Start with a set of vectors that are mutually orthogonal. (Although mutual orthogonality is the only condition, these vectors are usually constructed for ease of decoding, for example columns or rows from Walsh matrices.) An example of orthogonal functions is shown in the picture on the left. These vectors will be assigned to individual users and are called the "code", "chipping code" or "chip code". In the interest of brevity, the rest of this example uses codes (v) with only 2 digits.
An example of four mutually orthogonal digital signals.
Each user is associated with a different code, say v. If the data to be transmitted is a digital zero, then the actual bits transmitted will be –v, and if the data to be transmitted is a digital one, then the actual bits transmitted will be v. For example, if v=(1,–1), and the data that the user wishes to transmit is (1, 0, 1, 1) this would correspond to (v, –v, v, v) which is then constructed in binary as ((1,–1),(–1,1),(1,–1),(1,–1)). For the purposes of this article, we call this constructed vector the transmitted vector.
Each sender has a different, unique vector v chosen from that set, but the construction method of the transmitted vector is identical.
Now, due to physical properties of interference, if two signals at a point are in phase, they add to give twice the amplitude of each signal, but if they are out of phase, they "subtract" and give a signal that is the difference of the amplitudes. Digitally, this behaviour can be modelled by the addition of the transmission vectors, component by component.
If sender0 has code (1,–1) and data (1,0,1,1), and sender1 has code (1,1) and data (0,0,1,1), and both senders transmit simultaneously, then this table describes the coding steps:
Because signal0 and signal1 are transmitted at the same time into the air, they add to produce the raw signal:
(1,–1,–1,1,1,–1,1,–1) + (–1,–1,–1,–1,1,1,1,1) = (0,–2,–2,0,2,0,2,0)
This raw signal is called an interference pattern. The receiver then extracts an intelligible signal for any known sender by combining the sender's code with the interference pattern, the receiver combines it with the codes of the senders. The following table explains how this works and shows that the signals do not interfer with one another:
When the receiver attempts to decode the signal using sender1’s code, the data is all zeros, therefore the cross correlation is equal to zero and it is clear that sender1 did not transmit any data.
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