It has been recently shown that zero padding (ZP)-orthogonal frequency-division multiplexing (OFDM) is a promising candidate for 6G wireless systems requiring joint communication and sensing. In this paper, we consider a multiuser uplink scenario where users are separated in power domain, i.e., non-orthogonal multiple access (NOMA), and use ZP-OFDM signals. The uplink transmission is grant-free and users are allowed to transmit asynchronously. In this setup, we address the problem of time synchronization by estimating the timing offset (TO) of all the users. We propose two non-data-aided (NDA) estimators, i.e., the joint method of moment (JMoM) and the successive moment cancellation (SMC), that employ the periodicity of the second order moment (SoM) of the received samples for TO estimation. Moreover, the coding assisted (CA) version of the proposed estimators, i.e., CA-JMoM and CA-SMC, are developed for the case of short observation samples. We also extend the proposed estimators to multiuser multiple-input multiple-output (MIMO) systems. The effectiveness of the proposed estimators is evaluated in terms of lock-in probability under various practical scenarios. Simulation results show that the JMoM estimator can reach the lock-in probability of one for the moderate range of (Formula presented.) values. While existing NDA TO estimators in the literature either offer low lock-in probability, high computational complexity that prevents them from being employed in MIMO systems, or are designed for single-user scenarios, the proposed estimators in this paper address all of these issues.

The zero padding (ZP) variants of orthogonal frequency-division multiplexing (OFDM) exhibit a lower bit error rate (BER) and higher energy efficiency compared to their cyclic prefix (CP) counterparts. However, the employment of ZP-OFDM demands strict time synchronization, which is challenging in the absence of pilots or CP. Moreover, time synchronization in OFDM systems is even more challenging when impulsive noise is present. It is well known that urban noise, which consists largely of impulsive noise generated by spark plugs used in internal combustion engines, switching and industrial activities, and discharge of high voltage distribution lines, has a strong influence on digital mobile communications. In this paper, we propose a new low-complexity approximate maximum likelihood (A-ML) timing offset (TO) estimator for ZP multiple-input multiple-output (MIMO)-OFDM in impulsive-noise environments. Performance comparison of the A-ML estimator with existing TO estimators demonstrates a superior performance in terms of lock-in probability with similar computational complexity. Also, compared to the optimal ML TO estimator, it offers a significantly lower computational complexity with negligible performance loss. The A-ML estimator can be employed for both frame and symbol synchronization.