Max–Min Fairness Optimization for D2D Communications Coexisting with Cellular Networks
Abstract
:1. Introduction
- We formulate a max-min fairness optimization problem, which aims at providing a uniformly good QoS to everyone in the network where both cellular users and D2D users coexist, subject to the limited power budgets. In particular, a number of NOMA-based D2D device groups are allowed to reuse the bandwidth from that dedicated to the cellular users, which is controlled by a base station (BS). For a given QoS level, we then transfer the max–min fairness optimization problem into a minimum total transmit power consumption problem under the QoS requirements and the power constraints.
- We observe the quasilinear convexity of the proposed max-min fairness optimization problem and utilize the bisection method to obtain the global optimum. We rigorously find an upper bound on the QoSs that the system can provide to the cellular users and D2D devices. This upper bound offers a reduction of the computational complexity and also confirms that the proposed algorithm can be implemented in polynomial time. Our proposed algorithm balances between maximizing the worst spectral efficiency performance and minimizing the total transmit power consumption.
- The numerical results demonstrate the effectiveness of the proposed optimization framework in providing equally good QoS to all cellular users and D2D devices under the different subchannel assignments (either random assignment or a heuristic assignment that minimizes the mutual interference between cellular users and D2D devices), pairing techniques (either random paring or a heuristic pairing that reduces the total transmit power), and channel conditions.
2. System Model and Performance Analysis
2.1. System Model and Assumptions
2.2. Channel Model
2.3. Channel Capacity of D2D Devices and Cellular Users
2.3.1. Uplink Cellular Network Transmission
2.3.2. Downlink D2D Transmission
3. Max–Min QoS Optimization
Algorithm 1: Max–min quality of service (QoS) based on the bisection method. |
1Result: solve the optimization in (33). Input: Initial upper bound and line-search accuracy ; 2 Set ; ; 3 Calculate: 4 while do 13 Set and ; Output: Final interval and ; 14 final; |
4. Numerical Results
- (1)
- The diversity-based method (DBM) combined with heuristic pairing (denoted DBM + Heuristic Pairing in the figures): All cellular users have already been assigned to the subchannels. Subsequently, these subchannels are allocated to the D2D devices via channel diversity. In each D2D group, the devices are paired by the heuristic algorithm.
- (2)
- The DBM using random pairing (denoted DBM + Random Pairing in the figures): the system utilizes the heuristic algorithm to allocate the subchannels for the D2D groups; however, the devices in each group are paired randomly.
- (3)
- The random channel assignment using heuristic pairing (denoted NonDBM + Heuristic Pairing in the figures): the D2D groups are assigned randomly to the subchannels, and the devices in each group are paired by the heuristic algorithm.
- (4)
- The random channel assignment using heuristic pairing (denoted NonDBM + Random Pairing in the figures): the D2D groups are assigned randomly into subchannels, and the devices in each group are paired randomly.
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Cellular radius | 250 (m) |
Base station height | 6 (m) |
Beamforming technology | Maximum Ratio Combining (MRC) |
D2D group radius | 10 (m) |
Device and cellular user height | 1.5 (m) |
Operating frequency | 1.9 (GHz) |
Maximum transmit power of devices and cellular users | 23 (dBm) |
Noise power | −96 (dBm) |
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Nguyen, H.G.; Nguyen, X.T.; Nguyen, V.S.; Chien, T.V.; Nguyen, T.H.; Ro, S. Max–Min Fairness Optimization for D2D Communications Coexisting with Cellular Networks. Electronics 2020, 9, 1422. https://doi.org/10.3390/electronics9091422
Nguyen HG, Nguyen XT, Nguyen VS, Chien TV, Nguyen TH, Ro S. Max–Min Fairness Optimization for D2D Communications Coexisting with Cellular Networks. Electronics. 2020; 9(9):1422. https://doi.org/10.3390/electronics9091422
Chicago/Turabian StyleNguyen, Hoai Giang, Xuan Tung Nguyen, Van Son Nguyen, Trinh Van Chien, Tien Hoa Nguyen, and Soonghwan Ro. 2020. "Max–Min Fairness Optimization for D2D Communications Coexisting with Cellular Networks" Electronics 9, no. 9: 1422. https://doi.org/10.3390/electronics9091422