- Research
- Open Access
Power minimization of cooperative beamforming networks with spectrum sharing
- Cen Ling^{1},
- Xuefeng Yin^{1}Email author,
- Silvia Ruiz Boqué^{2} and
- Mario García-Lozano^{2}
https://doi.org/10.1186/s13638-015-0315-4
© Ling et al.; licensee Springer. 2015
- Received: 1 September 2014
- Accepted: 2 March 2015
- Published: 13 March 2015
Abstract
Cooperative communication with spectrum sharing has been proved to be an efficient way to reduce energy consumption. In this work, an optimal power allocation algorithm is proposed for mobile cooperative beamforming networks, where several secondary users (SUs) collaboratively act as relay nodes to assist the transmission of a primary user (PU) in reward of transmitting their own information. The optimal power allocation scheme is obtained by solving a convex optimization problem aiming at minimizing network energy consumption with guaranteed quality of service (QoS) for both PU and SUs. Simulation results show that with the consideration of overheads, circuit power, and energy costs for message sharing, a cooperative beamforming network augmented with our proposed power allocation algorithm performs better in scenarios of more SUs in terms of higher energy efficiency and less power consumption per unit throughput. Additionally, the proposed scheme outperforms the conventional best-relay selection approach in the aspects of power consumption per unit throughput, energy efficiency, and network power consumption. Furthermore, simulations also demonstrate that the derived cooperative beamforming algorithm exhibits superior performance in energy saving than conventional methods in high-speed scenarios.
Keywords
- Cooperative beamforming
- Power minimization
- Spectrum sharing
- Mobile network
1 Introduction
Towards the fifth generation (5G) of wireless/mobile broadband communication, many advanced key technologies are going to be implemented, including spectrum sharing management, exploiting the Cloud-RAN (CRAN) and mobile clouds concepts as well as heterogeneous network coordination, in order to meet the demand for larger bandwidth, higher data rate up to Gbit/s and seamless connection access [1-3]. Furthermore, reduction of unnecessary energy consumption becomes one of the major concerns in 5G communications, which not only reduces environmental impact but also cuts overall network costs and helps make communication more practical and affordable. These studies belong to the research of ‘green networking’ which aims in increasing energy savings while maintaining satisfactory users’ quality of service (QoS) [4-6]. Besides, cooperative techniques are promising in improving the reliability of the communications against channel impairments and achieved throughput through aggregating resources offered by different collaborative entities and realizing significant energy savings, targeting a so-called green and soft 5G system [7].
Apart from ‘cell breathing’ of base station coordination and clustered cooperative schemes [8,9], user cooperation, as a new form of spatial diversity, enables single-antenna mobiles in a multiuser environment to share their antennas and generate a virtual multiple-antenna transmitter, providing higher throughput, robustness to channel variations and ubiquitous mobile access for media-rich mobile devices. Recently, being extended with the concept of cognitive radio, user cooperation with spectrum sharing capability, i.e., secondary users (SUs) share the same spectrum with the primary user (PU), can further improve spectral efficiency. User-cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks and the outage capacity characterization of various relaying protocols, i.e., fixed relaying, selective relaying, and incremental relaying, are characterized [10]. In literature, numerous criteria have been proposed for relay node selection based on channel conditions [11], the distances between nodes [12], and the transmission contention [13], etc. It has been demonstrated in [14,15] that when more relay nodes, also called as cooperators, are involved in transmission, less energy costs and higher network throughput can be achieved simultaneously, compared with the single-relay transmission. This motivated the research on methodologies of selecting multiple entities to act as cooperators, also called as ‘cooperative beamforming’. However, several issues should be considered from a media access control (MAC) layer perspective when multiple cooperating entities are involved. The first issue is that more control signaling overhead should be considered for selecting and coordinating multiple cooperating entities [16]. The second issue is related to users’ willingness to cooperate. Furthermore, incentive mechanisms are of necessity for promoting user cooperation in order to prevent unwillingness and selfishness of the SUs via reputation evaluation, cost reduction, or increase of transmission time [17-20].
As the energy expenditure becomes a major concern for the operators of communication networks, constructing cooperative networks with the energy consumption minimized has become an important research field [21]. Multiple solutions of resource allocation were derived based on convex optimization or game theory via lowering power consumption under certain constraints, such as minimizing the outage probability [22-24], maximizing energy efficiency [25-28], maximizing overall throughput [29,30], maintaining service quality, or maximizing the sum of SUs’ capacities and signal-to-noise power ratio (SNR) [31]. Joint relay selection and power allocation schemes are proposed by factoring the cost of acquiring channel state information (CSI) to minimize the total energy consumption [32]. The allocation schemes obtained are applicable to adapting the transmission power, bandwidth, time, and accessibility for the nodes involved in the cooperative network. In addition, circuit power consumption model has been taken into account in calculating the energy efficiency of cooperative heterogeneous and beamforming networks in [25,33].
The aforementioned resource allocation methods share some common drawbacks which limit their applicabilities in cooperative spectrum sharing networks in cases where a PU and multiple SUs coexist. First, the energy consumption minimization strategies adopted in these methods usually consider a single relay node, which is typical merely for the best relay selection scheme. The adaptation of the strategies in the situation with multiple SUs selected simultaneously as relay nodes, as in the cooperative beamforming scenario, has not been investigated thoroughly so far. Furthermore, SUs may be reluctant to relay the traffic for the PU, if SUs do not forsee an immediate benefit or reward from their cooperation or they have some security and privacy concerns or encounter resource limitation, e.g., battery shortage [14]. This issue concerning the incentive mechanisms so as to prevent unwillingness and selfishness of the SUs has not been paid great attention in recent researches on cooperative beamforming networks. Moreover, the existing power allocation schemes are derived under an ideal channel assumption that channel coefficients for multiple links among the communication nodes are independent random variables following identical distributions. This leads to nonrealistic conclusions for performance evaluation. It is necessary to re-design the resource allocation methods by taking into account some new constraints posed by the existence of multiple relays, the energy costs of the communication coordination overheads, the influence of the rewards for the relay nodes, and realistic propagation scenarios.
In this paper, we propose an energy-saving strategy for cooperative beamforming by finding the optimal power allocation scheme. This method is particularly useful in cooperative beamforming for mobile spectrum sharing scenarios where a PU and multiple SUs co-exist. The proposed power allocation scheme is obtained by solving a convex optimization problem with the boundary conditions specifying the minimum QoS for the PU and SUs, similar to the approach described in [19]. A model of constant circuit power consumption originally introduced in [25] is considered for calculating the network power consumption. Simulations under the setting of realistic fast fading channels generated by using an infinite impulse response (IIR) filter demonstrate that the energy efficiency which is defined as the ratio of outage capacity over total energy consumed, i.e., a necessary extension from single-relay scenarios [22,34] to multi-relay cooperative beamforming cases, can be significantly improved by implementing the proposed optimization scheme. Furthermore, the proposed scheme exhibits superior performance compared with some conventional methods including the best relay selection approach.
The rest of the paper proceeds as follows. In Section 2, the considered cooperative beamforming scenario in a cognitive network is introduced. In Section 2, the optimization method of power allocation and the derivation of energy efficiency for cooperative beamforming are presented. Simulation results are elaborated in Section 2 for performance assessment of the proposed scheme. Eventually, conclusive remarks are given in Section 2.
2 System model
where γ _{ ij } is defined as the ratio between the transmission signal power over the noise variance.
Explanation of adopted symbols
Symbol | Explanation |
---|---|
y _{ j } | Received signal at the jth node |
h _{ i j } | Channel coefficient from ith to jth node |
P _{ ij } | Transmitting power per bandwidth from the ith node to the |
jth node | |
x _{ i } | Transmitting signal at the ith node |
W | Transmission bandwidth |
N _{ o } | Spectral density height of thermal noise |
n _{ j } | Thermal noise |
λ _{ ij } | Rate parameter of exponential distribution |
d _{ ij } | Distance between the ith and jth nodes |
R _{ d } | Direct transmission data rate |
γ _{ d } | Transmitting SINR of direct transmission |
h _{ d } | Channel coefficient of direct transmission |
R _{ c } | Data rate of PR |
\(R_{p{s_{k}}}\phantom {\dot {i}\!}\) | Data rate of the link of PT-SR _{ k } |
R _{MRC} | Data rate of MRC |
γ _{ p } | Ratio between the transmission signal power over the noise |
variance for PU | |
\(h_{p{s_{k}}}\phantom {\dot {i}\!}\) | Channel coefficient of the link PT-SR _{ k } |
\(\gamma _{{s_{k}}d}\phantom {\dot {i}\!}\) | Ratio between the transmission signal power over the noise |
variance between ST _{ k } and PR | |
\(h_{{s_{k}}d}\phantom {\dot {i}\!}\) | Channel coefficient of the link ST _{ k }-PR |
\(R_{{su}_{k}}\phantom {\dot {i}\!}\) | Data rate of the kth SU |
\(\gamma _{{su}_{k}}\phantom {\dot {i}\!}\) | Ratio between the transmission signal power over the noise |
variance for the kth SU | |
\(h_{{su}_{k}}\phantom {\dot {i}\!}\) | Channel coefficient of the link ST-SR |
R _{ N } | Cooperative network throughput |
T | Time for the 1st and 2nd phase transmission |
t _{ k } | Time for the third phase transmission |
P _{ p } | Transmitting power of PT |
P _{ d } | Transmitting power of non-cooperative scheme |
\(P_{{s_{k}}d}\phantom {\dot {i}\!}\) | Transmitting power of the ST _{ k } |
\({P_{s{u_{k}}}}\phantom {\dot {i}\!}\) | Transmitting power of the third phase |
w _{ k } | Beamforming weight of the ST_{ k } |
P _{OV} | Circuit power |
P _{SR} | Overheads of cooperative beamforming |
P _{TR} | Overheads of message sharing |
P _{ c } | Circuit power |
M | Number of cooperative SUs |
b _{RD} | Number of bits per symbol for cooperative beamforming |
b _{SR} | Number of bits per symbol for message sharing |
ρ | Amplifier efficiency |
N _{TR} | Number of symbols of training period |
N _{RD} | Number of symbols of cooperative beamforming |
P _{ b } | Power consumption per throughput |
β _{k} | Time allocation ratio of the kth SU |
Q _{ p } | QoS of PU |
Q _{ s } | QoS of SU |
\(P_{\mathrm {d}}^{\text {out}}\) | Outage probability of direct transmission |
\(C_{\text {d}}^{\text {out}}\) | Outage capacity of direct transmission |
Csuout | Outage capacity of SU |
ε | Outage probability threshold |
\(C_{\text {cb}}^{{\text {out}}}\) | Outage capacity of cooperative beamforming |
η | Energy efficiency |
θ _{1} | SNR threshold for decoding |
θ _{2} | SNR of the worst link between ST_{ k } and PR |
d _{ p } | Distance between PT and PR |
\({d_{{s_{k}}d}}\phantom {\dot {i}\!}\) | Distance between PT and PR |
d _{ su } | Distance between ST and SR |
\({d_{p{s_{k}}}}\phantom {\dot {i}\!}\) | Distance between PT and ST |
P _{max} | Maximum transmitting power |
γ _{ d } | Ratio between the direct transmission signal power over the |
noise variance | |
ζ | Network energy consumption for unit bit of throughput |
L _{ s } | Number of SUs |
v | Moving speed of users |
where γ _{ d } denotes the ratio of the direct transmitting power P _{ d } of the PT to the noise variance and h _{ d } is the channel coefficient for the direct link from the PT to the PR.
where γ _{ p } denotes the ratio of the transmission power P _{ p } of the PT to the noise variance N _{0}, \(\gamma _{{s_{k}}d}\) represents the ratio of the transmission power of the ST _{ k } and N _{0}, and \({{h_{{s_{k}}d}}}\) is the channel coefficient for the link between the ST _{ k } and the PR.
where \(\gamma _{{su}_{k}}\phantom {\dot {i}\!}\) and \({{h}_{{su}}}_{_{k}}\phantom {\dot {i}\!}\) denote respectively the ratio of transmission power of the ST _{ k } and the noise variance and the channel coefficient of the link between the ST _{ k } and the SR _{ k }.
where t _{ k } is the time utilized in the third phase for the kth ST, and \(\bar t\) represents the average of t _{ k }, k=1,…,M. In the system considered here, every SU transmits its own information in its allocated channel, and the individual transmission time t _{ k } is determined using an optimization algorithm described in the later sections of the paper.
where the optimal beamforming weight w _{ k } for the kth ST can be calculated as \(\left | {{h_{{s_{k}}d}}} \right |/\| \boldsymbol {h} \|\) with ∥·∥ being the norm of given vector and \(\boldsymbol {h} = {\left [ {\left | {{h_{{s_{1}}d}}} \right |,\left | {{h_{{s_{2}}d}}} \right |, \ldots,\left | {{h_{{s_{M}}d}}} \right |} \right ]^{T}}\) representing the vector consisting of the channel gains from the STs to the PR and P _{OV} denotes the power overheads required in the source message sharing and channel estimation phases [25].
where γ _{th}(b _{SR}) is the SNR required to achieve the target M-ary quadrature amplitude modulation (M-QAM) bit error probability, p _{th} and c _{1}=0.2,c _{2}=1.5.
3 An algorithm for energy consumption minimization and cooperative beamforming
3.1 Optimal power allocation for cooperative beamforming
The inequalities Equations 16 and 17 represent respectively the QoS requirements of the PU and of the SU. The left-hand sides of Equations 16 and 17 separately denote the transmission rate for PU during the cooperative communication (phases 1 and 2) and SU’s own transmission (phase 3).
This convex optimization problem in Equations 15 to 18 satisfies the Karush-Kuhn-Tucker conditions, and it can be solved using the Lagrangian equation [36,37]. Besides, T is normalized as 1. Detailed convexity analysis and the solution of the optimization problem are given in Appendix 1 and Appendix 2, respectively.
It can be readily shown in Appendix 2 that the left-hand side of Equation 20 has the derivative with respect to β _{ k } always larger than zero and, hence, increases monotonically along with β _{ k }. Thus, the optimal β _{ k } can be determined by applying the Newton’s iterative method as described in [38].
This scheme is used as a reference for evaluating the performance of the proposed method in simulations.
3.2 Energy efficiency of the cooperative beamforming scheme
where d _{su} represents the distance between an ST and the corresponding SR.
with \(z = \sum \limits _{k = 1}^{M} {{\gamma _{{s_{k}}d}}{{\left | {{h_{{s_{k}}d}}} \right |}^{2}}} + {\gamma _{p}}{\left | {{h_{p}}} \right |^{2}}\), \({\lambda _{k}} = d_{{s_{k}}d}^{\alpha } \), and \({\lambda _{M{\mathrm {+ }}1}} = d_{p}^{\alpha } /{\gamma _{p}}\).
where P_{ N } can be obtained from Equation 11.
A widely adopted metric for evaluating the validity for saving network energy consumption is the value of ‘bits-per-Joule’ for the network, i.e., the network energy consumption for unit bit of throughput, denoted with ζ and calculated as ζ=P _{N}/R _{N}. Energy efficiency, denoted with η, is defined as ratio of outage capacity over network power consumption.
4 Simulation results for performance evaluation
Parameter settings for simulation
Description | Value |
---|---|
Amplifier efficiency ρ | 38% |
Circuit power p _{ C } | 1 mw |
Power for training signals P _{TR} | 1 mw |
Bits per symbol of MS b _{RD} | 6 |
Bits per symbol of CB b _{SR} | 4 |
Number of training symbols N _{TR} | 1 |
Number of symbols for CB N _{RD} | 99 |
Outage probability threshold ε | 0.01 |
Required QoS of PU/SU | 1/0.5 bps/Hz |
Pathloss exponent α | 3.5 |
PT-PR distance d _{ p } | 0<d _{ p }≤1,000 m |
PT-ST distance \({d_{p{s_{k}}}}\phantom {\dot {i}\!}\) | \({{\mathrm {d}}_{{\mathrm {p}}{{\mathrm {s}}_{\mathrm {k}}}}} \le 800 m \phantom {\dot {i}\!}\) |
ST-PR distance \({d_{{s_{k}}d}}\phantom {\dot {i}\!}\) | \({d_{{s_{k}}d}} = 300\) m |
ST-SR distance d _{su} | d _{su}=200 m |
Maximum transmission power P _{max} | 40 mw |
Noise spectral density N _{ o } | 0.5 |
Number of snapshots per meter | 20 |
SNR threshold for decoding θ _{1} | 0.01 |
SNR of the worst link between ST_{ k } and PR θ _{2} | 0.0001 |
4.1 Performance evaluation with the number L _{ s } of SUs as a parameter
4.2 Comparison among three communication schemes
4.3 Performance evaluation in vehicular scenarios
The performance of the cooperative beamforming scheme with proposed power allocation strategy is also evaluated by simulations in time-variant cases where the nodes in the network move in high speeds. In the simulations, the speeds of the PU and of the SUs are set to be identical and represented with v. The channel coefficients among the nodes are generated by using a tap-delay-line (TDL) model with six discrete paths. The number L _{s} of SUs is fixed to be 5.
5 Conclusions
In this paper, a novel power allocation scheme has been proposed for energy-efficient mobile cooperative communication with spectrum sharing. In the system, SUs act collaboratively as beamforming relays and help the PU in data transmission in reward of transmitting their own information. The optimal power allocation derived solves a convex optimization problem of minimizing network energy consumption under the constraint of the guaranteed quality of service for both PU and SUs. Analytical expressions were derived based on the resultant optimal power allocation for outage capacity of the system. Numerical simulations have been conducted for evaluating the performance of the proposed scheme. The results demonstrated that the network power consumption exhibited different behaviors depending on whether the overhead power consumption is considered. By taking into account the overhead power consumption, circuit power, and message sharing energy costs, the cooperative beamforming cognitive network together with the proposed power allocation method performs better when more SUs are involved, in terms of enhanced energy efficiency and reduced power consumption per unit throughput. Furthermore, simulations demonstrated that the proposed cooperative beamforming scheme is superior to the conventional best relay selection scheme in the aspects of network power consumption, power consumption per unit throughput, and energy efficiency. In addition, the cooperative beamforming scheme with the optimal power allocation proposed here exhibited stable performance in the time-variant scenarios where both the PU and SUs move in high speeds.
6 Appendix 1
6.1 Convexity analysis of the optimization problem in Equations 15 to 18
Denoting \(f\left ({{P_{p}},{P_{{s_{k}}d}},{\beta _{k}}} \right) = {\beta _{k}}{Q_{p}} - {1 \over 2}{\log _{2}}\left (\!\!{1 + {{{P_{p}}{{\left | {{h_{p}}} \right |}^{2}}} \over {{N_{o}}}}} \!\right)- {1 \over 2}{\log _{2}}\left ({1 + {{{P_{{s_{k}}d}}{{\left | {{h_{{s_{k}}d}}} \right |}^{2}}} \over {{N_{o}}}}} \right)\), we can compute the Hessian matrix of \(f\left ({{P_{p}},{P_{{s_{k}}d}},{\beta _{k}}} \right)\) as:
Thus, the eigenvalues of H _{ f } are all above or equal to zero, which shows that H _{ f } is a positive semi-definite matrix, an implication that \(f\left ({{P_{p}},{P_{{s_{k}}d}},{\beta _{k}}} \right)\) is a convex function and Equation 16 is a convex constraint.
Thus, as long as the requirement of 2β _{ k } Q _{ s }−1≥0, i.e., Q _{ s }≥0.5 is satisfied, it is easy to show that Equation 17 is a convex constraint.
It can be seen that all leading principal minors of H _{ z } are equal to zero matrixes. Thus, \(z\left ({{P_{p}},{P_{{s_{k}}d}},{P_{s{u_{k}}}},{\beta _{k}}} \right)\) is a convex function in terms of \(\left ({{P_{p}},{P_{{s_{k}}d}},{P_{s{u_{k}}}},{\beta _{k}}} \right)\) and the objective function in Equation 15 is convex.
In addition, the constraint (18) is a linear function concerning to β _{ k }. Thus, the Hessian matrixes is zero matrix, indicating the convexity of the constraint (18).
Based on these analyses, we conclude that the formulated optimization problem in Equations 15 to 18 is convex, under the condition that QoS of SU is larger than or equal to 0.5.
7 Appendix 2
7.1 Solution of the optimization problem in Equations 15 to 18
until a sufficiently accurate value is reached.
Declarations
Acknowledgements
This work has been done as a collaboration between research institutions members of European COST IC1004 Action on Cooperative Radio Communications for Green Smart Environments. It has been jointly supported by the Spanish Ministry of Science under the project TEC2011-27723-C02-01, the Sino-Spanish Campus between Tongji University and UPC, the project ‘System design and demo-construction for cooperative networks of high-efficiency 4G wireless communications in urban hot-spot environments’ granted by the Science and Technology Commission of Shanghai Municipality, China, and the NSFC general project with Grant No. 61471268. Thanks for the technical guidance of Prof. Joan Olmos from the University of Polytechnic in Catalunya.
Authors’ Affiliations
References
- J Andrews, S Buzzi, W Choi, S Hanly, A Lozano, A Soong, J Zhang, What will 5G be. IEEE J. Sel. Areas Commun. 32, 1065–1082 (2014).View ArticleGoogle Scholar
- I C-Lin, C Rowell, S Han, Z Xu, G Li, Z Pan, Toward green and soft: a 5G perspective. IEEE Commun. Mag. 52, 66–73 (2014).Google Scholar
- P Demestichas, A Georgakopoulos, D Karvounas, K Tsagkaris, V Stavroulaki, J Lu, C Xiong, J Yao, 5G on the horizon: key challenges for the radio-access network. IEEE Veh. Technol. Mag. 8, 47–53 (2013).View ArticleGoogle Scholar
- S Chen, J Zhao, The requirements, challenges, and technologies for 5G of terrestrial mobile telecommunication. IEEE Commun. Mag. 52, 36–43 (2014).View ArticleGoogle Scholar
- Y Wu, Y Chen, J Tang, D So, Z Xu, C-L I, P Ferrand, J-M Gorce, C-H Tang, P-R Li, K-T Feng, L-C Wang, K Borner, L Thiele, Green transmission technologies for balancing the energy efficiency and spectrum efficiency trade-off. IEEE Commun. Mag. 52, 112–120 (2014).View ArticleGoogle Scholar
- X Hong, J Wang, C-X Wang, J Shi, Cognitive radio in 5G: a perspective on energy-spectral efficiency trade-off. IEEE Commun. Mag. 52, 46–53 (2014).View ArticleGoogle Scholar
- W Zhuang, M Ismail, Cooperation in wireless communication networks. IEEE Wireless Commun. 19, 10–20 (2012).View ArticleGoogle Scholar
- A Papadogiannis, D Gesbert, E Hardouin, in Proceedings of IEEE International Conference on Communications (ICC). A dynamic clustering approach in wireless networks with multi-cell cooperative processing (IEEEBeijing, China, 2008), pp. 4033–4037.Google Scholar
- Z Niu, Y Wu, J Gong, Z Yang, Cell zooming for cost-efficient green cellular networks. IEEE Commun. Mag. 48, 74–79 (2010).View ArticleGoogle Scholar
- J Laneman, D Tse, GW Wornell, Cooperative diversity in wireless networks: efficient protocols and outage behavior. IEEE Trans. Inf. Theory. 50, 3062–3080 (2004).View ArticleMATHMathSciNetGoogle Scholar
- A Bletsas, A Khisti, D Reed, A Lippman, A simple cooperative diversity method based on network path selection. IEEE J. Selec. Areas Commun. 24, 659–672 (2006).View ArticleGoogle Scholar
- YJ, H Jafarkhani, Network beamforming using relays with perfect channel information. IEEE Trans. Inf. Theory. 55, 2499–2517 (2009).View ArticleGoogle Scholar
- C Lo, S Vishwanath, R Heath, Relay subset selection in wireless networks using partial decode-and-forward transmission. IEEE Trans. Veh. Technol. 58, 692–704 (2009).View ArticleGoogle Scholar
- B Hamdaoui, T Alshammari, M Guizani, Exploiting 4G mobile user cooperation for energy conservation: challenges and opportunities. IEEE Wireless Commun. 20, 62–67 (2013).View ArticleGoogle Scholar
- Z Zhou, S Zhou, S Cui, J-H Cui, in Proceedings of IEEE Military Communications Conference (MILCOM). Energy-efficient cooperative communication in clustered wireless sensor networks (IEEEWashington, USA, 2006), pp. 1–7.Google Scholar
- H Shan, W Zhuang, Z Wang, Distributed cooperative MAC for multihop wireless networks. IEEE Commun. Mag. 47, 126–133 (2009).View ArticleGoogle Scholar
- D Yang, X Fang, G Xue, Game theory in cooperative communications. IEEE Wireless Commun. Mag. 19, 44–49 (2012).View ArticleGoogle Scholar
- G R Bella, G Costantino, Evaluating the device reputation through full observation in MANETs. J. Inf. Ass. Sec. 4, 458–465 (2009).Google Scholar
- D Liu, W Wang, W Guo, ‘Green’ cooperative spectrum sharing communication. IEEE Commun. Letters. 17, 459–462 (2013).View ArticleGoogle Scholar
- C Comaniciu, NB Mandayam, H Poor, J-M Gorce, An auctioning mechanism for green radio. J. Commun. Netw-s. Kor. 12, 114–121 (2010).View ArticleGoogle Scholar
- J Furthmuller, O Waldhorst, in Proceedings of Eighth International Conference on Wireless On-Demand Network Systems and Services (WONS). Energy-aware resource sharing with mobile devices (IEEEBardonecchia Italy, 2011), pp. 52–59.Google Scholar
- K Woradit, T Quek, W Suwansantisuk, H Wymeersch, L Wuttisittikulkij, M Win, Outage behavior of selective relaying schemes. IEEE Trans. Wireless. Commun. 8, 3890–3895 (2009).View ArticleGoogle Scholar
- E Larsson, Y Cao, Collaborative transmit diversity with adaptive radio resource and power allocation. IEEE Commun. Lett. 9, 511–513 (2005).View ArticleGoogle Scholar
- Y Cao, B Vojcic, M Souryal, in Proceedings of IEEE Vehicular Technology Conference (VTC2004-Fal). User-cooperative transmission with channel feedback in slow fading environmentA (IEEELos Angeles, USA, 2004), pp. 2063–2067.Google Scholar
- G Lim, J Cimini, LJ, Energy-efficient cooperative beamforming in clustered wireless networks. IEEE Trans. Wireless. Commun. 12, 1376–1385 (2013).View ArticleGoogle Scholar
- C Isheden, Z Chong, E Jorswieck, G Fettweis, Framework for link-level energy efficiency optimization with informed transmitter. IEEE Trans. Wireless. Commun. 11, 2946–2957 (2012).Google Scholar
- D To, T To, J Choi, in Proceedings of IEEE Vehicular Technology Conference (VTC Spring). Energy efficient distributed beamforming with sensor selection in wireless sensor networks (IEEEYokohama, Japan, 2012), pp. 1–5.Google Scholar
- Y Zhang, H Dai, Energy-efficiency and transmission strategy selection in cooperative wireless sensor networks. J. Commun. Netw-s. Kor. 9, 473–481 (2007).View ArticleGoogle Scholar
- X Zhang, Z Zheng, J Liu, X Shen, L-L Xie, in Proceedings of IEEE Global Communications Conference (GLOBECOM). Optimal power allocation and AP deployment in green wireless cooperative communications (IEEEAnaheim, USA, 2012), pp. 4000–4005.Google Scholar
- GB S Farshad, ML, in Proceedings of International Union of Radio Science General Assembly and Scientific Symposium (URSI GASS). A Q-learning game-theory-based algorithm to improve the energy efficiency of a multiple relay-aided network (IEEEBeijing, China, 2014), pp. 1–4.Google Scholar
- L Zhang, Y Liang, Y Xin, Joint beamforming and power allocation for multiple access channels in cognitive radio networks. IEEE J. Sel. Areas Commun. 26, 38–51 (2008).View ArticleMATHGoogle Scholar
- R Madan, N Mehta, A Molisch, J Zhang, Energy-efficient cooperative relaying over fading channels with simple relay selection. IEEE Trans. Wireless Commun. 7, 3013–3025 (2008).View ArticleGoogle Scholar
- G Lim, L Cimini, Energy-efficient cooperative relaying in heterogeneous radio access networks. IEEE Wireless Commun. Lett. 1, 476–479 (2012).View ArticleGoogle Scholar
- Q Guan, F Yu, S Jiang, V Leung, H Mehrvar, Topology control in mobile ad hoc networks with cooperative communications. IEEE Wireless Commun. 19, 74–79 (2012).View ArticleGoogle Scholar
- C Ling, X Yin, SR Boqule, M Garcia-Lozano, in Proceedings of International Union of Radio Science General Assembly and Scientific Symposium (URSI GASS). Optimal power allocation and relay selection in spectrum sharing cooperative networks (IEEEBeijing, China, 2014), pp. 1–4.Google Scholar
- RT Rockafellar, Convex Analysis (Princeton University Press, USA, 1996).Google Scholar
- LV Stephen Boyd, Convex Optimization (Cambridge University Press, UK, 2006).Google Scholar
- R Kress, Numerical analysis (World Book Publishing, China, 2003).Google Scholar
- WC Jakes, Microwave Mobile Communications (John Wiley & Sons, USA, 1974).Google Scholar
- C Komninakis, in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM). A fast and accurate Rayleigh fading simulator (IEEESan Francisco, USA, 2003), pp. 3306–3310.Google Scholar
- H Yu, Y Li, M Kountouris, X Xu, J Wang, in Proceedings of 12th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt). Energy efficiency analysis of relay-assisted cellular networks using stochastic geometry (IEEEHammamet, Tunis, 2014), pp. 667–671.Google Scholar
- J Chen, X Chen, T Liu, L Lei, in Proceedings of IEEE international conference on Communications in China (ICCC). Energy-efficient power allocation for secure communications in large-scale MIMO relaying systems (IEEEShanghai, China, 2014), pp. 385–390.Google Scholar
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