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https://www.gaussianwaves.com/tag/ofdm/

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Yes. The noise can be represented in four dimension as n1 + j n2 + k n3 + l n4.

To implement in Matlab or any programming language, each dimension is represented as a column vector in a Nx 4 matrix, where N represents the desired number of noise samples

Example:
To generate 10 I.I.D 4 dimensional noise samples that follow Gaussian distribution, each column represent a single dimension.

Noise = [randn(10,1) ; randn(10,1) ; randn(10,1) ; randn(10,1) ]

To understand, consider the case of 2 dimensional noise (complex noise)
Noise = [ randn(10,1) ; randn(10,1)] is equivalent to
Noise = randn(10,1) + i1* randn(10,1)

Hi Mathuranathan,
If i go for modulation using multiple basis functions (say 4), and if I introduce noise in them,
then the resulting noise will be N= n1 + jn2 + kn3 + ln4? Am I correct in representing the noise?
Or it should be N = n1+j(n2 + k(n3 + l n4))) ?

Thank you ,
That was very much informative

When talking about real normal distribution, it is one dimensional. The same concept can be extended to multivariate case, where the distribution across multi-dimension are jointly Gaussian. Complex normal distribution is a subset of multivariate normal distribution, where the number of dimension considered is just 2 (also bivariate normal distribution). We name these two dimensions as real and imaginary parts.

There are many applications to complex normal distribution. For example, A QPSK modulation is a two dimensional modulation, where each transmitted symbol is represented on two basis function – sine and cosine. Thus these symbols are represented as complex number. Actually, you cannot transmit a complex number. What happens really is that you are modulating the input message on two basis function – sine and cosine with same frequency but are offset 90* with respect to each other interms of phase.

If I would like to introduce noise in the QPSK modulation system, where the transmitted symbols are represented as complex number in the form S = s1 + j s2, then I would need a complex gaussian noise of form N = n1+jn2. The received signal is represented as Y = S+N, where everything is complex.

Yes, it is possible to generate complex distributions in matlab. Example
N = randn(1,100) + i1 * randn(1,100); %gives complex normal distributed samples

More applications :
Rayleigh fading: https://www.gaussianwaves.com/2010/02/fading-channels-rayleigh-fading-2/
Rician Fading: https://www.gaussianwaves.com/2012/07/ebn0-vs-ber-for-bpsk-over-rician-fading-channel/
AWGN noise (Complex case) : https://www.gaussianwaves.com/2015/06/how-to-generate-awgn-noise-in-matlaboctave-without-using-in-built-awgn-function/
Simulating white noise as multivariate Gaussian random vector: https://www.gaussianwaves.com/2013/11/simulation-and-analysis-of-white-noise-in-matlab/

-regards

thank you, I got the basics I needed