Abstract: In order to study the effect of spatial correlation on the performance of space-time codes,an angular spread of multipath signals received in Rayleigh fading channels is presented with the assumption that the power distribution versus the angle of arrival(AOA) of scatter components follows the von Mises distribution.An approximative spatial correlation coefficient with a form of Gaussian function is introduced, a spatial correlation matrix for the reception uniform linear array is constructed.It is proved that the matrix is positive definite and full rank,and the determinant value of the matrix is between 0～1.A performance loss of space-time codes transmission is not in diversity gain but in coding gain only,if the space-time codeword difference matrices are full rank and in presence of the spatial correlation at the receiving end only.The design criteria for optimal space-time codes over correlated Rayleigh channels are the same as that over uncorrelated Rayleigh channels.