The Problem with Simple PSK: Phase Ambiguity

To understand why DPSK is so useful, we must first look at the main challenge of standard Coherent PSK (CPSK). In CPSK, the receiver needs to know the exact reference phase to correctly interpret the transmitted bits. Imagine a compass: if your compass and my compass both point north, and I tell you "go east," you'll know where to go.

But what if your compass is miscalibrated and points south instead of north? Now, my instruction "go east" will send you west. This is the problem of phase ambiguity. In real communication systems, the signal's phase can be shifted by the transmission channel or by slight imperfections in the transmitter's and receiver's oscillators. The entire constellation of symbols might rotate. For example, a 180° phase shift would cause the receiver to interpret every '0' as a '1' and every '1' as a '0', leading to a complete inversion of the transmitted data and total communication failure.

The Differential Solution: Encoding the Change

DPSK cleverly solves the phase ambiguity problem by encoding information not in the absolute phase of the signal, but in the change in phase between consecutive symbols.

Instead of saying "go east" (an absolute direction), the instruction becomes "turn 90° clockwise from your current position." This relative instruction works even if our compasses are misaligned, as long as they are consistent.

Example: Differential BPSK (DBPSK)

In the simplest form, DBPSK, we use two phase shifts to represent the data:

• Input Bit '0': Keep the phase the same as the previous symbol (a $0^{\circ}$ shift).
• Input Bit '1': Change the phase by $180^{\circ}$ relative to the previous symbol.

The process requires an initial reference bit to start. Let's see how the sequence $1011$ is transmitted, starting with a reference phase of $0^{\circ}$:

Interactive DPSK – Differential Encoding and Time Waveform

DPSK modulated signal

Differential phase Δφ(t)

The Trade-Offs: Performance, Robustness, and Simplicity

Like every engineering solution, DPSK comes with a set of advantages and disadvantages compared to its coherent counterpart, CPSK.