Underwater wireless communication using ultrasound faces significant challenges due to narrower band channels and a lower transmission rate. Although higher-order quadrature amplitude modulation (QAM) is predominantly used for wireless communication in air, quadrature phase-shift keying (QPSK), with its constant envelope, remains crucial for underwater communication. On the other hand, with its narrower modulation bandwidth, military standard shaped-offset quadrature phase-shift keying (MIL-STD SOQPSK) is expected to provide better band efficiency than QPSK. In this paper, we studied the effectiveness of MIL-STD SOQPSK using numerical simulations, comparing its bit error rate (BER) performance with that of QPSK. We propose a detector for MIL-STD SOQPSK using 3-bit length matched filters and maximum likelihood estimation, assuming that the transmitting symbols are unknown and are independent and identically distributed. The results showe lower BERs for MIL-STD SOQPSK than for QPSK under the narrowband channel condition.