The Single Sideband (SSB) modulation through Hilbert transformation has successfully transmitted data using only half bandwidth for the same amount of contained information. Towards this line, the Four Single SideBand (4-SSB) using QPSK modulation over OFDM was proposed as a new applicable modulation for the next generation communication system, such as 5G. This approach can improve the network efficiency, however, the InterSymbol Interference (ISI) is substantially introduced in 4-SSB based modulation due to the wireless channel characteristics, especially when we are increasing the order of modulation. Particularly, the Widely Linear Minimum Mean Squared Error (MMSE) equalizer is impractical in high order modulation because of its high performance degradation. In this paper, we propose a 4-SSB M-QAM over OFDM approach to improve the modulation feasibility and data rate, compared to the previous 4-SSB using QPSK over OFDM. The proposal uses the Infinite Length MMSE Soft Input Soft Output (SISO) equalizer to deal with ISI induced by the Finite Impulse Response (FIR) of the Hilbert transform filter. The evaluation results show that the proposed 4-SSB-based modulation technique using MMSE SISO equalizer can considerably reduce the effect of ISI in non-ideal environments, including the Additive White Gaussian Noise (AWGN) and fading channel.