Code Division Multiple Access - Code Division Multiplexing (Synchronous CDMA)

Code Division Multiplexing (Synchronous CDMA)

Synchronous CDMA exploits mathematical properties of orthogonality between vectors representing the data strings. For example, binary string 1011 is represented by the vector (1, 0, 1, 1). Vectors can be multiplied by taking their dot product, by summing the products of their respective components (for example, if u = (a, b) and v = (c, d), then their dot product u·v = ac + bd). If the dot product is zero, the two vectors are said to be orthogonal to each other. Some properties of the dot product aid understanding of how W-CDMA works. If vectors a and b are orthogonal, then and:

\begin{align} \mathbf{a}\cdot(\mathbf{a}+\mathbf{b}) &= \|\mathbf{a}\|^2 &\quad\mathrm{since}\quad \mathbf{a}\cdot\mathbf{a}+\mathbf{a}\cdot\mathbf{b} &= \|a\|^2+0 \\ \mathbf{a}\cdot(-\mathbf{a}+\mathbf{b}) &= -\|\mathbf{a}\|^2 &\quad\mathrm{since}\quad -\mathbf{a}\cdot\mathbf{a}+\mathbf{a}\cdot\mathbf{b} &= -\|a\|^2+0 \\ \mathbf{b}\cdot(\mathbf{a}+\mathbf{b}) &= \|\mathbf{b}\|^2 &\quad\mathrm{since}\quad \mathbf{b}\cdot\mathbf{a}+\mathbf{b}\cdot\mathbf{b} &= 0+\|b\|^2 \\ \mathbf{b}\cdot(\mathbf{a}-\mathbf{b}) &= -\|\mathbf{b}\|^2 &\quad\mathrm{since}\quad \mathbf{b}\cdot\mathbf{a}-\mathbf{b}\cdot\mathbf{b} &= 0-\|b\|^2 \end{align}

Each user in synchronous CDMA uses a code orthogonal to the others' codes to modulate their signal. An example of four mutually orthogonal digital signals is shown in the figure. Orthogonal codes have a cross-correlation equal to zero; in other words, they do not interfere with each other. In the case of IS-95 64 bit Walsh codes are used to encode the signal to separate different users. Since each of the 64 Walsh codes are orthogonal to one another, the signals are channelized into 64 orthogonal signals. The following example demonstrates how each user's signal can be encoded and decoded.

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