## 3 System Model  
Consider a VANET where vehicles move along a one-way multi-lane road segment. Vehicles are distributed randomly along the road and move with the same average speed [30]. All vehicles have the same transmission range \(R_{T}\). If the distance between two nodes is less than \(R_{T}\), they can communicate with each other directly and are called each other's one-hop neighbor or neighbors. If two nodes (we use \"vehicle\" and \"node\" interchangeably throughout this paper) cannot communicate directly but have a same neighbor, they can communicate through the two-hop communication and are called each other's two-hop neighbor. Each node transmits the message with the same power \(P_{t}\). Let \(P_{r}\) denote the instantaneous received power at a receiving node. If \(P_{r}\) is equal to or greater than a threshold value, denoted as \(P_{th}\), the packet can be successfully decoded at the receiver; otherwise, the packet cannot be decoded at the receiver.  
Each vehicle is equipped with a Global Positioning System (GPS) receiver, and time is synchronized with the aid of GPS. If the GPS signal is lost, other distributed schemes can be used to synchronize vehicles [20]. In the system, channel time is partitioned into frames consisting of \(F\) equal time slots, as shown Figure 1. Each node maintains two sets of neighboring nodes: one-hop set (OHS) and two-hop set (THS) according to the frame information (FI) exchanged among its one-hop neighbors. The OHS or the THS is a group of vehicles that can communicate with each other with maximum one-hop or two-hop communication, respectively. To avoid hidden/exposed node problems, nodes in the same TTS are not allowed to reserve the same slot. Hence, before reserving a slot, a node must listen to the channel for at least \(F\) consecutive slots (not necessarily in the same frame). As shown in Figure 2, each node transmits its one-hop neighbors' IDs, and their reserved slots in the FI are contained in the header of a packet. Thus, by listening to the channel, a node can get its THS neighbors' IDs and their reserved slots and then choose one unreserved slot to access. A node releases its time slot if it fails to detect its ID in FIs from at least one of its one-hop nodes [7].  
Several helpers are selected to rebroadcast the packet to the failed nodes with the source node cooperatively. Thus, they form a multiple-input multiple-output (MIMO) system. Here, we do not consider coding gain and only focus on power gain of the cooperative MIMO. Then, the MIMO transmission can be seen as several multiple-input single-output (MISO) transmissions. Assuming a binary phase-shift keying (BPSK) modulation scheme, the average bit error rate (BER) in a Rayleigh fading channel for a maximal-ratio-combing (MRC) receiver with m-branch diversity is given by [31]:  
\[\overline{p_{b}}(\overline{r},m)=\frac{1}{\pi}\int_{0}^{\overline{n}}\!\! \left(1+\frac{\overline{r}}{\sin\varphi^{2}}\right)^{-m}\!\!d\varphi \tag{1}\]  
where \(\overline{r}\) is the average signal noise ratio (SNR) per link. Then, success probability \(p_{s}(m)\) of a \(\mu\) bit length packet can be calculated by:  
\[p_{s}(m)=[1-\overline{p_{b}}(\overline{r},m)]^{\mu} \tag{2}\]  
and the packet error rate \(p_{e}(m)\) is:  
\[p_{e}(m)=1-p_{s}(m) \tag{3}\]