We mainly study on the design of noncoherent space-time code based on Grassmannian with algebraic method.First of all
we present a new family of full-rate and full-diversity coherent space-time codes with arbitrary number of transmit antennas and coherent time.Then our noncoherent space-time codes can be built from the coherent space-time codes via a non linear map called exponential map.With the same number of transmit antennas
the new noncoherent space-time code have better performance than the present code.