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Pre-processing associated with massive multiple input-multiple output (MIMO) systems can lead to signals with high envelope fluctuations, which are very prone to nonlinear effects, especially when massive MIMO schemes are combined with orthogonal transform multiplexing (OFDM) modulations. If the nonlinear characteristics that affect a given system are known, we can design appropriate receivers that take into account the nonlinear effects introduced by the transmitter. Cubic systems are particularly important, not only because they can approximate many nonlinear effects (e.g., due to the power amplifier or clipping effects), but also because many more complex nonlinear characteristics in communication schemes can be replaced by equivalent lower-order nonlinear characteristics in general, and cubic characteristics in particular. To compensate the effects at the receiver side (e.g., by using the so-called Bussgang receivers), we need to estimate the nonlinear operation that was introduced at the transmitter, and this should be done blindly, without the need of training symbols. The paper contains a description of a mathematical approach for modeling and identification of nonlinear kernels in cubic systems. Based on theoretical tools of HOC in cubic systems, we build a new formula which relates the second- and fifth-order cumulants. Our performance results indicate that the proposed approach allows an accurate identification, yielding the desired kernels via fifth-order cumulants, and ensures a very good convergence, outperforming existing adaptive methods. This is achieved blindly, by exploiting the maximum information of the output system, making it suitable for many practical nonlinear effects.

Modeling and Identification of Nonlinear Effects in Massive MIMO Systems Using a Fifth-Order Cumulants-Based Blind Approach