Adaptive wireless transmission strategy for maximizing energy efficiency
 Caixia Cai^{1, 2},
 Runhe Qiu^{1, 2}Email authorView ORCID ID profile,
 XueQin Jiang^{1, 2} and
 Wanping Xu^{1, 2}
https://doi.org/10.1186/s1363801708075
© The Author(s) 2017
Received: 4 July 2016
Accepted: 2 January 2017
Published: 21 January 2017
Abstract
In a traditional wireless transmission system, studies about energy efficiency (EE) are usually for a fixed transmission mode. In this paper, we propose an adaptive wireless transmission (AWT) strategy with consideration of circuit power. In this AWT strategy, the transmission mode is switched between the direct transmission (DT) mode and the twoway relay transmission (TWRT) mode. The switch strategy is based on a transmission rate threshold R _{th} which makes the EEs of the DT mode and the TWRT mode equal. Furthermore, we propose a transmission rate threshold determining (TRTD) algorithm with a bisection method to find the threshold R _{th}. The simulation results also show that our AWT strategy has the maximum EE at a reasonable range of transmission rate.
Keywords
1 Introduction
Energy consumption in wireless transmission system has been continuously increasing to cater for the explosive growth in demand for highdatarate wireless applications and a wide variety of diverse quality of service (QoS) requirements during the last decade. Nowadays, the wireless terminals are usually powered by batteries. It is known that highlevel energy consumption has a profound influence on the wireless terminals due to the limit of battery capacity. Therefore, it is very important to reduce energy consumption of the wireless terminals and increase energy efficiency (EE) [1–3]. Recently, a lot of advanced wireless communication techniques, such as relay technique [4, 5] and small cells [6], have been adopted to provide a significant capacity improvement and reduce the energy consumption. In order to further reduce the energy consumption, there is also a lot of research work focusing on the optimal power allocation [7, 8].
A relay communication system, in which the relay forwards the signal transmitted from a source node to a destination node, has attracted a lot of attention, due to its ability in expanding the coverage, increasing the capacity, and reducing the power consumption. Twoway relay communication is a promising spectralefficient transmission protocol for it only needs two time slots to complete a process of signal exchange [9, 10]. In such a communication technique, two source nodes exchange signals with the help of relay(s). As a result, there are two traffic flows in a twoway relay transmission (TWRT) process and they are supported by the same physical channels concurrently, which enhances spectral efficiency (SE) [11].
Most current studies on the twoway relay technique mainly focus on the relay schemes, relay selection, and resource allocation from the perspective of SE [12]. However, there are less research work focusing on EE. In [13], authors studied maximizing aggregated EE utility while provisioning proportional fairness. The power allocation schemes to improve the EE in multiuser multicarrier twoway relay networks have been designed in [14]. The issue of resource allocation problem in orthogonal frequency division multiple access (OFDMA) twoway relay networks has been considered in [15]. Its objective is to minimize the total transmit power to improve EE. However, in these research works, only transmit power has been considered. Actually, in practical wireless transmission system, energy consumption does not only include transmit power but also include circuit power for nonideal transmitter [16]. In [17], it has been demonstrated that the circuit power is consumed by signal processing and the device working in the active mode. The authors in [18] designed an optimal power allocation scheme to maximize EE for twoway amplify and forward (AF) relay networks with consideration of circuit power. Furthermore, the discussions above mainly focus on a fixed transmission mode, in which EE is not always the maximum at a range of transmission rate.
In this paper, to improve EE, we propose an adaptive wireless transmission (AWT) strategy in which the transmission mode is switched between the direct transmission (DT) mode and the TWRT mode. The switch strategy is based on a transmission rate threshold R _{th}, which makes EEs of the DT mode and the TWRT mode equal. However, the traditional metric for EE is not suitable for the subsequent analysis, and the certain threshold R _{th} cannot be found. In this work, we first investigate the transmission rates of the DT mode and the TWRT mode when the scenario of two source nodes exchanging signals is considered. Then, energy consumption ratio (ECR) which is used to evaluate EE of various kinds of transmission modes is introduced with consideration of the circuit power. The ECR is defined as minimum power consumption of unit transmission rate. Finally, we propose a transmission rate threshold determining (TRTD) algorithm with a bisection method to find the threshold R _{th}.

We give a detailed analysis of ECRs with consideration of the circuit power.

We propose the AWT strategy in which the transmission mode is switched between the DT mode and the TWRT mode based on the threshold R _{th}. With this strategy, it can be seen that EE is always the maximum at a range of transmission rate.

We also propose the TRTD algorithm with a bisection method to find the threshold R _{th}.
The remainder of this paper is as follows. Section 2 describes the system model. Section 3 introduces the power consumption and the metric of EE. Comparison and analysis of EE are presented in Section 4. Simulation results are presented in Section 5, followed by the conclusions in Section 6.
Notation: y _{(·)} denotes received signal at relay and source nodes. The transmission rate of source nodes S _{1} and S _{2} are denoted by \(R_{s_{1}}\) and \(R_{s_{2}}\). R _{s} denotes the sum transmission rate. The ECRs of the DT mode and the TWRT mode are denoted by η _{d}and η _{t}. The ECR of the AWT strategy is defined by η _{a}= min{η _{d},η _{t}}. The EEs of the DT mode and the TWRT mode are denoted by e _{d}and e _{t}. The EE of the AWT strategy is defined by e _{a}= max{e _{d},e _{t}}. w _{ i }∼(0,σ ^{2}) denotes a zeromean complexvalued additive white Gaussian noise (AWGN) with variance σ ^{2}. The transmit power of the source nodes and the relay node are denoted by \(\phantom {\dot {i}\!}P_{\mathrm {s}_{j}}(j=1,2)\) and P _{r}. P _{t} denotes the power consumption. P _{c} and P _{sic} denote the circuit power and selfinterference cancelation power. E _{(·)} represents the expectation. f(·) denotes the primitive function, and \(f^{'}{(\cdot)}\phantom {\dot {i}\!}\) denotes the derived function.
2 System model
2.1 DT mode
In the DT mode, the two source nodes S _{1} and S _{2} transmit signals to each other without the assistance of the relay node R. Two time slots are required to complete the process of signal exchange. The DT mode is shown in Fig. 1 a.
where \(w_{s_{1}}\) and \(w_{s_{2}}\) denote the noise at the source nodes S _{1} and S _{2}.
2.2 TWRT mode
In a relay communication system, it can be seen that each transmission time interval (TTI) also composes of two time slot periods. In the TWRT mode, the two source nodes S _{1} and S _{2} transmit signal to each other through the relay node R. The TWRT mode is demonstrated in Fig. 1 b.
G is an amplification factor.
3 Power consumption and metric of energy efficiency
In this section, we formulate the power consumptions and the metric of EEs in the DT mode and the TWRT mode. It is shown in [19] that during the entail transmission process, in addition to the transmit power \(P_{s_{1}}\) and \(P_{s_{2}}\), mobile devices also incur additional circuit power P _{c} which is relatively independent of the transmission rate. Therefore, the power consumptions in the DT mode and the TWRT mode are mainly composed of the transmit power and the circuit power.
3.1 Power consumption in DT mode
It is stated in [20] that P _{c}is incurred by signal processing and the device working in active mode, and it can be modeled as a linear function of the transmission rate. Then, P _{c}is given by P _{c}=P _{s}+α R _{s}, where P _{s} is the static circuit power, α is the dynamic circuit power per unit transmission rate, and \(R_{\mathrm {s}}=R_{s_{1}}+R_{s_{2}}\phantom {\dot {i}\!}\) is the sum transmission rate. In order to simplify the calculation and analysis, α=0 and the constant circuit power consumption model P _{c}=P _{s} [19] is used in this paper.
3.2 Power consumption in TWRT mode
3.3 Metric of energy efficiency
We assume that η e=1. From the relationship of η and e, we can know that the denominator of the ECR can be more simple. It also can be known that the EE in this paper can be determined by the power consumption per unit transmission rate. It means that the transmission mode which consumes less power with the lower ECR will have a higher EE.
In practice, the transmission rates \(R_{s_{1}}\) and \(R_{s_{2}}\) may differ. Moreover, for 0<R _{s}<∞, there exist various rate pairs of \(R_{s_{1}}\) and \(R_{s_{2}}\) that satisfy \(R_{\mathrm {s}}=R_{s_{1}}+R_{s_{2}}\phantom {\dot {i}\!}\), but the ECRs of the DT mode and the TWRT mode with different rate pairs are different. In order to compare the ECRs of the modes and transform them into a unified form which is represented by R _{s}, we define \(R_{s_{1}}=\beta {R_{\mathrm {s}}}\) and \(R_{s_{2}}=(1\beta){R_{\mathrm {s}}}\) to reflect such an asymmetric rate scenario, where β∈(0,1) [22] and β is just a ratio of \(R_{s_{1}}\) in R _{s}.
3.3.1 ECR of DT mode
3.3.2 ECR of TWRT mode
It is easy to see that (32) includes only one variable \(P_{s_{2}}\). The optimal \(P_{s_{2}}\) can be found by setting the derivative of \(f(P_{s_{2}})\) to zero. Substituting the optimal \(P_{s_{2}}\) into \(f_{s_{1}}(P_{s_{2}})\phantom {\dot {i}\!}\) and \(f_{r}(P_{s_{2}})\phantom {\dot {i}\!}\), then, the transmit power \(P_{s_{1}}\), \(P_{s_{2}}\), and P _{r} in the TWRT mode can be calculated as
4 Comparison and analysis of energy efficiency
4.1 Comparison of energy efficiency
In this section, the ECRs of the DT mode and the TWRT mode will be compared to get a comparison between e _{d}and e _{ t }. An AWT strategy will also be designed to achieve the minimize ECR, that is to achieve the maximum EE.
We assume that \(\theta =\frac {1}{g_{s_{1}s_{2}}}\left (\frac {1}{{\sqrt {g_{s_{1}r}}}}+\frac {1}{{\sqrt {g_{s_{2}r}}}}\right)^{2} \), then, when θ≤0, f(R _{s})<0 as \(\frac {P_{\text {sic}}}{R_{\mathrm {s}}}>0\). Otherwise, θ>0, then, there is a uncertainty about which one of η _{d} and η _{t} is the larger. However, it can be seen that when f(R _{s})=0, there is a threshold R _{th} which makes the ECRs of the two kinds of transmission modes equal, that is, makes the EEs of the DT mode and the TWRT mode equal. With the threshold R _{th}, we can design an AWT strategy to decrease the ECR, namely as mentioned above to improve the EE of the wireless transmission system. The threshold R _{th} will be considered in the next section.
4.2 Analysis of energy efficiency
Substituting (46) into (42), the range of the threshold R _{th} which makes the ECRs of the DT mode and the TWRT mode equal can be determined.
Based on the analysis above, it is clear that the threshold R _{th} is just a range of transmission rate. The threshold R _{th} varies with β which is also a variable rather than a certain value. Therefore, the certain threshold R _{th} cannot be found. From the perspective of a certain threshold R _{th}, the TRTD algorithm with the bisection method which is offline will be used to find the threshold R _{th}. This TRTD algorithm is presented in Algorithm 1.
With the TRTD algorithm, the threshold R _{th} will be found. Then, we can design the AWT strategy to achieve an energyefficient adaptive transmission. The ECR of the AWT strategy is defined by η _{a} and η _{a}= min{η _{d},η _{t}}. In the AWT strategy, at first the wireless transmission system is working in the DT mode. When θ≤0, then η _{a}=η _{d}, and the system keeps working in the DT mode. Otherwise, when θ>0, then, we compare R _{s} and R _{th} according to Algorithm 1. If R _{s}≤R _{th}, and η _{a}=η _{d}, the system still keeps working in the DT mode. The system will change its working mode to the TWRT mode unless θ>0, R _{s}>R _{th}, and η _{a}=η _{t}.
From the AWT strategy, we can know that when f(R _{s})≤0, the transmission mode of the wireless transmission system will be the DT mode and the relay node is in a state of sleep. When f(R _{s})>0, the transmission mode of the wireless transmission system will be the TWRT mode and the source node sends a request (REQ) to the relay node. The relay node changes it state into active and meanwhile the relay node sends an acknowledgement (ACK) to the source node. Then, the TWRT mode will be set up. With the AWT strategy, the ECR is the minimum, then the EE of the wireless transmission system is always the maximum at a range of transmission rate.
5 Simulation results
In this section, in order to confirm the validity of the analytical expressions, the simulation results are conducted. The EE of the AWT strategy is denoted by e _{a}, where e _{a}=max{e _{d},e _{t}}. To evaluate and compare the EEs with various transmission modes, without loss of generality, the Rayleigh fading channel and the AWGN model is considered in the Monte Carlo simulation. It is assumed that c=4, and the noise variance is 1.
5.1 EE comparison with ideal and practical power systems
As a baseline for comparison, we first compare the EEs of the DT mode and the TWRT mode with consideration of the ideal and the practical power system. In the ideal power system, P _{s}=0. In the practical power system, P _{s}=1 W and P _{sic}=0.1 W. The other simulation parameters are given as β=0.5 and d=0.5.
5.2 EE comparison with effects of different parameters
In this subsection, the EE comparison with the effects of different parameters will be presented based on the theories mentioned above.
5.3 EEs comparison with various transmission schemes
In this subsection, the EEs comparison with various transmission schemes are provided. The simulation parameters are β=0.9, d=0.5, P _{s}=1 W, and P _{sic}=1 W.
It can be seen from the simulation results that the theoretical analysis is correct. The EE is closely related with the relevant parameters, such as P _{c}, P _{sic}, β, and d. The EE in our AWT strategy is always the maximum at a range of transmission rate. Evidently, it demonstrates the effectiveness of our proposed AWT strategy.
6 Conclusions
In this paper, to improve EE, we have proposed an AWT strategy with consideration of the circuit power in which the transmission mode was switched between the DT mode and the TWRT mode. The switch strategy was based on a transmission rate threshold, which made the EEs of the DT mode and the TWRT mode equal. The TRTD algorithm with a bisection method has been used to find the threshold. The analytical and simulation results have also shown that our AWT strategy was more efficient at a reasonable range of transmission rate. Future work can consider the position of the relay node more specifically and practically. The twoway fullduplex model to improve EE and SE at the same time can also be considered.
Declarations
Acknowledgements
This work was sponsored by the Shanghai RisingStar Program (15QA1400100), Innovation Program of Shanghai Municipal Education Commission (15ZZ03), and DHU Distinguished Young Professor Program (16D210402).
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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