Multiplexing means putting several things onto one resource and recovering them at the far end. The second half of that sentence is the hard half, and it is what every named technique on this page exists to guarantee. The four classic ones differ only in which property of the signal they use to keep the streams apart.

• What does multiplexing mean ?
• What are the four classic types ?
• Why does every one of them need orthogonality ?
• How does multiplexing differ from multiple access ?
• How do real systems combine them ?

What does multiplexing mean ?

The definition below is short enough to read without noticing it, so it is worth reading twice. Several things go in, one signal travels, and the same several things come out at the far end. Everything else on this page exists to make that last step possible.

When some "multiple things" are carried by the same physical resources, we call the multiple things being "multiplexed".

When you multiplex something, you always have to think about how to "de-multiplex" them. It means that you have to multiplex somethings in such a way that they can be easily separated into individual things. If you multiplex things and those things cannot be demultiplexed, it is called a garbage -:).

That warning states the whole subject in one line, and it is worth restating as a requirement. The receiver gets one signal, which is the sum of everything that was combined. To recover any one stream it has to undo that sum. A sum can be undone only when the parts differ in some property the receiver can measure.

That property is what gives each technique below its name. Each one picks a dimension in which the streams will differ, and then keeps them separated in that dimension. Nothing else about the four is different, which is why they can be combined freely and usually are.

The resource being shared is worth naming too. It is not really a cable or a band of spectrum. It is a stretch of time multiplied by a stretch of frequency, and a system spends that product the same way whichever technique it uses. Splitting it one way rather than another changes who gets which part, and it does not change how much there is.

• Demultiplexing is the requirement, not the afterthought : any scheme can combine signals. A scheme earns its name by guaranteeing that the combination can be taken apart again.
• Each technique names the dimension it separates in : time, frequency, code or space. The name of the technique tells you which one, and that is most of what the name carries.
• The resource is time multiplied by bandwidth : dividing it differently moves the boundaries and never creates more of it. No multiplexing scheme is free capacity.

What are the four classic types ?

There are many different types of multiplexing that has been used in communication and you'd better know of at least some name of these techniquest. (Details of each of these technique is a huge topics on their own). There are some communication system that is using only one of these technique and there are some other communication systems that are using multiples of these techniques in combination.

• TDM (Time Division Multiplexing) : This would be the most straightfoward method. We split the data exchange time into multiple small slots and transmit/receive different data onto different slot. GSM is one of example of communication system that is extensively using this technology)
• FDM (Frequency Division Multiplexing) : In this technique, we split a communication channel(physical resource) into different frequency blocks and transmit/receive different stream of data through different frequency blocks. OFDM (Orthogonal Frequency Division Multiplexing) is one typical example.
• CDM (Code Division Multiplexing) : In this technique, we split a communication channel(physical resource) into different code (orthogonal code) and allocate each stream of data onto different code. CDMA and WCDMA is the most widely used example.
• SDM (Space Division Multiplexing) or Spatial Multiplexing : In this technique, we split a communication channel(physical resource) into multiple different physical locations and allocate each stream of data onto each of the location. In real implementation, 'differet physical location' mean 'different transmission or reciever antenna'. MIMO (Multiple Input Multiple Output) is the most common example of SDM.

Those four are easier to compare drawn than listed, because all four are dividing the same thing. Figure 1 puts each one on the same time and frequency grid, with two streams marked A and B.

Figure 1. The same resource under the four schemes. The first two cut the grid in different directions. The second two do not cut it at all, and rely instead on a code or a spatial path to separate the streams afterwards.

• TDM and FDM cut the same rectangle at right angles : one divides along time and the other along frequency. Neither creates capacity, and both simply decide who gets which part of it.
• CDM and SDM do not divide the grid at all : both streams occupy every part of it. The separation happens after the signals have already been added together, which is why both need more work at the receiver.
• SDM is the only one that can add capacity : a second antenna pair gives a second path rather than a share of the first. The other three split what is already there.

Why does every one of them need orthogonality ?

The four techniques look unrelated in a list and behave identically underneath. Each one gives every stream a signature, sends the sum of all of them, and expects the receiver to undo the sum. That last step is the one with a condition attached.

The condition is that the signatures must be distinguishable. Write the received signal as a weighted sum of signatures. The receiver has to recover the weights, and that is possible only when no signature can be built from the others. Engineers call that orthogonality. For TDM and FDM it is obvious, because two streams that never share a moment cannot be confused, and neither can two that never share a frequency.

CDM is where the idea stops being obvious and becomes useful. Two streams occupy the same time and the same band. Their spreading codes are chosen so that correlating against one code recovers that stream and cancels the other. The Gold code page covers how such families are built, and channelization covers how they are assigned.

OFDM is the case worth looking at twice, because its name claims orthogonality and its subcarriers overlap heavily in frequency. They are separable because each subcarrier falls to zero exactly where the others peak. That is a property of their spacing rather than of their separation. The OFDM page draws that condition.

SDM relies on the channel rather than on the waveform, which is what makes it the fragile one. Two antennas are separable only when the paths between transmitter and receiver differ enough. The guarantee therefore comes from the environment rather than from the design. A receiver recovers the layers by inverting a channel matrix, which is an equalization problem and fails when the matrix is close to singular.

• One requirement, four ways of meeting it : the signatures must be distinguishable. Separate slots, separate bands, orthogonal codes and independent spatial paths are four answers to the same question.
• Three of them are guaranteed by design and one is not : time, frequency and code separation are properties of the transmitted signal. Spatial separation is a property of the channel, and it varies with where the terminal stands.
• Orthogonality is fragile in exactly the way the technique is : a timing error damages TDM and a frequency offset damages FDM. A correlated channel damages SDM. Each failure attacks the dimension the scheme depends on.

How does multiplexing differ from multiple access ?

Every name on this page has a near twin with an A on the end. TDM has TDMA, FDM has FDMA, CDM has CDMA and OFDM has OFDMA. The mechanisms are the same, and the words are not interchangeable. That difference catches people constantly.

The difference is about ownership rather than about signal processing. Multiplexing combines streams that one node already has, and multiple access shares one medium between nodes that are independent of each other. Figure 2 puts the two side by side.

Figure 2. The same separation mechanism, arranged two different ways. On the left one transmitter holds every stream and can schedule them freely. On the right the transmitters cannot see each other, so something has to hand out the resource before anyone transmits.

• The physical layer cannot tell the two apart : a receiver separating two OFDM streams does the same arithmetic either way. The difference lives above it. The difference lives above it.
• Multiple access needs an allocator and multiplexing does not : independent transmitters need a scheduler, a contention rule or a fixed assignment. A single transmitter already knows what it is sending.
• The A is not decoration : OFDM is a waveform. OFDMA is that waveform plus a rule for giving different subcarriers to different users. LTE uses both words for that reason.

How do real systems combine them ?

The author's point above is the one to keep : some systems use one technique and most use several. No real system picks a single row from the list. The four divide different dimensions, and nothing stops a design from dividing more than one.

Read the table as a progression rather than as four unrelated designs. GSM divided time inside frequency. WCDMA replaced the time division with codes. LTE went back to dividing time and frequency, and added spatial layers on top. Each generation kept the techniques that were cheap and changed the one that limited capacity.

The reason for combining rather than choosing is also worth stating. Dividing one dimension finely makes a system sensitive in that dimension, which the OFDM page shows for subcarrier spacing. Spreading the division across several dimensions keeps each one coarse enough to survive real hardware. That is a design argument rather than an accident of history.

• Combination is the normal case : every system in the table uses at least two of the four, and the modern ones use all four.
• The dimensions are independent, so the techniques stack : dividing frequency leaves the freedom to divide time untouched. OFDMA grants a rectangle of both at once for that reason.
• Each generation changed one technique rather than all of them : GSM to WCDMA swapped time division for codes. WCDMA to LTE reversed that and added space.