I am struggling to find the correlation between two complex r.vs; X and 1/Y i.e. E{X*/Y}, where '*' denotes the conjugation operator. The complex r.s X and Y are correlated with each other with known covariance matrix. Moreover, E{X/Y} is also known.
can anyone help?
Best Answer
Complex numbers are inherently two-dimensional, so you will have a set of numbers, not just one. A good "real valued" analog is the multivariate gaussian. In essense, what you are tyring to do is similar to getting a correlation between two vectors of two variables each, whcih partition the dimentions of a 4-dimensional gaussian distribution.
The complex case is a litte more nuanced because the real and complex parts of each "complex number" must bear a certain relationship to each other.
This paper will help you a great deal.