The Problem with Standard QPSK

In standard Quadrature Phase Shift Keying (QPSK), data is encoded by shifting the phase of a carrier wave to one of four positions, allowing each state (symbol) to represent a two-bit pair, or dibit. While efficient, a critical issue can arise: when both bits of the dibit change at the same time (e.g., a transition from '00' to '11'), the signal's phase must instantly jump by 180 degrees.

This abrupt 180-degree phase shift causes problems when the signal passes through the necessary filters in a radio system. These filters can cause the signal's amplitude to fluctuate significantly, even dropping close to zero momentarily.

Why Are Amplitude Fluctuations a Problem?

• Non-Linear Amplifiers: High-power amplifiers used in transmitters work most efficiently when the signal they are amplifying has a constant amplitude. Large amplitude variations can push the amplifier into its non-linear region.
• Spectral Regrowth: When a signal with fluctuating amplitude passes through a non-linear amplifier, it can cause the signal's spectrum to "spread out" into adjacent frequency channels. This phenomenon, known as spectral regrowth, is a form of interference that can disrupt other communications.

The Solution: Offset QPSK (OQPSK)

OQPSK, or Offset Quadrature Phase Shift Keying, is an elegant modification of standard QPSK that prevents 180-degree phase jumps. The key modification is simple but powerful: the bitstream in one of the channels is deliberately delayed.

Specifically, the bitstream for the quadrature component (Q-channel) is shifted in time by half a symbol period ($T_s/2$), which is equivalent to one bit period ($T_b$), relative to the in-phase component (I-channel).

The Consequence of the Offset

Because of this time offset, the I and Q components of the signal can never change at the exact same moment. At any given transition time, only one of the two bits (either the I bit or the Q bit) can change its value. By preventing simultaneous bit changes, OQPSK eliminates the possibility of a 180-degree phase shift. The maximum possible phase change at any single transition point is now limited to $\pm 90^{\circ}$.

Visualizing OQPSK: Constellation and Transitions

At first glance, the constellation diagram for OQPSK looks identical to the one for standard QPSK. It has the same four points, typically assigned bit pairs using Gray coding to minimize bit errors.

The crucial difference lies not in the points themselves, but in the allowed transitions between them. Since only one bit (I or Q) can change at a time, transitions are restricted to movements along the horizontal or vertical axes. Diagonal transitions, which represent a 180-degree phase shift, are forbidden.

For example, from the point representing '00', the signal can transition to '01' (a vertical move, changing the Q bit) or to '10' (a horizontal move, changing the I bit). A direct transition to '11', which would require changing both bits simultaneously, is not possible. To get from '00' to '11', the signal must first pass through either '01' or '10'.

Advantages and Applications of OQPSK

The primary benefit of using OQPSK is the improved quality of the transmitted signal, especially in systems where power efficiency is critical.

• Reduced Amplitude Variations: By eliminating 180-degree phase jumps, OQPSK significantly reduces the amplitude fluctuations that occur after signal filtering.
• Improved Amplifier Performance: The more constant signal envelope makes OQPSK well-suited for systems with non-linear power amplifiers, allowing them to operate more efficiently without causing significant spectral regrowth.
• Maintained Spectral Efficiency: OQPSK offers these benefits while maintaining the same spectral efficiency as standard QPSK (2 bits/symbol/Hz). The trade-off is not in data rate, but in slightly increased complexity at the transmitter and receiver.

Due to these advantages, OQPSK and its derivatives are widely used in satellite communication systems, cellular standards like CDMA2000, and short-range wireless protocols such as Zigbee, where power amplifier efficiency and signal integrity are paramount.

Interactive OQPSK (offset) – Constellation and Time Waveform

OQPSK (offset) modulated signal

Constellation diagram