## 1 Introduction  
The Third Generation Partnership Project (3 GPP) introduced Long Term Evolution (LTE) Fourth Generation (4G) technology in Release-8 (Rel-8). It is based on Orthogonal Frequency Division Multiple Access (OFDMA). After doing a significant improvement in Rel-9, LTE provides higher data rates and better Quality of Service (QoS) than Third Generation (3G) mobile technology. The QoS is better in the cell-center area as users are close to the eNodeB (eNB), which strengthens the received signal. However, users in the cell-edge area are experiencing low data rates and poor QoS due to low received signal, high interference from adjacent eNBs and various fading effects [1].  
The packet scheduler implemented in eNB plays a vital role to enhance the QoS. This can be done by allocating time-frequency blocks known as Resource Blocks (RBs) to different users according to their current situations and priorities [2]. RBs of the OFDMA system is defined by the time and frequency domains in the \(x\)- and \(y\)-axes, respectively. A 10 ms long radio frame in the time domain is divided into 10 sub-frames each with 1 ms duration. Each sub-frame consists of two equal-sized time slots with duration of 0.5 ms. Each slot is composed of six or seven OFDMA symbols for extended and normal cyclic prefix respectively. In the frequency domain, one RB has 12 consecutive subcarriers with in total 180 kHz, where each subcarrier has 15 kHz bandwidth [3; 4]. Figure 1 shows the basic RB structure of LTE with a normal cyclic prefix.  
The packet scheduler in the LTE system calculates the metric of all users according to the corresponding algorithm. It considers various factors, such as instantaneous and previous throughput, spectral efficiency, head of line (HOL) packet delay, the number of packets waiting in the queue and several scheduling constants. The user with higher metric value will be in front of the queue to get the service. An efficient packet scheduler can reduce the traffic congestion in the network. Different downlink scheduling algorithms have different approaches to determine the user priority. Proportional fairness (PF) is the basic scheduler [5], which is based on prioritizing the user with maximum metrics from the ratio of the instantaneous and previous data rates. This scheduling algorithm does not consider any kind of packet delay or queue length. Therefore, real-time data are experiencing low QoS and high rate of packet loss. The Modified Largest Weighted Delay First (MLWDF) algorithm ensures ideal throughput to the system and maintains better fairness to all users than other algorithms [6; 7; 8]. This scheduler largely depends on QoS and packet delay. The throughput optimal MLWDF algorithm has less complexity among all other scheduling algorithms and it considers the real-time traffic. The primary goals of this scheduler are to provide better QoS, to enhance the spectral efficiency and to provide good fairness to the user. Other scheduling algorithms such as exponential proportional fairness (EXP/PF), exponential rule (EXP/Rule) and Logarithmic rule (LOG/Rule) are comparatively more complex to implement [9]. Therefore, this paper extends the MLWDF algorithm to provide services.  
PF and basic MLWDF algorithms are considered in the simulation process to compare the performance with the proposed extended MLWDF (EMLWDF) algorithm. This proposed algorithm gives more priority to the cell-edge users by considering the distance between user and eNB, downlink Signal to Interference plus Noise Ratio (SINR) and packet delay while maintaining the cell performance.  
Figure 1: Time-frequency Resource block (RB) structure of Long Term Evolution (LTE).  
The remaining paper is organized as follows. Section 2 describes the related work followed by the system model of the proposed algorithm in Section 3. Section 4 has results and discussion, Section 5 describes limitations and future work and conclusions are presented in Section 6.