SCIENCE CHINA Information Sciences, Volume 60, Issue 10: 102304(2017) https://doi.org/10.1007/s11432-016-9012-7

Energy-efficient resource allocation for hybrid bursty services in multi-relay OFDM networks

• AcceptedJan 11, 2017
• PublishedMay 19, 2017
Share
Rating

Abstract

In this paper, we propose mapped two-way water filling (MTWF) scheme to maximize energy efficiency (EE) for hybrid bursty services with quality of services (QoS) requirements in two-way multi-relay (TWMR) OFDM networks. The bursty traffic is first analyzed by strictly proved equivalent homogeneous Poisson process, based on which the QoS requirements are converted into sum-rate constraints. The formulated non-convex EE maximization problem, including subcarrier assignment, relay selection (RS) and rate allocation, is NP-hard involving combinatorial optimization. To conduct optimal RS on each subcarrier without priori bursty traffic knowledge, we utilize some approximate relationships under high data rate demands to remove its dependence on two-way data rates, and simplify the whole optimization problem as well. After the optimal channel configuration is obtained, which only depends on channel conditions, subcarrier assignment is attained through elitist selection genetic algorithm (ESGA), and rate allocation of each service is fulfilled by deducing two-way water filling principle. A new equivalent optimization objective function is proposed next as the simple evaluating index in ESGA to reduce complexity. Finally, simulations are carried out to verify the superiority and convergence of our scheme, as well as the applicability for different scenarios.

Acknowledgment

The work was supported by National Nature Science Foundation of China Project (Grant No. 61471058), Hong Kong, Macao and Taiwan Science and Technology Cooperation Projects (Grant Nos. 2014DFT10320, 2016YFE0122900), Beijing Nova Program (Grant No. xx2012037), Shenzhen Science and Technology Project (Grant No. 20150082), and Beijing Training Project for the Leading Talents in S&T (Grant No. Z141101001514026).

Supplement

Appendix

Proof of the average performance equivalent

With the same data packet departure (that is homogeneous Poisson process), there are two kinds of data packet arrival, which are equivalent about the average performance, i.e., delay in this paper. The two types of data packet arrival can be described as follows.

Homogeneous Poisson arrival: The data packets arrive with a fixed rate $\lambda$ with a period of time $T$.

Heterogeneous Poisson arrival: The data packets arrive with a changed rate $\lambda(t)$ with regard to time $t$ within a period of time $T$, and the following constraint is satisfied, as given by $$\lambda \cdot T = \int_0^T \lambda(t) \cdot {\rm d}t. \tag{39}$$

Since the departure process is identical, the equivalence of the two queue systems can be ensured if the equivalence of the two arrival processes can be proved within time duration $T$. Observing the whole queue system at time $T$, it is seen that the waiting time, depending on the state of queue system, will be same for different queue systems as long as the probability of queue length is identical. It is noted that only same average performance at time $T$ is guaranteed, but not the transient performance or any time before $T$.

As for homogeneous poisson arrival, the probability of arriving $k$ data packets within time $T$ can be expressed as $$P_k^1(T)=\frac{(\lambda \cdot T)^k}{k!}{\rm e}^{-\lambda \cdot T}.$$

Similarly, for heterogeneous poisson arrival, this probability of arriving $k$ data packets can be obtained, as given by $$P_k^2(T)=\frac{\left(\int_0^T\lambda(t) \cdot {\rm d}t\right)^k}{k!}{\rm e}^{-\int_0^T\lambda(t) \cdot {\rm d}t}.$$ According to 39, $P_k^1(T)=P_k^2(T)$ is obtained which indicates that the probability of arriving $k$ data packets within time $T$ is identical. It is obvious that the probability of leaving $q$ data packets within time $T$ is identical too due to the same departure process, resulting in the same state of queue system. Therefore, it is proved that the two kinds of process are equivalent if the constraint 39 is satisfied.

The average time duration can be written as $T_1^s+\frac{1}{\Lambda_1^s}$ for service $s$ in downlink from a burst arrival to another burst arrival periodically. The burst data packet arrival is a heterogeneous poisson process, thus the following relationship can be obtained with the arrival rate $\lambda_1^s$ during bursty duration while $0$ during bursty interval, as given by $$\int_0^{T_1^s+\frac{1}{\Lambda_1^s}} \lambda(t) \cdot {\rm d}t = \int_0^{T_1^s} \lambda_1^s \cdot {\rm d}t + \int_{T_1^s}^{T_1^s+\frac{1}{\Lambda_1^s}} 0 \cdot {\rm d}t=\lambda_1^s \cdot T_1^s.$$

Since ${\lambda_1^s}^*=\frac{\lambda_1^s~\cdot~T_1^s}{{T_1^s+\frac{1}{\Lambda_1^s}}}$, the new homogeneous poisson arrival with the parameter of ${\lambda_1^s}^*$ can meet the constraint 39 due to the following relationship, as given by $${\lambda_1^s}^*\left({T_1^s+\frac{1}{\Lambda_1^s}}\right)= \lambda_1^s \cdot T_1^s =\int_0^{T_1^s+\frac{1}{\Lambda_1^s}} \lambda(t) \cdot {\rm d}t.$$

Therefore, it is completely proved that it is equivalent on average performance for the bursty arrival and the homogeneous poisson arrival with the parameter of ${\lambda_1^s}^*$.

References

[1] Daquan Feng , Chenzi Jiang , Gubong Lim . A survey of energy-efficient wireless communication. IEEE Commun Surv Tutorials, 2013, 15: 167-178 CrossRef Google Scholar

[2] Cui Q, Wang H, Hu P. Evolution of Limited-Feedback CoMP Systems from 4G to 5G: CoMP Features and Limited-Feedback Approaches. IEEE Veh Technol Mag, 2014, 9: 94-103 CrossRef Google Scholar

[3] Miao G, Himayat N, Li Y G. Cross-layer optimization for energy-efficient wireless communications: a survey. Wirel Commun Mob Comput, 2009, 9: 529-542 CrossRef Google Scholar

[4] Liu Y, Lu L, Li G Y. Joint User Association and Spectrum Allocation for Small Cell Networks With Wireless Backhauls. IEEE Wireless Commun Lett, 2016, 5: 496-499 CrossRef Google Scholar

[5] Min Zhou , Qimei Cui , Jantti R. Energy-efficient relay selection and power allocation for two-way relay channel with analog network coding. IEEE Commun Lett, 2012, 16: 816-819 CrossRef Google Scholar

[6] Li Y, Louie R H Y, Vucetic B. Relay selection with network coding in two-way relay channels. IEEE Trans Veh Technol, 2010, 59: 4489-4499 CrossRef Google Scholar

[7] Peters S, Panah A, Truong K, et al. Relay architectures for 3GPP LTE-advanced. EURASIP J Wirel Commun Netw, 2009, 2009: 1--14. Google Scholar

[8] Rankov B, Wittneben A. Spectral efficient protocols for half-duplex fading relay channels. IEEE J Select Areas Commun, 2007, 25: 379-389 CrossRef Google Scholar

[9] Fu S, Lu K, Zhang T, et al. Cooperative wireless networks based on physical layer network coding. IEEE Wirel Commun, 2010, 17: 86--95. Google Scholar

[10] Popovski P, Yomo H. Physical network coding in two-way wireless relay channels. In: Proceedings of IEEE International Conference on Communications (ICC), Scotland, 2007. 707--712. Google Scholar

[11] Kim S J, Mitran P, Tarokh V. Performance bounds for bidirectional coded cooperation protocols. IEEE Trans Inform Theor, 2008, 54: 5235-5241 CrossRef Google Scholar

[12] Cui Q, Yuan T, Tao X. Energy Efficiency Analysis of Two-Way DF Relay System With Non-Ideal Power Amplifiers. IEEE Commun Lett, 2014, 18: 1254-1257 CrossRef Google Scholar

[13] Ngo H Q, Quek T Q S, Shin H. Amplify-and-forward two-way relay networks: error exponents and resource allocation. IEEE Trans Commun, 2010, 58: 2653-2666 CrossRef Google Scholar

[14] Cui Q, Yuan T, Ni W. Energy-efficient two-way relaying under non-ideal power amplifiers. IEEE Trans Veh Tech, 2016, 99: 1257--1270. Google Scholar

[15] Kim S, Lee Y H, Shahbazpanahi S. Energy-efficient power allocation for OFDM signaling over a two-way AF relay. IEEE Trans Veh Tech, 2014, 64: 4856--4863. Google Scholar

[16] Sun C, Cen Y, Yang C. Energy efficient OFDM relay systems. IEEE Trans Commun, 2013, 61: 1797-1809 CrossRef Google Scholar

[17] Pang L, Zhang Y, Gong F. Energy Aware Resource Allocation for Incremental AF-OFDM Relaying. IEEE Commun Lett, 2015, 19: 1766-1769 CrossRef Google Scholar

[18] Tain-Sao Chang , Kai-Ten Feng , Jia-Shi Lin . Green Resource Allocation Schemes for Relay-Enhanced MIMO-OFDM Networks. IEEE Trans Veh Technol, 2013, 62: 4539-4554 CrossRef Google Scholar

[19] Do T P, Wang J S, Song I. Joint relay selection and power allocation for two-way relaying with physical layer network coding. IEEE Commun Lett, 2013, 17: 301-304 CrossRef Google Scholar

[20] Talwar S, Jing Y, Shahbazpanahi S. Joint Relay Selection and Power Allocation for Two-Way Relay Networks. IEEE Signal Process Lett, 2011, 18: 91-94 CrossRef ADS Google Scholar

[21] Wang X M, Zheng F C, Zhu P C, et al. Energy-efficient resource allocation for OFDMA relay systems with imperfect CSIT. Sci China Inf Sci, 2015, 58: 082311. Google Scholar

[22] Chen Y, Fang X, Huang B. Energy-Efficient Relay Selection and Resource Allocation in Nonregenerative Relay OFDMA Systems. IEEE Trans Veh Technol, 2014, 63: 3689-3699 CrossRef Google Scholar

[23] Cheung K T K, Shaoshi Yang K T K, Hanzo L. Achieving Maximum Energy-Efficiency in Multi-Relay OFDMA Cellular Networks: A Fractional Programming Approach. IEEE Trans Commun, 2013, 61: 2746-2757 CrossRef Google Scholar

[24] Xiong K, Fan P, Lu Y. Energy Efficiency With Proportional Rate Fairness in Multirelay OFDM Networks. IEEE J Select Areas Commun, 2016, 34: 1431-1447 CrossRef Google Scholar

[25] Cheung K T K, Yang S, Hanzo L. Spectral and Energy Spectral Efficiency Optimization of Joint Transmit and Receive Beamforming Based Multi-Relay MIMO-OFDMA Cellular Networks. IEEE Trans Wireless Commun, 2014, 13: 6147-6165 CrossRef Google Scholar

[26] Zhou M, Cui Q, Valkama M, et al. Energy-efficient resourse allocation for OFDMA-based two-way relay channel with physical-layer network coding. EURASIP J Wirel Commun Netw, 2012, 66: 1--11. Google Scholar

[27] Liew S C. Performance of various input-buffered and output-buffered ATM switch design principles under bursty traffic: simulation study. IEEE Trans Commun, 1994, 42: 1371-1379 CrossRef Google Scholar

[28] Jacob L, Kumar A. Delay performance of some scheduling strategies in an input queuing ATM switch with multiclass bursty traffic. IEEE/ACM Trans Networking, 1996, 4: 258-271 CrossRef Google Scholar

[29] Yu M, Zhou M. A Performance Modeling Scheme for Multistage Switch Networks With Phase-Type and Bursty Traffic. IEEE/ACM Trans Networking, 2010, 18: 1091-1104 CrossRef Google Scholar

[30] Jagannathan K, Jiang L, Naik P L, et al. Scheduling strategies to mitigate the impact of bursty traffic in wireless networks. In: Proceedings of International Symposium and Workshops on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt), Japan, 2013. 468--475. Google Scholar

[31] Wu J, Bao Y, Miao G, et al. Base station sleeping and power control for bursty traffic in cellular networks. In: Proceedings of IEEE International Conference on Communications Workshops (ICC), Sydney, 2014. 837--841. Google Scholar

[32] Wu Y, Min G, Yang L T. Performance analysis of hybrid wireless networks under bursty and correlated traffic. IEEE Trans Veh Technol, 2013, 62: 449-454 CrossRef Google Scholar

[33] Ng T, Doan Hoang T. Joint optimization of capacity and flow assignment in a packet-switched communications network. IEEE Trans Commun, 1987, 35: 202-209 CrossRef Google Scholar

[34] Cidon I, Khamisy A, Sidi M. Analysis of packet loss processes in high-speed networks. IEEE Trans Inform Theor, 1993, 39: 98-108 CrossRef Google Scholar

[35] Gurewitz O, Sidi M, Cidon S. The ballot theorem strikes again: packet loss process distribution. IEEE Trans Inform Theor, 2000, 46: 2588-2595 CrossRef Google Scholar

[36] Jianming Liu , Xiaohong Jiang , Horiguchi S. Recursive formula for the moments of queue length in the M/M/1 queue. IEEE Commun Lett, 2008, 12: 690-692 CrossRef Google Scholar

[37] Medhi J. Stochastic Models in Queueing Theory. San Diego: Academic Press, 2003. Google Scholar

[38] Miao G, Himayat N, Li G. Energy-efficient link adaptation in frequency-selective channels. IEEE Trans Commun, 2010, 58: 545-554 CrossRef Google Scholar

[39] Holland J H. Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press, 1975. Google Scholar

[40] Goldberg D E. Genetic Algorithms in Search, Optimization, and Machine Learning. New York: Addsin-Wesley Publishing Company, 1989. Google Scholar

[41] Jiang H, Zheng L, Liu Y, et al. Multi-constratined QoS routing optimization of wireless mesh network based on hybrid genetic algorithm. In: Proceedings of International Conference on Intelligent Computing and Integrated Systems (ICISS), Guilin, 2010. 862--865. Google Scholar

[42] Hu X M, Zhang J, Yu Y. Hybrid genetic algorithm using a forward encoding scheme for lifetime maximization of wireless sensor networks. IEEE Trans Evol Computat, 2010, 14: 766-781 CrossRef Google Scholar

[43] Rudolph G. Convergence analysis of canonical genetic algorithms.. IEEE Trans Neural Netw, 1994, 5: 96-101 CrossRef PubMed Google Scholar

• Figure 1

(Color online) Hybrid bursty services transmission in TWMR OFDM networks.

• Figure 2

(Color online) Bursty traffic of single service.

•

Algorithm 1 The mapped two-way water filling allocation

Require:Chromosome number in ESGA: Popsize, iteration number in ESGA: $g_c$, service number: $S$, channel conditions: $\{h_m^n,~g_m^n\}$, QoS requirements, and bursty traffic features;

Obtain sum-rate constraints from the QoS requirements through equivalent queue analysis for all services;

According to the integrated-noise-channel selection criterion, the optimal relay for each subcarrier is selected and the optimal channel conditions are recorded;

Calculate the comprehensive two-way channel coefficients for each subcarrier;

for $i=1:$ Popsize

Initialize the subcarrier assignment sequence satisfying the $\{C_s^n\}$ constraints of each service for chromosome $i$;

end for

for $g=1:g_c$

for $i=1:$ Popsize

for $j=1:S$

Resolve water level according to 33 for service $j$;

Conduct the rate allocation and obtain the data rate ${r_1}$ and ${r_2}$ according to water level for service $j$;

if $\forall~{r_1}~<~0$, $\forall~{r_2}~<~0$ then

Let these negative data rates be 0 and exclude these subcarriers. Turn to Step Cal_water;

end if

end for

Calculate the fitness according to the equivalent optimization function (37) as evaluating indicator;

end for

Select and record the best assignment scheme;

Obtain the next generation by crossover and mutation;

end for

• 2

Citations

• Altmetric

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有