ML-based Tracking Algorithms for MIMO-OFDM

This article addresses the problem of tracking the carrier frequency offset (CFO) and sampling frequency offset (SFO) in burst MIMO-OFDM systems. The goal is to accomplish those tasks with the smallest possible piloting overhead (highest spectral efficiency). For that, we derive a precise mathematical model that describes the joint effect of a CFO and SFO on the received MIMO-OFDM subcarriers. The model unifies simpler, well-known results found in the literature. We use it for deriving maximum likelihood (ML) estimators for both impairments based on observations of received pilot subcarriers at the output of the FFTs of the receiver branches. This approach yields estimators that are independent of the type of MIMO decoder, located further downstreams. At the same time, the estimators are the ML-optimal processors of pilot information at the MIMO channel´s output. A pair of corresponding tracking algorithms based on the estimators is proposed and evaluated by simulation. The results show that the variance of our estimators decreases with larger MIMO configurations, allowing for increased synchronization accuracy at low SNR, or for reducing the number of pilot subcarriers to maintain equal estimator variance. We also show that the proposed tracking algorithms operate robustly under imperfect channel state information and with modulation sizes ranging from 4-QAM to 64-QAM. The SNR loss of the proposed algorithms is below 0.1 dB in all the cases, while a conventional tracking approach is shown to have an SNR loss between 0.8 dB and 1.2 dB.