Energy Efficiency Optimization in Multi-Antenna Wireless Powered Communication Network with No Channel State Information

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1 Vol.141 (GST 016), pp Energy Efficiency Optimization in Multi-Antenna Wireless Powered Communication Networ with No Channel State Information Byungjo im 1,, Jae-Mo ang, yung-myung im, Joohyun Lee 1, 1 Electronics and Telecommunications Research Institute (ETRI) {imbj, juehyun}@etri.re.r School of Electrical Engineering, orea Advanced Institute of Science and Technology (AIST) {jmang, imhm}@aist.ac.r Abstract. This paper presents QoS-constrained energy efficiency maximization scheme in multi-antenna Wireless Powered Networ. Specifically, considering No channel state information (CSI) at the users, we optimize energy transmit beamforming, user power allocation and time resource allocation for energy and information transfer. The simulation results show that the proposed scheme provides better EE performances than those of the conventional schemes and outperforms the other schemes in terms of the minimum user EE. eywords: Energy efficiency, energy harvesting, resource allocation, wireless powered networ. 1 Introduction Wireless energy transfer can be one of ey technologies for future energy constrained or battery-limited wireless networs [1] []. They can be readily applied to wireless sensor networ, without changing or recharging batteries periodically. In [3] and [4], wireless-powered communication networs (WPCNs) have recently received significant attention since they are well-suitable for energy harvested sensor networs. The harvest-then-transmit (TT) protocol has been introduced in [4], where wireless energy is first transmitted from a hybrid access point (-AP) for energy harvesting at user terminals and, then, then, the users send their information signals based on their harvested energies. Since the energy harvesting sensor nodes may have limited battery capacity, the bit-per-joule EE can be a more critical criterion for system design. But most wors in WPCNs considered the maximum rate without efficient energy usage. The aforementioned wor in [5] has proposed the energy efficient scheme in single-antenna WPCN with full CSI at all the users. In [6], the authors have proposed EE resource allocation schemes in multi-antenna WPCN with full CSI. In practical WPCNs, RF energy harvesting nodes may be allowed due to limited signal processing capability transfer. And feedbac of CSI or transmission strategy introduces an additional overhead. In this letter, we consider the practical situations with no CSI at all the users, and ISSN: ASTL Copyright 016 SERSC

2 Vol.141 (GST 016) optimize energy transmit beamforming, user power allocation and time allocation for energy and information transfer. System Model We consider a multiuser WPCN considering of power transmitter with N antennas supplied with electricity from an external power source, information receiver with M antenna and single-antenna user terminals. All the nodes operate in the same frequency band. The users have no fixed energy suppliers. Let and h M 1 denote the channel vectors between the power transmitter and the th user and between the information receiver and the th user, respectively. The channels are assumed quasi static bloc-fading. For simplicity, we assume the unit transmission time, T = 1. In the first energy transfer phase, wireless energy transfer (WET) is carried out from the power transmitter to users and in the second phase, wireless information transfer (WIT) is carried out from the users to information receiver. We denote the fraction of time assigned to the first phase by 0 < < 1 and that dedicated to the th user in the second phase by, 1,,. In the first WET phase, the harvested energy can be expressed ad E 0g Sg at the th user 0 NN where (0,1] is the energy conversion efficiency and S E[ ss ] is the N1 energy transmit covariance of the energy-bearing signal s from the power transmitter. In second WIT phase each users transmit the information signal to the receiver using TDMA scheme. The achievable rate of the th user is given by x h R log 1, 1,, (1) g N1 3 Energy Efficiency Optimization In this section, we address the optimization problem to maximize the energy efficiency with the rate constraints and the energy harvesting constraints. By adopting the EE criterion from harvested energy and (1), the EE optimization problem with the NpNp Z variable changes 0S can be formulated as Copyright 016 SERSC 159

3 Vol.141 (GST 016) max Z, τ log 1 g Zg 1 0 Pmax Pc 1 g Zg Subject to Tr( Z) P, 0 max Z±0, 1, 0, 0,1,,, 0 log 1 g Zg 1 R min () Q where is power amplifier inefficiency, is some initial energy for user, R min P c h is the circuit power consumption, is the effective SNR for user, and is the minimum required throughput. We assume the users have no initial energy and all the harvested energy is consumed. The problem () can be easily showed for a concave-convex fractional problem with the pseudo concave objective function. We convert the EE problem into a more tractable form, which can be easily tacled max log 1 g Zg 0 Pmax Pc, 1 1 g Zg Z τ s.t. Tr( Z) P, Z±0, 1 0 max 1, 0, 0,1,, 0 log 1 g Zg Rmin, From (3), it can be straightforwardly shown that the optimal Z can be expressed as Proof: g Zg (1 ), 1,, å 0 j1 jg j Zg j (3) (4) 160 Copyright 016 SERSC

4 Vol.141 (GST 016) The function log 1 g Zg (1 0) log 1 g Zg is concave in { }.Therefore, applying the Jensen's inequality, we obtain 1 (1 0) log 1 g Zg (1 0) log The equality holds when g Zg c, 1,, Thus, considering the constraint =1, the optimal { } is g Zg g Zg (1 ), 1,, å 0 j1 jg j Zg j Optimal transmit covariance and time allocation for energy transfer given by the solution of the following problem 1 s.t. Tr( Z) P, Z± 0, (5) max (1 0)log 1 0 max c, 0 1 g Zg P P g Zg Z max , (1 0)log 1 g Zg Rmin, For above jointly concave functions, we can obtain solution through Solved by the interior-point method. 3 Simulation Results We consider the system with N = M = = 4, and compare the performances of the proposed schemes with the sum-throughput maximization scheme (STM) [4]. The elements channel vectors { h} and { g} are generated with the rayleigh fading with 30dB attenuation. In Fig. 1, the EE performance of the proposed scheme is shown versus the SNR for various values of R min ere, Rmin is set to R min = Rmax with 0, 1 and Rmax denotes the throughput obtained by the throughput maximization scheme. Copyright 016 SERSC 161

5 Vol.141 (GST 016) Fig. 1. EE performance versus the SNR for different rate constraints. We observe the EE optimization scheme outperforms the throughput maximization scheme in the sense of the energy efficiency. As the value of Rmin decreases, the EE performance is improved. Because the larger value of Rmin reduces the feasible set of the optimal solution. As a result, the EE performance is best when there is no rate constraint. 4 Conclusion In this paper, we proposed energy-efficient transmission scheme in multi antenna WPCN with no CSI cases. The EE problems were converted into the equivalent parameterized subtractive forms and, then, we optimized energy transmit beamforming, user power allocation and time allocation for energy and information transfer. The simulation results showed the proposed scheme outperforms the through maximization scheme in terms of the EE. Acnowledgments. This wor was supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the orea government (MSIP) (No. B , 100 Gbps Coherent/OFDM DSP Development). References 1. Varshney, L. R.: Transporting information and energy simultaneously, in Proc. 008 IEEE Int. Symp. Inf. Theory, pp (008). 16 Copyright 016 SERSC

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