# Time and frequency domain spreading in CDMA and MC-CDMA?

For time domain CDMA transmitter, how the spreading sequences should look like? Is it necessary to be from $\{ -1,+1\}$ like PN sequences ? How will the codes be in frequency domain?
I am confused in spreading codes used for MC-CDMA and CDMA.
If I use a PN sequence $\in \{ -1,+1\}$ and then take FFT, it is MC-CDMA.
Now, If I directly use a DFT matrix as spreading codes, is it equivalent to MC-CDMA?

• PN sequences generally take on values in $\{+1, -1\}$ and not in $\{+1, 0, -1\}$. – Dilip Sarwate Apr 4 '17 at 15:43
• Note some interesting similarities between OFDM and CDMA: OFDM can be viewed as spreading with symbols that are the complex roots of unity just like forms of CDMA done with spreading with Walsh Codes (symbols that are +1/-1). In 2 points they converge to the same spreading matrix ([1 1; 1 -1]), so in that sense OFDM is in itself a form of CDMA! But MC-CDMA specifically is a system of using the user's spread data (with PN sequences consisting of +/-1 and assigning each chip in the sequence to a different subcarrier before taking the IFFT to create the transmit waveform (as in OFDM) – Dan Boschen Apr 4 '17 at 16:12

The spectrum of DS-CDMA without pulse shaping is equivalent to the sinc function. The Matlab code below illustrates the difference between DS and MC-CDMA. For MC you need the IFFT not the FFT function.

clear,clc

N=2;
% BPSK data
d=sign(randn(1,N));

% 7-chip m-sequence code
c=[1 1 1 -1 1 -1 -1];

% DS-CDMA
s1=kron(d,c);

% MC-CDMA
L=sqrt(length(c));
s2=L*ifft(d(1)*c);
s3=L*ifft(d(2)*c);
% etc, better to use a for loop for more symbols


PN Sequence in Frequency Domain will look like what a White Noise should look like. The only difference is that since PN sequence is real valued, hence, the frequency domain magnitude will be symmetric around 0Hz.

This is because single most desirable property of a good PN sequence is that it cross-correlation should $$\rightarrow 0$$ and its auto-correlation should $$\rightarrow$$ $$\delta[n]$$.

I am pasting the plot of GPS L2C Data PN's FFT: As expected, it is like White Noise and Symmetric.