Offset QPSK (OQPSK) | Teleinf Edu

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 . Under the usual Gray mapping, a transition between opposite points such as '00' and '11' changes both bits and requires a 180-degree phase reversal.

This abrupt 180-degree phase shift causes problems when the signal passes through the necessary filters in a radio system. After filtering, the signal's amplitude can vary and may approach zero at some instants.

Why are amplitude fluctuations a problem?

Non-linear amplifiers: Power amplifiers used in transmitters operate most efficiently with signals whose envelope varies little. 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, its spectrum can extend into adjacent frequency channels. This phenomenon, known as , is a form of interference that can disrupt other communications.

The solution: Offset QPSK (OQPSK)

OQPSK, or Offset Quadrature Phase Shift Keying, delays one branch of standard QPSK so that the two branches do not switch at the same instant. This prevents direct 180-degree phase reversals in the ideal rectangular-pulse model.

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

With ideal timing, the I and Q components of the signal switch at different instants. At a transition, only one branch changes its value, so the phase moves to an adjacent constellation point. OQPSK therefore limits the phase change at a single transition to $\pm 90^{\circ}$ instead of 180 degrees.

Visualizing OQPSK: constellation and transitions

The OQPSK constellation has the same four points as standard QPSK, typically assigned bit pairs with Gray coding to reduce bit errors.

OQPSK changes the allowed transitions between those points. Since only one bit (I or Q) changes at a time, transitions follow the horizontal or vertical axes. Diagonal transitions, which represent a 180-degree phase shift, are excluded.

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 main benefit of OQPSK is lower envelope variation after pulse shaping, which helps systems that use power-efficient but non-linear amplifiers.

Reduced amplitude variations: By eliminating direct 180-degree phase reversals, OQPSK reduces the amplitude fluctuations that can occur after signal filtering.
Improved amplifier performance: The more stable signal envelope suits OQPSK to systems with non-linear power amplifiers and can reduce spectral regrowth when the amplifier is operated within its design limits.
Maintained spectral efficiency: OQPSK carries the same two bits per symbol as QPSK and has the same spectral efficiency with identical pulse shaping. For a raised-cosine Nyquist pulse with roll-off factor $\alpha$ , the ideal spectral efficiency is $\eta = 2/(1 + \alpha)$ bit/s/Hz. The added cost is the offset timing and synchronization circuitry, with the symbol rate unchanged.

OQPSK and related offset or filtered schemes are used in satellite and spread-spectrum systems. IEEE 802.15.4-based short-range protocols such as Zigbee use OQPSK, while cdma2000 uses HPSK on its reverse link rather than plain OQPSK.