The phase response of a passband waveform at receiver is given by $$\varphi \,(f) = - 2\,\pi \,\alpha \,(f - {f_c}) - \,2\pi \beta \,{f_c}$$

where $${f_c}$$ is the centre frequency, and $$\alpha $$ and $$\beta $$ are positive constants. The actual signal propagation delay from the trasmitter to receiver is