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1.3.1 A Frame for Time Division

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Let us first consider downlink traffic, such that Basil has data to transmit to each of the devices. Then a straightforward idea is the one in which Basil divides the time into slots, where each slot has a duration of , which corresponds to the duration of the transmission of a single packet. In each slot, Basil can send a single packet to a particular device. For the moment we are ignoring the possibility that Basil can broadcast a common packet to all devices, using the shared property of the wireless medium. Keep in mind that we are still assuming that all packets have the same size. This mode of communication is a simple variant of time division multiple access (TDMA): at a given time, the whole shared medium is allocated to a single user, that is, the terminal to which Basil transmits. The simplest TDMA scheme with users is depicted in Figure 1.5(a), where each device gets an equal fraction of the shared channel. It is convenient to define a TDMA frame, which is periodically repeated, and see how one can define a logical channel by using the physical, shared communication channel. For the example in Figure 1.5(a), the logical communication channel between Basil and Zoya is the first slot in each TDMA frame, as depicted in Figure 1.5(b). The data rate of the logical channel is easily calculated as follows. The data rate of each packet is , such that in each frame a total of bits are sent to Zoya. If frames are observed, Zoya receives in total bits over a duration of s, which makes the equivalent data rate for Zoya

(1.1)

Figure 1.5 Downlink time division multiple access (TDMA). (a) Periodic equal allocation to all terminals. (b) The downlink communication channel from the perspective of Zoya. (c) Periodic allocation, but unequal across the terminals.

This very simple fact is, surprisingly, often neglected in practice. For example, a wireless system may have a nominal speed of, e.g., (Mbps, megabits per second), but this data speed is rather instantaneous and valid during the times when the user receives the data. However, if a lot of data needs to be sent by the user over a long period, then the average data rate is decreased because there are time intervals in which no data is sent to the user and thus their data rate in those time intervals is strictly zero. This leads to the conclusion that, for a consistent definition, we should always keep in mind that there is a particular time interval over which the data rate is calculated:

(1.2)

Most of the time is implicitly clear from the context.

If Basil is certain in advance that sending bits each s is sufficient for each terminal, then the simple TDMA is an easy and, in fact, perfect solution. In addition, the frame structure can be established once and kept indefinitely, as long as the devices stay synchronized to the frame defined by Basil. This is the essence of a circuit-switched connection in communications, where the usage of a certain communication resource is agreed in advance for a long period of time. In this particular example, Basil may have agreed with the mobile devices in the past that Zoya will use the first slot in a frame, Yoshi the second, etc. This means that whenever the time slot allocated to Zoya comes, Basil does not need to use a part of the bits to send signaling information and thus label the packet “This packet is for Zoya”. Instead, it is sufficient to send pure data to Zoya as every other device in the network knows that what is being sent in that slot is data for Zoya.

Circuit-switched operation is useful in minimizing signaling whenever it is known in advance which resources are required over a certain period. In practice, TDMA allocation can be more complex than what is described above. Let the demanded data rates be: for Zoya, for Yoshi and for Xia. An example of a TDMA allocation that can satisfy these data rate demands is depicted in Figure 1.5(c).

In real systems, even in the case of static, circuit-switched allocation, it is unrealistic to assume that the logical channels and frames will stay ideally allocated for an indefinite period. For example, there might be a period of time in which Basil has no data to send to Zoya. If Zoya does not receive anything within several consecutive frames, she might easily get out of synchronization with Basil, which would result in irrecoverable errors. If the internal clocks of Zoya and Yoshi have a large relative drift, then Zoya might start to receive the data for Yoshi, not knowing that it is not intended for her. This cannot be prevented in the described simple TDMA scheme, since no resources are spent in sending control information after the initial, circuit-switched allocation. This control information would be used to describe what kind of data is sent in a particular slot. Therefore the periodic frame structure with fixed allocations to the users is only an approximation, as there must be flexibility to change the allocation in the frame when new devices are coming in the system, as well as to release slots when some devices are leaving the system.

Wireless Connectivity

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