A Contract-Based Model for Multiuser Cooperative Relay in Wireless Communication Networks

Abstract

Cooperative communication utilizes multi-user spatial diversity to improve spectrum efficiency and channel capacity. However, due to the limited wireless network resource, the selfish relay nodes may be unwilling to offer their relay assistance without any extra incentive. In this paper, the incentive issue between multiple wireless nodes’ relay service and multiple sources’ relay selection is investigated. By modelling multi-user cooperative relay as a labour market, a contract model is proposed with the combination of relay power and basic wage. A relay factor is introduced to describe the contract-relay strategy in cooperative communication. To incentivize the relay nodes to participate in multiple sources’ relay efficiently and credibly, an optimization problem of multi-user relay incentive is formulated to obtain the sources’ maximum cooperative utility under the individually rational restraints. By exploiting the hidden convexity of the non-convex problems in both single-source and multi-source scenarios, the efficient iterative algorithms are developed. Numerical results show that the performance of our approach yields a significant enhancement compared with the equal relay-power and equal relay-factor strategies.

Appendix

In this appendix, how the RNs’ power constraint affects the performance of cooperative communication is investigated. First, we focus on the single source scenario. Suppose that the maximum relay power of the ith RN at the source’s receiver as $\bar{P}$, then, the source’s utility maximization problem can be designed as follows

$$\begin{aligned} &\mathop {\hbox{max} }\limits_{{\{ p_{i} ,\alpha_{i} ,\lambda_{i} \} }} \quad \sum\limits_{i \in \varOmega } {N_{i} \lambda_{i} [\rho \log (1 + p_{i} ) - \alpha_{i} - \beta p_{i} ]} , \hfill \\ & s.t.\quad \alpha_{i} + \beta p_{i} - \theta_{i} p_{i} \ge 0,\quad \forall i \in \varOmega ,\qquad \hfill \\ &\, \lambda_{i} = \{ 0,1\} ,\qquad 0 \le p_{i} \le \bar{P}_{i} . \hfill \\ \end{aligned}$$

(20)

Similar to Sect. 3, we can obtain the optimal basic wage $\alpha_{i}^{*} = \theta_{i} p_{i} - \beta p_{i}$. Then, the source’s utility maximization problem in (20) can be simplified as

$$\begin{aligned} &\mathop {\hbox{max} }\limits_{{\{ p_{i} ,\lambda_{i} \} }} \quad \sum\limits_{i \in \varOmega } {N_{i} \lambda_{i} [\rho \log (1 + p_{i} ) - \theta_{i} p_{i} ]} , \hfill \\ & s.t.\quad 0 \le \lambda_{i} \le 1,\qquad 0 \le p_{i} \le \bar{P}_{i} . \hfill \\ \end{aligned}$$

(21)

which can be solved by Algorithm 1 similarly.

Next, simulation result is given to analyze the performance of the optimal contract design method with one source and two RNs (N ₁ = N ₂ = 1). Figure 10 plots the source’s optimal utility with the two typical RNs’ power constraint scenarios. Scenario S1 describes the situation in which the optimal $p_{i}^{*}$ in Problem P2 is smaller than $\bar{P}_{i}$. Scenario S2 describes the situation in which the optimal $p_{i}^{*}$ in Problem P2 is more than $\bar{P}_{i}$ With the power constraint $\bar{P}_{i}$ above the optimal $p_{i}^{*}$, Scenario S1 achieves the higher source’s optimal utility. And as the optimal $p_{i}^{*}$ is more than $\bar{P}_{i}$ in Scenario S2, the source cannot get the enough relay help from the two RNs, thus, Scenario S2 obtains the lower source’s optimal utility. However, even with such power constraints, the source’s utility is also enhanced compared with the non-cooperative communication.

Fig. 10

The source’s optimal utility $U_{S}^{*}$ versus the equivalent profit ρ for fixed β ₁ = 0.1, θ ₁ = 0.1, θ ₂ = 0.3

As for the multiple sources’ relay incentive scenario, the sources’ utility maximization problem can be rewritten by considering the RNs’ power constraint $0 \le p_{i} \le \bar{P}_{i}$. From the IC and the power constraints, we can also get the optimal relay power and relay factor with Algorithm 2. Similar to the above analysis, the sources’ utility can be similarly enhanced with the optimal contract design even with the relay power constraints. Introducing the relay power constraints will not change this result. Due to the page limits, we skip the detailed analysis of the multiple sources scenario.