Joint Channel and Nonlinearity Estimation for Memoryless Nonlinear Systems

System nonlinearity due to hardware impairments has always been a challenging issue. Distortion cancellation and iterative detection based receivers such as the Bussgang Noise Cancelling (BNC) receiver are used to detect the original data in the presence of strong nonlinear (NL) effects. However, these receivers require knowledge of the system nonlinearity which is usually unknown in practical systems. Bussgang decomposition and its general form denoted Generalized Bussgang decomposition (GBD), have been commonly used to model system nonlinearity. In GBD the nonlinearity output is decomposed as the sum of uncorrelated terms of increased orders and provides spectral characteristics of the useful and distortion terms. In this paper we consider nonlinearity at the transmitter side and model it with GBD. We aim to estimate the scalar weights in the GBD to later use them at the BNC receiver. However, knowledge of the channel is required to make a reliable estimate of the NL parameters. On the other hand the pilots for channel estimation are affected by the system nonlinearity, which can preclude reliable channel estimation. Therefore, in this paper we propose a joint channel and NL parameter estimation technique by designing appropriate training signals for each estimation phase (i.e. channel estimation and NL parameter estimation). We also derive a closed form expression for the average power of residual distortion in GBD with estimated parameters to see how well this model can characterize the nonlinearity. The results show that the proposed estimation technique has good accuracy and enables quasi-ideal performance for a BNC receiver.