Fisher information matrix, Rao test, and Wald test for complex-valued signals and their applications

• We show some important features of the FIM with respect to complex-valued signals.
• The Rao and Wald tests for complex-valued signals are given.
• We present the CRB of unbiased estimates involved complex FIM.
• Several examples about their application are also given.

The Fisher information matrix (FIM) is an important tool in signal processing. In this paper, we investigate the FIM with respect to the complex-valued quantities, and show its application in signal processing, such as the design of the Rao and Wald tests, and the derivation of the Cramér–Rao bound for the unbiased estimate. Some examples are also given.