One of the major purposes for fifth generation (5G) communications waveform design is to relax the synchronisation requirements for supporting efficient massive machine type communications (MTC). Polynomial cancellation coded orthogonal frequency-division multiplexing (PCC-OFDM) and universal filtered multi-carrier (UFMC) are designed to reduce the sidelobes of the orthogonal frequency division multiplexing (OFDM) waveform to protect against intercarrier interference (ICI) in the 5G uplink. To the best of our knowledge, there is no analysis of the effect of ICI for the UFMC system with time offset transmissions that many arise in MTC scenarios. Furthermore, there is no study on reducing the computational complexity of the UFMC system. This paper provides closed-form expressions for time offsets interference in such a case for OFDM, PCC-OFDM and UFMC. This paper also presents theoretical analysis for the signal-to-interference-plus-noise ratio (SINR), achievable rate and bit error ratio (BER) performance. The results show that PCC-OFDM significantly protects against ICI at the cost of halving the spectral efficiency. UFMC improves the ICI and intersymbol interference (ISI) protection performance, especially when the length of time offset is very small, at the cost of significantly increasing the computational complexity. Finally, this paper proposes the overlap and add UFMC (OA-UFMC) and a variant of UFMC using infinite impulse response prototype filter banks (IIR-UFMC) to reduce the processing complexity.