A randomized algorithm for joint power and channel allocation in 5G D2D communication☆
Introduction
In 5G device to device (D2D) communication, two users residing within the transmission range of each other can communicate directly among themselves over a common channel without involving the base station (BS) [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. Also, users not residing within the transmission range of each other can use other devices to relay signal to them [11]. A cellular user communicates with the BS by forming a cellular link (CL) and a pair of D2D users communicates among themselves by forming a D2D link (DL). In D2D underlaid cellular network, DLs reuse the same uplink channel resources of CLs [12], [13], [14]. Each link (CL or DL) includes a transmitter and a receiver. The transmitter of each link has to be allocated sufficient power such that it can communicate with its receiver in the presence of noise and interference from other links operating on the same channel. More specifically, the allocated power of a transmitter must satisfy the required signal to interference plus noise ratio (SINR) at the receiver of that link. Each link requires certain level of SINR depending on its data rate requirement. Moreover, the allocated power at a transmitter must not exceed the residual power available at it.
Note that under a BS only one CL can use a particular channel. However, the channel of a CL may be shared by multiple DLs provided the required SINR is satisfied for each link sharing the channel. Hence we have to find a channel vector for the links , where represents the channel allocated to link . Due to the scarcity of channels, we always have to minimize total number of distinct channels used in the communication.
It is evident that maximum power that can be allocated to the transmitter of a link is a limited quantity. If link is activated with power then , where is the residual power available at the transmitter of link . Hence we have to find a power vector for the links such that the total power requirement is minimized.
The links activated with the same channel will interfere to each other. If more links are activated with the same channel to keep the channel requirement at low, the power requirement of the corresponding links would be high. On the other hand, if each link is activated with a different channel, the power requirement will be minimum but the channel requirement will be maximum. It is thus evident that and have a natural trade-off. Owing to this natural trade-off, we define our minimization objective as a cost function . Here is a constant reflecting the relative weights of and , where the weight of is normalized to . The joint power and channel allocation problem (JPCAP) deals with the problem of finding the channel vector and the power vector such that the required SINR criteria for each link is satisfied and the cost is minimized.
Several authors [15], [16], [17], [18], [19] have studied the problem of sizing the orthogonal channels in D2D communication. A nice survey of various resource allocation schemes in D2D communication can be found in [7]. In [20] authors discussed an analytical model of resource allocation. In [16], [17], [21], the energy efficient mode selection techniques were discussed. In [22], [23], [24], [25], [26] authors adopted graph coloring approach to solve channel assignment problem in D2D communication. In [27], a power minimization solution with joint sub-carrier allocation, adaptive modulation, and mode selection was proposed. In [28], [29] different strategies to minimize power were discussed. In [30] authors adopted a energy saving coding design. Spectral efficiency (SE) [31] and energy efficiency (EE) [32], [33] are two well adopted maximization objective in power and channel allocation in D2D communication. In SE data rate per spectrum is maximized whereas, in EE, data rate per spectrum per energy unit is maximized. In [34] authors formulate the resource allocation problem as a non-convex optimization problem to minimize power. In [35], [36], [37] authors propose channel assignment algorithms where both cellular and D2D users share channels. In this underlaid scenario, cellular and D2D users may interfere with each other. Here, one channel could be used by one cellular user only whereas, a single channel might be used by multiple D2D users. In [18] authors discussed the method to maximize the minimum weighted energy efficiency of D2D links while ensuring maximum data rate in cellular links. The main features of the existing approaches which are similar to our proposed approach are summarized in Table 1. The difference between these approaches and our proposed approach are also summarized in Table 1.
In contrast to the above mentioned existing approaches, we propose a randomized joint channel and power allocation (RJCPA) algorithm to solve the power and channel allocation problem in a combined setup where multiple DLs can be paired with one CL. More specifically our contributions are summarized below.
We formulate JPCAP as a cost minimization problem where the cost is designed such a manner that by properly tuning we can set the goal of JPCAP to minimize only or only or a joint objective of and . Then we reduce JPCAP to the classical graph coloring problem and thereby show that it is NP-hard and also providing approximation to JPCAP is NP-hard. Next we propose a mixed integer linear programming (MILP) formulation for JPCAP and subsequently develop a greedy channel and power allocation (GCPA) algorithm for it. GCPA works by taking an order of the links as input. We show that there exists an order of the links on which if GCPA is applied it will provide an optimal solution. Then we develop a method to search orders efficiently. We show that an order is equivalent to many orders. We develop an incremental algorithm (IA) which searches orders from different equivalent sets and thereby evaluating less number of orders, it essentially explores large number of orders. Finally, using IA, we design a randomized joint channel and power allocation (RJCPA) algorithm to find the near optimum solution. We also theoretically calculate the expected cost produced by RJCPA. Moreover, we identify some special cases where RJCPA can produce optimal result in expected polynomial time. We also compute the expected energy efficiency (EE) produced by RJCPA. We perform extensive simulations to show that RJCPA outperforms both the two-step approach [14] and RSBI algorithm [9] with respect to both cost and EE. Finally we validate our theoretical findings through simulation.
Suppose there are links within the coverage region of a BS where each link is either a CL or a DL. Let be the set of CLs and be the set of DLs where . Let channels are represented by positive integers and be the set of available channels. Each link requires a channel and power for its activation, where is the residual power available at the transmitter of link . It is evident that consists of power consumption of transmitter of link and power loss at circuitry blocks of both transmitter and receiver of link [9]. When communication is not taking place is considered to be by neglecting the minute leakage current [44]. We assume that each link undergoes distance dependent pathloss and small-scale fading. If power is allocated at the transmitter of link then the power received at the receiver of link can be expressed as , where [34] is the gain at the receiver of link from the transmitter of link , is a log-normally distributed random variable representing slow fading, is a exponentially distributed random variable representing fast fading, is the Euclidean distance between the transmitter of link and the receiver of link and is a path loss exponent. Note that our solution technique is independent of how is computed. For simulation purpose we have computed as stated in [34].
Note that each link will receive interference from every other link for which where . Let be minimum SINR required at the receiver of link to satisfy its data rate requirement. Link can be activated with and if , the SINR received at the receiver of link , is greater than or equals to . That is, where is the constant noise over each link.
We denote if channel is allocated to at least one link, else . Note that each CL requires a different channel to communicate [14] and hence for all where . But a DL may share channel with other CL and/or DL. Clearly total number of distinct channels used is given by and total power used in the communication is given by .
Given a constant , our objective is to find a channel vector and a power vector such that (1) cost is minimized, (2) each activated CL gets different channel and (3) , the SINR received at the receiver of each activated link , satisfies Constraint (1).
Rest of the paper is organized as follows. In Section 2 we prove the hardness of JPCAP and propose a mixed integer linear programming formulation of JPCAP. In Section 3 we propose GCPA and present a detailed analysis of the algorithm. In Section 4 we present the randomized joint channel and power allocation (RJCPA) algorithm. In Section 5 we find the expected cost and energy efficiency generated by RJCPA. In Section 6 we simulate RJCPA and compare with two existing approaches of [14] and [9] respectively. Finally in Section 7 we conclude the paper. All notations used in this paper are summarized in Table 2.
Section snippets
Hardness and MILP formulation
In this section we first formally show that JPCAP is NP-hard and then provide a MILP formulation of this problem.
Greedy channel and power allocation algorithm
In this section, we propose a greedy channel and power allocation (GCPA) algorithm to allocate channels and powers to the links. Let be an arbitrary order of the links. In GCPA, we visit the links one by one following and allocate channels and powers to them. Thus while allocating link , all the links have already been allocated. In other words, and , , are already known before the allocation of and . Let be a channel. We now
Randomized algorithm
In this section we first propose an incremental algorithm (IA) to minimize the cost and then propose a randomized joint channel and power allocation algorithm (RJCPA) which uses IA with parameter to further minimize the cost. Next we present the analysis of RJCPA. Since the optimum hitting probability of RJCPA is a function of , we then compute the expected value of to find the optimum.
Expected cost and energy efficiency
We now analyze the expected cost and energy efficiency (EE) produced by RJCPA. For the analysis purpose we will first state some assumptions and notations. We assume that DLs are situated inside a radius cell with the base station placed at its center and . Let , where , and , where and . Also . Let , , , and . Let be the energy efficiency and . We also assume that expected
Simulation
This section comprises of three subsection. In the first subsection we elaborate the simulation environment. In the second subsection we compare RJCPA with two existing algorithms. In the third subsection we validate our analytical findings through simulation.
Conclusion
In this paper, we have formulated the joint power and channel allocation problem (JPCAP) in D2D underlaid cellular network as a cost minimization problem, where cost is defined as a linear combination of and . We first showed that JPCAP is NP-hard and even providing a approximation for it is also NP-hard. Then we proposed a MILP formulation of this problem. As solving MILP is also NP-hard we proposed a GCPA algorithm which runs on an order of links. We proved that there exists an order
CRediT authorship contribution statement
Subhankar Ghosal: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Visualization, Investigation. Sasthi C. Ghosh: Supervision, Editing, Validation, Visualization, Investigation.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (48)
- et al.
A randomized algorithm for joint power and channel allocation in 5G D2D communication
- et al.
Firefly inspired improved distributed proximity algorithm for D2D communication
- et al.
Analytical modeling of mode selection and power control for underlay D2D communication in cellular networks
IEEE Trans. Commun.
(2014) - et al.
Cognitive and energy harvesting-based D2D communication in cellular networks: Stochastic geometry modeling and analysis
IEEE Trans. Commun.
(2015) - et al.
Device-to-device communication in 5G cellular networks: Challenges, solutions, and future directions
IEEE Commun. Mag.
(2014) - et al.
Stochastic geometry analysis of achievable transmission capacity for relay-assisted device-to-device networks
- et al.
Device-to-device communication in LTE-advanced networks: A survey
IEEE Commun. Surv. Tutor.
(2014) - et al.
On the outage probability of device-to-device-communication-enabled multichannel cellular networks: An RSS-threshold-based perspective
IEEE J. Sel. Areas Commun.
(2015) - et al.
Energy-efficient D2D communications with dynamic time-resource allocation
IEEE Trans. Veh. Technol.
(2019) - et al.
D2D communication mode selection and resource allocation in 5G wireless networks
Comput. Commun.
(2020)
Resource sharing for device-to-device communications underlaying full-duplex cellular networks
Device-to-device communication as an underlay to LTE-advanced networks
IEEE Commun. Mag.
Design aspects of network assisted device-to-device communications
IEEE Commun. Mag.
A two-stage energy-efficient approach for joint power control and channel allocation in D2D communication
IEEE Access
Energy efficiency and delay tradeoff in device-to-device communications underlaying cellular networks
IEEE J. Sel. Areas Commun.
Mode switching for energy-efficient device-to-device communications in cellular networks
IEEE Trans. Wireless Commun.
Energy-efficient resource sharing for mobile device-to-device multimedia communications
IEEE Trans. Veh. Technol.
Energy-efficient resource allocation for D2D communications in cellular networks
IEEE Trans. Veh. Technol.
Energy-efficient resource allocation for D2D communications underlaying cloud-RAN-based LTE-A networks
IEEE Internet Things J.
Analytical modeling of resource allocation in D2D overlaying multihop multichannel uplink cellular networks
IEEE Trans. Veh. Technol.
Energy efficient D2D communications in dynamic TDD systems
IEEE Trans. Commun.
Graph coloring based resource sharing (GCRS) scheme for D2D communications underlaying full-duplex cellular networks
IEEE Trans. Veh. Technol.
Channel assignment in mobile networks based on geometric prediction and random coloring
A decentralize algorithm for perturbation minimization in 5G D2D communication
Cited by (9)
Mobility aware resource allocation for millimeter-wave D2D communications in presence of obstacles
2023, Computer CommunicationsCitation Excerpt :In [10] authors deal with the resource allocation problem through vertex coloring in combination with branch-and-bound method in order to maximize the system throughput with guaranteed fairness. Authors of [21] uses a randomized approach for the resource allocation problem and minimizes the number of channels. The resource allocation in relay-aided D2D communication has also been well explored in the existing literature.
Network-Compute Co-Optimization for Service Chaining in Cloud-Edge-Radio 5G Networks
2023, IEEE Transactions on Vehicular TechnologyAn Approach of Resource Allocation for Vehicle-to-Vehicle Communication using Cuckoo Search based Grey Wolf Optimization
2023, International Journal of Intelligent Systems and Applications in EngineeringResource Allocation and Power Control for D2D Communications With Spread Unsent-Data Strategy
2023, IEEE Transactions on Vehicular TechnologyEnergy Efficient Resource Allocation for D2D Communications using Reinforcement Learning
2023, Proceedings - Conference on Local Computer Networks, LCNNon-optimal is Good! Resource Allocation in Presence of Dynamic Obstacles in D2D Networks
2023, Proceedings - Conference on Local Computer Networks, LCN
- ☆
A preliminary version of this paper appeared in Proceedings of the 18th IEEE International Symposium on Network Computing and Applications, IEEE NCA, 2019: 1-5 (Ghosal and Ghosh, 2019).