 The standard complex normal random variable or standard complex Gaussian random variable is a complex random variable formula_8 whose real and imaginary parts are independent normally distributed random variables with mean zero and variance formula_9.Formally,

where formula_10 denotes that formula_8 is a standard complex normal random variable.Suppose formula_12 and formula_13 are real random variables such that formula_14 is a 2-dimensional normal random vector.