Tensor-Based Receiver for Joint Channel, Data, and Phase-Noise Estimation in MIMO-OFDM Systems

Phase-noise is a system impairment caused by the mismatch between the oscillators at the transmitter and the receiver. In OFDM systems, this induces inter-carrier-interference (ICI) by rotating the transmitted symbols. Thus it can cause severe system performance degradation. To reduce its effects, the phase-noise must be estimated or compensated. In this work, we propose a two-stage tensor-based receiver for a joint channel, phase-noise (PN), and data estimation in MIMO-OFDM systems. In the first stage, we show that the received signal at the pilot subcarriers can be modeled as a third-order PARAFAC tensor. Based on this model, we propose two algorithms for channel and phase-noise estimation at the pilot subcarriers. The first algorithm, based on the BALS (Bilinear Alternating Least Squares), is an iterative algorithm that estimates the channel gains and the phase-noise impairments. The second is a closed-form algorithm based on the LS-KRF (Least Squares - Khatri-Rao Factorization) that estimates the channel gains and the phase-noise terms through multiple rank-one factorizations. Both algorithms achieve similar performance, but in terms of computational complexity, we show that the LS-KRF becomes more attractive than the BALS as the number of receive antennas is increased. The second stage consists of data estimation, for which we propose a ZF (Zero-Forcing) receiver that capitalizes on the PARATuck tensor structure of the received signal at the data subcarriers using the Selective Kronecker Product (SKP) operator. Our numerical simulations show that the proposed receiver achieves an improved performance compared to the state-of-art receivers in terms of symbol error rate (SER) and normalized mean square error (NMSE) of the estimated channel and phase-noise matrices.