The Laurent Decomposition is the approximation for GMSK as a sum of PAM signals.
This technique is most useful for GMSK with partial response signaling, which is when we overlap subsequent pulses to send more date in less time which serves to increase the spectral efficiency at the expense of introducing intentional inter-symbol interference (ISI).
This does not simplify the transmitter, as compared to the very simple implementation I have detailed here with a Gaussian filter and NCO (which supports partial response signaling directly), but the Laurent decomposition shines in the receiver implementation for partial response GMSK. This is because the optimum receiver would need to correlate to every possible phase trajectory over the duration of symbol overlap, which creates a trellis of possibilities, with complexity increasing by the number of symbols that are overlapped. A Viterbi decoder is an efficient but still computationally intensive operation for implementing such an optimum receiver. The use of the Laurent Decomposition simplifies the Viterbi decoder by reducing the number of states in the trellis.
More details on Laurent Decomposition for GMSK can be found here. and the original paper by Pierre A. Laurent is:
"Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP)", IEEE Transactions on Communications, Vol. COM-34 No 2 February 1986. pp 150-160