Many of the systems in various signal processing applications are nonlinear due to, for example, hardware impairments, such as nonlinear amplifiers and finite-resolution quantization. The Bussgang decomposition is a popular tool used when analyzing the performance of systems that involve such nonlinear components. In a nutshell, the decomposition provides an exact probabilistic relationship between the output and the input of a nonlinearity: the output is equal to a scaled version of the input plus uncorrelated distortion. The decomposition can be used to compute either exact performance results or lower bounds, where the uncorrelated distortion is treated as independent noise. This lecture note explains the basic theory, provides key examples, extends the theory to complex-valued vector signals, and clarifies some potential misconceptions.

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非线性系统的 Bussgang 分解：基本理论和 MIMO 扩展 [讲义]

各种信号处理应用中的许多系统都是非线性的，例如由于硬件损伤，如非线性放大器和有限分辨率量化。Bussgang 分解是分析涉及此类非线性组件的系统性能时常用的工具。简而言之，分解提供了非线性的输出和输入之间的精确概率关系：输出等于输入的缩放版本加上不相关的失真。分解可用于计算精确的性能结果或下限，其中不相关的失真被视为独立噪声。本讲义解释了基本理论，提供了关键示例，将理论扩展到复值矢量信号，并澄清了一些潜在的误解。