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An incremental selection hybrid decode-amplify forward (ISHDAF) scheme for the two-hop single relay systems and a relay selection strategy based on the hybrid decode-amplify-and-forward (HDAF) scheme for the multirelay systems are proposed along with an optimized power allocation for the Internet of Thing (IoT). Given total power as the constraint and outage probability as an objective function, the proposed scheme possesses good power efficiency better than the equal power allocation. By the ISHDAF scheme and HDAF relay selection strategy, an optimized power allocation for both the source and relay nodes is obtained, as well as an effective reduction of outage probability. In addition, the optimal relay location for maximizing the gain of the proposed algorithm is also investigated and designed. Simulation results show that, in both single relay and multirelay selection systems, some outage probability gains by the proposed scheme can be obtained. In the comparison of the optimized power allocation scheme with the equal power allocation one, nearly 0.1695 gains are obtained in the ISHDAF single relay network at a total power of 2 dB, and about 0.083 gains are obtained in the HDAF relay selection system with 2 relays at a total power of 2 dB.

Recently, multiple-input multiple-output (MIMO), as a milestone in the development of wireless communications, brought an efficient transmission rate and reliability. To put it into practice, a cooperative communication scheme was then proposed in time [

Meanwhile, power allocation in cooperation communications had always been one of the research hot-spots. In wireless uplink transmissions, successive interference cancellation (SIC) was combined with the power allocation method to obtain the optimal power allocation ratio for efficient resource allocation [

In this paper, by analyzing a two-hop single relay cooperative network with an ISHDAF scheme and the multirelay selection strategy with a HDAF scheme, an optimized power allocation is proposed. The main contributions are summarized as follows:

The power allocation is optimized in both the ISHDAF single relay and the HDAF multirelay systems. In the case of link status change, the preferred links are allocated with much more power for transmission according to the well-known water filling principle in information theory, which reduces the entire power consumption under the same system performance. The proposed scheme also provides a new hybrid automatic repeat request (ARQ) retransmission and relay forward mechanism, where the source node can retransmit messages to the destination node when the first direct transmission failed. It differs from the source node sending new messages to the destination node directly in the incremental relaying protocol. So it can be more suited for all kinds of the multiple relay channel status and obviously improves the systematic outage probability without any complexity increase.

The approximate closed-form expression of the systematic outage probability with relation to the node power and channel coefficients is derived by the equivalent infinitesimal replacement of the probability distribution function at high SNR. And it can be taken as the objective function of the optimization. Then, the minimization is achieved under fixed total power by Lagrange multiplier method, and the objective function is related to the power of the source node and the relay nodes. The power allocation coefficients between the source and the relay nodes are then obtained to achieve optimized power allocation. Moreover, the power allocation changes the location selection of the relay nodes, which can be calculated indirectly from the above closed-form expression. It can adaptively satisfy the link conditions to optimize the entire system performance.

By introducing the path loss factor, the powers of the source and the relay nodes are modeled as the objective function related to the distance among all nodes. According to both the property of the objective function and the related numerical analyses, the relationships of the varied power to the distance of the nodes are obtained. Then, the optimized node positions are obtained to improve the power efficiency with minimized systematic outage probability. Also the power allocation of all relay nodes with respect to their relative location to the source and destination nodes can be clearly and quantitatively analyzed by this model. Therefore, the link status associated with the proposed relay position obviously affects the selection of the cooperative schemes, which can be adopted in practice.

This paper is organized as follows. In Section

For a classic three-node relay model shown in Figure

System model of a single relay communication.

In an ISHDAF cooperative network, the whole transmission is divided into two time slots. In the first slot, node S sends a signal to node R and node D, while in the second slot, either node S or node R sends the signal to node D, which depends on the link status. Suppose that the transmitted power of the source node S is

For the first situation, if the destination node successfully receives the signal sent by the source in the first slot, the transmission from node S to node D is not interrupted. In this case, the mutual information is defined in [

For another situation, if the direct transmission fails in the first slot, or the destination does not receive the correct information from the source, the source would retransmit the message to the destination in the second slot. In this case, the mutual information is deduced and presented in [

To ensure the success retransmission, (

The relay node starts the cooperative transmission when there is

If the DF scheme is adopted for the cooperative transmission, the mutual information is obtained by the maximum ratio combining (MRC) for the destination as

If the relay node transmits in the AF protocol, the mutual information is expressed in [

In summary, the mutual information in the ISHDAF cooperative network is concluded as follows. When

There is a typical two-hop multirelay cooperative network shown in Figure

System model of the multiple relay communication.

Based on the system model, there is a relay selection strategy as the HDAF scheme, which chooses the AF or DF scheme to forward signals adaptively according to the channel status. If the channel status of link S-R_{i} is good enough for the relay to decode the source information, the DF protocol is selected to forward signals in the relay. Otherwise, the AF protocol is just used to prevent from the error propagation. According to the above strategy, the

At first, there are some symbol definitions about the transmission power of the source and relay, respectively, that is, _{i}, and R_{i}-D, respectively. They are subjected to the exponential distribution with parameters of _{i}. For this case, the mutual information in the transmission is deduced as

Equation (

Therefore, the candidate relays are divided into two sets according to whether successful decoding occurs or not in the relays, where the relays in set

Since the optimal relay means to the maximized SNR in the destination, there are two steps to obtain it. Firstly, the best relays of

For the cooperation system with the AF scheme, the destination combines the signals from the source and the relay together by the maximum ratio combination (MRC) mechanism, and the instantaneous SNR at the destination is expressed as

For the cooperation system with the DF protocol, the signals from the source and the relay are combined by the MRC scheme, and the instantaneous SNR at the destination is obtained as

Finally, the optimal relay

Meanwhile, the mutual information of the cooperative transmission of the HDAF scheme by the proposed relay selection strategy is _{b}.

The power allocation is optimized to obtain high power efficiency, where the entire power is taken as the constraint condition and the outage probability as the objective function. Then, the outage probability of the whole cooperation system is deduced analytically. And the Lagrange multiplier method is used to solve the optimal power allocation equation.

Outage probability is defined as the probability of failure in a transmission, which is one of the most used measures to evaluate the entire wireless communications. The transmission interruption occurs when the link capacity can not attain the required user rate

By replacing (

The

In addition, the probability distribution function

Based on the above discussion, at high SNRs, the outage probability of the ISHDAF scheme can be calculated as follows:

According to (

With (

Therefore, the outage probability of a single relay ISHDAF cooperative network is expressed as

Similarly, the outage probability in the HDAF relay selection strategy is denoted as

It is obvious that

Using the Lagrange multiplier method, the optimized power allocation among the source and relay nodes to minimize the outage probability is produced as follows. For the ISHDAF scheme, with entire power as the constraint, as long as the fixed power

Let

Take partial derivation of (

By combining (

According to the root of (

From (

Similarly, the power allocation optimization for the HDAF scheme can be defined as

Finally, the optimized powers

The power allocation depends on the channel coefficients, which are related to the distance between the relay and the source or the destination. To obtain the maximum outage probability gain by the proposed power allocation, an optimal relay location is deduced as follows.

To simplify the analysis of power allocation, we just constrain the situations where the distance between the link S-D and the link S-R-D is approximately equal, especially when the distance is quite large. Otherwise, under the same channel noise variance

Taking the derivation of variable

Equation (

Substituting (

From (

Given the diversity gain in the proposed ISHDAF scheme, it should be divided into three cases as follows.

First, when

Second, the direct transmission is failed, but the retransmission is successful in the second time slot, when there is

Third, the relay node starts to forward signals in the AF protocol or the DF protocol. In these two cases, the destination node receives signals from two links. So the system achieves two diversity gains in the cooperative transmission by the relay nodes. In addition, for the multirelay selection strategy under the HDAF scheme, it employs DF or AF mode to forward signals adaptively according to the channel status. Because both forward modes are required for R-D transmission, the full diversity gain of 2 is then obtained.

In summary, the proposed ISHDAF scheme obtains much more outage probability performance gain by the direct link retransmission rather than the relay forwarding, when compared with the IHDAF one in [

To validate the proposed power allocation optimization algorithm for the ISHDAF and the HDAF relay selection strategy, two typical kinds of cooperative network are simulated and analyzed. For a single relay network, the outage performances by the proposed HDAF and ISHDAF strategy are compared. Besides, the optimized power allocation (OPA) and the equal power allocation (EPA) algorithms are employed in the two strategies, respectively, for comparison. In addition, for a HDAF multirelay selection network, the outage performances of the whole system with different relay numbers are simulated and compared. And the simulations for the validation of the optimal relay location are also performed in both the HDAF and the ISHDAF single relay network.

The simulation parameters are set as follows. The transmission rate is set as

Figure

Outage probabilities between the OPA and the EPA in different forwarding strategies.

The outage performances of different schemes with the distance parameters of

Outage probabilities between the OPA and the EPA under the specific relay location.

There is also a comparison of outage performance between the OPA and the EPA scheme, in the HDAF multirelay selection network. They are simulated with different number of relays, under the distance parameters of

Outage probabilities among different number of the relays in the HDAF scheme.

To verify the theoretical analysis of the optimal relay location for the proposed algorithm, some simulations are performed in the cooperative single relay network. For the different relay locations, the outage probabilities of the ISHDAF and the HDAF strategies are illustrated in Figure

Outage probabilities among different relay locations in the OPA scheme.

In this paper, an optimized power allocation algorithm is proposed, which mainly employs the two-hop single relay network with ISHDAF scheme and the multirelay selection strategy with HDAF scheme. The optimization of the proposed algorithm is just to minimize the outage probability of system under the constraints of total power of the source and relay nodes. In addition, the proposed scheme can only occupy a small amount of time complexity to obtain the power allocation optimization in a cooperative communication system. In the simulations, the proposed algorithm is applied in the ISHDAF and the HDAF scheme with the well-known three-node models, respectively. Simulation results show that the proposed algorithm can achieve much larger gain by the ISHDAF scheme than that by other ones. Also, for different number of the relay nodes in a cooperative network, the simulation comparisons show that the proposed algorithm by the HDAF relay selection strategy has a significant validity in power allocation. Simultaneously, the optimal relay location by the suggested algorithm is also established for an even better gain over current schemes. Therefore, the proposed optimized power allocation and relay location selection algorithm can be effectively adopted in cooperative IoT relay systems in practice for high power efficiency and good outage probability performance.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (no. LZ14F010003, no. LY17F010019), the National Natural Science Foundation of China (no. 61471152), the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (no. 2014D02), and the Zhejiang Provincial Science and Technology Plan Project (no. 2015C31103, no. LGG18F010011).