--- title: "OQPSK transmitter/receiver and π/4-QPSK" subject: "Wireless Communication" chapter: 4 key: "semester_7/wireless_communication:oqpsk-pi4-qpsk" source: https://www.bctengineer.com/q/semester_7/wireless_communication/oqpsk-pi4-qpsk site: BCT Engineering --- # OQPSK transmitter/receiver and π/4-QPSK Wireless Communication · Chapter 4: Modulation and Demodulation in Mobile Communication - Asked in: 2071 Bhadra, 5+2 marks - Video: [OQPSK and pi/ 4 QPSK](https://www.youtube.com/watch?v=YLBR-fAO_u0) — Sheershendu Bhattacharya - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/oqpsk-pi4-qpsk - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-4 ## Question Explain the transmitter and receiver of OQPSK modulation. Discuss why π/4-QPSK is more preferred than OQPSK modulation. ## 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. ## Answer **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 ```text +->[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** ```text I: | a0 | a2 | a4 | Q: | a1 | a3 | a5 | <-Tb-> ``` #### OQPSK receiver ```text +->(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). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the offset in OQPSK? A. The Q stream is delayed by T_b relative to I, so the phase changes at most 90 degrees B. I and Q change simultaneously every 2T_b C. The carrier frequency is offset by R_b D. The Q stream is advanced by 2T_b Answer: A. I and Q never change at the same instant, avoiding 180 degree jumps and reducing envelope fluctuation. (Key point: OQPSK offset) 2. How does OQPSK's BER compare with QPSK? A. Twice as bad B. The same, Q(sqrt(2Eb/N0)) C. Much better by 3 dB D. Worse by 3 dB because of the delay Answer: B. The offset only changes timing, not the orthogonal detection. (Key point: OQPSK BER) 3. What phase changes does pi/4-QPSK produce? A. Only +/-90 degrees B. 0 or 180 degrees C. +/-45 or +/-135 degrees at each symbol D. Only 0 degrees Answer: C. Two QPSK constellations rotated by 45 degrees are used alternately; maximum jump is 135 degrees. (Key point: pi/4-QPSK phase) 4. Why is pi/4-QPSK preferred to OQPSK in mobile systems? A. It has a perfectly constant envelope B. It needs coherent detection C. It has lower BER than OQPSK coherently D. It allows differential (non-coherent) detection, which suits fast-fading channels Answer: D. pi/4-DQPSK avoids carrier recovery and always has a phase change that aids timing, so it was chosen for IS-54/IS-136 and PDC. 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