## 1 Introduction  
Wireless ad hoc networks are widely used in military and civil mobile communication, where fixed communications infrastructures (i.e., base station) are not available. Different from WLAN (Wireless Local Area Network), the ad hoc network is a multi-hop wireless network without a centralized coordinator. Each node works as a router to forward the packets from other nodes. In this special wireless network, TCP (Transmission Control Protocol) flows traverse multiple hops before reaching the destination node or sink node. To provide reliable communications in wireless ad hoc networks, it is critical to design an efficient TCP congestion control mechanism [1].  
However, the performance of the wireless ad hoc network will be degraded if the traditional TCP protocol is utilized. The reason is that TCP congestion control has an implicit assumption that any packet loss is due to the buffer overflow. In fact, as long as the buffer size at each wireless node is reasonably large, most packet losses are due to wireless channel contention, namely, MAC (Media Access Control) layer competition [2; 3; 4].  
Therefore, several cross-layer schemes are proposed to alleviate congestion in the wireless channel [5; 6; 7; 8]. For example, a cross-layer ECN (Explicit Congestion Notification) scheme was proposed to perceive the link congestion according to the retransmission counter at the MAC layer. In this scheme, the retransmission counter at the MAC layer is used as the congestion metric to trigger the ECN mechanism. ECN is the explicit congestion notification mechanism of the IP layer. When network congestion occurs, the sender can adjust the congestion window and reduce the sending rate by the ECN mark from the receiver. Differently from [9], [PERSON] et al. utilized the frame service delay at the MAC layer as the congestion metric to mark or drop packets [10; 11; 12]. WCCP (Wireless Congestion Control Protocol) was proposed to dynamically adjust the congestion window of TCP according to the channel business ratio, which presents the extent of channel congestion in a more accurate way [13]. These cross-layer methods improve the efficiency and fairness of wireless ad hoc networks [14; 15]. However, the retransmission counter and the frame service delay are not precise enough to detect congestion from the MAC layer, while WCCP is too complex to implement in existing transport protocols.  
Therefore, this paper proposes an MAC congestion metric called frame transmission efficiency, describing channel congestion in a more precise manner. Furthermore, combining this congestion metric with ECN, we propose a cross-layer ECN mechanism, RECN (ECN and the ratio of successful transmission delay to the frame service delay in the MAC layer, namely, the frame transmission efficiency), which is based on frame transmission efficiency and adjusts the transport sending rate through a standard ECN signaling method, without any modification to transport protocols.  
The remainder of this paper is structured as follows. Section 2 describes several congestion metrics at the MAC layer and proposes a congestion notification scheme RECN. Section 3 gives the definition and analysis of the frame transmission efficiency to demonstrate the relationship between the frame transmission efficiency and the link layer congestion. Section 4 gives the protocol design of RECN. In Section 5, the simulation results show that our proposed congestion notification mechanism significantly outperforms traditional TCP in wireless multi-hop ad hoc networks. Section 6 is our conclusion.