## 2 Related Work
### Preamble Sampling-Based MAC Protocols  
The idea of MAC protocols based on preamble sampling is that every node toggles periodically the radio from sleep to active mode, with the aim of sampling the channel to detect incoming packets. The interval between two consecutive samplings of the channel is the sampling interval, also called _check interval_, and its length is \(\tau_{check}\). If during the sampling there are no packets to be received, the node toggles the radio to sleep. Otherwise, the node keeps the radio on for the time necessary to receive the incoming packets, and then it turns the radio off. The goal of this strategy is to reduce the energy consumed by idle listening. This concept, with small differences, was proposed independently by two authors ([PERSON] _et al_. [15] and [PERSON] [5]), and given two different names: _Low Power Listening_ (LPL) and _preamble sampling_. Both names are currently used in the literature to refer to the same concept. Hereafter we use them interchangeably.  
To ensure that a packet is correctly received by its recipient, the LPL sender transmits a very long preamble immediately before the actual packet. This preamble spans the whole check interval to ensure that, when the receiver starts its check interval, it detects the preamble and remains in active mode for the time necessary to receive the packet. Figure 1 illustrates the strategy used in this technique. The protocol presents some disadvantages, such as an excessive amount of energy consumption as compared to approaches based on check intervals as well as a high overhead as a consequence of the transmission and reception of very long preambles. The overhearing is also very high, since the packet has to be completely received to determine its destination. Another limitation of these approaches is that they cannot be applied to all types of networks, specifically, those networks where the preamble is fixed and limited to a few bytes, such as IEEE 802.15.4-compliant networks [16; 17] (note that, however, to address the latest point, there exist other approaches based on sending short preambles such as X-MAC [18]). For these reasons, many variants and modifications of the original protocol have been proposed. In particular, we highlight WiseMAC [6], an energy efficient MAC protocol based on synchronized preamble sampling. WiseMAC considers infrastructure networks and assumes multiple access points that are usually energy unconstrained. WiseMAC focuses on the downlink problem: the communication from the access point to the nodes. The basic idea behind WiseMAC is to reduce the length of the preamble based on the knowledge of the receiver's sampling schedule, which is piggybacked into the acknowledgment packets. Thus, the sender starts to transmit the preamble just a short time before the wake-up time of the receiver. Another approach is VLPM [19] that considers both the downlink and uplink problem for Wireless Body Area Networks (WBAN). In VLPM, the nodes are equipped with both a low-power transmitter (employed for sending wake-up packets before sending data) and a receiver (employed for continuous monitoring of the activity on channels).