Particle Filter Based Nonlinear Data Detection in Presence of CFO for Frequency Selective mmWave MIMO-OFDM Systems

The nonlinear distortions attributed by the radio frequency (RF) power amplifier (PA) and other RF circuits from the enormous bandwidth of millimeter wave (mmWave) and high frequency design limitations of the integrated circuits involved, degrade the performance of the hybrid mmWave multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. This nonlinear distortions in the hybrid mmWave systems cause nonlinear coupling of the hybrid precoder with the data signals. Further, it induces intercarrier interference (ICI) in the OFDM systems, which also involves the interference from the precoders of other subcarriers. These difficulties in collusion with frequency selective channel and carrier frequency offset (CFO) may pose great challenges to the estimation accuracy of these parameters (channel gains and CFO) and signal detection. The nonlinearity causes the target posterior distribution for data detection as non-Gaussian and analytically intractable. In this work, we present a novel pilot assisted maximum likelihood (ML) based framework for estimating the CFO with PA impairment in the time domain by formulating a low dimensional equivalent channel matrix. The low dimensional equivalent channel matrix is composed of hybrid precoders-combiners, high dimensional MIMO channel, and the nonlinearly distorted components from PA. We further propose a group-sparse Bayesian learning (G-SBL) based semi-blind channel estimator in the time domain, which incorporates the CFO and nonlinearity of PA in its estimation process. With the estimated channel, a procedure to obtain the hybrid precoder and combiner matrices for data transmission is developed next. An iterative algorithm based on particle filter (PF) that effectively handles the nonlinear coupling of precoder matrix with data, and ICI is also proposed for data detection. The performance of the algorithms are evaluated on two different channel models: (a) synthetic geometric based mmWave channel (b) realistic mmWave channel for an urban microcell (UMi) environment. To validate the efficacy of the CFO and channel estimator, the Cramer-Rao bound (CRB) and Bayesian CRB (BCRB) are derived respectively.