  This paper addresses the development of analytical tools for the computation
of the moments of random Gram matrices with one side correlation. Such a
question is mainly driven by applications in signal processing and wireless
communications wherein such matrices naturally arise. In particular, we derive
closed-form expressions for the inverse moments and show that the obtained
results can help approximate several performance metrics such as the average
estimation error corresponding to the Best Linear Unbiased Estimator (BLUE) and
the Linear Minimum Mean Square Error LMMSE or also other loss functions used to
measure the accuracy of covariance matrix estimates.
