# Reasoning Behind Additional Phase Shift in DPSK

In MATLAB's Comm System Toolbox there is an option for 'Phase Rotation', defined as the phase difference between previous and current modulated symbols when the input is zero. This is the first time I've heard of this concept.

Let's take DQPSK as an example. Say my previous symbol had an absolute phase of $0$, (1+j0) and I am trying to encode '01'. Under the DQPSK scheme I'm familiar with, '01' corresponds to a phase shift of $\pi/2$. Therefore the absolute phase of this symbol would be $\pi/2$, (0+j1). MATLAB would describe this scheme as having a phase rotation of 0.

If the same example were to use a phase rotation as $\pi/2$ then the absolute phase of the symbol would be:

$0$ (phase of last symbol) + $\pi/2$ (shift due to modulation) + $\pi/2$ (additional phase rotation) = $\pi$

This brings me to my question. Performing the additional phase shift requires increased complexity at the receiver and transmitter. So what is to be gained from the process of adding an additional phase shift? Why do it in the first place?

• A $\pi/4$-DQPSK system changes the phase by an additional $\pi/4$ over and above the phase change (if any) dictated by the differential modulation. Thus, even a stream of $(00), (00), (00), \cdots$ data symbols causes the carrier to change phase by $\pi/4$ each time, while a stream of $(11), (11), (11),\cdots$ does not cause transitions of the carrier envelope through the origin (which helps in satellite channels with traveling-wave-tube amplifiers. – Dilip Sarwate Apr 21 '16 at 18:39

A QPSK constellation could in theory have any rotation. For example, $$\mathcal{S}=\lbrace 1, j, -1, -j \rbrace$$ is a QPSK constellation, and $e^{j\phi}\cdot\mathcal{S}$ is also a QPSK constellation. Matlab's phaserot parameter in the dpskmod command is $\phi$ in the equation above.
What is to be gained depends on the particular application I guess. In particular, note that $\phi=\pi/4$ is nice because then the ML decoding rule is equivalent to finding what quadrant the received point is in.