I try to utilize this formula to a similar case, but the result seems too complicated. What if one of two RVs is a circular (mod 2 pi) uniformly distributed in [0, 2 pi) and the other one is an independent uniform RV in the range [-2^(-q) pi, 2^(-q) pi], where q is a nonnegative integer greater...
Hello,
I would like to know the analytical steps of deriving the distribution of sum of two circular (modulo 2 pi) uniform RVs in the range [0, 2 pi).
Any help would be useful
Thanks in advance!
Yes. I would like to know if (and how) is this result true for generally random matrices A and B (where their elements are particularly independent complex-valued Gaussian distributed).
Any suggestion could be useful. Thanks in advance.
Hello,
I am puzzled about the following condition. Assume a matrix A with complex-valued zero-mean Gaussian entries and a matrix B with complex-valued zero-mean Gaussian entries too (which are mutually independent of the entries of matrix A).
Then, how can we prove that...
Hi,
I would like to expand the following expression:
1/[((a+s)*(1+b/s)^m)], where a, b, and s are real nonnegative values and m is an arbitrary positive integer.
Particularly, according to partial fraction expansion, it becomes:
Sum[A_j/[(1+b/s)^j],{j,1,m}]+B/(a+s). I look for a closed-form...
Hi,
Let y = x + z, where x and z are mutually independent RVs. Also, z is a complex gaussian RV with zero mean and variance sigma^2.
My question is as follows:
For x = y - z, what is the variance of (-z) ?
Any help could be useful.
Thanks in advance.
Hi,
Let the following function:
X = ∑^{L}_{k=1} f(k)/L, where f(k) is a continuous random function and L is a random discrete number. Both L and f(k) are non negative random variables. Thus, X is the average of f(k) with respect to L.
Is it right to say that X equals (or approximately) to...
Hi,
If E[wwH]=T, where w is a zero-mean row-vector and H is the Hermitian transpose then assuming that H is another random matrix, it holds that
E[H w (H w)H] = T H HH or T E[H HH] ??
In other words, the expectation operation still holds as in the latter expression or vanishes as in the...
Hi, I would like to know if the inequality sign plays any role to the following optimization problem:
minimize f0(x)
subject to f1(x)>=0
where both f0(x) and f1(x) are convex. The standard form of these problems require a constraint such as: f1(x)<=0, but i am interested in the opposite...
Indeed, they have different dimensions. However their non-zero eigenvalues are the same. This is a fact. If you hold reservations about the latter just implement it in Matlab and see with the command eig their corresponding eigenvalues.
My question is: if they also have the same probability...
Hello,
Assume that H is a n \times m matrix with i.i.d. complex Gaussian entries each with zero mean and variance \sigma. Also, let n>=m. I ' m interested in finding the relation between the distribution of HHH and HHH, where H stands for the Hermittian transposition. I anticipate that both...
Hello,
Assume that H is a n \times m matrix with i.i.d. complex Gaussian entries each with zero mean and variance \sigma. Also, let n>=m. I ' m interested in finding the relation between the distribution of HHH and HHH, where H stands for the Hermittian transposition. I anticipate that both...
Hello,
Assume that H is a n \times m matrix with i.i.d. complex Gaussian entries each with zero mean and variance \sigma. Also, let n>=m. I ' m interested in finding the relation between the distribution of HHH and HHH, where H stands for the Hermittian transposition. I anticipate that both...
Hi,
Assume a matrix H n\times m, with random complex Gaussian coefficients with zero-mean and unit-variance. The covariance of this matrix (i.e., expectation [HHH]) assuming that m = 1 is lower than another H matrix when m > 1 ??
If this holds, can anyone provide a related reference?
Thanks...