Kalman filter application for mitigation of nonlinear effects in multicarrier communication systems

The extension of Bussgang´s theorem for multicarrier signals states that the effect of a memoryless band-pass nonlinearity consists in an attenuation of the input signal and its corruption by additive nonlinear noise (Dardari, D. et al., IEEE Trans. Commun., vol.48, no.10, p.1755-64, 2000). In spite of the fact that, before the fast Fourier transform (FFT) block at the receiver, nonlinear noise is non-Gaussian, the Kalman filter is applied (which is known to provide the minimum mean-square estimate when the informative Gaussian signal is corrupted by additive Gaussian noise). Thus the structure of the useful signal is taken into account as well as the relationship between the powers of the useful signal and nonlinear noise. Hence the procedure of Kalman filtering, as applied to the above problem, consists in the simple multiplication of the received samples by the ´Kalman gain´. This gain can be calculated in advance because it depends only on the input signal power and the transfer characteristic of the nonlinearity. If the communication system is operated in an AWGN channel, the noise characteristics should also be taken into account when the above gain is calculated. Theoretical analysis and simulation results show that this simple procedure decreases the noise variance before the decision device and thus improves the performance of the system.