A blind equalization approach called

l

0

-norm constraint fractionally spaced sparse adaptive dual-mode algorithm is proposed for multiple phase shift keying (MPSK) signal in deep fading sparse multipath channels.Based on the traditional fractionally spaced dual-mode blind equalization algorithm

and motivated by the sparse adaptive filter theory

a fractionally spaced dual-mode least mean square error cost function with the

l

0

-norm penalty on the equalizer tap coefficients is constructed.Then

the u

pdate formula of the tap coefficients is derived according to the gradient descent method.Moreover

the iteration step is updated adaptively by drawing upon the normalized proportionate factor.Theoretical analysis and simulation results show that compared with the sparse blind equalization algorithm based on the threshold

the blind equalization algorithm based on the fractional order norm and the fractionally spaced dual-mode blind equalization algorithm

the proposed algorithm has advantages in increasing the convergence rate and decreasing the residual inter-symbol interference.The presented blind equalization algorithm provides a fast and effective method for receivers to recover transmitted signals in underwater acoustic communication systems.