Wireless Connectivity. Petar Popovski

rel="nofollow" href="#fb3_img_img_e8fc3dae-a493-5a56-8ab0-fb6b614ce769.png" alt="images"/>. Let us use the term minislot to denote the time unit corresponding to an idle slot. After arrives and Zoya has it available for transmission, she waits until the start of the next minislot and then starts to listen during that minislot. If the minislot is idle, Zoya starts transmission after the minislot ends. The packet arrives at Xia during a minislot in which Xia is not in a transmission state. Since Zoya transmits during that minislot, Xia detects a carrier and concludes that the medium is busy from a transmission carried out by somebody else. After the transmission of is finished, Xia waits for one idle minislot to verify that the transmission of Zoya has finished. In other words, Xia cannot learn that the transmission of Zoya will finish during the minislot in which it actually finishes and she has to verify the end of Zoya's transmission by detecting the subsequent idle minislot. After that idle minislot, Xia transmits .

Note that the introduction of a minislot has drastically reduced the number of collisions. This is because the minislot is cheap in terms of time duration, offers a better time resolution, and the system operation can benefit from the asynchronism among the arrivals of the packets across the different devices. However, the minimal resolution is brought to the level of a minislot, such that if two packets arrive at the same minislot, then collision cannot be avoided. This is illustrated by the packets and . Upon collision, Zoya picks a random number of minislots (not slots!) to wait until the next transmission and Xia does the same. In this way, they create the required asynchronism and likely avoid another collision between the packets of Zoya and Xia.

      While the idea of minislots and CSMA is introduced here in the context of spectrum sharing, the same mechanism can also be used to design a random access protocol. We can reuse Figure 1.1(b) and think of a system in which Zoya, Yoshi, and Xia use random access to transmit to Basil. Recall that, when we were using the same setting to describe random access, the devices received signals only from the base station Basil and it was not relevant to consider the fact that a device can detect the transmission of another device. By contrast, the new requirement in CSMA is that a device should listen to find out whether the medium has been taken by a transmission from another device.

      Figure 2.4(b) presents a rather basic version of CSMA. For example, there can be a variant in which, upon detecting that the medium is not busy, a node waits for a random number of time slots before starting the transmission. The rationale is that, while the medium is busy, there could have been multiple packet arrivals at different transmitters, and if all of them wait only for a single idle slot then a collision occurs. A similar argument is valid for the following feature that is used in practical systems, such as Wi-Fi. Assume that Zoya experienced a collision and decided to wait for 10 minislots. While waiting, Zoya detects that the medium has been busy for 15 minislots. If Zoya counts down the waiting minislots when the medium is busy, then she finishes the countdown while the medium is still busy and transmits after the idle minislot that follows the busy period. Again, the main problem is that many other nodes could have done the same and thus they get synchronized towards a collision. An elegant solution to this is to stop the counter while the medium is busy, thus removing the synchronizing effect that the busy medium may have on the waiting nodes.

      We note that, as the minislot becomes the basic time reference of the protocol, then this removes the need to assume that all packets are of the same length. The example in Figure 2.4(b) can be easily reworked by assuming that each of the packets or has a different length, expressed as an integer number of minislots.

      The gains of carrier sensing improve when the minislot is shorter. Ideally, it should be equal to zero. However, there are practical constraints that put a lower bound on the minislot duration. While it is not part of our collision model, in practice there is always a propagation delay in the wireless signals. This means that, when Zoya starts to transmit in Figure 2.4(b), Xia does not immediately detect that there is a transmission, and only detects one after a certain time that is required for the wireless signal to travel from Zoya's transmitter to Xia's receiver. The duration of the minislot should be set to be equal to the maximal propagation delay that a carrier signal can experience. In our communication model, depicted in Figure 1.1(a), we work with the (very artificial) assumption that no signal propagates beyond a distance of ; then the minislot duration can be determined as:

      (2.7)

where is the propagation speed, equal to the speed of light. We can soften the propagation assumption and enrich our collision model by assuming the following: the communication range is , but the range within which the carrier can be sensed, called the sensing range, is larger, say . The rationale can be drawn from the analogy with speech: as Yoshi goes away from Zoya, after some distance he can hear that she is speaking, but cannot understand the words. If Zoya and Yoshi are terminals that are situated at the opposite ends of Basil's cell, then the distance between them is and the duration of the minislot should be chosen to be . In practice, it gets more complicated as not all signals travel over a straight line, as some of the waves that carry wireless information are reflected and arrive later.

      We remark that carrier sensing is well suited for ALOHA type protocols, where collisions are avoided. On the other hand, the random access protocols based on splitting tree are good at resolving collisions once they occur, such that the gains that CSMA introduces in splitting tree type protocols are rather modest, as the main effect of CSMA is to decrease the probability of occurrence of a collision.

      2.3.3 Feedback to the Transmitter

      The way we have described the system operation in Figure 2.4 assumes that a transmitter, Zoya or Xia, knows perfectly if their packet has been received successfully or was subject to collision. On the other hand, collision or success is a phenomenon that occurs at the receiver, such that it is the receiver that needs to inform the transmitter about the outcome. In addition, Zoya's transmitter is half-duplex and she cannot detect the collision with Xia while transmitting, although Xia is within the communication/interfering range and her signal reaches Zoya. In fact, due to the use of half-duplex transmission, after sending the packet, Zoya should go into receiving mode. In this mode she waits for a packet from Yoshi that carries feedback to inform her whether the packet reception outcome was