First, we must agree on how the system operates and what it takes to have a signal from one communication node received correctly at another node. In other words, we need to settle on a suitable system model: a set of assumptions that will allow us to talk about communication protocols and principles in a setting that is simple, but sufficient to contain the necessary properties of a shared wireless medium. We build the initial model by relying on a common sense analogy with the spoken conversation, as it captures three fundamental properties of wireless communication: broadcast, interference, and half-duplex operation. We illustrate these features by observing a conversation between Zoya, Yoshi, and Xia:
Half–duplex: A given person, e.g. Zoya, cannot speak and listen at the same time.
Broadcast: If Zoya has information to convey to Yoshi and Xia, then, provided that both Yoshi and Xia are listening, Zoya needs to say her message only once, and not repeat it individually to Yoshi and to Xia.
Interference: If Yoshi and Xia speak simultaneously, Zoya will not understand either of them.
The descriptions above are arguably not always correct, but they do represent what is common sense for a conversation. Furthermore, the analogy of the communication problems with the conversation between Zoya, Yoshi, and Xia is useful, but it has its limitations, which will be pointed out when necessary.
1.1.2 Communication Channel with Collisions
For the purpose of this chapter, we define a communication channel to be the physical resource that is used for a wireless transmission. In that sense, in spoken communication, the channel is created by the audible vibrations that take place in air or even another sound-propagating medium. It is useful to note that the communication channel is not the whole physical medium with all the vibrations, since there are vibrations that cannot be registered by ear and thus do not carry useful audio information. Furthermore, spoken communication uses a single communication channel: one cannot switch to another channel, such as in a TV receiver, in order to listen to the desired speaker and avoid the undesired one.
As already stated above, our discussion will be limited to the case in which all nodes use a single communication channel. In reality that can be, for example, a certain frequency to which all the nodes are “tuned”. Here we use the term “frequency” as it is used in a common language for, say, a TV frequency. One may argue that Zoya and Yoshi can agree to one frequency, while Xia and Walt can agree to tune to another frequency and in this way they do not need to share the channel with the link Zoya–Yoshi. This is indeed possible and we will discuss it in later chapters, when we introduce the notion of separation in frequency. On the other hand, it is also true that Zoya and Yoshi should first use some communication channel to agree upon which frequency they will use for communication. This agreement is, again, metadata or control information, such that the corresponding channel is often denoted as a control channel and can be shared by multiple nodes to come to an agreement about the frequency. For example, if Zoya decides to communicate with Xia, then she knows that she should try to find Xia at the control channel and, upon contacting her, use the control channel to decide which channel/frequency they should both be tuned to in order to communicate the useful data. However, the control channel is a common, shared communication channel and therefore the question of how to share that channel to send metadata remains valid.
The communication model used in this chapter is called a collision model. This is because the central assumption of the model is that if two or more nodes transmit simultaneously, then the interference that they cause to each other is manifested as a collision at the receiver. Upon collision, the receiver does not manage to retrieve any data successfully. Another assumption in the model, not really related to the issue of collision, is that a node operates in a half-duplex manner and cannot receive while transmitting. Most of the wireless systems that we encounter today are not full-duplex, that is, do not transmit and receive simultaneously at the same frequency channel. However, although technologically more complex, it is also possible to have full-duplex operation. Therefore, throughout the chapter we will occasionally revise the half-duplex assumption and discuss the changes that the full-duplex can bring into the design of a specific protocol or algorithm.
The communication between the wireless nodes is based on data packets. A transmitting node is capable of sending
1 Yoshi is in the communication range of Zoya such that the distance between them is less than m;
2 No other communication node that is within m of Yoshi transmits while Yoshi is receiving the packet from Zoya.
The first condition above indicates that each transmission is omnidirectional. Due to the basic property of reciprocity in electromagnetic/radio propagation (see Section 10.9), each reception in our model is also omnidirectional. From this it follows that Yoshi receives a signal as long it is sent from a distance less than
