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Energy-efficient resource allocation is investigated for a relay-based multiuser cooperation orthogonal frequency division multiple access (OFDMA) uplink system with amplify-and-forward (AF) protocol for all relays. The objective is to maximize the total energy efficiency (EE) of the uplink system with consideration of some practical limitations, such as the individual power constraint for the users and relays and the quality of service (QoS) for every user. We formulate an energy-efficient resource allocation problem that seeks joint optimization of subcarrier pairing, relay selection, subcarrier assignment, and power allocation. Unlike previous optimization throughput models, we transform the considered EE problem in fractional form into an equivalent optimal problem in subtractive form, which is solved by using dual decomposition and subgradient methods. To reduce computation costs, we propose two low-complexity suboptimal schemes. Numerical studies are conducted to evaluate the EE of the proposed algorithms.

Transmit diversity generally requires more than one antenna at the transmitter and receiver. However, many wireless devices are limited to single antenna because of size or hardware complexity. Cooperation communication is a promising solution to address this problem in various wireless systems, such as ad hoc and cellular networks [

Relaying protocols have three main types, namely, amplify-and-forward (AF), decode-and-forward (DF), and compress-and-forward (CF). In AF, the signal received by relay is amplified and retransmitted to the destination. The noise is also amplified at the relay. This protocol is simple and of low cost. In DF, the relay attempts to decode the received signal. If successful, DF reencodes the information and retransmits the signal. CF attempts to generate an estimate for the received signal. Hoping the estimated value provides some assistance in decoding the original codeword at the destination. Given the limited available space, we only study the energy-efficient resource allocation with AF protocol. The other relaying protocols will be studied in future works.

Compared with previous studies on single-carrier relay networks or multicarrier noncooperation networks, more technical challenges exist in the study of multicarrier cooperation networks. We not only consider the relaying protocols (AF, DF, and CF) but also solve the problems about relay selection and power allocation between users and relays in relaying networks. Several results have been reported recently about relaying networks [

We have discussed only the throughput maximum problem in resource allocation for relay-assisted cooperative OFDMA systems. However, explosively growing data traffic and the requirement for ubiquitous access have triggered the escalation of energy, which results in increased greenhouse gas emission [

For relaying networks, limited study about EE exists. The authors in [

Considerable research exists about the optimal resource allocation mechanisms in relaying networks, including power allocation, subcarrier pairing, and relay selection; see, for example, [

The remainder of this paper is organized as follows. Section

We consider a multirelay-assisted cooperation OFDMA system, as shown in Figure

System model.

The noise variances of the source-to-relay (SR) links, relay-to-destination (RD) links, and source-to-destination (SD) links are denoted by

In this relaying system, the base station controls all users and relays. The resource allocation information, including subcarrier pairing, relay selection, subcarrier assignment, and power allocation, is sent to users and relays by the base station via downlink control channel.

The achievable rate for the

The above approximation is jointly concave in

Our objective is to maximize the uplink system total EE subject to a set of constraints. The relay selection and subcarrier assignment constraints are as follows:

The individual power constraint of the users and relays can be expressed as follows:

Aside from transmit power, the energy consumption also includes circuit energy consumption [

The optimization EE problem can be formulated as

The integer assignment variables

For the fraction objective function in (

Consider

Based on the above theorems, we can use binary search method to find

Obtaining the joint optimal

The Lagrange dual function of problem (

In (

The literature in [

Computing the dual function

For the fixed

A detailed derivation is given in Appendix

According to the Lagrange dual decomposition method, the optimal power allocation can be determined by solving the following problem:

Appendix

A detailed derivation is given in Appendix

Substituting the optimal power allocation expressions (

Therefore, the function

In the operation, the optimal power allocation can first be computed by using (

After finding the optimal

We can then find the optimal subcarrier pairing

We need to select one element in each row and each column in matrix (

We have obtained the optimal variables

(1)

(2) (i)

(ii)

(a) Obtain the optimal power via (

(b) Obtain (

(c) Obtain (

(d) Update the dual variables

(e) Repeat (a) → (d) until convergence;

(3) If

(4)

We analyze the complexity of the proposed optimal scheme. For every subcarrier pair, the number of computations needed to perform relay selection is

Similar to the literature in [

To reduce the complexity of the subcarrier pairing, we let the subcarrier pairing be prefixed, rather than seeking the optimal subcarrier pairing. Similar to the previous suboptimal scheme [

Thus, the source and relay use the same subcarrier to transmit and forward a signal in different phases, respectively. We do not need to make the subcarrier pair.

In the two suboptimal schemes, we only reduce the complexity for subcarrier pairing. The dual variables still need to be updated to compute

In this section, simulation results are presented to demonstrate the performance of the three proposed schemes. In the simulation, we consider quasistatic frequency-selective Rayleigh fading channels with a six-tap equal-gain, equal-space delay profile. The delay interval between adjacent taps is equal to the inverse of the OFDM system bandwidth. We consider

EE of the energy-efficient design that optimizes EE and the spectral-efficient design that maximizes the weight sum rate with the same constraints is evaluated in Figures

Energy efficiency versus channel variance of

Energy efficiency versus channel variance of

For comparison with EE performance under different number of relays, we also plot EE with 12 relays with equal weight factor for all the users in Figure

Energy efficiency versus channel variance of

Figures

Throughput versus channel variance of

Throughput versus channel variance of

Throughput versus channel variance of

Figure

Energy efficiency versus different numbers of relays with

Energy efficiency versus different numbers of relays and circuit energy consumption with

In this paper, we formulate an energy-efficient resource allocation problem for a cooperative multirelay OFDMA uplink system with AF protocol. This paper determines the joint optimization of subcarrier pairing, relay assignment, subcarrier assignment, and power allocation with the objective of maximizing EE. Individual power constraint for every user and relay is applied. To solve the complex fraction problem, we transform the considered EE problem in fractional form into an equivalent optimal problem in subtractive form. However, the mixed integer programming problem is NP-hard. We utilize the dual method to solve the problem efficiently. To reduce the complexity of the problem, we propose two low-complexity schemes for subcarrier pairing. The simulation results show greater EE improvement of the energy-efficient design than that of the spectral-efficient design, and the performance of the proposed suboptimal algorithm OSP-based is close to that of the optimal algorithm. EE differs under different relay numbers and is also affected by circuit energy consumption. In future work, we will study the fundamental tradeoff between EE and SE in cooperative communication.

We define the function as

For any

We assume that

Considering the integer variables

We define problem 1 as follows:

If we have known

According to (

If we know

Using (

We present the detailed derivation about (

We can obtain the partial derivative of

For simplicity, variables

When

The authors declare that there is no conflict of interests regarding the publication of this paper.

This study is funded by the National Natural Science Foundation of China (Grant no. 61271421).