Complex‐Valued B‐Spline Neural Networks for Modeling and Inverse of Wiener Systems

Nonlinear Equalization of Hammerstein OFDM Systems

“…We then propose an efficient algorithm for jointly estimating H n and Ψ( ) based on the CV B-spline modelling of Ψ( ). A significant advantage of our CV B-spline neural network is that its inversion can be effectively calculated [15]. Before introducing the B-spline modelling of Ψ( ), we point out that the HPA Ψ( ) of (8) and (9) satisfies the following conditions.…”

“…The inverse of Hammerstein system's static nonlinear function based on B-spline neural network was introduced in [56], and this is described in below for completeness for solving (20).…”

“…Note that the CV HPA's nonlinearity, (8) and (9), is completely unknown to the receiver and w is unobserved. We adopt the CV B-spline neural network [15], [16] to represent the mapping w = Ψ(…”

“…The reason that we adopt the B-spline neural network is because it has been demonstrated to be very effective in identification and inversion of CV Wiener systems [14], [15]. Specifically, we propose an efficient alternating least squares (ALS) identification algorithm for estimating the channel impulse response (CIR) coefficients together with the parameters of the B-spline neural network that models the HPA static nonlinearity of the OFDM Hammerstein channel.…”

B-spline neural network based single-carrier frequency domain equalisation for Hammerstein channels

“…In our previous works [18], [19], the B-spline neural network has been demonstrated to be very effective in identification and inversion of CV Wiener systems. We adopt two real-valued (RV) B-spline neural networks to model the amplitude response and the phase response of the CV static nonlinearity of the Hammerstein channel, and we develop a highly efficient alternating least squares (ALS) identification algorithm for estimating the channel impulse response (CIR) coefficients as well as the parameters of the two RV B-spline neural networks that model the HPA's CV static nonlinearity.…”