The graded quotients of the logarithmic higher ramification groups of a local field of characteristic p¿0 are abelian groups killed by p. Their character groups are canonically embedded in some spaces of twisted differential forms. Using the embeddings, we define the characteristic cycle of an l-adic sheaf, satisfying a certain conditions, as a cycle on the logarithmic cotangent bundle and prove that the intersection with the 0-section gives the characteristic class.