In this article, we explore the theoretical foundations of statistical signal processing as they apply to complex-valued data. Unlike real-valued signals, complex signals have a phase component in addition to their amplitude, which adds an additional layer of complexity. We delve into techniques for analyzing these signals, including maximum likelihood estimation and Bayesian inference. Additionally, we discuss the challenges inherent in working with complex signals, such as phase ambiguity. Overall, this article provides a comprehensive overview of statistical signal processing for complex-valued data.