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International Journal of Distributed Sensor Networks
Volume 2011 (2011), Article ID 946258, 8 pages
http://dx.doi.org/10.1155/2011/946258
Research Article

Modeling and Performance Analysis of Energy Efficiency Binary Power Control in MIMO-OFDM Wireless Communication Systems

1Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
2Department of Information and Communication Technology, University of Agder (UiA), 4879 Grimstad, Norway

Received 31 March 2011; Accepted 30 June 2011

Copyright © 2011 Yuming Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The energy efficiency optimization of the binary power control scheme for MIMO-OFDM wireless communication systems is formulated, and then a global optimization solution of power allocation is derived. Furthermore, a new energy efficiency binary power control (EEBPC) algorithm is designed to improve the energy efficiency of MIMO-OFDM wireless communication systems. Simulation results show that the EEBPC algorithm has better energy efficiency and spectrum efficiency than the average power control algorithm in MIMO-OFDM wireless communication systems.

1. Introduction

It is beyond question that information and communication technology (ICT) industries play a significant role in current global economy. Among all energy-consuming industries, the ICT industry takes 2% of global total CO2 emissions while consuming 3% of global energy storage [1, 2]. Within the 3% consumption, 57% is caused in mobile and wireless communication systems [3]. From another perspective of ICT growth, there has risen a high demand for broadband data transmission with high-quality services, which is further triggering the Multi-Input and Multi-Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) techniques to be adopted in the next generation wireless communication systems [46]. Therefore, the optimization of energy efficiency in MIMO-OFDM wireless communication systems has become an urgent requirement.

In wireless communication systems, the transmission power consumption of base station is controlled by power allocation schemes. In early analog mobile communication systems, the key aim of transmission power allocation scheme is to improve user signal-to-noise (SNR). Therefore, some transmission power allocation schemes of base station are developed to enhance the SNR of terminal users [79]. In digital mobile communication systems, the traditional transmission power allocation schemes sought to realize the maximization of wireless channel capacity [1012]. One of the most popular power allocation schemes of base station is the power water-filling scheme, which performs power allocation based on the state of wireless channels to close the wireless channel capacity to the Shannon capacity limit [10]. To overcome the requirement of continuous-rate adaptation in the power water-filling scheme, a new scheme based on a fixed number of codes, was proposed to maximize average spectral efficiency (ASE) of dual-branch MIMO systems with perfect transmitter and receiver channel state information (CSI) [11]. To formulate the link adaptation problem as a convex optimization problem, Kim and Daneshrad proposed a link adaptation power strategy to maximize energy efficiency or data throughput subject to a given quality of service (QoS) constraint [12]. Considering the complexity of optimization transmission power allocation scheme, a simple transmission power allocation scheme, that is, the binary power control scheme was proposed to maximize wireless channel capacity in practical engineering applications [13, 14]. However, the energy efficiency problem in the traditional binary power control scheme of MIMO-OFDM wireless communication systems is not considered.

In this paper, we investigate the energy efficiency problem of the binary power control scheme and formulate the binary power control scheme with energy efficiency constraint. Moreover, a new algorithm is designed to address the energy efficiency power allocation in MIMO-OFDM wireless communication systems. The contributions and novelty of this paper are summarized as follows.(1)We formulate the energy efficiency problem of the binary power control scheme in MIMO-OFDM wireless communication systems. (2)A global optimization solution of power allocation in MIMO-OFDM wireless communication systems is derived. Furthermore, two derivation results can be used for potential engineering application with the low calculation complexity. (3)A new algorithm is designed to realize the energy efficiency binary power control scheme in communication systems. (4)Performance of the new algorithm is analyzed and some interesting observations are presented.

The rest of paper is organized as follows. In Section 2, the energy efficiency concept is introduced and the binary power control scheme is introduced. In Section 3, we investigate optimal conditions for energy efficiency transmission with the binary power control scheme. Moreover, the global optimization solution of power distribution model is derived and a new algorithm is proposed. Furthermore, we apply the new algorithm in a MIMO-OFDM communication system and provide simulation results to demonstrate energy efficiency improvement in Section 4. Finally, we conclude the paper in Section 5.

2. Energy Efficiency in Wireless Communication Systems

As introduced in this section, more and more energy efficiency optimization schemes in wireless communication systems were studied. To estimate the energy efficiency, the definition of energy efficiency should be first declared. In this paper, a definition of energy efficiency is described as follows.

2.1. Definition of Energy Efficiency in Wireless Communication Systems

Typically, the energy consumption of transmitting per bit is a main concern in evaluating the energy efficiency of a communication system. In addition, the definition should include the transmission power from the base station and the capacity of wireless channels. Considering the Shannon capacity theory [15], the maximum achievable capacity of a wireless channel is related to the transmission power from a base station. Therefore, an energy efficiency used in wireless communication systems is defined as follows:𝑃𝜂=𝑓𝑖=𝑛𝑖=1𝐶𝑖𝑃𝑖𝑛𝑖=1𝑃𝑖[],𝑖1,𝑛,(1) where 𝜂 is the energy efficiency of wireless communication systems which is denoted as a function of transmission power 𝑃𝑖 over wireless channel 𝑖𝑛 is the number of wireless channels in wireless communication systems. 𝐶𝑖(𝑃𝑖) is a wireless channel capacity which is denoted as a function of transmission power 𝑃𝑖 over wireless channel 𝑖.

2.2. Binary Power Control Scheme

For wireless communication systems, the transmission power 𝑃 over wireless channels is allocated from the minimum value 𝑃min to the maximum value 𝑃max, that is, 𝑃min𝑃𝑃max. According to the binary power control scheme of wireless communication systems, the transmission power 𝑃 over wireless channels is allocated a value from two elements, that is, 𝑃min and 𝑃max. Moreover, the binary power control scheme is formulated as follows [16]:𝑃Ω,Ω=𝑃𝑃=𝑃minor𝑃=𝑃max.(2)

From research results in [13, 14, 17], when there are many wireless channels in wireless communication systems, the capacity and rate performance of wireless communication systems adopting the binary power control scheme can approximate the Shannon capacity limit. However, when the energy efficiency of wireless communication systems is considered as an optimal aim, how to adopt the binary power control scheme of wireless communication systems to approximate the global energy efficiency optimal solution is a great challenge.

3. Problem Formulation of Energy Efficiency Binary Power Control Scheme

To investigate the binary power control scheme in energy efficiency of wireless communication systems, a single cell MIMO-OFDM wireless communication system is illustrated in Figure 1. One base station integrated with 𝑀𝑇 antennas is located in the center of cell. There are 𝐾 users uniformly scattering in the cell and every user is integrated with 𝑀𝑅 antennas. To simplify the modeling complexity of the OFDM scheme, all orthogonal 𝑁 subcarriers are regrouped into 𝑁 subchannels by the OFDM scheme. Moreover, interference between users is assumed to be ignored in this single cell. Every subchannel of MIMO-OFDM communication system in Figure 1 is assumed as a quasistatic channel, which means there is no change within a block of transmission. The bandwidth of MIMO-OFDM communication system is normalized as 1. For one moment, without loss of generality, only 𝑁 subchannels are enabled for data transmission. The CSI of MIMO-OFDM wireless communication system is assumed to be known by the base station in Figure 1. In this paper, our research focuses on the downlink performance of wireless communication systems.

946258.fig.001
Figure 1: System model of MIMO-OFDM wireless communication systems.
3.1. Problem Formulation

Based on the system model in Figure 1, the total capacity of MIMO-OFDM communication system is described as𝐶total=𝑁𝑖=1log2𝑃1+𝑖𝑛0𝐻𝑖2𝐹,(3) where 𝑃𝑖 is the transmission power over wireless subchannel 𝑖, 𝑛0 is the additive white Gaussian noise (AWGN) in wireless subchannels, and 𝐻𝑖𝐹 is the 𝐹 norm over wireless subchannel 𝑖.

In this case, the total transmission power in the downlink of MIMO-OFDM communication system is denoted as𝑃total=𝑁𝑖=1𝑃𝑖.(4)

Furthermore, the energy efficiency of MIMO-OFDM communication system is given by𝜂total=𝑁𝑖=1log2𝑃1+𝑖/𝑛0𝐻𝑖2𝐹𝑁𝑖=1𝑃𝑖.(5)

The wireless subchannel set 𝐾 is defined as follows:CH𝑖𝐾,𝐾=CHCH=𝑁𝑖=1CH𝑖,(6) where CH is the wireless subchannel element in set 𝐾 and CH𝑖 is the wireless subchannel 𝑖.

Assume that the binary power control scheme is used to allocate the transmission power for the wireless subchannel set 𝐾. In this case, the set 𝐾 is divided into two subsets: one is the maximum power transmission subchannel subset 𝐾𝑀𝑝max with 𝑀 wireless subchannels; the other is the minimum power transmission subchannel subset 𝐾𝑁𝑀𝑝min with 𝑁𝑀 wireless subchannels. Moreover, the total transmission power of 𝐾𝑀𝑝max is denoted as 𝑃max_total and the total transmission power of 𝐾𝑁𝑀𝑝min is denoted as 𝑃min_total. The relationship of 𝑃total,𝑃max_total, and 𝑃min_total is described as follow:𝑃total=𝑃max_total+𝑃min_total,𝑃max_total=𝑀×𝑃max,𝑃min_total=(𝑁𝑀)×𝑃min.(7)

To optimize the global energy efficiency of MIMO-OFDM wireless communication system, some basic assumptions and a principle are defined as follows.

Assumption 1. The total transmission power of MIMO-OFDM wireless communication system is fixed as a constant.

Assumption 2. 𝑃max_total in the maximum power transmission subchannel subset is fixed as a constant.

Principle 1. A wireless subchannel CH𝑘 is assigned into the maximum power transmission subchannel subset 𝐾𝑀𝑝max only when the energy efficiency of 𝐾𝑀𝑝max including CH𝑘 is no less than the energy efficiency of 𝐾𝑀𝑝max without CH𝑘, otherwise, the wireless subchannel should be assigned into the minimum power transmission subchannel 𝐾𝑁𝑀𝑝min.

3.2. Optimization of Power Allocation

For the energy efficiency binary power control scheme, how to optimize the power allocation in the maximum power transmission subchannel subset and the minimum power transmission subchannel subset is a key problem. Based on assumption, principle and (7) in Section 3.1, we find that 𝑃max_total and 𝑃min_total can be derived if the value of 𝑃max is determined. Therefore, the global optimal solution of 𝑃max is a key problem in this binary power control scheme.

When a candidate wireless subchannel CH𝑘 is assigned into the maximum power transmission subchannel subset, the maximum transmission power 𝑃max_1 used for the maximum power transmission subchannel subset is given by𝑃max_1=𝑃max_total𝑀.(8) Furthermore, the energy efficiency of MIMO-OFDM communication system with the wireless subchannel CH𝑘 is derived as𝜂1=𝑀𝑖=1log2𝑃1+max_1/𝑛0𝐻𝑖2𝐹𝑃max_total.(9)

When a candidate wireless subchannel CH𝑘 is not assigned into the maximum power transmission subchannel subset, the maximum transmission power 𝑃max_2 used for the maximum power transmission subchannel subset is given by𝑃max_2=𝑃max_total𝑀1.(10) Furthermore, the energy efficiency of MIMO-OFDM communication system without the wireless subchannel CH𝑘 is derived as𝜂2=𝑀1𝑖=1,𝑖𝑘log2𝑃1+max_2/𝑛0𝐻𝑖2𝐹𝑃max_total.(11)

Based on Principle 1, the candidate wireless subchannel CH𝑘 can be finally assigned into the maximum power transmission subchannel subset and the maximum transmission power 𝑃max can be derived under the condition of 𝜂1𝜂2. From Principle 1, the optimization relationship of maximum transmission power is derived in the Appendix and is expressed by𝑃1+max_2𝑛0𝐻𝑘2𝐹𝑀1𝑖=1,𝑖𝑘𝑛0+𝑃max_total/𝐻(𝑀1)𝑖2𝐹𝑀1𝑖=1,𝑖𝑘𝑛0+𝑃max_total𝐻/𝑀𝑖2𝐹.(12)

Compared with the transmission power over wireless subchannels, the value of AWGN 𝑛0 is obviously less than the value of (𝑃max_total)/(𝑀1)𝐻𝑖2𝐹 or (𝑃max_total/𝑀)𝐻𝑖2𝐹. Therefore, the right side of (12) can be approximated as𝑃1+max_2𝑛0𝐻𝑘2𝐹𝑀1𝑖=1,𝑖𝑘𝑛0+𝑃max_total/𝐻(𝑀1)𝑖2𝐹𝑀1𝑖=1,𝑖𝑘𝑛0+𝑃max_total𝐻/𝑀𝑖2𝐹𝑀1𝑖=1,𝑖𝑘𝑃max_total𝐻/(𝑀1)𝑖2𝐹𝑀1𝑖=1,𝑖𝑘𝑃max_total𝐻/𝑀i2𝐹.(13) Furthermore, (13) can be derived as follows:𝑃1+max_2𝑛0𝐻𝑘2𝐹𝑀1𝑖=1,𝑖𝑘(1/(𝑀1))𝑀1𝑖=1,𝑖𝑘(,𝑃1/𝑀)(14a)1+max_2𝑛0𝐻𝑘2𝐹(1/(𝑀1))𝑀1(1/𝑀)𝑀1,𝑃(14b)1+max_2𝑛0𝐻𝑘2𝐹(𝑀/(𝑀1))𝑀1.(14c)

Based on (14c), we can derive a current global optimization solution of maximum transmission power 𝑃max_2 with the CSI of wireless communication system and the subchannel number of the maximum power transmission subchannel subset.

When the number of subchannels 𝑀 approaches to infinite, we have the following result:lim𝑀𝑀𝑀1𝑀1=𝑒.(15)

From the numerical simulation of threshold values (𝑀/(𝑀1))𝑀1 and limitation values 𝑒 in Figure 2, the difference between the threshold values (𝑀/(𝑀1))𝑀1 and limitation values 𝑒 is less than 1.67% when the number of subchannel is large than or equal to 30. Therefore, we further derive two simple results for possible engineering applications.

946258.fig.002
Figure 2: Threshold values versus number of subchannels.

Result 1. When the number of current subchannel in the maximum power transmission subchannel subset is less than 30, the value of maximum transmission power 𝑃max is derived by 𝑃max𝑛0𝐻𝑖2𝐹𝑀𝑀1𝑀11.(16)

Result 2. When the number of current subchannel in the maximum power transmission subchannel subset is larger than or equal to 30, the value of maximum transmission power 𝑃max are derived by 𝑃max𝑛0𝐻𝑖2𝐹𝑒1.(17)
From above results, especially from Result 2, the complexity of maximum transmission power derivation can be reduced.

3.3. Algorithm Design

Based on Results 1 and 2, an energy efficiency binary power control (EEBPC) algorithm is designed for improving energy efficiency of MIMO-OFDM wireless communication systems. The detailed EEBPC algorithm is illustrated in Algorithm 1. Morever, an assumption of Algorithm 1 is that all subchannels of wireless subchannel set 𝐾 are degressively ordered.

alg1
Algorithm 1: Energy efficiency binary power control.

4. Simulation Results and Performance Analysis

Based on the new EEBPC algorithm, the energy efficiency and spectrum efficiency performance of MIMO-OFDM wireless communication systems is simulated and analyzed. In the following simulation, some parameters of the system model in Figure 1 are configured as follows: the total transmission power of base station is ranged from 0.6 to 1.4 watt (W); considering the OFDM scheme used in MIMO wireless communication system, the number of subchannels is ranged from 8 to 128; the AWGN 𝑛0 in wireless subchannels is assumed as 0.1 W. Wireless subchannels are simulated by a Monte Carlo approach based on AWGN wireless subchannels with zero mean values.

From Figure 3, the impact of the number of subchannels on the spectrum efficiency of MIMO-OFDM communication system with the EEBPC algorithm is investigated. The spectrum efficiency of MIMO-OFDM communication system increases with the number of subchannels and the total transmission power of base station.

946258.fig.003
Figure 3: Spectrum efficiency analysis with number of subchannels limited by different total transmission power.

From Figure 4, the impact of number of subchannels on the energy efficiency of MIMO-OFDM communication system with the EEBPC algorithm is analyzed. The energy efficiency of MIMO-OFDM communication system increases with the number of subchannels, but the energy efficiency of MIMO-OFDM communication system decreases with the total transmission power of base station.

946258.fig.004
Figure 4: Energy efficiency analysis with number of subchannels limited by different total transmission power.

From Figure 5, the EEBPC algorithm is compared with the traditional average power control algorithm [16] in the spectrum efficiency of MIMO-OFDM communication system with different number of subchannels. Assume that the total transmission power of base station is configured as 1 W. When the number of subchannels is less than 12, the spectrum efficiency of MIMO-OFDM communication system with average power control algorithm is larger than that with EEBPC algorithm. When the number of subchannels is larger than or equal to 12, the spectrum efficiency of MIMO-OFDM communication system with EEBPC algorithm is larger than that with average power control algorithm. Moreover, the spectrum efficiency gain of EEBPC algorithm increases with the number of subchannels.

946258.fig.005
Figure 5: Comparison spectrum efficiency of EEBPC and average power control algorithms with different number of subchannels.

From Figure 6, the EEBPC algorithm is compared with the traditional average power control algorithm in the energy efficiency of MIMO-OFDM communication system with different number of subchannels. Assume that the total transmission power of base station is configured as 1 W. When the number of subchannels is less than 12, the energy efficiency of MIMO-OFDM communication system with average power control algorithm is larger than that with EEBPC algorithm. When the number of subchannels is larger than or equal to 12, the energy efficiency of MIMO-OFDM communication system with EEBPC algorithm is large than that with average power control algorithm. Moreover, the energy efficiency gain of EEBPC algorithm increases with the number of subchannels.

946258.fig.006
Figure 6: Comparison energy efficiency of EEBPC and average power control algorithms with different number of subchannels.

From Figure 7, the EEBPC algorithm is compared with the traditional average power control algorithm in the spectrum efficiency of MIMO-OFDM communication system with different total transmission power of base station. Assume that the number of subchannels is configured as 64. The spectrum efficiency of MIMO-OFDM communication system with EEBPC algorithm is large than that with average power control algorithm. Moreover, the spectrum efficiency gain of EEBPC algorithm is invariable with the total transmission power of base station.

946258.fig.007
Figure 7: Comparison spectrum efficiency of EEBPC and average power control algorithms with different total transmission power.

From Figure 8, the EEBPC algorithm is compared with the traditional average power control algorithm in the energy efficiency of MIMO-OFDM communication system with different total transmission power of base station. Assume that the number of subchannels is configured as 64. The energy efficiency of MIMO-OFDM communication system with EEBPC algorithm is large than that with average power control algorithm. Moreover, the energy efficiency gain of EEBPC algorithm decreases with the total transmission power of base station.

946258.fig.008
Figure 8: Comparison of energy efficiency of EEBPC and average power control algorithms with different total transmission power.

5. Conclusion

In this paper, the energy efficiency of binary power control scheme is investigated and formulated by three principles. Furthermore, a global optimalsolution of the maximum transmission power of MIMO-OFDM wireless communication system is derived. Moreover, a simple engineering application result is proposed for reducing the complexity of calculation. Based on them, a new EEBPC algorithm is designed for performance analysis. The exact impact of EEBPC algorithm on the spectrum efficiency and the energy efficiency has been fully investigated under different number of subchannels and total transmission power of base station. Simulation results have shown that the energy efficiency and spectrum efficiency of EEBPC algorithm is better than that of traditional average power control algorithm when the number of subchannels is larger than 11. Our future work includes a further investigation of the impact of multicell on the EEBPC algorithm.

Appendix

Appendix of (12)

In this appendix, we derive the optimization relationship of maximum transmission power. Based on Principle 1, only satisfying the condition of 𝜂1𝜂2, the candidate wireless subchannel CH𝑘 can be finally assigned into the maximum power transmission subchannel subset. Therefore, this condition is expressed by𝑀𝑖=1log2𝑃1+max_1/𝑛0𝐻𝑖2𝐹𝑃max_total𝑀1𝑖=1,𝑖𝑘log2𝑃1+max_2/𝑛0𝐻𝑖2𝐹𝑃max_total.(A.1) Based on (A.1), we can further derive this expression as follows:𝑀𝑖=1log2𝑃1+max_1𝑛0𝐻𝑖2𝐹𝑀1𝑖=1,𝑖𝑘log2𝑃1+max_2𝑛0𝐻𝑖2𝐹,(A.2)log2𝑀𝑖=1𝑃1+max_1𝑛0𝐻𝑖2𝐹log2𝑀1𝑖=1,𝑖𝑘𝑃1+max_2𝑛0𝐻𝑖2𝐹,(A.3)𝑀𝑖=1𝑃1+max_1𝑛0𝐻𝑖2𝐹𝑀1𝑖=1,𝑖𝑘𝑃1+max_2𝑛0𝐻𝑖2𝐹.(A.4)

Assume that the total transmission power of the maximum power transmission subchannel subset 𝑃max_total is fixed, so we can derive the following expression considering (8) and (10):𝑃max_2𝑃max_1.(A.5) Based on (A.5), and (A.4) is further derived as follows:𝑃1+max_2𝑛0𝐻𝑘2𝐹M1𝑖=1,𝑖𝑘𝑃1+max_1𝑛0𝐻𝑖2𝐹𝑀𝑖=1𝑃1+max_1𝑛0𝐻𝑖2𝐹𝑀1𝑖=1,𝑖𝑘𝑃1+max_2𝑛0𝐻𝑖2𝐹,𝑃1+max_2𝑛0𝐻𝑘2𝐹𝑀1𝑖=1,𝑖𝑘𝑃1+max_1/𝑛0𝐻𝑖2𝐹𝑀1𝑖=1,𝑖𝑘𝑃1+max_2/𝑛0𝐻𝑖2𝐹,𝑃1+max_2𝑛0𝐻𝑘2𝐹𝑀1𝑖=1,𝑖𝑘𝑛0+𝑃max_total𝐻/(𝑀1)𝑖2𝐹𝑀1𝑖=1,𝑖𝑘𝑛0+𝑃max_total𝐻/𝑀𝑖2𝐹.(A.6)

This completes the derivation.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (NSFC), Contract/Grant number: 60872007, 61103177; National 863 High Technology Program of China, Contract/Grant number 2009AA01Z239; The Ministry of Science and Technology (MOST), China, International Science and Technology Collaboration Program, Contract/Grant number 0903; EU FP7-PEOPLE-IRSES, project acronym S2EuNet, Contract/Grant number 247083.

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