International Journal of Interactive Mobile Technologies (iJIM) – eISSN: 1865-7923 – Vol. 14, No. 10, 2020 Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks https://doi.org/10.3991/ijim.v14i10.14389 Nada M. Elshennawy(*) Tanta University, Tanta, Egypt Nada_elshennawy@f-eng.tanta.edu.eg Abstract—Growing of time-sensitive applications such as streaming multimedia, voice over IP and online gaming required strongly support from mobile communication technology. So, the persistent need for wireless broadband technologies such as LTE-A is essential. LTE-A can achieve QoS in an efficient manner by using a reliable packet scheduling algorithm. It also sup- ports good cell coverage by using heterogeneous capability. In this paper, modi- fications of proportional fair (PF) algorithm are proposed with different methods to compute the average throughput, which is the main and important parameter in the PF cost function. These methods are geometric mean, root mean square and arithmetic mean. Vienna simulator is used to study the performance of the proposed algorithms. A comparison between PF modifications and the most fa- mous algorithms (the original PF and Best CQI algorithms) with various UE ve- locities is introduced. Average UE throughput, spectral efficiency, energy per bit, cell throughput and fairness are used as performance indicators. The results ex- pose that QPF has best improved values for spectral efficiency, energy per bit and fairness by 8.4%, 14%, and 9.3%, respectively than original PF. However, Best CQI has a better value of average UE and cell throughput than all algorithms of 2% and 1.8% in low and medium UE velocity, respectively, but the best value of all types of throughput at high speed is gained by QPF. QPF and GMPF has the same performance in fairness with all UEs speeds. Keywords—Long Term Evolution Advanced (LTE-A), Heterogeneous net- work (HetNet), QoS Scheduling Algorithms, Proportional Fair (PF), root mean square (RMS). 1 Introduction Increasing in mobile applications needs special wireless communication technology which should have special features such as quality of services (QoS) support and high data rate. It is essential to develop a viable and powerful wireless technology. Long term evolution (LTE) is developed by the third Generation Partnership Project (3GPP) to introduce the mobile service requirements strongly. It also supports high data rates, low latency, better coverage and better QoS [1]. 3GPP is still developing its LTE to face the rapid growth in the multimedia applications and it has introduced an LTE im- provement named LTE advanced (LTE-A) which provides users with better services, 22 http://www.i-jim.org Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks has ability of servicing users with better performance and an improved the overall net- work performance [2]. LTE-A has provided many advanced features: Carrier Aggregation (CA), Multiple- input and multiple-output (MIMO), Coordinated multipoint (CoMP) and Heterogene- ous Networks (HetNets) [2]. In LTE-A, heterogeneous networks are presented by using many base stations with different levels of power to increase the coverage area [3]. In LTE-A, the main part which responses for allocating the resources fairly between users is the radio resources management (RRM). It is a very important aspect, espe- cially in heterogeneous networks [4]. The distribution of the resource between the users is very critical and difficult process, and it should be done at each Transmission Time Interval (TTI). Each user has different types of applications; therefore, the network technology should be able to support different quality of service (QoS) needs. Because, the system performance indicators like throughput and fairness between users are af- fected by choosing the scheduling algorithm [4].RRM has two main tasks: Radio Ad- mission Control (RAC) and Packet Scheduler (PS) which can be considered as the two wings of QoS. RAC has the capability of testing the network availability for new trans- missions in both downlink and uplink before the acceptance of new users. PS has the responsibility of allocating the Resource Blocks (RBs) efficiently in TTI between users to improve the overall network performance [4]. The most important phase in QoS in LTE-A is the packet scheduling which allocates sub-carriers resources for User Equipment (UEs) in each TTI in a manner that maxim- izes the overall network performance [2]. LTE-A scheduling algorithms can be classi- fied into: channel-aware and unaware algorithms. In channel-unaware algorithms, the algorithm takes parameters as throughput, delay, fairness and energy consumption in its priority function such as proportional fair (PF) algorithm. But, in channel-aware, the channel status is the main parameter of its function such as Best Channel Quality Indi- cator (Best CQI) algorithm [4].PF is the most powerful, efficient and fair used algo- rithm in LTE-A, because it maximizes fairness with an acceptable values in the other performance parameters: average throughput, spectral efficiency and used energy [4]. In the literature, many modifications of PF are developed presenting different methods to calculate the average throughput value in its cost function. In [5], the difficulties designing issues for downlink scheduling algorithms are in- troduced. To illustrate the importance of the relation between fairness and throughput. In [6], performance analysis between Open Loop Spatial Multiplexing (OLSM) and Closed Loop Spatial Multiplexing (CLSM), for PF and Round Robin (RR) algorithms with a variety of UE velocities for LTE-A heterogeneous networks are introduced. The results highlight that at low UEs velocity, CLSM-PF has best performance with the desired MIMO-scheduler combination. However, at high velocities, OLSM-RR is the preferred combination. Resource allocation study in Femto cell for LTE-A networks is reviewed in [7]. A resource allocation strategy is also suggested. It uses the Heteroge- neous Channel Quality Index (CQI) based Scheduling Techniques (HCBST) with in- dexed adaptive modulation and coding technique by referring the various CQI param- eters. Finally, the results show that HCBST system is better in term of throughput and spectral efficiency than the existing scheduling algorithms. iJIM ‒ Vol. 14, No. 10, 2020 23 Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks In [8], a packet scheduling algorithm for the downlink LTE system is developed based on Kalman filter to restore the true CQI from erroneous channel quality feedback. Then, a time domain grouping of PF and Modified Largest Weighted Delay First (M- LWDF) algorithms is also used. The results illustrate that the throughput and packet loss ratio of the proposal has better performance.In this paper, modifications on PF are developed, by using different methods to calculate the average throughput in its cost function. These methods are the root mean square, arithmetic mean, and geometric mean which were used in LTE-A homogenous networks in the literature [9, 10, 11]. In these methods. Proposed algorithms performance is studied by comparing their perfor- mance with the original PF and Best CQI algorithms at various UE velocities. Average throughput for UE and cell, fairness, average used energy per bit and spectral efficiency are used as performance indicators. The paper is organized as follows. In Section II, an overview of LTE-Advanced and its heterogeneous type is introduced. Section III describes the scheduling algorithms. In Section IV, the proposed modifications are explained. The simulation results and discussion are reviewed in Section V. Finally, conclusion and future works are pre- sented in Section VI. 2 LTE-A and Heterogeneous Networks LTE-A stands for long term evolution–advanced. It is developed by 3rd Generation Partnership Project (3GPP) as a viable wireless technology. LTE-A architecture is shown in fig. 1. As declared from the figure, the two main parts of LTE-A: E-UTRAN (Evolved Universal Terrestrial Radio Access Network), also called base stations, (eNBs) and Evolved Packet Core (EPC) [1]. Fig. 1. LTE-A Architecture LTE-A uses in its physical layer, OFDMA (the Orthogonal Frequency Division Mul- tiple Access) for downlink (DL) and Single Carrier FDMA for uplink (UL) [12, 13]. It also has many features like: achieving a high level of data rate, supporting low latency for real time applications, using Multiple Input Multiple Output (MIMO), Carrier 24 http://www.i-jim.org Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks Aggregation (CA), Coordinated Multipoint (Comp), and finally, introducing strong coverage in its cell by using Heterogeneous Network (Het Net). Wireless network layout is classified into [14]: homogeneous networks and hetero- geneous network. All used base-stations have the same: power transmission level, an- tenna patterns, receiver noise floors, and similar backhaul connectivity to the data net- work, in homogeneous networks. Also, base stations have unrestricted assess to user terminals and support different applications with various QoS requirements. Their lo- cations are chosen to maximize the coverage and control the interference between them. Heterogeneous networks have many types of base stations based on the power levels to improve the network coverage area as shown in fig. 2. This type of networks consists of a regular macro base-stations which have high power transmission level (~5W - 40 W), overlaid with several pico stations, femto base-stations and relay base-stations, which have transmission power at lower levels (~100 mW – 2 W) [14]. Fig. 2. Heterogenous Networks [13] QoS in LTE-A can be considered as a main and important concept. The hardest chal- lenge in wireless communication technologies is supporting strong QoS to satisfy dif- ferent user requirements and applications over the network. Scheduling algorithm is one of the principal methods used to preserve QoS which prioritizes applications in the network based on the service type, as each application requires special characteristics like delay, high data rate and correct jitter [15]. There are different packet scheduling algorithms which are used in LTE-A: Round Robin, Best CQI Scheduler, and Proportional Fair and more where the researchers every day seek to enhance the performance of LTE networks [16]. PS is used to allocate resource blocks for users depending on their Qos requirements and channel condition [17]. 3 Packet Scheduling Algorithms In LTE-A, there are many types of PS algorithms. The most famous and powerful algorithms are PF and a best channel quality indicator (Best CQI) [11]. The choice of the suitable PS is an essential design issue in LTE-A and should be based on the traffic types in the network. Moreover, between all PSs there is a trade off in their performance iJIM ‒ Vol. 14, No. 10, 2020 25 Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks between throughput and the other performance indicators: fairness, spectral efficiency and used energy per bit. PF aims to maximize fairness between users with an agreeable performance in the other performance indicators: average throughput, spectral efficiency and average sys- tem energy [11]. Best CQI is a channel-aware scheduling algorithm. It assigns RB to the user which has the best channel quality [11]. This scheduler aims to maximize the average throughput and spectral efficiency while giving an acceptable value of fairness. 3.1 Proportional Fair Algorithm PF is used in wireless communications. It is the most powerful and efficient algo- rithm used in LTE-A [11, 12]. Its priority function is shown in Eq. (1) [18, 19]. K* the priority value or each user which used to assign resource blocks for users. K* is calculated using the following equation [18,19, 20]: (1) Where, rk,n Service rate of kth user on the nth Resource Block (RB) Pk,n Assignment indicator variable (Pk,n =1, if nth RB is as- signed to kth user and = 0 if it’s not) tc Average window size Tk Average throughput information of kth user. It is com- puted by equation (2) k User index n Resource Block index (2) Where, Tk Previous average throughput kth , which assigned to UE in its all previous TTI Rk Throughput that UE gets in that TTI k User index k=K* when the kth user gets resources in the previous TTI. ) )1( (maxarg , 1 , ,* nk N n nkkc nk k rPTt r K å = +- = ïî ï í ì =+ +- - ),( 1 )() 1 1( ),() 1 1( , , )1( tR t tT t tT t k k c nk c nk c tT k=K* k≠K* 26 http://www.i-jim.org Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks Average throughput for UEs is the main factor in the PF priority function. It is com- puted from the history of Ues used throughput. Therefore, the overall performance of the network is affected by the methods used to compute the average throughput. 3.2 3.2 Best CQI Algorithm It belongs to channel-aware algorithms. It uses a channel indicator that is carrying the information on how good/bad the communication channel quality is in order to get the RB allocation for each time, without any care about fairness. Best CQI maximizes the throughput by selecting the user with the highest CQI value as shown in Eq. (3) [11]. (3) Where, Mk,n Maximum value of channel quality indicator CQI k,n Channel quality indicator value kth User index nth Resource Block index CQI sends from each UE to the eNodeB to inform it with its current channel quality Fig. 3 depicts the flow chart of Best CQI scheduler [11]. It creates a 2D array with row represents a UE and column represents assigned RB to each UE. It then chooses the largest element to each UE on a specific RB. After that, it sets the element of the cor- responding value of the row i and column j of array element equals 0. These steps are repeated for all users. Fig. 3. Flowchart of Best CQI scheduler algorithm. )(maxarg ,, nk k nk CQIM = iJIM ‒ Vol. 14, No. 10, 2020 27 Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks 4 Proposed Scheduling Algorithm The role of PS is allocating of resources in each TTI to UEs to achieve maximization in network performance. In LTE-A, the most famous and powerful algorithm is Pro- portional Fair (PF) [18]. Many modifications in the PF priority function are introduced in the literature by using different methods to find the average UE throughput. Some PF modifications are: Midrange Fair Mean, Arithmetic Mean, Median, Mid- range Mean, Geometric Mean and Range. These modifications of PF are used for ho- mogeneous LTE-A [4,5]. In this paper, PF modifications performance evaluation is presented for HetNet in LTE-A and a scheduling algorithm is proposed by modifying PF cost function to cal- culate the average throughput using the root mean square (RMS) method and it is named: Quadratic Proportional Fair (QPF). To calculate the average for a set of numbers, RMS can be used. It is finding the square root of the average squared values of these numbers. It has the same value as or a little bit larger than the average values which computed by the other used methods. RMS increases the associated resource block per UE. Hence, the total cell throughput and overall network performance are improved. QPF priority function equation is shown in (4) Tk, Tk(N+1) = (𝑅𝑘 2(1)+𝑅𝑘 2(2)+⋯……+𝑅𝑘 2(𝑁) 𝑁 ) 1/2 (4) Where, Rk(1), Rk(2), ………..,Rk(N), is the historical used throughput for kth UE and N is the number of recently computed throughput values for UE. This proposed method is compared with other PF modifications which used Arith- metic Mean and Geometric Mean as depicted in [10, 11]. 5 Simulation networks and results The proposed algorithm is implemented using Vienna LTE System Level Simulator [21]. The performance evaluation of QPF is to prove that it is able to support strongly the QoS with different users' requirements. The impact of user mobility is used in our performance study. QPF is compared with the original PF, Best CQI, PF with arithmetic mean (APF) and PF with geometric mean (GPF) algorithms with various UE velocities for LTE-A HetNet. LTE-A heterogeneous networks used in QPF performance evaluation with some per- formance indicators: Average throughput, cell throughput, spectral efficiency, energy per bit and Fairness. The simulation parameters are listed in Table 1 [14]. 28 http://www.i-jim.org Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks Table 1. Simulation Parameters Hexagonal grid, 26 cells, 3 sectors per BS, and 1 femto per sector Topology 2 GHz Carrier Frequency 20 MHz Bandwidth FDD Duplexing 2 No. of transmitter 2 No. of receiver CLSM Transmission mode 20m BS height 15dBi Antenna Gain 1.5m Receiver height 45dBm BS power 30 dBm Femto power 10 Number of UEs per femto 20 Number of UEs per BS Uniform User distribution in site area 10 TTI Simulation time 5.1 Network layout An LTE-A heterogeneous network with hexagonal geometry is used. The used net- work layout contains 26 Tri-sector antennas BSs and one femto BS for each sector with 500m distance between the BSs. Fig. 4 illustrates the simulated network layout. Fig. 4. Simulated Network Layout iJIM ‒ Vol. 14, No. 10, 2020 29 Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks 5.2 Results Analysis In this paper, the performance evaluation of QPF is introduced by comparing its performance with the most used algorithms in LTE-A networks: the original PF, Best CQI, PF with arithmetic mean (AMPF) and PF with geometric mean (GMPF) with the impact of user velocity. UEs speed is considered from low speed 3Km/h, through me- dium speed 60 Km/h and finally, high speed 120 Km/h. Average UE throughput is shown in fig.5 at different UEs speed: 3, 60, and 120 Km/h. As the results illustrate, Best CQI has the largest throughput at low and medium speeds. But, in high speed QPF has the best throughput value. This is due to that the channel status can be poor with high UEs velocity and it is also caused by using the RMS value to compute the average throughput in QPF, which gives an average value greater than the average value calculated by other methods (PF, Arithmetic Mean Method which used in (AMPF) and Geometric Mean Method which used in (GMPF)). The average UE Spectral efficiency is depicted in fig. 6. It also experiences decreas- ing when the velocity increases in all algorithms. However, QPF exceeds all algorithms in spectral efficiency because spectral efficiency is functioning in average throughput. QPF uses RMS to compute the average throughput to achieve a large value of average throughput. Fig. 5. Average UE Throughput (Mbps) vs. UEs Speed (Km/h) Fig. 6. Average UE Spectral Efficiency (bits/Hz) vs. UEs Speed (Km/h) Average Energy per bit is shown in fig. 7. As clearly shown, QPF has the least av- erage energy per bit in all velocities. QPF also outperforms the others in energy use. As clearly shown in Fig. 8, Best CQI has the best value of cell throughput at low and 0 1 2 3 4 3 Km/h 60 Km/h 120 Km/h PF Best CQI QPF AMPF GMPF 0 2 4 6 3 Km/h 60 Km/h 120 Km/h PF Best CQI QPF AMPF GMPF 30 http://www.i-jim.org Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks medium velocities. However, in high UE velocity QPF exceeds all algorithms. The increasing of the average cell throughput in QPF is caused by using of the RMS with all UEs speeds. Fairness performance indicator is shown in fig. 9. As the figure clearly depicts, QPF and AMPF have better value of fairness than the others in all UEs speeds. Fig. 7. Average Energy per bit (J) vs. UEs Speed (Km/h) Fig. 8. Average cell Throughput (Mbps) vs. UEs Speed (Km/h) Fig. 9. Fairness vs. UEs Speed (Km/h) As illustrated from the previous performance evaluation of the algorithms. QPF has best improved for spectral efficiency, energy per bit and fairness by 8.4%, 14%, and 9.3%, respectively than original PF. However, Best CQI has the best average UE and cell throughput than all algorithms by 2% and 1.8% in low and medium UE velocity, 0 500 1000 1500 3 Km/h 60 Km/h 120 Km/h PF Best CQI QPF AMPF 0 20 40 60 3 Km/h 60 Km/h 120 Km/h PF Best CQI QPF AMPF GMPF 0 0,1 0,2 0,3 0,4 0,5 3 Km/h 60 Km/h 120 Km/h PF Best CQI QPF AMPF GMPF iJIM ‒ Vol. 14, No. 10, 2020 31 Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks respectively. But, QPF has the best value of all types of throughput at high speed. QPF and GMPF has the same performance in fairness with all UEs speeds. 6 Conclusion and Future Works The new mobile communication technologies offer many solutions for assuring QoS for the advanced real-time applications. Strong cell recovery is needed also. So, there is a persistent need for wireless broadband technologies such as LTE-A which can strongly support QoS by selecting a reliable and powerful packet scheduling algorithm and introduce good cell coverage by using of heterogeneous capability. In this paper, modifications of PF algorithm are proposed, by using different meth- ods for computing the average throughput value which is the main and important pa- rameter in the PF cost function. These methods are the root mean square, arithmetic mean, and geometric mean which is used in LTE-A homogenous networks in the liter- ature [9, 10]. Complete performance evaluation of the proposed algorithms is intro- duced by comparing their performance with the original PF and Best CQI algorithms with various UE velocities. The performance indicators are average UE throughput, spectral efficiency, energy per bit, cell throughput and fairness. The results reveal that QPF has best improved spectral efficiency, energy per bit and fairness by 8.4%, 14%, and 9.3%, respectively than original PF. However, Best CQI has a better value of average UE and cell throughput than all algorithms with an im- provement of 2% and 1.8% in low and medium UE velocity, respectively, but QPF has the best value of all types of throughput at high speed. QPF and GMPF have the same performance in fairness with all UEs speeds. The evaluation of the proposed algorithm in 5G communication technology with the effective of admission control is considered as our future works. 7 References [1] G.Enzo,L.James and Z.Yang, ''The Performance Analysis of LTE Network", Communication Networks Spring, 2014. [2] T. Girici,C. Zhu, J. R. Agre, and A. Ephremides''Proportional Fair Scheduling Algorithm in OFDMA-Based Wireless Systems with QoS Constraints'', Journal of Communications and Networks, Vol. 12, No. 1, FEB. 2010. https://doi.org/10.1109/jcn.2010.6388432 [3] A.Khanderkar , et.al, ''LTE-Advanced: Heterogeneous Networks'', European Wireless Conference, San Diego, 2010. [4] S. Fouziya Sulthana and R. Nakkeeran, “Study of Downlink Scheduling Algorithms in LTE Networks”, Journal of Networks, Vol. 9, No. 12, Dec. 2014. https://doi.org/10.4304/ jnw.9.12.3381-3391 [5] S.Schwarz,C. Mehlführer and M. Rupp "Throughput Maximizing Multiuser Scheduling with Adjustable Fairness", Proceedings of the IEEE International Conference on Communications (ICC), pp. 1-5, June 2011. https://doi.org/10.1109/icc.2011.5963489 [6] A. B. Shams, S. R. Abied, Md. Asaduzzaman and Md. F. Hossain," Mobility Effect on the Downlink Performance of Spatial Multiplexing Techniques under Different Scheduling Algorithms in Heterogeneous Network", International Conference on Electrical, Computer 32 http://www.i-jim.org Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks and Communication Engineering (ECCE), 2017. https://doi.org/10.1109/ecace.2017.7913 032 [7] A. Rajesh, and R. Achar, "A Review of Heterogeneous Resource Allocation in LTE-A based Femto cell Networks with CQI Feedback", Indian Journal of Science and Technology, Vol. 9, No. 36, 2016. https://doi.org/10.17485/ijst/2016/v9i36/102109 [8] Y. Wang, K. S.garan2, X. Zhu, J. Fei, X. Kong and C. C. Lin," Frequency and Time Domain Packet Scheduling Based on Channel Prediction With Imperfect Cqi In Lte", International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013. https://doi.org/10.5121/ijwmn.2013.5412 [9] Nada M. Elshennawy,” Quadratic Proportional Fair Scheduling Algorithm for LTE-A Networks”, International Journal of Engineering Research and Technology. ISSN 0974- 3154, Volume 12, Number 11, pp. 1957-1963, 2019. [10] A. Büyükoğlu, M. İzzet Sağlam, A. Kavas, and M. Kartal, "An Efficient Throughput Averaging Method for Proportional Fair Algorithm Used in Mobile Networks," Proceedings of the IEEE Conference on Advances in Wireless and Optical Communications (RTUWO), 2016. https://doi.org/10.1109/rtuwo.2016.7821876 [11] Mai Ali Ibraheem, Nada M. El-Shennawy, A Sarhan, “A Proposed Modified Proportional Fairness Scheduling (MPF-BCQI) Algorithm with Best CQI Consideration for LTE-A Networks”, 13th International Conference Computer Engineering and Systems (ICCES), pp. 360-368, Cairo, Egypt, 2018. https://doi.org/10.1109/icces.2018.8639213 [12] M. W. Akhtar,R. Ghaffar, I. Rashid," A Q Learning and Fuzzy Q Learning Approach for Optimization of Interference Constellations in Femto–Macro Cellular Architecture in Downlink",Springer Science+Business Media, New York ,2016. https://doi.org/10.1007/ s11277-016-3206-z [13] F. Capozzi, G. Piro, LA .Grieco, G. Boggia and P. Camarda, "Downlink Packet scheduling in LTE cellular networks: Key design issues and a survey", IEEE Transaction on Vehicular Technoly, Vol. 15, No. 2, pp. 678–700, 2012. https://doi.org/10.1109/surv.2012.060912. 00100 [14] S.V. George, L. Mathews and S.S. Pillai, "Physical Layer Frame Structure in 4G LTE/LTE- A Downlinkbased on LTE System Toolbox", IOSR Journal of Electronics and Communication Engineering (IOSR-JECE) ,Vol. 10, Issue 3, pp. 12-16, 2015. https://doi. org/10.9790/2834-1203025153 [15] A. Khandekar, N. Bhushan, J. Tingfang and V. Vanghi, " LTE-Advanced: Heterogeneous Networks ", European Wireless Conference, Italy, 2010. https://doi.org/10.1109/ew.2010. 5483516 [16] Y. Wang, K. S.garan2, X. Zhu, J. Fei, X. Kong and C. C. Lin," Frequency and Time Domain Packet Scheduling Based on Channel Prediction With Imperfect Cqi In Lte", International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 4, August 2013. https://doi.org/10.5121/ijwmn.2013.5412 [17] A. Ebrahim ,E. Alsusa, and M. W. Baidas,'' An Uncoordinated Frequency Allocation Scheme for Future Femtocell Networks '', IEEE ,School of Electrical and Electronic Engineering, University of Manchester, 2016. https://doi.org/10.1109/iwcmc.2016.7577 064 [18] F. Capozzi, G. Piro, LA .Grieco, G. Boggia and P. Camarda, "Downlink Packet scheduling in LTE cellular networks: Key design issues and a survey", IEEE Transaction on Vehicular Technoly, Vol. 15, No. 2, pp. 678–700, 2012. https://doi.org/10.1109/surv.2012.060912. 00100 iJIM ‒ Vol. 14, No. 10, 2020 33 Paper—Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks [19] R. Kwan, C. Leung, and J. Zhang, “Proportional fair multiuser scheduling in LTE,” IEEE, Signal Processing Letters, vol. 16, pp. 461 –464, June 2009. https://doi.org/10.1109/lsp. 2009.2016449 [20] M. K. Ismail et. al., "Design and Analysis of Modified-Proportional Fair Scheduler for LTE Femtocell Networks," Journal of Telecommunication, Electronic and Computer Engineer- ing, 2017. [21] M. Rupp, S. Schwarz and M. Taranetz, "TheVienna LTE-Advanced Simulators Up and Downlink, Link and System Level Simulation", Springer Science+Business Media, Singapore 2016. https://doi.org/10.1007/978-981-10-0617-3 8 Author Nada M. Elshennawy, is an Assistanat Professor, Faculty of Engineering at Tanta University, Tanta in Egypt. Article submitted 2020-03-16. Resubmitted 2020-04-13. Final acceptance 2020-04-13. Final version published as submitted by the authors. 34 http://www.i-jim.org iJIM – Vol. 14, No. 10, 2020 Modified Proportional Fair Scheduling Algorithm for Heterogeneous LTE-A Networks