Error performance of QAM GFDM waveform with CFO under AWGN and TWDP fading channel

Generalized frequency division multiplexing (GFDM) is a strong contender waveform for 5G cellular communications. This letter derives closed form symbol error rate (SER) expressions with carrier frequency offset (CFO) in the presence of additive white gaussian noise (AWGN) channel for 1. normal BPSK, QPSK and 16-QAM-GFDM and 2. Time shift and Frequency shift, offset QPSK (OQPSK) and offset 16-QAM GFDM waveforms. This letter also derives SER expressions under TWDP fading channel for BPSK and QPSK GFDM waveforms. It is observed that under AWGN channel 1. SER performance of frequency shift offset QAM (FS-OQAM) GFDM is better than conventional MF, ZF and MMSE receivers and 2. FS-OQAM-GFDM slightly outperforms time shift OQAM(TS-OQAM) GFDM at higher values of CFO. The performance analysis studies show that TWDP fading can result in a performance poorer than Rayleigh fading when two specular components which are equal in strength and antiphase cancel each other for $\bar{K} > 6\mathbf{dB}$. The numerically evaluated results are in close agreement with the simulated results.