This paper proposes a study of performances of the Orthogonal Four Single Sideband elements modulation previously proposed by Ohta . Realistic parameters such as receiver noise and various channel effects are introduced in the derivation of the modulation. Transmission of two QPSK signals multiplexed in one 4-SSB (Single Sideband) signal over OFDM (Orthogonal frequency-division multiplexing) is considered and a demodulation process exploiting a turbo equalizer is presented. Computer simulations are used to verify the performances of the proposed modulation scheme. Results show that 4-SSB QPSK signal over OFDM can achieve performances close to QPSK-OFDM scheme while carrying twice more information, provided perfect channel equalization. However, we also show that in a non-ideal equalization case, performances of 4-SSB QPSK OFDM become highly sensitive to channel effects.