Effective 5G Wireless Downlink Scheduling and Resource Allocation in Cyber-Physical Systems ^†

Abstract

In emerging Cyber-Physical Systems (CPS), the demand for higher communication performance and enhanced wireless connectivity is increasing fast. To address the issue, in our recent work, we proposed a dynamic programming algorithm with polynomial time complexity for effective cross-layer downlink Scheduling and Resource Allocation (SRA) considering the channel and queue state, while supporting fairness. In this paper, we extend the SRA algorithm to consider 5G use-cases, namely enhanced Machine Type Communication (eMTC), Ultra-Reliable Low Latency Communication (URLLC) and enhanced Mobile BroadBand (eMBB). In a simulation study, we evaluate the performance of our SRA algorithm in comparison to an advanced greedy cross-layer algorithm for eMTC, URLLC and LTE (long-term evolution). For eMTC and URLLC, our SRA method outperforms the greedy approach by up to 17.24%, 18.1%, 2.5% and 1.5% in terms of average goodput, correlation impact, goodput fairness and delay fairness, respectively. In the case of LTE, our approach outperforms the greedy method by 60%, 2.6% and 1.6% in terms of goodput, goodput fairness and delay fairness compared with tested baseline.

1. Introduction

Cyber-Physical Systems (CPS) and the Internet of Things (IoT) support numerous important applications, such as connected cars, factory automation, intelligent surveillance, smart homes and smart agriculture. The total number of IoT devices has already exceeded seven billion in the second quarter of 2018 without including two billion smartphones in the world [1]. It is projected that there will be approximately 50 billion connected devices by the end of 2020 [2]. Further, 70% of IoT devices will use cellular technology with better connectivity and reliability [3]. Thus, massive cellular traffic and connectivity requirements should be handled gracefully, dramatically increasing the demand for higher wireless communication performance and enhanced connectivity. It is difficult to support the demand using today’s wireless technology [3,4].

To address these challenges, the International Telecommunication Union (ITU) and International Mobile Telecommunication (IMT) have envisioned the fifth generation of cellular communication technology, called 5G for brevity. A 5G base station needs to support efficient Scheduling and Resource Allocation (SRA) via Time Division Duplexing (TDD), as well as Frequency Division Duplexing (FDD) [5,6,7]. In 5G, user applications are classified into three broad categories: (1) enhanced Mobile Broadband (eMBB), (2) enhanced Machine Type Communication (eMTC) and (3) Ultra-Reliable Low Latency Communication (URLLC) [8]. To support different 5G use-cases, as illustrated in Figure 1, a base station needs to use different numbers of Resource Blocks (RBs) along the time axis for TDD and different sub-carrier bandwidth allocations on the frequency axis to support FDD. For eMBB, typically, a 100-MHz bandwidth in the frequency domain and at least 500 RBs in the time domain are needed. For URLLC, the latency and reliability are critical. It uses a modest bandwidth up to 5 MHz with an RB sequence of 25 symbols for FDD and TDD, respectively. In addition, eMTC uses 1.4 MHz bandwidth and six RBs in the frequency and time domain, respectively.

These use-cases show that a 5G base station needs to handle diverse traffic at each transmission interval. It is challenging to schedule and allocate resources at each transmission interval for many devices with diverse use-cases. In addition, the first generation of 5G comes as a Non-Stand-Alone (NSA) architecture that requires backward compatibility with the previous generation Long-Term Evolution (LTE) technology [9,10,11,12], making Scheduling and Resource Allocation (SRA) even more challenging.

To address the challenges of 5G, Feminias et al. [13] have recently proposed a novel cross-layer SRA framework by extending their previous work [14]. In their work, the utility function is defined in terms of the weighted goodput for cross-layer SRA. It provides a greedy cross-layer optimization over the Physical (PHY) and Data Link Control (DLC) layers to support effective SRA for massive Multiple-Input-Multiple-Output (MIMO) systems by taking advantage of higher bandwidth [15] and adaptive Modulation and Coding Schemes (MCSs) [16]. However, their SRA algorithm is greedy, potentially producing sub-optimal results; hence, it may not perform well for broader 5G use-cases. To address this issue, we have designed a new SRA algorithm based on dynamic programming [17]. It formulates the utility function based on the available bandwidth and required RBs, while allocating resources to maximize the total utility. Although the knapsack-like problem of dynamic SRA is usually NP-hard, we show that the time complexity of our algorithm is polynomial in a practical sense. In this paper, we further extend our conference publication [17] as follows:

• This paper discusses the need for SRA based on dynamic programming at the base station to support diverse 5G use-cases, as depicted in Figure 1.
• We extend our SRA algorithm for 5G use-cases: eMTC, URLLC and eMBB. The problem formulation shows the scalability of the utility function to adopt all these use-cases with LTE to support the first generation 5G NSA architecture.
• An extended discussion of related work is given in Section 2 to review state-of-the-art SRA techniques and discuss the need for our work presented in this paper.
• In this paper, we extend the performance evaluation to consider the eMTC and URLLC in addition to LTE. For LTE, our SRA algorithm outperforms the greedy approach [13] by up to 60%, 2.6% and 1.6% in terms of goodput, goodput fairness and delay fairness, conforming to [17]. For eMTC and URLLC associated with more demanding performance requirements, our SRA algorithm continues to outperform the greedy cross-layer approach [13] by up to 17.24%, 18.1%, 2.5% and 1.5% in terms of average goodput, correlation impact, goodput fairness and delay fairness, respectively.

The remainder of this paper is organized as follows. Section 2 reviews state-of-the-art SRA algorithms. Section 3 formulates the SRA problem. In Section 4, our SRA algorithm is described and its time complexity analyzed. In Section 5, the performance of the proposed SRA algorithm is evaluated in comparison to [13] for LTE, eMTC and URLLC use-cases. Finally, the paper is concluded and future work is discussed in Section 6.

2. Related Work

In a mobile network, when a user requests data from the Internet, the request is sent to the base station. The base station retrieves the data through the Internet and provides them to the user in the form of data packets. These data packets are framed into larger data frames and transmitted from the base station towards the User Equipment (UE). These data frames consist of time and frequency resources in terms of RBs and the number of subcarriers, respectively. Allocating resources to multiple users in a single data frame is known as the SRA problem at the base station. SRA has been studied over the decades from a variety of performance perspectives: (1) spectral efficiency, (2) scalability, (3) computational complexity, (4) Quality of Service (QoS), (5) fairness, (6) target delay, (7) queue length, (8) priority, (9) Guaranteed Bit-Rate (GBR), etc. [18,19,20,21]. In this paper, we classify state-of-the-art approaches for SRA into two broad categories: (1) channel-dependent and (2) channel-independent SRA algorithms, as summarized in

Table 1. Taxonomy of Scheduling and Resource Allocation (SRA) algorithms.

Category	Dependent Parameter	Algorithm Name	Resource Allocation Summary
Channel-Independent	Classical Algorithms	Proportional Fair (PF) [22,23,24]	Allocate resources to users in proportion to their weights
		First-In-First-Out (FIFO) [25,26,27]	Allocate resources based on their arrival order
		Round Robin [28,29,30]	Allocate resource to each user for a fixed time interval
		Weighted Fair Queuing [31,32]	Allocate resources based on users’ weights inversely proportional to costs
		Blind Equal Throughput [33,34,35]	Allocate resources to maintain minimum throughput requirements
		Largest Weighted Delay First [36,37,38]	Allocate resources based on users’ weights and delay sensitivities
	VoIP	Delay sensitive [39,40,41,42,43]	Prioritize VoIP traffic and provide best effort service to other traffic
	Video Streaming	Dynamic Adaptive Streaming Over HTTP (DASH) [44,45,46,47]	Ensure a guaranteed bit-rate to high-rank users based on the channel quality
Channel-Dependent	Guaranteed Bit-Rate (GBR)	Priority Based [48,49,50,51]	Allocate resources based on user priority
		Quality of Service (QoS) Aware Scheduler [52,53,54]	Prioritize users and allocate resources accordingly
		Hybrid Schedulers [55,56]	Allocate resources based on users’ QoS and delay sensitivity requirements
	Delay-Sensitive	Weighted Delay First [57,58,59]	Assign a higher weight and more resources to a user close to its target
		Hybrid Automatic Repeat Request (HARQ) Aware Scheduling  [60,61,62]	Prioritize users based on the average throughput and delay
		Exponential/Proportional Fair (Exp/PF) [63,64]	Maximize throughput while providing a fair level of services
		Two-Level Scheduler [65,66]	Prioritize real-time and non-real-time data to allocate resources
		Delay-Prioritized Scheduling [38,67]	Assign resources based on users’ delay requirements
		Exp and Log Rule [68,69]	Assign resources to a user based on his/her position in the queue
		Game Theory-Based Scheduling [70,71]	Fairly distribute the resources among the participating users based on game theory
	Cross-Layer Algorithm	Overload-State Downlink Resource Allocation [72,73,74]	Assign resources based on the queue state information
		Greedy Resource Block (RB) Allocation [13]	Assign resources based on the queue and channel state information

. Within each category, they are further classified into subcategories.

All the algorithms in Table 1 are used to handle either a single type of traffic or multiple QoS classes at the base station. In the case of 5G, SRA decisions take place based on the queue and Channel State Information (CSI); hence, the channel-independent SRA algorithms are not relevant. In the case of channel-dependent algorithms, most work has been focused on supporting a GBR and dealing with delay-sensitive traffic. However, in the case of 5G, the base station needs a cross-layer SRA algorithm, which can make cross-layer SRA decisions considering the queue and CSI. Table 1 shows the state-of-the-art system-centric cross-layer SRA algorithms that make SRA decisions considering both the queue and channel state. However, none of them has specifically been designed from the 5G perspective. In 5G, the base station needs to serve diverse traffic of different use-cases in each transmission interval. An advanced cross-layer approach [13] considers the queue state and CSI together for SRA decisions; however, it is a greedy algorithm that may produce suboptimal results. To address this problem, we have proposed a new cross-layer SRA algorithm based on dynamic programming in [17] that makes optimal SRA decisions at 5G base stations with polynomial time complexity. In this paper, we extend our previous SRA framework [17] to accommodate various 5G use-cases.

3. Problem Formulation

Figure 2 shows the downlink time-slotted architecture inspired by [13]. It consists of mainly two parts: a base station and User Equipment (UE), as shown in the figure. The base station has $N_T$ transmit antennas with transmitting power $P_T$. In a real environment, multiple mobile stations are connected with a base station. For simplicity, we show just one UE in the figure and assume that all the Mobile Stations $MS=\{M{S}_1,\dots ,M{S}_N\}$ follow the same architecture. Each of these mobile stations supports multiple-input-multiple-output (MIMO) technology with an array of $N_T\times N_R$ transmitting and receiving antennas.

In this architecture, we have considered a busy base station with an infinite traffic queue: there is a continuous traffic flow from the upper layer to the DLC and PHY layers of the base station, as shown in Figure 2. Requests from different mobile stations are queued at the base station. Requests can consists of a variety of 5G use cases, such as eMBB, URLLC and eMTC. SRA decisions in this architecture are cross-layer in that decisions are made considering the DLC and PHY layers, as shown in Figure 2. It takes input from the queue state and the CSI, which is three-dimensional information consisting of time (symbols), frequency (number of sub-bands) and space (number of antennas), as shown in Figure 2. At each transmission interval, a CSI exchange takes place between the base station and a mobile station. The mobile station CSI tells the base station about the channel properties of a communication link such as delay-Doppler spread, Signal-Interference-to-Noise-Ratio (SINR), angle-of-arrival, angle-of-departure and PHY layer configurations such as Modulation and Coding Schemes (MCS) and the rank indicator, precoding matrix indicator and channel quality indicator received from the mobile station. The scheduled resources are then transferred to the PHY layer for transmission, as shown in the figure. At the PHY layer, the information goes through the Adaptive Modulation and Coding (AMC) process, which decides the appropriate modulation schemes for individual users. Data modulation is followed by MIMO processing and data transmission using transmit antennas [14,75,76] in the base station. In a mobile station, the reverse process takes place: the PHY layer performs multi-carrier post-processing and MIMO equalization on the received signals through the receiving antennas. The AMC and MIMO precoding matrices are exchanged and known by the mobile station during the CSI exchange. Finally, the demodulation process extracts the coded data.

In the case of multi-carrier time-slotted downlink architecture, resources, called RBs, are allocated in the time domain across multiple sub-bands. For each transmission time interval t, RBs consist of $N_{sym}$ symbols for a duration $T_p$, along the time axis and sub-bands of $\Delta f=\frac{1}{T_p}$ in the frequency domain. On the time axis, each RB holds a fixed number of time slots $T_s^{PHY}$. In this paper, PHY represents either orthogonal frequency division multiplexing (OFDM) or filter bank multi-carrier (FBMC) symbols.

3.1. Orthogonal Frequency Division Multiplexing

OFDM has been used over a decade and has proved its robustness in multi-carrier technologies, such as Wi-Fi and cellular technology. It uses multiple smaller subcarriers to avoid the Inter-Channel Interference (ICI) and Inter-Symbol Interference (ISI) over the network. It adds a Cyclic Prefix (CP) to demodulate the signal effectively on the receiver side. It is assumed that the transmitter and receiver are synchronized properly to avoid the misinterpretation of symbols [77]. It uses the Inverse Fast Fourier Transform (IFFT) to convert the symbol from the time domain to the frequency domain at the transmitter, while applying the Fast Fourier Transform (FFT) to transform the symbols from the frequency domain to the time domain at the receiver. Since OFDM uses the Cyclic Prefix (CP) to cancel out ISI, there are $N_{sym}^{long}$ OFDM symbols prefixed with a long CP of duration $T_{CP}^{long}$. Furthermore, there are $N_{sym}^{short}=N_{sym}-N_{sym}^{long}$ symbols prefixed with a short CP of duration $T_{CP}^{short}$. Thus, for OFDM systems, the fixed time slot size is:

$$T_s^{OFDM}=(N_{sym}\times T_p)+(N_{sym}^{long}\times T_{CP}^{long})+(N_{sym}^{short}\times T_{CP}^{short})$$

(1)

where $T_p$ is the symbol duration and $T_{CP}$ is the symbol duration with CP. Hence, OFDM is spectrally inefficient since it adds $(N_{sym}^{long}\times T_{CP}^{long})+(N_{sym}^{short}\times T_{CP}^{short})$ cyclic prefixes, which consume additional resources in the frequency domain. The CPs usually consume about 25% of the subcarrier bandwidth $\Delta f$ [78].

Filter Bank Multi-Carrier

In 5G, a base station needs to serve a large number of users; thus, it needs a spectrally-efficient PHY waveform. FBMC uses a chain of filters at each subcarrier to make it spectrally efficient, unlike OFDM, which uses CPs. Hence, FBMC can enhance the spectral efficiency and improve the network performance. For FBMC, the fixed time slot size $T_s^{FBMC}$ is:

$$T_s^{FBMC}=N_{sym}\times T_p$$

(2)

We assume that the SRA process happens at the beginning of a Transmission Time Interval (TTI) between two consecutive time slots, similar to [13]. By comparing Equations (1) and (2), we observe that FBMC achieves higher spectral efficiency compared to OFDM due to the absence of CPs. However, FBMC applies a filter chain at each individual subcarrier. Hence, the base station needs to spend more time and computational resources compared to OFDM.

3.2. DLC Layer

The queue $Q_u$ at the base station may contain a variety of traffic such as eMBB, URLLC and eMTC. At each TTI, the base station allocates a spatial stream, $L_u$, for each user u. The total transmission capacity at each TTI is ${\gamma }_{u,l}(t,N_{B{}_u})$, where $lϵL_u=\{1,\dots ,L_u\}$ and $N_{B{}_u}$ is the number of RBs required by user u. The total queue length at each TTI at the base station is:

$$\begin{array}{c}\hfill Q_u(t+1)=Q_u\left(t\right)+A_u\left(t\right)-S_u\left(t\right)\end{array}$$

where $A_u\left(t\right)$ and $S_u\left(t\right)$ represent the number of the arriving data bits to transmit for the user u during TTI t and that successfully transmitted to the user, respectively. These queues are then forwarded to the PHY layer for SRA.

3.3. PHY Layer

When there are $N_{MS}$ mobile stations, at the beginning of TTI t, the SRA unit of the BS is required to derive the RB allocation set $N_B=\{N_{B1},\dots ,N_{B{N}_{MS}}\}$, where $N_{Bu}$ is the number of RBs allocated to MS u, and the MCS allocation set $\mu =\{{\mu }_1,\dots ,{\mu }_{N_{MS}}\}$, where ${\mu }_u=\{{\mu }_{u,1},\dots ,{\mu }_{u,L_u}\}$ represents a set of MCSs assigned to each spatial stream l of MS u, to effectively allocate RBs and MCSs, respectively. For simplicity, t is dropped in our problem formulation presented hereafter. We formulate the SRA optimization problem to maximize the total utility V, i.e., the total weighted goodput, as follows:

$$\begin{array}{cc}\hfill V=& \underset{{\mathcal{N}}_B,\mu }{\max }\sum _{u=1}^{N_{\mathit{MS}}}\sum _{l=1}^{L_u}{w}_u{r}_{u,l}\left({{\mathcal{N}}_B}_u\right)\left[1-{\mathit{BLER}}_{u,l}^{\left({\mu }_{u,l}\right)}\left({{\mathcal{N}}_B}_u\right)\right]\hfill \\ & \mathrm{subject}\mathrm{to}{{\mathcal{N}}_B}_k\cap {{\mathcal{N}}_B}_j=\varnothing \forall k\ne j\hfill \\ & \phantom{\mathrm{subject}\mathrm{to}}\sum _{l=1}^{L_u}{r}_{u,l}\left({{\mathcal{N}}_B}_u\right)\le Q_u\forall (u,l)\hfill \\ & \phantom{\mathrm{subject}\mathrm{to}}{\mathit{BLER}}_{u,l}^{\left({\mu }_{u,l}\right)}\left({{\mathcal{N}}_B}_u\right)\le {\mathit{BLER}}_0\forall (u,l)\hfill \end{array}$$

where $w_u$ is the weight of user u and $BLE{R}_{u,l}^{\left({\mu }_{u,l}\right)}$ is the Block Error Rate of user u’s spatial stream l to which the MCS ${\mu }_{u,l}$ is assigned.

The SRA unit is required to maximize the utility function V subject to these three constraints:

• An RB should be exclusively allocated to one user.
• The scheduler should allocate no more maximum transmission capacity than the number of bits in its queue to maintain the frugality constraint.
• The average $BLER$ of u does not exceed the upper bound, $BLER$${}_0$, for a minimum quality guarantee.

The proposed methodology in [13] uses an adaptive MCS [14] for each user u considering his/her Channel State Information (CSI) and Queue State Information (QSI). Moreover, the authors proposed a greedy algorithm to allocate RBs to users efficiently. Essentially, it allocates the first RB to the user with the largest utility increase. It repeats this greedy approach until the set of non-allocated RBs becomes empty or there are no more active users to whom to allocate RBs. In this paper, we propose a cost-effective algorithm based on dynamic programming to allocate RBs optimally to active users, while applying the same adaptive MCS scheme used in [13].

4. Dynamic Scheduling and Resource Allocation

In general, a greedy algorithm makes a choice deemed best according to a certain criterion regardless of the choices it made before or will make in the future. Although it may find an effective solution in a reasonable time, it also results in a suboptimal solution when a series of local decisions fails to lead to a global optimum. The basic idea for dynamic programming is to solve subproblems optimally only once and store the results and look up the stored optimal solutions to the subproblems instead of recomputing them to compute the optimal solution for a given problem efficiently [79,80].

In this paper, we design a new SRA algorithm by adapting the dynamic programming method for the 0/1 knapsack problem to optimize the utility of SRA for allocating RBs to active users with non-empty queues. It is challenging to design a cost-effective algorithm for RB allocation, since the 0/1 knapsack problem is NP-complete. In this section, we design a dynamic programming algorithm to maximize the utility defined in Section 3 in polynomial time and analyze the time complexity.

To this end, we first design the recursive structure of utility function V to allocate free RBs, $N_B^{free}$, optimally to an arbitrary user u where $Q_u>0$ as follows:

$$V[u,k]=\{\begin{array}{cc}\hfill max\left(V[u-1,k],V[u-1,k-m\left[u\right]]+w\left[u\right]\times r_{u,l}\left(m\left[u\right]\right)\right)& \mathrm{if}m\left[u\right]\le k;\\ V[u-1,k]\hfill & \mathrm{otherwise}.\end{array}$$

Here, k is the number of the available RBs, $m\left[u\right]$ is the number of RBs required by the MS u and $r_{u,l}\left(m\left[u\right]\right)$ is the transmission capacity provided to MS u by $m\left[u\right]$ RBs. If $m\left[u\right]\le k$, MS u can be assigned the required number of RBs. In this case, our dynamic programming method for SRA optimizes the total utility by assigning $m\left[u\right]$ RBs to MS u, if $V[u-1,k-m\left[u\right]]+w\left[u\right]\times r_{u,l}\left(m\left[u\right]\right)>V[u-1,k]$ and updates the total utility as $V[u-1,k-m\left[u\right]]+w\left[u\right]\times r_{u,l}\left(m\left[u\right]\right)$. Otherwise, it does not assign the RBs to MS u and maintains the utility as $V[u-1,k]$. If $m\left[u\right]>k$; however, the RBs required by MS u are unavailable; therefore, our approach cannot meet the requirement of MS u. As a result, the utility remains as $V[u-1,k]$. With this, we design the dynamic programming algorithm for SRA based on these recursive properties, as shown in Algorithm 1.

Algorithm 1: SRA via dynamic programming.

As discussed earlier, the base station has limited transmission capacity $r_{u,l}(t,N_{B_u})$ at each TTI t, where the spatial stream, l, and number of RBs, $N_{B_u}$, represent the resources in the frequency and time domain, respectively. At the 5G base station, the user requests in a queue may be of eMBB, URLLC and eMTC types. As a result, it may demand various $m\left[u\right]$ RBs, such as 100, 25 and 6 for the eMBB, URLLC and eMTC use-cases, respectively. In this case, our utility function V allocates the required RBs only if $m\left[u\right]\le k$ and tries to maximize the transmission capacity $r_{u,l}$. If $m\left[u\right]>k$, it holds the request of user u till the next TTI and schedules it later. Hence, the user requests of diverse use-cases at the 5G base station can be scheduled together by our SRA algorithm based on dynamic programming. By leveraging dynamic programming, we fully optimize the allocation of the transmission capacity at the base station at every TTI.

Time Complexity Analysis

The time complexity of Algorithm 1 is $O(N_{MS}\times N_{all})$, where $N_{all}$ is the total number of RBs in a wireless communication frame at the BS. In general, when the number of items to consider is n and the total capacity of the knapsack is W, the time complexity of the dynamic programming algorithm for the 0/1 knapsack problem is $O\left(nW\right)$ [81]. $O\left(nW\right)$ is pseudo-polynomial complexity, since there is no guarantee that W is a polynomial function of n, but it could be arbitrarily large (e.g., exponential with respect to n). In practice, however, $N_{all}$ during a wireless communication frame is a fixed constant known a priori. For example, in LTE, one frame is 10 ms, and $N_{all}$ is six and 100 when the channel bandwidth is 1.4 MHz and 200 MHz, respectively. Each RB consists of 84 resource elements when each RB consists of seven symbols (time slots) in the time axis and 12 subcarriers (15 kHz each) in the frequency axis [82]. As long as $N_{all}$ remains a constant or is a polynomial function of $N_{MS}$ in practical implementations of the 5G standard, the time complexity of our algorithm remains polynomial.

5. Performance Evaluation

We have compared the performance of the proposed SRA algorithm based on dynamic programming to that of the novel greedy algorithm [13], which is used as the baseline for performance comparisons in this paper. To evaluate the proposed SRA algorithm, we use the MATLAB LTE toolbox (version 2017a, Mathworks, Natick, MA, USA), with a 5G library that supports the system architecture as per the 3GPP recommendations [83], similar to the state-of-the-art work, such as [13,14]. For fair comparisons, we use the same simulation settings as the baseline [13]. To implement the greedy SRA and dynamic programming algorithms, we have modified the lteDLResourceGrid function.

Performance is measured in terms of goodput and fairness [84] for the two dominant 5G waveforms, i.e., OFDM and FBMC [85,86,87]. In the rest of this section, we call the proposed method dynamic and the baseline method [13] as greedy for brevity. The greedy-FBMC and greedy-OFDM conventions are used to address the reproduced baseline approach [13] for the FBMC and OFDM waveforms, respectively. Their results are plotted using dotted lines. Similarly, dynamic-FBMC and dynamic-OFDM refer to the proposed SRA algorithm with the FBMC and OFDM waveforms, respectively. The results of dynamic-FBMC and dynamic-OFDM are plotted with solid lines for clarity of presentation.

In our previous work [17], we evaluated performance for LTE with a 20-MHz bandwidth and 100 RBs, since the 5G standardization was still underway at that time. As the 5G standardization has been finalized, we have three broad categories of use cases: eMBB, URLLC and eMTC for 5G NSA, as discussed before. From the scheduling perspective, we can distinguish these use cases as different requirements for bandwidth and RBs: (1) eMBB with a 100-MHz bandwidth with 500 RBs or more; (2) URLLC with up to 5 MHz and 25 RBs; and (3) eMTC with 1.4 MHz and 6 RBs or less. Using these settings, we compare the performance of greedy-FBMC, greedy-OFDM, dynamic-FBMC and dynamic-OFDM. Unfortunately, during the performance evaluation, we found two limitations of the LTE toolbox: (1) for a single cell, only up to 16 users can be simulated; and (2) a maximum of 100 RBs can be modeled in the PHY layer; hence, we cannot evaluate the eMBB case in this paper. A more extensive evaluation is reserved for future work. The results of the URLLC and eMTC use-cases are shown in Figure 3 and Figure 4 for goodput and in Figure 5 and Figure 6 for fairness measurements. A detailed discussion of goodput and fairness measurements is given in the following subsections.

5.1. Goodput Measurements

Goodput measurements are important at the application-level, since it shows the rate of successful data packet delivery observed on the UE side. Different from throughput, a goodput measurement excludes packet retransmissions; hence, the goodput can be comparatively lower than the throughput. However, in the case of noisy environments, it is important to measure the goodput to verify the successful delivery of packets received at a UE in a cell. To measure the goodput, we consider the delay and Doppler parameters as shown in

Table 2. Channel model parameters [83].

Channel Model	Doppler Frequency (Hz)	Correlation Profiles
		Low		Medium		High
		$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\alpha }$	$\mathit{\beta }$
EPA	5	0	0	0.3	0.9	0.9	0.9
EVA	5, 50	0	0	0.3	0.9	0.9	0.9
ETU	70, 300	0	0	0.3	0.9	0.9	0.9

.

As shown in Table 2, we consider three delay spread channel models: (1) the Extended Pedestrian A (EPA), (2) the Extended Vehicular A (EVA) and (3) the Extended Typical Urban (ETU) models. Each of these channel models has different delay profiles. EPA has the lowest delay and interference. EVA and ETU have higher delay and interference, in that order. We have also considered different correlation profiles as: (1) low, (2) medium and (3) high between the base station $\alpha$ and mobile station $\beta$, as shown in Table 2.

5.1.1. Average Goodput for Different Doppler Frequencies

In a dense environment, signals may be reflected or the mobility of users may cause the Doppler effect in signals. The Doppler effect may reduce the overall performance of the network. Hence, in this paper, we have tested the proposed SRA and the baseline [13] against the standard Doppler frequencies for 5, 50 and 300 Hz, as suggested in [83]. Figure 3 shows the average goodput for different Doppler frequencies suggested for the EPA, EVA and ETU channel models. The performance is evaluated for the LTE, URLLC and eMTC use-cases.

The overall trend shows that the goodput increases as the number of users in a cell increases. It also shows that dynamic-FBMC outperforms dynamic-OFDM, greedy-FBMC and greedy-OFDM. For three users in a cell, dynamic-FBMC outperforms dynamic-OFDM, greedy-FBMC and greedy-OFDM by approximately 6 Mbps (≈11.7%), 13 Mbps (≈29.5%) and 17 Mbps (≈42.5%), as shown in Figure 3a–c for the LTE use case. For URLLC and eMTC, its goodput is higher than the others’ by up to approximately 1–3 Mbps, as shown in Figure 3d–f for URLLC and Figure 3g–i for eMTC. In the case of more than six users in a cell, dynamic-FBMC outperforms greedy-FBMC by up to 1–3 Mbps (≈1.3–5.4%) and dynamic-OFDM by up to 10 Mbps (≈17.24%) with different Doppler frequencies, as shown in Figure 3d–f for URLLC and Figure 3g–i for eMTC. Similarly, dynamic-OFDM outperforms greedy-OFDM by 2–3 Mbps (≈5.4%) for the EPA, EVA and ETU channels with different Doppler frequencies, as shown in Figure 3. Overall, dynamic-FBMC outperforms dynamic-OFDM by up to 8–10 Mbps (≈12.12–17.24%) for different Doppler frequencies, as shown in Figure 3a–c for LTE, Figure 3d–f for URLLC and Figure 3g–i for eMTC when more than six users are present in the cell.

5.1.2. Impact of Correlation on Average Goodput

The incoming signal can be correlated with the transmitting and receiving antennas. The higher correlation of antennas leads to degradation of the overall system performance. As 5G uses MIMO technology, it is important to measure the correlation. In this paper, we have considered the standard high, low and medium correlation profiles, as shown in Table 2, where $\alpha$ means the base station and $\beta$ means the UE side correlation, as per [83]. The results are shown for the LTE, URLLC and eMTC use cases in Figure 4 with EPA, EVA and ETU channel models and low, medium and high correlation.

The overall trends show that the proposed dynamic approach achieves similar performance to that of the baseline for the low correlation profile as plotted in Figure 4a–c for LTE, Figure 4d–f for URLLC and Figure 4g–i for eMTC. When there are less than six users in a cell with respect to the LTE use case, dynamic improves the goodput by approximately 8–10 Mbps (≈11.1–18.1%), as shown in Figure 4a–c. The biggest goodput enhancement is approximately 14 Mbps (≈60%), achieved by dynamic-FBMC-high over greedy-FBMC-high (the black solid and dotted curves in Figure 4a). The dynamic-FBMC outperforms the greedy-FBMC by up to 4 Mbps (≈7.27%) in the case of medium correlation and up to 5 Mbps (≈9.09%) for high correlation profiles, as shown in Figure 4d–f for URLLC and Figure 4g–i for eMTC, respectively. Overall, dynamic-FBMC outperforms dynamic-OFDM by up to 8 Mbps (≈16%), as shown in Figure 4d–f for URLLC and Figure 4g–i for eMTC, respectively.

5.2. Fairness Measurements

Fairness is a measure to calculate how fairly the base station is allocating resources to the requests made by multiple users. In the case of heavy traffic, a user request may have to wait longer to get resources and may even starve. Hence, a fairness analysis is important for any scheduling scheme. To ensure the fairness of our proposed SRA algorithm, we have used Jain’s fairness measure. Jain et al. [84] proposed a methodology to calculate the fairness index among the users. If the measured goodput of the users is $T=\{T_1,\dots ,T_n\}$ and the required fair goodput is $O=\{O_1,\dots ,O_n\}$, then the normalized goodput is $X_n=\frac{T_n}{O_n}$. The overall goodput fairness is measured as follows:

$$FairnessIndex=\frac{(\sum X_n^2)}{n\sum X_n^2}$$

The delay fairness can be derived similarly from the above equation. Figure 5 and Figure 6 show the results of fairness analysis in terms of average goodput and delay. The fairness is bounded between zero and one (i.e., 100%). If Jain Fairness Index equals to 1, perfect fairness is achieved. On the other hand, zero fairness means starvation. There are more general fairness indicators [88,89]. In this paper, however, our main objective is to compare the performance of our approach to that of the advanced greedy baseline [13]. For fair comparisons, we use the same fairness metric and simulation settings as [13]. Using the more general fairness indicators and using other waveforms are reserved for future work.

In this paper, we consider two dominant 5G waveforms, OFDM and FBMC, as discussed before. A major implementation comparison between them is the number of complex symbol multiplications. In OFDM, the number of multiplications per symbol that the split-radix algorithm has is:

$$C_{FFT/IFFT}=M((log\left(M\right)-3)+4)$$

where M is the number of complex symbols. FFT and IFFT stand for the FFT and IFFT on the receiver and transmitter side, respectively.

In FBMC, the number of multiplications per symbol is:

$$C_{SFB/AFB}=2M((log\left(M\right)-3)+4K)$$

where the $SFB$ and $AFB$ are the Synthesis and Analysis Filter Banks at the transmitter and receiver side, respectively.

OFDM suffers from poor spectral selectivity, which leads to marginal degradation in fairness as the number of users increases, as plotted in Figure 5 and Figure 6. FBMC has higher selectivity, but requires more symbol multiplications.

5.2.1. Goodput Fairness

Goodput fairness measures how fairly the scheduler allocates the bandwidth. Figure 5 shows the goodput fairness for LTE, URLLC and eMTC use-cases with the EPA, EVA and ETU channel. The overall results show that the JFI index of the FBMC waveform is slightly lower than that of the OFDM due to its complex nature. For all these cases, the proposed SRA and baseline approaches show full fairness (100%) for up to three users. In the case of the URLLC and eMTC use-cases, dynamic and greedy show similar performance for OFDM and FBMC waveforms, as shown in Figure 5d–i. In the case of LTE and URLLC, the JFI index remains more than 96%, and for eMTC, it is more than 95%, as shown in Figure 5. Dynamic-OFDM outperforms dynamic-FBMC by up to 0.02% (≈2.5%), as shown in Figure 5a–c for LTE and in Figure 5d–f for URLLC. In the case of eMTC, dynamic-OFDM outperforms dynamic-FBMC by up to 0.01% (≈1.5%), as shown in Figure 5g–i.

5.2.2. Delay Fairness

Delay fairness measures how long an arbitrary user needs to wait for resource allocation. Figure 6 plots the delay fairness for LTE, URLLC and eMTC with the EPA, EVA and ETU channel models. For all these cases, the proposed SRA and baseline approaches show full fairness (100%) for up to three users. In the case of the URLLC and eMTC use-cases, dynamic and greedy show similar performance for OFDM and FBMC waveforms, as shown in Figure 6d–i. Dynamic-OFDM outperforms dynamic-FBMC by up to 0.01% (≈1.5%), as shown in Figure 6a–c for LTE and Figure 6d–f for URLLC. In the case of eMTC, dynamic-OFDM outperforms dynamic-FBMC by up to 0.01% (≈1%), as shown in Figure 6g–i. In the other cases, its fairness is slightly higher than or similar to the fairness of greedy.

6. Conclusions and Future Work

The upcoming 5G technology is envisioned to support diverse use-cases such as enhanced Mobile Broadband (eMBB), enhanced Machine Type Communication (eMTC), and Ultra-Reliable Low Latency Communication (URLLC). These use cases may generate different types of traffic at the base station. The first generation of 5G comes with backward LTE compatibility, which generates even more diversity in traffic at the base station. Hence, we need an effective Scheduling and Resource Allocation (SRA) at the 5G base station. In this paper, we have proposed a new SRA algorithm based on dynamic programming that can accommodate diverse use-cases of 5G and make effective SRA decisions. The simulation results show the robust performance of the proposed SRA for the two dominant waveforms for 5G, i.e., Orthogonal Frequency Multiplexing (OFDM) and Filter Bank Multi-Carrier (FBMC). For LTE, our SRA method outperforms the advanced greedy SRA algorithm [13] by up to approximately 60%, 2.6% and 1.6% in terms of goodput, goodput fairness and delay fairness, as observed in [17]. In the case of URLLC and eMTC, our SRA algorithm continues to outperform [13] by up to 17.24%, 18.1%, 2.5% and 1.5% in terms of average goodput, correlation impact, goodput fairness and delay fairness. In the future, we will explore other 5G New Radio (NR) waveforms and leverage them in our SRA framework. We will also investigate if the dynamic programming algorithm for SRA can be further extended to support V2X communication, which is significantly more challenging due to high-speed mobile stations.