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Intuitive Guide to Principles of Communications www.complextoreal.com

Code Division Multiple Access (CDMA)

The Concept of signal spreading and its uses in communications Let’s take a stright forward binary signal of symbol rate 2.

Figure 1 – A binary information signal To modulate this signal, we would multiply this sequence with a sinusoid and its spectrum would look like as In figure 2. The main lobe of its spectrum is 2 Hz wide. The larger the symbol rate the larger the bandwidth of the signal.

Figure 2 – Spectrum of a binary signal of rate 2 bps Now we take an another binary sequence of data rate 8 times larger than of sequence shown in Fig. 1.

Copyright 2002 Charan Langton

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CDMA Tutorial

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Figure 3 – A new binary sequence which will be used to modulate the information sequence Instead of modulating with a sinusoid, we will modulate the sequence 1 with this new binary sequence which we will call the code sequence for sequence 1. The resulting signal looks like Fig. 4. Since the bit rate is larger now, we can guess that the spectrum of this sequence will have a larger main lobe.

Figure 4 – Each bit of sequence 1 is replaced by the code sequence The spectrum of this signal has now spread over a larger bandwidth. The main lobe bandwidth is 16 Hz instead of 2 Hz it was before spreading. The process of multiplying the information sequence with the code sequence has caused the information sequence to inherit the spectrum of the code sequence (also called the spreading sequence).

Figure 5 – The spectrum of the spread signal is as wide as the code sequence The spectrum has spread from 2 Hz to 16 Hz, by a factor of 8. This number is called the the spreading factor or the processing gain (in dBs) of the system. This process can also

Copyright 2002 Charan Langton

www.complextoreal.com

CDMA Tutorial

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be called a form of binary modulation. Both the Data signal and the modulating sequence in this case are binary signals. If original signal is x(t) of power Ps, and the code sequence is given by g(t), the resultant modulated signal is s (t ) = 2 Ps d (t ) g (t )

The multiplication of the data sequence with the spreading sequence is the first modulation. Then the signal is multiplied by the carrier which is the second modulation. The carrier here is analog. s (t ) = 2 Ps d (t ) g (t ) sin(2πf c t ) On the receive side, we multiply this signal again with the carrier. What we get is this. rcv(t ) = 2 Ps d (t ) g (t ) sin 2 (2πf c t ) By the trigonometric identity sin 2 (2πf c t ) = 1 − cos(4πf c t ) we get rcv (t ) = 2 Ps d (t ) g (t )(1 − cos(4π fc t ))

Where the underlined part is the double frequency extraneous term, which we filter out and we are left with just the signal. rcv(t ) = 2 Ps d (t ) g (t ) Now we multiply this remaining signal with g(t), the code sequence and we get rcv(t ) = 2 Ps d (t ) g (t ) g (t ) Now from having used a very special kind of sequence, we say that correlatation of g(t) with itself (only when perfectly aligned) is a certain scalar number which can be removed, and we get the original signal back. rcv(t ) = 2 Ps d (t )

Copyright 2002 Charan Langton

www.complextoreal.com

CDMA Tutorial

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In CDMA we do modulation twice. First with a binary sequence g(t), the properties of which we will discuss below and then by a carrier. The binary sequence modulation ahead of the carrier modulation accomplishes two functions, 1. It spread the signal and 2. It introduces a form of encryption because the same sequence is needed at the receiver to demodulate the signal. In IS-95 and CDMA 2000 we do this three times, once with a code called Walsh, then with a code called Short Code and then with one called Long code.

Properties of spreading codes Multiplication with the code sequence which is of a higher bit rate, results in a much wider spectrum. The ratio of the code rate to the information bit rate is called...

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