Contents
Is there a way to generate a random correlation matrix?
Here are some ways to generate random correlation matrices that I know of, but that do not work for me here: Generate random X of s × n size, center, standardize and form the correlation matrix C = 1 s − 1 X ⊤ X. If s > n, this will generally result in all off-diagonal correlations being around 0.
Which is the correct formula for the correlation matrix C?
Generate random X of s × n size, center, standardize and form the correlation matrix C = 1 s − 1 X ⊤ X. If s > n, this will generally result in all off-diagonal correlations being around 0. If s ≪ n, some correlations will be strong, but C will not be full rank. Generate random square A and make symmetric positive definite B = A A ⊤.
Start by generating two uncorrelated sequences of random numbers { x i } i = 1 N and { y i } i = 1 N with any desired distributions. Let C by the desired value of the correlation coefficient. Then do the following: 5) If | C − c n e w | < | C − c o l d | then keep the swap.
How to generate a sample with a given correlation?
Now, we can combine these four facts to create two standard normal variables whose populations will have a given correlation, r (more properly, ρ ), although the samples you generate will have sample correlations that vary.
How is vine used to generate correlation matrices?
The so called “vine” method allows to generate random correlation matrices with any distribution of partial correlations and can be used to generate correlation matrices with large off-diagonal values. Here is the example figure from that thread:
How to generate data with a prespecified matrix?
Let’s say you start with (mean zero) uncorrelated data (i.e. the covariance matrix is diagonal) – since we’re talking about the correlation matrix, let’s just take Σ = I. You can transform this to data with a given covariance matrix by choosing A to be the cholesky square root of Ω – then A x would have the desired covariance matrix Ω.
When is the spatial correlation matrix known to the transmitter?
Analogous to [28,30], let us now investigate how to modify the codebook design when the channel is spatially correlated Rayleigh distributed and the spatial correlation matrix is known to the transmitter. For simplicity, we assume a MISO transmission, so that the channel matrix is written as h = hwR1 / 2t, with h and hw being 1 × nt vectors.
Which is best codebook for spatial correlation matrix?
In general, it is more appropriate to design a CDIT-based codebook (also called adaptive codebook) that changes as a function of the spatial correlation matrix.
How to generate a random square with all positive elements?
Generate random orthogonal Q (e.g. by generating random square A and doing its QR decomposition, or via Gram-Schmidt process) and random diagonal D with all positive elements; form B = Q D Q ⊤.