# A Joint Strategy for Fair and Efficient Energy Usage in WLANs in the Presence of Capture Effect
## 1 Introduction
If AP receives packets from both nodes simultaneously, it evaluates the receiving signal strengths of both receiving packets and accepts one of the packet whose signal strength is higher than the other by a certain ratio. This ratio is called capture threshold. Obviously packet from the other node is discarded. Capture effect reduces the number of collisions and increases the number of successful transmissions. In this paper, at first we present an analytical model that takes into account the capture effect, unlike previously proposed analytical models for calculating the energy efficiency of WLAN that ignore taking into account the capture probability [4; 7]. We validate the presented analytical model via simulations in various network settings such as different values of capture threshold, erroneous channel and unsaturated traffic load. Secondly, we show that although capture effect improves overall energy efficiency of WLAN by about 20% but it causes unfairness; a group of nodes located far away from AP is less energy efficient than the group of nodes located closer to the AP. Finally, to reduce the stated unfairness problem we propose a joint strategy based on adaptive transmission power control (ATXPR) and contention window adjustment (CWAD). ATXPR additively or multiplicatively increases or decreases transmission power of a node whose transmission is unsuccessful due to capture failure. Capture failure is considered when transmitter does not receive an ACK but instead overhears it. In other words, two or more transmitters send data frames simultaneously but only one of them has successfully captured the channel and therefore only that transmitter receives ACK frame whereas the remaining nodes only overhear the ACK frame. When a node's transmission is unsuccessful because of a capture failure, it (i) increases the transmission power level to the next available transmission power among a set of predefined transmission power  
Figure 1: A simple scenario of two nodes communicating with an AP (Access Point) in the presence of physical layer (PHY) capture effect. levels according to additive increase (AI) or multiplicative increase (MI) and (ii) stays in the same backoff stage without increasing its CW according to CWADJ. This increase in power helps the node avoid another capture failure in the next round of transmission. A node after successful transmission decreases its transmission power additively (additive decrease) or multiplicatively (multiplicative decrease) and resets its CW. Our proposed mechanism on one hand increases the probability of successful transmission and on the other hand lets the node conserve energy by not spending more time in contention. Simulation results show that our proposed algorithm is 99% fair. This paper is organized as follows: Section 2 presents the literature review. Section 3 explains the analytic model to calculate energy efficiency of WLAN in the presence of capture effect, unsaturated traffic conditions and erroneous channel. Section 4 discusses the results obtained from analytical models and simulation. Section 5 highlights the unfairness caused by the capture effect in terms of energy efficiency and proposes several strategies to overcome the unfairness problem. The proposed strategies are evaluated via simulations and results are compared. Section 6 finally concludes the paper.