A kind of receiver is designed for underwater acoustic communications to cope with the combined limitations of timevarying multipath and phase instabilities of the underwater channel. After quadrature demodulation and mathematical transform, the carrier phase error can be eliminated. As phaselocked loop (PLL) is not needed to track the carrier phase shift during equalization, the computational complexity can be reduced. Simulations on two different types of multipath and phase shift channels show that good performance can be achieved for the simple channel model, while satisfactory results can be obtained through multichannel diversity combining for the other channel.