \( {C}_{k^{{\prime\prime}}}^{\ast }=1 \) (\( {C}_{k^{{\prime\prime} }}=0 \)) represents that the k ^{″}th pico UE is assigned to the protected UE set; Eq. (9) represents that the sum of the allocated power \( {p}_{k^{\prime },n,q}^{\left(\mathrm{Macro}\right)}\left[i\right] \) is less than the total power of the macro eNBP ^{(Macro)}[i]; Eq. (10) represents the transmit power constraint of the pico eNB P ^{(Pico)}[i]; Eq. (11) denotes that each RB in the macro eNB is only allocated to one macro UE; each RB in one eNB is not allowed to be shared among UEs served in the eNB; Eq. (12) denotes that each RB in the pico eNB is only allocated to one pico UE; Eq. (13) means that each subframe is only classified as either the normal subframe or the protected subframe; the sum of ε[i]and ε ^{∗}[i] for a particular subframe i is equal to 1; Eq. (14) implies that one pico UE can only be in the normal UE set or the protected UE set.
\( {G}_{k^{{\prime\prime} },n,q}^{\left(\mathrm{Pico}\right)} \)  the channel gain between the pico eNB and the k ^{″}th pico UE on the qth subcarrier of the nth RB 
\( {p}_{k^{{\prime\prime} },n,q}^{\left(\mathrm{Pico}\right)} \)  the amount of power for the k ^{″}th pico UE on the qth subcarrier of the nth RB 
\( {G}_{k^{{\prime\prime} },n,q}^{\left(\mathrm{Macro}\right)} \)  the channel gain between the macro eNB and the k ^{″}th pico UE on the qth subcarrier of the nth RB 
\( {p}_{k^{\prime },n,q}^{\left(\mathrm{Macro}\right)} \)  the amount of power for the k ^{′}th macro UE on the qth subcarrier of the nth RB 
ε[i]  the binary indicator. Subframe configuration 
\( {r}_{k^{{\prime\prime} },n}^{\left(\mathrm{normal}\right)} \)  the data rate for thek ^{″}th pico UE on the nth RB in the normal UE set 
\( {r}_{k^{{\prime\prime} },n}^{\left(\mathrm{protected}\right)} \)  the data rate for thek ^{″}th pico UE on the nth RB in the protected UE set 
\( {\rho}_{k^{{\prime\prime} },n}^{\left(\mathrm{Pico}\right)} \)  the binary indicator. RB assignment 
Ω ^{(normal)}  the normal UE set 
Ω ^{(protected)}  the protected UE set 
\( {R}_{k^{{\prime\prime}}}^{\left(\mathrm{normal}\right)} \)  the sum of data rate for thek ^{″}th pico UE in the normal UE set 
\( {R}_{k^{{\prime\prime}}}^{\left(\mathrm{protected}\right)} \)  the sum of data rate for thek ^{″}th pico UE in the protected UE set 
\( \overline{R} \)  the average data rate 
I  the number of subframes in one frame 
J  the windows size which is the number of the frames in a PF period 
\( {C}_{k^{{\prime\prime} }} \)  the indicators for the UE k ^{″} assigned to the normal UE set 
\( {C}_{k^{{\prime\prime}}}^{\ast } \)  the indicators for the UE k ^{″} assigned to the protected UE set 
F ^{(Macro)}[i]  denotes that the sum rate of all macro UEs in the ith subframe 
\( {F}_{\left(\mathrm{protected}\right)}^{\left(\mathrm{Pico}\right)}\left[i\right] \)  denotes that the sum rate of pico UEs in the protected UE set in the ith subframe 
\( {F}_{\left(\mathrm{normal}\right)}^{\left(\mathrm{Pico}\right)}\left[i\right] \)  denotes that the sum rate of pico UEs in the normal UE set in the ith subframe 
α,β,μ,\( {\psi}_{k^{{\prime\prime} }} \),\( {\phi}_{k^{{\prime\prime} }} \), \( {\zeta}_{k^{{\prime\prime} }} \),\( {\zeta}_{k^{{\prime\prime}}}^{\prime } \),\( {\lambda}_{k^{{\prime\prime} }} \)  nonnegative Lagrangian multipliers 
N  the number of resource block in a system 
Q  the number of subcarriers per resource block 
3 Proposed ABS pattern design
Based on the derived result, ΔF[i] implies that the sum rate difference of the ith subframe configured as the normal subframe or the protected subframe. If the value of ΔF[i] is greater than zero, the ith subframe is configured as the normal subframe because it may achieve higher sum rate. Otherwise, the ith subframe is categorized as the protected subframe. After the development of the configuration of an ABS pattern, the UE grouping design will be shown in the next section.
4 Proposed UE grouping strategy
\( \varDelta {C}_{k^{{\prime\prime} }} \) is the indicator difference of the normal UE set and the protected UE set when UE k ^{″}is assigned to them. If the value of \( \varDelta {C}_{k^{{\prime\prime} }} \) is more than zero, UE k ^{″} should be assigned to the normal UE set; otherwise, UE k ^{″} should be assigned to the protected UE set.
5 Proposed joint allocation scheme
In this section, the joint ABS configuration and UE grouping scheme is described to resolve the resource allocation problem while achieving high system performance and fairness among all UEs. The proposed scheme by utilizing the designed functions includes the designs of the ABS pattern, the pico UE grouping, and the RB allocation. The procedures of the proposed scheme are as follows:

Step 1: ABS Configuration. Start fromi = 1,i ∈ {1, … , I}, Iis the number of subframes in one frame. Each subframe is determined as the normal subframe or the protected subframe in one frame. The designed function ΔF[i] (24) determines which subframes should be configured as protected subframes in one frame. In order to find a better ABS pattern, we may sort the values of the designed function (24) in a descending order. And then, the number of protected subframes is limited to an upper bound of ABS density [22]. Therefore, the ABS pattern for a frame would be configured.

Step 2: Pico UE Grouping. After the ABS pattern is configured for a frame, we will assign pico UEs to the normal UE set or the protected UE set and allocate the RBs for each subframe. The initial UE set is determined by using Eq. (1). Pico UEs which are handed over from macro eNB to pico eNB because of bias values are assigned to the protected UE set Ω ^{(protected)}, i.e., \( {C}_{k^{{\prime\prime}}}^{\ast }=1 \). The others are assigned to the normal UE set Ω ^{(normal)}, i.e., \( {C}_{k^{{\prime\prime} }}=1 \).

Step 3: RB Allocation, for n = 1, …, N. After the protected UE set Ω ^{(protected)}and the normal UE set Ω ^{(normal)}are determined, the RB allocation of each subframe is performed. For the normal subframes, only pico UEs which are assigned to the normal UE set can use the RBs; similarly, the RBs in the protected subframes can only be used by UEs in the protected UE set. We assume that power is equally distributed to each RB in the view of base station. In the initial stage, equal power is assumed for each subcarrier of each UE. A simple strategy is to assign RBs to UEs with a higher value of data rate. Since it is the first run of the solution, a better solution is achieved after iterations by the proposed scheme.

Step 4: Fast Adjustment . We would redistribute pico UEs into the two UE sets by using \( {C}_{k^{{\prime\prime} }} \) (32) and \( {C}_{k^{{\prime\prime}}}^{\ast } \) (33) in a group basis. If the k ^{″}th UE is assigned to the normal UE set, we can get the \( {C}_{k^{{\prime\prime} }} \) according to Eq. (32); then, we temporarily move the k ^{″}th UE from the normal UE set to the protected UE set; and repeat Step 3 to allocate the RBs for each subframe. We can get the \( {C}_{k^{{\prime\prime}}}^{\ast } \) according to Eq. (33). Similarly, if the k ^{″}th UE is assigned to the protected UE set, the same approach is used to get \( {C}_{k^{{\prime\prime} }} \) and \( {C}_{k^{{\prime\prime}}}^{\ast } \). After that, \( \varDelta {C}_{k^{{\prime\prime} }} \) (34) is obtained for each pico UE. The value of \( \varDelta {C}_{k^{{\prime\prime} }} \)would be used to determine if the k ^{″}th UE is reassigned to the normal UE set or the protected UE set. If \( \varDelta {C}_{k^{{\prime\prime} }}\ge 0 \), the pico UE k ^{″}is assigned to the normal UE set; otherwise, the pico UE k ^{″} is assigned to the protected UE set.

Step 5: Refinement Mechanism. Based on the result of the fast adjustment, the refinement mechanism is performed to exchange or move pico UEs between two UE sets on a perUE basis. The main concept of the refinement mechanism is to reassign only one UE to the normal UE set Ω ^{(normal)} or the protected UE set Ω ^{(protected)} in one iteration. In the exchanging operation, originally two pico UEs, e.g., xandy, are assigned toΩ ^{(normal)}andΩ ^{(protected)}, i.e., x ∈ Ω ^{(normal)} andy ∈ Ω ^{(protected)}. After the exchanging operation, two pico UEs are exchanged between two pico UE sets, i.e., y ∈ Ω ^{(normal)} and x ∈ Ω ^{(protected)}. In this fashion, two pico UEs are exchanged in each time and the number of pico UEs in each set is not changed. The sum rate (25) of all combinations is calculated correspondingly. The sum rate increment can be defined as:

Step 6: Update the average data rates\( {\overline{R}}_{k^{\prime}}^{\left(\mathrm{Macro}\right)}\left[i\right] \)and \( {\overline{R}}_{k^{{\prime\prime}}}^{\left(\mathrm{Pico}\right)}\left[i\right] \) for the current frame. The proposed joint scheme is ready to be performed for the next framej = j + 1. Return to Step 1 until the window size of frames j = J is met.
We incorporate the computation and evaluation of related equations into Fig. 2a to complete the allocation procedures. Figure 2b illustrates the procedures of the proposed joint allocation scheme across the frequency domain and the time domain.
6 Computational complexity analysis
In this section, we focus on the computational complexity analysis of the RB allocation and UE grouping strategies in one frame in terms of BigOh notation. All compared schemes are based on the same system model, so the computational complexity of calculating the data rate associated with an SINR is the same, which is represented as O(Q) by referring to Eq. (3) and Eq. (6). The complexities of the processing steps in the algorithm are the focus, in terms of calculating the SINR and the data rate.
Step 1 of the proposed joint allocation scheme is the ABS configuration for one frame. Regarding the proposed ABS pattern design, the calculation of the sum rate for each subframe in one frame is needed. Therefore, the complexity of the proposed ABS pattern design is O(IK ^{″} NQ). Step 2 uses Eq. (1) to determine the initial UE set. In that, K ^{″} UEs are considered which requires O(K ^{″}). RB allocation is operated in Step 3. For the macro eNB, N RBs are considered for K ^{′} UEs per subframe. One frame contains I subframes. The computational complexity of the RB allocation needs O(INK ^{′} Q). For the pico eNB, we assume that K ^{″} UEs are equally distributed in each set. Each set needs the complexity of O(INK ^{″} Q/2) for the RB allocation. Therefore, O(INK ^{″} Q) is required for RA allocation of the pico UEs. Step 4 focuses on the moving operation of the pico UEs. K ^{″} pico UEs are evaluated along with the RB allocation for one iteration. The complexity is calculated as O((INK ^{″} Q)K ^{″} T _{1}). T _{1} denotes the number of iterations. The refinement mechanism in Step 5 comprises the exchanging operation and the moving operation. We also assume that the average number of pico UEs in each set is approximately K ^{″}/2. For the exchanging operation, there are (K ^{″}/2) ⋅ (K ^{″}/2) ≈ (K ^{″})^{2} possible combinations per iteration. For the moving operation, the number of combinations is the number of total pico UEs K ^{″}. Therefore, the complexity of the refinement mechanism along with the RB allocation is O(INK ^{″} Q((K ^{″})^{2} + K ^{″})T _{2})≈O(IN(K ^{″})^{3} QT _{2}).T _{2} is the number of iterations. In summary, the complexity of the joint allocation scheme for one frame is O(K ^{″} INQ + K ^{″} + INQ(K ^{′} + K ^{″}) + INQ(K ^{″})^{2} T _{1} + INQ(K ^{″})^{3} T _{2})≈O(INQK ^{′} + INQ(K ^{″})^{2} T _{1} + INQ(K ^{″})^{3} T _{2}).
For the compared schemes, the computational complexity of the fixed ABS pattern [22] is O(1) where it fixes the ABS density and determines an ABS pattern at random. Regarding pico UE grouping strategies, the full search scheme [25] is to search all UE grouping combinations of pico UEs in each ABS pattern. The complexity of all UE grouping combinations is \( O\left({\sum}_{j=1}^{K^{{\prime\prime} }}{C}_j^{K^{{\prime\prime} }}\right)\approx O\left({2}^{K^{{\prime\prime} }}\right) \). So, the total computational complexity along with RB allocation is \( O\left( INQ{K}^{\prime }+ INQ{K}^{{\prime\prime} }{\sum}_{j=1}^{K^{{\prime\prime} }}{C}_j^{K^{{\prime\prime} }}\right) \) ≈ \( O\left( INQ{K}^{\prime }+ INQ{K}^{{\prime\prime} }{2}^{K^{{\prime\prime} }}\right) \), including K ^{′} macro UEs and K ^{″} pico UEs. O(INQK ^{′}) is the complexity of RA allocation for macro UEs. In [27], pico UE grouping is determined by CRE bias, which requires O(K ^{″}). Therefore, the computational complexity along with RB allocation is O(K ^{″} + INQK ^{′} + INQK ^{″}). In [24], an indicator which involves the data rate is used to determine that each UE may be assigned to either the normal UE set or the protected UE set. The computational complexity of pico UE grouping is O(K ^{″} T _{3}). T _{3} denotes the number of iterations. So, the total computational complexity along with RB allocation is O(INQK ^{′} + INQK ^{″} K ^{″} T _{3})=O(INQK ^{′} + INQ(K ^{″})^{2} T _{3}).
7 Simulation results
The simulation results will demonstrate the performance of the proposed scheme compared to those of the existing schemes [22, 24, 25, 27]. The network topology consists of one macro eNB and one pico eNB based on the 3GPP case 1 [37]. The radius of the macro eNB is 289 m, and the pico eNB is randomly distributed with a minimum distance of 75 m to the macro eNB. The frequency selective wireless channel model [38] is employed. We adopt Jake’s model to generate the Rayleigh fading channel. The mobile speed is 4 km/h. The standard deviation of shadowing is 8 dB. N _{0}is −174 dBm/Hz. The channel power of the received signal for each UE is varied because of the various path losses at the different locations. The macro path loss model [39] is 128.1 + 37.6*log(d1) in decibels. d1 is in kilometers. The pico path loss model [39] is 38 + 30*log(d2) in decibels. d2 is in meters. The carrier frequency is 2 GHz. UEs are uniformly distributed within the coverage of the macro cell with the numbers from 12 to 36. Transmit power is 46 dBm for the macro eNB and 30 dBm for the pico eNB. Eightdecibel bias is considered for cell range expansion. The downlink FDD system is used for simulation with a bandwidth of 10 MHz comprising 50 RBs. Each RB has 12 subcarriers. Subcarrier spacing Δfis 15 kHz. The ABS pattern period is set to be 10 ms, i.e., 10subframe duration. All results are the average values from 600 frames.
8 Conclusions
A strategy with the help of the derived evaluation function to determine the ABS pattern is designed in this paper. With a proper design of ABS pattern, the performance would be further improved in term of sum rates. The novel UE grouping strategies are presented to improve the performance of the system without a prohibitive computational complexity. The proposed joint allocation scheme obtains the balance in the computational complexity and the performance, and also considers the fairness among UEs. The proposed joint allocation scheme outperforms the existing schemes about 10% gains in term of sum rate, and approaches 99.5% of the full search scheme while having a much lower complexity.
Declarations
Acknowledgements
There is no other person who contributed toward the article who does not meet the criteria for authorship.
Funding
This work was supported by the Information and Communications Research Laboratories, Industrial Technology Research Institute (ITRI), Hsinchu, Taiwan, under Grant 2017–41–5G0301.
Authors’ contributions
WCP is responsible for the development of the most parts of the algorithms and conducting simulations. JWLin is responsible for the development of some parts of the algorithms and conducting simulations. YFC is responsible for the development of the algorithms, verification of the derivations and simulation results, writing the paper for the whole idea, and supervising the process of the research. CLW is responsible for providing the whole concept of the algorithms to develop and supervising the process of the research. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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