I red that 180 degree phase shift causes spurious high frequency components which As a result methods such as OQPSK are invented, but I can't understand how it can happens? In fact, I can't find any connection between 180 degree phase shift and the creation of high frequency components. or for example why 90 degree doesn't cause such an effect?! I would appreciate it if you could explain.


1 Answer 1


OQPSK is used specifically to limit the peak-avg ratio of the QPSK waveform, as it avoids transitions from going through the origin. When the modulation in QPSK changes from one point in the constellation to another that is opposite (which is a 180 degree phase transition), the transition with go through or near the origin and with that result in larger variations in the magnitude of the modulated waveform. What is the real concern is the magnitude, specifically the variation in the envelope of the waveform. This leads to requiring greater back-offs in average input power to power amplifiers, to keep them running in their linear regions. The non-linearity in amplitude (not phase) leads to spectral regrowth in the output of the power amplifier. OQPSK limits transitions at any give time to adjacent instead of opposite points in the constellation, so never goes through or near the origin.

Linearity for amplifiers is often specified as "1 dB compression (P1dB)" and "2-tone third order Intercept (IP3)". Running an amplifier closer to their P1dB levels results in much greater power efficiency, which motivates waveforms with reduced peak-avg ratio such as OQPSK, pi/4 QPSK, GMSK, etc. Please also see DSP.SE #41130 where I provide further examples and details of this. This also motivates significant efforts in crest factor reduction and pre-distortion for waveforms that do have very high peak-avg ratios (such as OFDM).

To help illustrate the significance of this, below is a plot I have used to demonstrate the motivation for "pulse-shaping". The blue is if we transmitted QPSK with rectangular pulses: instantly going from one point on the constellation to any other with no transition time. The red is what we get by slowly transitioning with carefully shaped pulses so that we limit the bandwidth without introducing inter-symbol interference:

QPSK spectrum

If we drive that carefully shaped waveform into a non-linearity, in the worst case a hard limiter, we would return this to the rectangular pulse case and "regrow" the blue spectrum- hence "spectral regrowth". A typical result we may see is as shown in the plot below, the growth adjacent to the spectrum limits our ability to space two channels closer together, and ultimately frequency regulatory bodies such as the US FCC will impose a spectral mask on what can be transmitted adjacent to and within assigned frequencies, and driving a PA too hard will cause the spectral mask to fail. As another consideration, that noise adjacent to the spectrum is also within the spectrum and with that degrades waveform quality (EVM).

Spectral regrowth

Like what you see? These plots and other cool demonstrations are part of my DSP courses where I try to bring intuition together with the math involved for a deeper and more creative understanding of signal processing concepts. You can find the latest course listings at https://dsprelated.com/courses and https://ieeeboston.org/courses/ Course registration is open now for courses starting very soon in April 2024!


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