Communication Systems/Time-Division Multiplexing

Consider a situation where there are multiple signals which would all like to use the same wire (or medium). For instance, a telephone company wants multiple signals on the same wire at the same time. It certainly would save a great deal of space and money by doing this, not to mention time by not having to install new wires. How would they be able to do this? One simple answer is known as Time-Division Multiplexing.

What is TDM?

In Time-Division Multiplexing (TDM), each signal is transmitted for a certain period of time, and is then "turned off". When one signal has been turned off, another signal is "turned on". On the other end of the wire is a switch that will then move each signal to its correct destination.

Benefits of TDM

TDM is all about cost: fewer wires and simpler receivers are used to transmit data from multiple sources to multiple destinations. TDM also uses less bandwidth than Frequency-Division Multiplexing (FDM) signals, unless the bitrate is increased, which will subsequently increase the necessary bandwidth of the transmission.

Synchronous TDM

Synchronous TDM is a system where the transmitter and the receiver both know exactly which signal is being sent. Consider the following diagram:

Signal A ---> |---| |A|B|C|A|B|C|   |------| ---> Signal A
Signal B ---> |TDM| --------------> |De-TDM| ---> Signal B
Signal C ---> |---|                 |------| ---> Signal C

In this system, starting at time-slice 0, every third time-slice is reserved for Signal A; starting at time-slice 1, every third time-slice is reserved for Signal B; and starting at time-slice 2, every third time-slice is reserved for Signal C. In this situation, the receiver (De-TDM) needs only to switch after the signal on each time-slice is received.

Statistical TDM

Synchronous TDM is beneficial because the receiver and transmitter can both cost very little. However, consider the most well-known network: the Internet. In the Internet, a given computer might have a data rate of 1kbps when hardly anything is happening, but might have a data rate of 100kbps when downloading a large file from a fast server. How are the time-slices divided in this instance? If every time slice is made big enough to hold 100Kbps, when the computer isn't downloading any data, all of that time and electricity will be wasted. If every time-slice is only big enough for the minimum case, the time required to download bigger files will be greatly increased.

The solution to this problem is called Statistical TDM, and is the solution that the Internet currently uses. In Statistical TDM, each data item, known as the payload (we used time-slices to describe these earlier), is appended with a certain amount of information about who sent it, and who is supposed to receive it (the header). The combination of a payload and a header is called a packet. Packets are like envelopes in the traditional "snail mail" system: Each packet contains a destination address and a return address as well as some enclosed data. Because of this, we know where each packet was sent from and where it is going.

The downside to statistical TDM is that the sender needs to be smart enough to write a header, and the receiver needs to be smart enough to read the header and (if the packet is to be forwarded,) send the packet toward its destination.

Packets

Packets will be discussed in greater detail once we start talking about digital networks (specifically the Internet). Packet headers not only contain address information, but may also include a number of different fields that will display information about the packet. Many headers contain error-checking information (checksum, Cyclic Redundancy Check) that enables the receiver to check if the packet has had any errors due to interference, such as electrical noise.

Duty Cycles

Duty cycle is defined as " the time that is effectively used to send or receive the data, expressed as a percentage of total period of time." The more the duty cycle , the more effective transmission or reception.

We can define the pulse width, τ, as being the time that a bit occupies from within it's total alloted bit-time T_b. If we have a duty cycle of D, we can define the pulse width as:

$\tau =D{T}_b$

Where:

$0<\tau \le T_b$

The pulse width is equal to the bit time if we are using a 100% duty cycle.