  Many of the systems that appear in various signal processing applications are
non-linear, for example, due to hardware impairments such as non-linear
amplifiers and finite-resolution quantization. The Bussgang decomposition is a
popular tool for analyzing the performance of systems that involve such
non-linear components. In a nutshell, the decomposition provides an exact
probabilistic relationship between the output and the input of a non-linearity:
the output is equal to a scaled version of the input plus uncorrelated
distortion. The decomposition can either be used to compute 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.
