--- title: "QPSK transmission and detection" subject: "Wireless Communication" chapter: 4 key: "semester_7/wireless_communication:qpsk-transmission-detection" source: https://www.bctengineer.com/q/semester_7/wireless_communication/qpsk-transmission-detection site: BCT Engineering --- # QPSK transmission and detection Wireless Communication · Chapter 4: Modulation and Demodulation in Mobile Communication - Asked in: 2081 Bhadra, 8 marks; 2075 Bhadra, 6 marks; 2074 Magh, 5 marks; 2072 Magh, 8 marks (asked 4 times) - Video: [QPSK Quadrature Phase Shift Keying (Basics, Modulator, Waveforms, Demodulator & Applications)](https://www.youtube.com/watch?v=ij760lCUtfw) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/qpsk-transmission-detection - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-4 ## Question Explain the transmission and detection process of QPSK modulation technique with appropriate figure and constellation diagram. ## Short answer QPSK maps 2 bits per symbol to one of four phases via S/P split into I and Q BPSK streams on cosine and sine carriers. Coherent receiver multiplies by recovered cos and sin, integrates, decides, then P/S combines bits. BER equals BPSK. ## Answer **Quadrature Phase Shift Keying (QPSK)** is a 4-level PSK in which each symbol carries **2 bits**, and the carrier takes one of four phases (π/4, 3π/4, 5π/4, 7π/4). For the same bandwidth it carries twice the data rate of BPSK, so it has twice the bandwidth efficiency (2 bps/Hz ideally) with the same bit error rate. ```text s_i(t) = √(2E_s/T_s) cos(2π f_c t + (2i − 1)π/4), i = 1..4 ``` It can be written as two BPSK signals in quadrature: an in-phase (I) part on cos and a quadrature (Q) part on sin. #### Constellation diagram ```text Q | 01 • | • 00 | -----------+----------- I | 11 • | • 10 | ``` Gray coding is used, so neighbouring points differ by only one bit. Distance between neighbouring points = √(2E_s). #### QPSK transmitter ```text +-> [I: odd bits ] -> (x) --+ | [NRZ, Rb/2 ] ^ | bits ->[S/P] cos ωct (+)-> QPSK (Rb) | v | +-> [Q: even bits] -> (x) --+ [NRZ, Rb/2 ] sin ωct ``` 1. The unipolar data at rate R_b is converted to bipolar NRZ (±1). 2. A serial-to-parallel converter splits it into the I stream (odd bits) and Q stream (even bits), each at R_b/2. 3. Each stream may pass a pulse-shaping filter (e.g. raised cosine) to limit bandwidth. 4. The I stream multiplies cos(ω_c t) and the Q stream multiplies sin(ω_c t); the two BPSK signals are added to give QPSK. #### QPSK receiver (coherent detection) ```text +-> (x) -> [LPF/Integ] -> [Decision] -+ | cos ωct | QPSK -> [BPF] [P/S]-> bits | sin ωct | +-> (x) -> [LPF/Integ] -> [Decision] -+ ^ [Carrier recovery] ``` 1. The input passes a band-pass filter to remove out-of-band noise. 2. A carrier recovery circuit produces coherent cos and sin references. 3. Two correlators (multiplier + integrator over T_s) recover the I and Q components. 4. Decision circuits compare each output with zero to decide 1 or 0. 5. A parallel-to-serial converter combines the two streams into the original bit stream. #### Properties - Bit error rate: P_b = Q(√(2E_b/N₀)), same as BPSK. - Phase changes of up to 180° can occur, which causes envelope dips after filtering; OQPSK and π/4-QPSK reduce this. - Used in satellite links, CDMA (IS-95), WCDMA and LTE. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How many bits does each QPSK symbol carry? A. 1 B. 2 C. 4 D. 8 Answer: B. QPSK has four phases, each carrying 2 bits, for twice the bandwidth efficiency of BPSK. (Key point: Bits per symbol) 2. The QPSK transmitter splits bits into I and Q streams, which are: A. Both multiplied by cos B. Multiplied by cos (I) and sin (Q) and added C. Multiplied and subtracted from noise D. Sent without carrier Answer: B. Two BPSK signals in quadrature are added to form QPSK; each stream runs at Rb/2. (Key point: Transmitter structure) 3. What does Gray coding ensure in QPSK? A. Neighbouring points differ by one bit B. All points have the same bits C. Higher power D. No phase jumps Answer: A. Adjacent constellation points differ by a single bit, so a neighbour-decision error gives one bit error. (Key point: Gray coding) 4. In the coherent receiver, each decision circuit: A. Compares the correlator output with zero to decide 1 or 0 B. Uses the carrier phase only C. Measures delay D. Applies FFT Answer: A. Two correlators recover I and Q, each compared with zero, then P/S combines the bits. (Key point: Detection) ## Close variants set in other exams - [GMSK transmission and detection](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Agmsk-transmission-detection) — Wireless Communication, chapter 4, asked 5× ## Related in Wireless Communication - [Short note: GMSK modulation technique](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Agmsk-short-note) — Wireless Communication, chapter 4 - [Digital vs analog modulation; GMSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adigital-modulation-gmsk) — Wireless Communication, chapter 4 - [OQPSK transmitter/receiver and π/4-QPSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aoqpsk-pi4-qpsk) — Wireless Communication, chapter 4 ## Related in other subjects - [QAM modulation, demodulation and constellation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aqam-mod-demod-constellation) — Communication Systems, chapter 7 - [Multilevel modulation significance; QPSK](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amultilevel-modulation-qpsk) — Communication Systems, chapter 7 - [QPSK modulation and demodulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aqpsk-mod-demod) — Communication Systems, chapter 7 - [Constellation diagram significance; E1 vs T1](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aconstellation-significance-e1-t1) — Communication Systems, chapter 5