In wikipedia of covariance matrix as well many textbooks on probability and statistics, the cross-covariance matrix $X$ and $Y$ is defined as $$K_{XY} = E[(X - E[X])(Y - E[Y])]$$
However, in a lot of book in the field of electrical engineering (e.g., in "Baseband Receiver Design for Wireless MIMO-OFDM Communications"), it seems that the cross-covariance matrix between $X$ and $Y$ is defined as $$K_{XY} = E[XY^{H}],$$ where $(\cdot)^{H}$ is conjugate transpose operation. Also it seems that in the aforementioned book the terms "cross-correlation matrix" and "cross-covariance matrix" are used interchangably.
So is this difference of definition due to the specific field? Or the authors have misused the term in the books?