As my understanding GSM is GMSK modulation.
It is a kind of FSK with Gaussian filter to filter the
output data bit. With GMSK we can have minimum
transmission bandwith and higher channel efficiency.
Not quite. You should filter the square bipolar
pulses representing data bits and then
pass them through the integrator to yield the phase
of the baseband signal and then take sine and
cosine of the phase and later mix the I/Q components obtained during the previous step with
the quadrature components of the carrier.