As the Hilbert transform is known as the main cause of intersymbol interference (ISI) in single-sideband generation (SSB), the design and performance evaluation of relevant equalizers over Hilbert transform with different numbers of taps is critical to minimize the ISI effect. In this paper, we develop a mathematical model of Hilbert transform with the different number of taps with the relevant equalizers over four single-sideband (4-SSB), given that 4-SSB modulation can carry a double amount of information while using half of the bandwidth compared to the conventional modulation of SSB. As expected, the evaluation results demonstrate that the soft-input soft-output (SISO) Turbo equalizer has degraded the ISI issue with small number of tap since the Hilbert transform is showed to work empirically in the case of small tap number. Similarly, the Shadow equalizer verifies the benefits and robustness of the Hilbert transform effect with the lowest number of taps, particularly Bit Error Rate (BER) performance is converged when the number of taps is greater than 15. This demonstrates a new insight into applying the SISO Turbo and Shadow equalizer using the novel concept of 4-SSB modulation for data transmission in the case of coded and uncoded wireless environments, respectively, toward 5G communication networks and beyond.