Recent content by nikozm

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...

Hi, I was wondering if two matrices with the same eigenvalues share the same PDF. Any ideas and/or references would be helpful. Thanks in advance

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...

Hi, If f'(x) >= f'(y) can we say that f''(x) >= f''(y) also holds ? And if yes under which conditions ? Thanks

Ok, I redifine the expression: (Σ^{m}_{i=0}x^i*Σ^{i}_{j=0}y^j)^n, where x,y are nonnegative real numbers and m,n are nonnegative integers