Throughput in A Cooperative Network and Channel State Information

Abstract

Cooperative communications greatly enhance the point-to-point link capability to against channel fading, and such performance gain is expected to large wireless ad hoc networks. However, current cooperative networking is based on ideal assumptions of completely known network information and centralized optimization, which is practically infeasible to large ad hoc networks requiring unscalable control signaling overhead. In this paper, the exact throughput of practical cooperative ad hoc network is provided, in which users make autonomous decisions with regard to their network usage based on the current network conditions and their individual preferences. Since preference of each node is shown by the achievable data rate estimated from the channel state information (CSI) of links of each source-destination pair, the cost of acquiring CSI is considered in the throughput analysis. Furthermore, the cooperation beneficial condition and the operation algorithm of each node to guarantee the network operating at the highest throughput are proposed. The proposed algorithm provides a way to control network-level performance by local operations among nodes.

Appendix

1.1 Proof of Lemma 1

The proof is similarly presented in [21, 46]. The term $(1+P_{hr}\phi )p\lambda$ denotes the transmitting node density of the network.

1.2 Proof of Lemma 2

We rewrite

$$\begin{aligned} P_{SP}^{CC}&( R )\nonumber \\ =&{\mathbb {P}}\left( \frac{P_t\min \{h_{S,r} d_{S,r}^{-\alpha }, h_{S,D} d^{-\alpha }+h_{r,D} d_{r,D}^{-\alpha }\}}{I_S+I_r+\sigma ^2}\ge R \right) \nonumber \\ =&\left( 1-P_S \right) {\mathbb {P}}\left( \frac{P_th_{S,r} d_{S,r}^{-\alpha }}{I_S+I_r+\sigma ^2}\ge R \right) \nonumber \\&+P_S{\mathbb {P}}\left( \frac{P_th_{S,D} d^{-\alpha }+P_th_{r,D} d_{r,D}^{-\alpha }}{I_S+I_r+\sigma ^2}\ge R \right) \end{aligned}$$

(33)

The rest of proof is similar to [21, 46].

1.3 Proof of Theorem 3

From other player’s decisions only changed the interference level, that is, $\phi$ in (16), (17) and (18). No matter what other players’ decisions are, (19) and (20) are the dominant strategies for players with $P_th_{S,r}d_{S,r}^{-\alpha }>P_th_{S,D}d^{-\alpha } +P_th_{r,D}d_{r,D}^{-\alpha }$ and $P_th_{S,r}d_{S,r}^{-\alpha }<P_th_{S,D}d^{-\alpha } +P_th_{r,D}d_{r,D}^{-\alpha }$, respectively.

1.4 Proof of Theorem 3

According to Lemma 3, when $p\le p_{max}$, all players would choose strategy DT if $\lambda <\lambda _{th}(p)$, and choose strategy CC if $\lambda \ge \lambda _{th}(p)$. $\lambda _{th}(p)$ depends on $p$. When $p> p_{max}$, each player whose type satisfies $P_th_{S,r}d_{S,r}^{-\alpha }>P_th_{S,D}d^{-\alpha } +P_th_{r,D}d_{r,D}^{-\alpha }$ would choose strategy CC and each player whose type satisfies $P_th_{S,r}d_{S,r}^{-\alpha }<P_th_{S,D}d^{-\alpha } +P_th_{r,D}d_{r,D}^{-\alpha }$ would choose strategy DT.