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OQPSK transmitter/receiver and π/4-QPSK

Short answer

OQPSK delays the Q stream by one bit so only plus or minus 90 degree phase jumps occur, keeping the envelope nearly constant. pi/4-QPSK alternates two 45-degree-rotated constellations, allowing differential non-coherent detection, easier timing recovery, and maximum 135 degree jumps, so it is preferred for mobile cellular standards.

Explain the transmitter and receiver of OQPSK modulation. Discuss why π/4-QPSK is more preferred than OQPSK modulation.

Offset QPSK (OQPSK) is QPSK in which the Q bit stream is delayed by one bit period T_b (half a symbol) relative to the I stream. Because I and Q never change at the same instant, the phase can change by at most ±90°, never 180°. This keeps the envelope nearly constant after filtering and non-linear amplification.

OQPSK transmitter

           +->[I: even bits]------------>(x)--+
           |   (2T_b each)                ^   |
bits->[S/P]                          cos ωct (+)->OQPSK
           |                              v   |
           +->[Q: odd bits]->[Delay T_b]->(x)-+
                                     sin ωct
  1. NRZ data is split into I (even) and Q (odd) streams, each of duration 2T_b.
  2. The Q stream is delayed by T_b.
  3. I modulates cos ω_ct, Q modulates sin ω_ct, and the two are added.

Timing

I: |  a0  |  a2  |  a4  |
Q:    |  a1  |  a3  |  a5  |
      <-Tb->

OQPSK receiver

       +->(x)->[∫ 2T_b]->[Decide]-----------+
       |  cos ωct                           |
r(t)-->+                                 [P/S]-> bits
       |  sin ωct                           |
       +->(x)->[∫ 2T_b, offset T_b]->[Decide]+

Coherent I and Q correlators recover each stream; the Q integrator is offset by T_b. Decisions are combined by a parallel-to-serial converter. BER equals that of QPSK/BPSK: Q(√(2E_b/N₀)).

Why π/4-QPSK is preferred over OQPSK

In π/4-QPSK, two QPSK constellations rotated by 45° are used alternately, so each symbol causes a phase change of ±45° or ±135°.

  • Non-coherent (differential) detection is possible. π/4-QPSK can be differentially encoded and detected, which avoids carrier recovery and works well in fast-fading mobile channels. OQPSK needs coherent detection.
  • The maximum phase jump (135°) is smaller than QPSK's 180°, so envelope fluctuation is still low (between QPSK and OQPSK).
  • There is always a phase change every symbol, which helps timing recovery.

For these reasons π/4-DQPSK was chosen for IS-54/IS-136 (US digital cellular) and PDC (Japan).

✓ Answer checked by Claude Opus 5.5 (high effort)

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