The energy efficiency and bandwidth efficiency are two important criterion in designing a modulation scheme Especially the constant envelope property must be considered as in the non-linear channel tht exit, for example in the nonlinear amplifiers for satellite repeater. The Q$^{2}$AM(Quadrature Quadrature Amplitude Modulation) is a new modulation scheme which combines the Q$^{2}$PSK(Quadrature Quadrature Phase Shift Keying) scheme which increases the signal space dimension and the QAM scheme which increases the bandwidth efficiency using the multi-level signal. The Q$^{2}$AM scheme has by far superior spectrum efficiency compared with the existing modulation schemes. Applying this scheme in the non-linear communication system increses the bandwidth efficiency but cannot envelop property. In this paper, a new system architecture is suggested which satisfies the large spectrum efficiency and constant envelope property by implementing the linear block coding prior to the Q$^{2}$AM modulation. the system has improved in performance by gaining the constant envelope and the additional coding gain. We able to observe the performance improvement of the suggested system(at BER=10$^{-5}$ ) of 4.4 dB for the 16-QAM and 0.7 dB for the Q$^{2}$PSK under the exact spectrum efficiency.