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I'm trying to build an SOQPSK-TG signal in MATLAB/Octave. I am following this paper for formulas.

I'm trying to generate a waveform for the phase, equation 2.4:

enter image description here

Where q(t) is the phase pulse, equation 2.3:

enter image description here

f is the partial-response frequency pulse (L=8 for SOQPSK-TG):

enter image description here

and w is the window function:

enter image description here

for SOQPSK-TG, we have the following values:

p = 0.7, A = 0.3112, B = 1.25, T1 = 1.5, T2 = 0.5, L = 8, h = 0.5, T = 1

One point of confusion I am seeing is that when I plot ftg(t) as written, the pulse is centered around t=0:

enter image description here

However the image of ftg in the paper shows an unexplained shift in time:

enter image description here

The formula for q(t) also supports this time shift, showing that the integral must start at t=0, and should end up at 0.5.

I can just accept for now that there is a time shift by L*T/2, so I can adjust my integration indices, and shift everything in time, no big deal: enter image description here

When I plot the resulting phase using the time shifted version of ftg, I end up with a smooth moving waveform, which is the desired behavior:

enter image description here

However, when I look at the mod(2*pi) results, and sample once per symbol-duration-period, I am seeing 8 discrete phase states:

enter image description here

The document claims I should only see 4 discrete phase states. Interestingly enough, if I don't time shift ftg, I end up with a non-smooth phase state:

enter image description here

But with this waveform I am seeing the 4 discrete phase states:

enter image description here

How can I get a smooth looking waveform with 4 discrete phase states?

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Nice! I'm trying to implement SOQPSK too... Answering the question, You actually have 8 phases since the IQ (qpsk) symbols pass through one precoder that works with 3 bits (2³ = 8 states), these are -1, 0, 1 increments that get mapped to -pi/2, 0, pi/2 changes in the phase... About the time shift on the plot that's just a different notation for time, this equation set is for the windowed RC filter coefficients and you could generate them by having the time start from 0 and go to N or by substracting (N/2) from that range yielding -N/2 to N/2. This "time" axis isn't that relevant since you just want the coefficients h(t)... Fig from paper Paper about SOQPSK

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