I would like to generate CSCG in MATLAB with zero mean and certain variance. I would be pleased to know all the possible ways of generating CSCG noise.
Thanks
I agree with answers above, but if "var" should be the true variance then you write it as
sqrt(var/2)*(randn(1,N)+1i*randn(1,N))
so that the real and imaginary parts each contribute to one half of the variance.
What is meant by circularly symmetric Gaussian noise is that the noise looks the same in all directions. Imagine a certain Gaussian complex noise that (for some physical reason) produces larger noise in specific directions; for example, along a line at an angle of π/4 on the complex plane. You could then design a QAM constellation (and detector) that takes advantage of this behavior to get better than expected performance given the noise power in the channel. When a problem states that the noise is circularly symmetric, it's saying that you can't play this kind of game.
Below is a pdf attached which generates the circular symmertic gauusian noise. Hope that helps
if h be CSCG ,
h=randn(1,N)+1i*randn(1,N).
N is the number of sample noise
The command sqrt(var)*(randn(1,N)+1i*randn(1,N)) works in case of uncorrelated noise. If you want to implement a correlation among samples, you should exploit Cholesky factorization or a filter in frequency domain.
I agree with answers above, but if "var" should be the true variance then you write it as
sqrt(var/2)*(randn(1,N)+1i*randn(1,N))
so that the real and imaginary parts each contribute to one half of the variance.
Circularly-Symmetric Complex Normal and corresponds to the case of zero relation matrix and zero mean:µ = 0 and C = 0. Circular symmetric complex normal random variables are used extensively in signal processing.
Let Z = (Z1, Z2,... ,Zn)T be a complex jointly-Gaussian random vector.
For E[eiφZ ] = eiφE[Z ], any circularly-symmetric complex random vector must have E[Z ] = 0, i.e., must have zero mean. In a moment, we will see that a circularly-symmetric jointly-Gaussian complex random vector is completely determined by its covariance matrix, KZ = E[Z Z † ], where Z † = Z T∗ is the complex conjugate of the transpose. A circularly-symmetric jointly-Gaussian complex random vector Z is denoted and referred to as Z ∼ CN (0,KZ ), where the C denotes that Z is both circularly symmetric and complex. Most communication engineers believe that vectors of Gaussian random variables (real or complex) are determined by their covariance matrix
I agree with the previous answers. To put into different words, a complex random variable Z is circularly symmetric Gaussian if both its real and imaginary parts are Gaussian, zero mean and identically distributed (iid), namely present the same variance. Such a random variable is called circularly symmetric because the probability density of its phase is uniformly distributed.
For additional information, a very good material is chapter 7 in the Digital Communications course available at MIT OCW.
Prof. Robert Gallager talks about this in Lecture 17, starting from minute 51. Take a look in the attached lecture link if interested.
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-450-principles-of-digital-communications-i-fall-2006/lecture-notes/
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-450-principles-of-digital-communications-i-fall-2006/video-lectures/lecture-17-detection-for-random-vectors-and-processes/
In case of Rician fading, I saw many papers address that the channel follows CN(muy,sigmal^2) (circularly symmetric complex Gaussian variable). So can the mean be non-zeros?
Please refer to the recent paper: Preprint Massive MIMO with Spatially Correlated Rician Fading Channels
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