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This paper is devoted to the performance study of the Linear Minimum MeanSquared Error estimator for multidimensional signals in the large dimensionregime. Such an estimator is frequently encountered in wireless communicationsand in array processing, and the Signal to Interference and Noise Ratio (SINR)at its output is a popular performance index. The SINR can be modeled as arandom quadratic form which can be studied with the help of large random matrixtheory, if one assumes that the dimension of the received and transmittedsignals go to infinity at the same pace. This paper considers the asymptoticbehavior of the SINR for a wide class of multidimensional signal models thatincludes general multi-antenna as well as spread spectrum transmission models.  The expression of the deterministic approximation of the SINR in the largedimension regime is recalled and the SINR fluctuations around thisdeterministic approximation are studied. These fluctuations are shown toconverge in distribution to the Gaussian law in the large dimension regime, andtheir variance is shown to decrease as the inverse of the signal dimension.

A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large Dimensional Signals