Multiple-input multiple-output (MIMO) technology in conjunction with orthogonal frequency division multiplexing (OFDM) transmission is widely adopted in fifth-generation mobile networks to support multiple users. However, in these mobile communication systems, high power amplifiers (HPAs) at user terminals’ transmitters are driven into their saturation regions, which makes the multiuser frequency-selective MIMO-OFDM uplink channel nonlinear and renders the standard multiuser detection (MUD) at the base station (BS) ineffective. In this paper machine learning is employed to combat the distortions in the uplink of this multiuser frequency-selective MIMO-OFDM communication system. More specifically, a powerful complex-valued B-spline neural network (BSNN) based design is developed to simultaneously identify the system’s channel impulse response (CIR) matrix and the BSNN model for the nonlinear transmitters’ HPA together with the BSNN inversion for the nonlinear HPA at transmitters. This enables the BS to effectively implement MUD by utilizing the estimated MIMO-OFDM CIR matrix as well as to compensate for the transmitter HPAs’ saturation distortions using the estimated BSNN inversion. A simulation study is included to evaluate the effectiveness of this novel BSNN assisted design in combating multiuser and dispersive channel interference as well as nonlinear distortions for multiuser MIMO-OFDM nonlinear uplink.

For the multiple-input multiple-output (MIMO) uplink employing high-order quadrature amplitude modulation (QAM) signaling and with nonlinear high power amplifiers (HPAs) at mobile users' transmitters, the existing multiuser detection methods can no longer be applied. We propose a novel nonlinear multiuser detection scheme for the nonlinear MIMO uplink. Specifically, we adopt an effective B-spline parameterization of the nonlinear transmit HPAs and derive an efficient and accurate algorithm to identify the nonlinear MIMO uplink channel, including the nonlinear B-spline model of the nonlinear transmit HPAs and the estimate of the linear MIMO channel matrix. Moreover, as the direct result of this nonlinear MIMO channel identification, the B-spline inverse model of nonlinear transmit HPAs can readily be identified. The nonlinear multiuser detection can be effectively implemented by the zero-forcing linear detection based on the estimated linear MIMO channel and followed by compensating the nonlinear distortion of the nonlinear transmit HPAs based on the estimated B-spline inverse model. An extensive simulation investigation is performed to demonstrate the effectiveness of our proposed nonlinear multiuser detection scheme for nonlinear MIMO uplink with high-order QAM signaling.

Complex-valued (CV) B-spline neural network approach offers a highly effective means for identifying and inverting practical Hammerstein systems. Compared with its conventional CV polynomial-based counterpart, a CV B-spline neural network has superior performance in identifying and inverting CV Hammerstein systems, while imposing a similar complexity. This paper reviews the optimality of the CV B-spline neural network approach. Advantages of B-spline neural network approach as compared with the polynomial based modeling approach are extensively discussed, and the effectiveness of the CV neural network-based approach is demonstrated in a real-world application. More specifically, we evaluate the comparative performance of the CV B-spline and polynomial-based approaches for the nonlinear iterative frequency-domain decision feedback equalization (NIFDDFE) of single-carrier Hammerstein channels. Our results confirm the superior performance of the CV B-spline-based NIFDDFE over its CV polynomial-based counterpart.

We propose a nonlinear hybrid decision feedback equalizer (NHDFE) for single-carrier (SC) block transmission systems with nonlinear transmit high power amplifier (HPA), which significantly outperforms our previous nonlinear SC frequency-domain equalization (NFDE) design. To obtain the coefficients of the channel impulse response (CIR) as well as to estimate the nonlinear mapping and the inverse nonlinear mapping of the HPA, we adopt a complex-valued (CV) B-spline neural network approach. Specifically, we use a CV B-spline neural network to model the nonlinear HPA, and we develop an efficient alternating least squares scheme for estimating the parameters of the Hammerstein channel, including both the CIR coefficients and the parameters of the CV B-spline model. We also adopt another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can be estimated using the least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. The effectiveness of our NHDFE design is demonstrated in a simulation study, which shows that the NHDFE achieves a signal-to-noise ratio gain of 4dB over the NFDE at the bit error rate level of 10-4.

Complex-valued (CV) B-spline neural network approach offers a highly effective means for identification and inversion of Hammerstein systems. Compared to its conventional CV polynomial based counterpart, CV B-spline neural network has superior performance in identifying and inverting CV Hammerstein systems, while imposing a similar complexity. In this paper, we review the optimality of CV B-spline neural network approach and demonstrate its excellent approximation capability for a real-world application. More specifically, we develop a CV B-spline neural network based approach for the nonlinear iterative frequency-domain decision feedback equalization (NIFDDFE) of single-carrier Hammerstein channels. Advantages of B-spline neural network approach as compared to polynomial based modeling approach are extensively discussed, and the effectiveness of CV neural network based NIFDDFE is demonstrated in a simulation study.