Generalized frequency-division multiplexing is one of the multi-carrier modulation schemes currently under study for beyond fifth generation (B5G) cellular systems. The main characteristics of generalized frequency-division multiplexing (GFDM) are the flexible time-frequency structure of data blocks, making it customizable according to various service requirements in B5G scenarios, and the low out of band (OOB) emission, which can be achieved by means of a flexible time-domain pulse shaping of individual sub-carriers. With this motivation, a new pulse shaping filter is proposed and its benefits on the OOB emission and on the symbol error probability (SEP) are demonstrated. The eye diagram, used as a performance evaluation parameter at the transmitter, shows that the proposed pulse has better vertical sharpness than root-raised cosine (RRC) filter and, therefore, it gives better OOB emission. Along with vertical sharpness, it has better horizontal sharpness, which means that the proposed pulse has better tolerance to inter-symbol interference (ISI). The SEP performance is evaluated by means of Monta Carlo simulations in case of 16-QAM transmission over an AWGN channel. Analytical expressions of SEP are also presented.

Due to its low out-of-band emission and high spectral efficiency, the generalized frequency division multiplexing (GFDM) has been adopted as one of the most prominent waveform techniques for the 5G networks. To further combat the deep fading, the space time coding (STC) can be integrated with the GFDM system which provide high diversity gain that results into low symbol error rate at the receiver. In this article, a generalized model of space time coded GFDM system (STC-GFDM) has been proposed. More precisely, a comprehensive analytical framework to compute the average symbol error rate (ASER) is introduced, which can be used for any MIMO configuration, code rate, and arbitrary fading channel. The proposed framework has wider applicability over generalized fading channels and having more accurate exact solution along with easy to evaluate approximate solution. Thus, the proposed framework extends the horizon of performance analysis of STC-GFDM system over any fading scenario, that is not covered so far in the literature. In general, the closed from expressions of exact and approximate along with asymptotic ASER are derived for different fading channels using moment generating function (MGF) approach. Particularly, the ASER analysis has been performed analytically using derived expression over Rayleigh, TWDP, Nakagami-q, and Nakagami-m fading channels for 𝜇-ary quadrature amplitude modulation (𝜇-QAM). This analysis confirms that with the increase in transmit and receive antenna and decrease in modulation order, the ASER performance improves for all fading channels. Also, the improvement in ASER is observed as the power of specular components (ie, LOS paths) increases. Furthermore, these analytical results are validated using Monte-Carlo simulation.