Algebraic relations among periods and logarithms of rank 2 Drinfeld modules

For any rank $2$ Drinfeld module ρ defined over an algebraic function field, we consider its period matrix Pρ, which is analogous to the period matrix of an elliptic curve defined over a number field. Suppose that the characteristic of the finite field Fq is odd and that ρ does not have complex multiplication. We show that the transcendence degree of the field generated by the entries of Pρ over Fq(θ) is $4$. As a consequence, we show also the algebraic independence of Drinfeld logarithms of algebraic functions which are linearly independent over Fq(θ).