A coded excitation has been studied to improve the performance for ultrasound imaging in term of SNR, imaging frame rate, contrast to tissue ratio, and so forth. However, it requires a complicated arbitrary waveform transmitter for each active channel that is typically composed of a multi-bit Digital-to-Analog Converter (DAC) and a linear power amplifier (LPA). Not only does the LPA increase the cost and size of a transmitter block, but it consumes much power, increasing the system complexity further and causing a heating-up problem. This paper proposes an optimized 1.5bit fourth order sigma-delta modulation technique applicable to design an efficient arbitrary waveform generator with greatly reduced power dissipation and hardware. The proposed SDM can provide a required SQNR with a low over-sampling ratio of 4. To this end, the loop coefficients are optimized to minimize the quantization noise power in signal band while maintaining system stability. In addition, the decision level for the 1.5 bit quantizer is optimized for a given input waveform, which results in the SQNR improvement of more than 5dB. Computer simulation results show that the SQNR of a FM(frequency modulated) signal generated by using the proposed method is about 26dB, and the peak side-lobe level (PSL) of its compressed waveform on receive is -48dB.