--- title: "MSK as CPFSK/OQPSK; compare OQPSK, MSK, GMSK" subject: "Wireless Communication" chapter: 4 key: "semester_7/wireless_communication:msk-oqpsk-gmsk-comparison" source: https://www.bctengineer.com/q/semester_7/wireless_communication/msk-oqpsk-gmsk-comparison site: BCT Engineering --- # MSK as CPFSK/OQPSK; compare OQPSK, MSK, GMSK Wireless Communication · Chapter 4: Modulation and Demodulation in Mobile Communication - Asked in: 2080 Baisakh, 3+3+2 marks - Video: [What is Minimum Shift Keyed (MSK) Modulation in Digital Communications?](https://www.youtube.com/watch?v=O87gVMLkMJY) — Iain Explains Signals, Systems, and Digital Comms - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/msk-oqpsk-gmsk-comparison - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-4 ## Question How can Minimum Shift Keying (MSK) be defined as a special type of continuous phase FSK and Orthogonal Quadrature Phase Shift Keying (OQPSK)? Compare OQPSK, MSK and GMSK in terms of their bandwidth efficiency and power efficiency. Which of them are suitable for modulation in GSM and why? ## Short answer MSK is CPFSK with modulation index h=0.5 and tone spacing Rb/2, and is OQPSK with half-sinusoidal pulse shaping. OQPSK has a narrower main lobe but slow side-lobe roll-off; MSK has a wider main lobe (1.5Rb) with faster roll-off; GMSK has the narrowest spectrum with slightly lower power efficiency. GMSK suits GSM because of its constant envelope, narrow spectrum, and allowance for nonlinear class-C amplifiers. ## Answer #### MSK as continuous phase FSK **Minimum Shift Keying (MSK)** is a binary continuous phase FSK (CPFSK) with modulation index **h = 0.5**, the minimum index for which the two tones are orthogonal over one bit (coherent detection). ```text s(t) = √(2E_b/T_b) cos(2π f_c t + θ(t)), θ(t) = ± π t / (2T_b) + θ(0) f_H − f_L = 1 / (2T_b) = R_b / 2 ``` The phase changes linearly by exactly ±π/2 in each bit and has no jumps, so the waveform is continuous and the spectrum falls off fast. #### MSK as a special OQPSK MSK can also be written as **OQPSK with half-sinusoidal pulse shaping** instead of rectangular pulses: ```text s(t) = a_I(t) cos(πt/2T_b) cos(2π f_c t) + a_Q(t) sin(πt/2T_b) sin(2π f_c t) ``` - a_I and a_Q are the even and odd bits, each lasting 2T_b. - The Q stream is offset by T_b from I (as in OQPSK). - The half-sine weighting makes the envelope constant and the phase continuous. #### Comparison | Scheme | Bandwidth efficiency | Power efficiency | Envelope | |---|---|---|---| | OQPSK | Good: main lobe R_b, but slow side-lobe roll-off | Good, BER = Q(√(2E_b/N₀)) | Nearly constant (no 180° jumps) | | MSK | Wider main lobe (1.5R_b) but fast side-lobe roll-off | Same BER as BPSK/QPSK | Constant | | GMSK | Best: very narrow spectrum (BT = 0.3) | Slightly lower (≈ 0.5–1 dB loss from ISI) | Constant | Notes on the table: in null-to-null terms, OQPSK main lobe width is R_b (narrower than MSK's 1.5R_b), but its side lobes fall slowly (1/f²); MSK side lobes fall as 1/f⁴; GMSK shrinks side lobes further. #### Suitable for GSM **GMSK** is used in GSM because: - Its **constant envelope** lets mobiles use non-linear class-C amplifiers, which are power efficient and save battery. - Its **narrow spectrum and low side lobes** give low adjacent channel interference, allowing 270.833 kbps in a 200 kHz channel. - It can be detected coherently or non-coherently, and the small ISI is handled by GSM's Viterbi equalizer. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is MSK called a special continuous phase FSK? A. It is binary CPFSK with modulation index h = 0.5, the minimum tone spacing (R_b/2) keeping tones orthogonal B. It is CPFSK with h = 1 so the phase jumps each bit C. It is CPFSK with a Gaussian filter and BT = 0.3 D. It is CPFSK with PN-code hopping Answer: A. MSK has f_H - f_L = 1/(2T_b) = R_b/2, h = 0.5, the minimum spacing for orthogonality, and the phase is continuous. (Key point: MSK as CPFSK) 2. How can MSK be viewed as OQPSK? A. As OQPSK with Gaussian pulse shaping B. As OQPSK with half-sinusoidal pulse shaping instead of rectangular pulses C. As OQPSK with no offset between I and Q D. As OQPSK with raised-cosine pulses and 180 degree jumps Answer: B. Weighting I and Q with half-sine pulses (Q offset by T_b) makes the envelope constant and the phase continuous. (Key point: MSK as OQPSK) 3. Which statement correctly compares the spectra? A. MSK has the narrower main lobe and slower side-lobe decay than OQPSK B. OQPSK has both the narrower main lobe and the faster side-lobe decay C. OQPSK has the narrower main lobe (R_b) but slow side-lobe decay; MSK has a 1.5R_b lobe but faster roll-off D. All three have identical side-lobe roll-off Answer: C. OQPSK side lobes fall as 1/f^2 and MSK's as 1/f^4, while OQPSK's main lobe is narrower. GMSK reduces side lobes further. (Key point: Spectrum comparison) 4. Why is GMSK chosen for GSM? A. It has the best BER of all three because it has no ISI B. It has a varying envelope that suits linear amplifiers C. It needs no equalizer because it has no ISI D. Constant envelope allows efficient class-C amplifiers, and its compact spectrum gives low adjacent channel interference Answer: D. GMSK keeps a constant envelope and very narrow spectrum (270.833 kbps in 200 kHz). Its slight ISI loss is handled by the Viterbi equalizer. (Key point: Why GMSK for GSM) ## Related in Wireless Communication - [MSK, GMSK and advantages of spread spectrum](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amsk-gmsk-spread-spectrum-advantages) — Wireless Communication, chapter 4 - [MSK, GMSK and OFDM modulator/demodulator](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amsk-gmsk-ofdm-modem) — Wireless Communication, chapter 4 - [MSK modulation and DSSS](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amsk-dsss) — 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 - [Short note: GMSK modulation technique](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Agmsk-short-note) — Wireless Communication, chapter 4 - [CDMA merits/demerits; GSM frame efficiency](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amultiple-access-cdma-frame-efficiency) — Wireless Communication, chapter 7 ## Related in other subjects - [Need for shift keying; ASK vs FSK vs PSK](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ashift-keying-ask-fsk-psk) — Communication Systems, chapter 7 - [ASK, FSK and PSK modulation](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aask-fsk-psk) — Data Communication, chapter 5, asked 3× - [MSK modulation scheme](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amsk-modulation) — Communication Systems, chapter 7 - [Multi-tone AM: spectrum, bandwidth, power efficiency](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aam-50-0-3-0-2-spectrum) — Communication Systems, chapter 2