# BT value in GMSK signal equations

I am studying MSK/GMSK modulation technique. Before I posted 2 questions:

Mr Boschen was so kind to answer my questions. I have googles the equation to derive GMSK signal for my case and didnt find it.

In "An Approximation Method of the Continuous Phase Encoder in the Concatenated Coded GMSK System " as given the following equation:

or "Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP)"

i don’t understand how BT ( Bandwidth Time Product) is used in the equation? Is it affect to it?

For a pulse of duration $$L$$, $$BT = 1/L$$, where $$B$$ is the single-sided 3-dB bandwidth of the Gaussian filter used. In the OP's formula, it is each PAM pulse $$C_K(t)$$ that is determined by the Bandwidth-Time product. Changing $$BT$$ will both change the Gaussian frequency function (pulse shape for one symbol) and result in a different set of $$C_K(t)$$ in the decomposition.
• $C$ pulse shapes : If i convolve them with upsampled NRZ sequences, will I get an approximated or constant amplitede? I tested $c0$ and $c1$ with IQ-GMSK modulator ( work with gaussian fiter), and I got a constant amplitude of the sequence. In precoded linear approximated gmsk modulator and laurent decomposition, we speeak about approximation ... i cant undertand then my results I got Apr 7, 2022 at 9:16
• @FrHart64 Yes if you use all the $2^{L-1}$ Laurent PAM signals and convolve with the zero-stuffed NRZ sequence with proper real and imag mapping you will get the GMSK modulation. If you less than the complete set, approximately so. Be sure that your PAM pulses extend over multiple symbols properly which means to get back to constant envelope there should be a lot of overlap from pulse to pulse. Did you find Laurent's original paper (IEEE Transactions on Communications, Vol COM-34 No 2 Feb 1986)? Probably best to start with that as it explains the decomposition and combining in specific detail. Apr 7, 2022 at 9:48