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Underwater acoustic communication systems need Doppler compensation for the server Doppler effects. OFDM (Orthogonal Frequency Division Multiplexing) is widely applied in the underwater acoustic communication systems. FFT is the most computational kernels in the OFDM systems. By exploring the two typical digital signal processing kernels and other basic kernels, an ASIP (Application Specific Instruction set Processor) has been proposed. The proposed composite function unit can reach high MOPS in most DSP kernels with less read/write ports. Also, the proposed composite function unit reduce the memory access and register file access of the FFT, which is the bottleneck of the certain implementation of the FFT. The clock speed of the proposed ASIP can reach up to 600MHz under the CMOS 90nm technology.