Hi, as you may know, there are only three independent variables for the log periodic antenna design, which can be chosen from the directivity, length of the antenna, apex angle, the upper frequency and the lower frequency. [Huang, Yi and Boyle, Kevin, Antennas: From Theory to practice, Wiley, 2008 ]
Once you've choosed these three parameters (lower frequency, upper frequency and one another ) two other parameters and also construction specifications such as the number of elements, spacing between them, etc. can be obtained through the designing procedure.
Your antenna's frequncy band includes some GSM types band: GSM-750, GSM-810, GSM-850, P-GSM-900, E-GSM-900, R-GSM-900, T-GSM-900, T-GSM-900.
You should also choose proper diameter for dipoles and gap between the poles to achieve good impedance matching and VSWR < 2 for GSM. The formula is g=d*cosh(Z0/120) where g is gap and d is diameter of a dipole.