--- title: "PSK generation and detection; GMSK" subject: "Communication Systems" chapter: 7 key: "semester_6/communication_systems:psk-generation-detection-gmsk" source: https://www.bctengineer.com/q/semester_6/communication_systems/psk-generation-detection-gmsk site: BCT Engineering --- # PSK generation and detection; GMSK Communication Systems · Chapter 7: Digital Modulation Techniques - Asked in: 2081 Baisakh (CS II), 5+1 marks - Video: [Gaussian Minimum shift Keying-GMSK](https://www.youtube.com/watch?v=AU00f3jEXHo) — deva Sena - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/psk-generation-detection-gmsk - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-7 ## Question Briefly explain generation and detection of Phase Shift Keying (PSK) with necessary illustration. Discuss Gaussian Minimum Shift Keying (GMSK) with its advantage. ## Short answer PSK is generated by multiplying polar NRZ data (±1) with the carrier, causing 180° phase shifts. Detection uses coherent multiplication with a recovered carrier, integration, and zero-threshold decision. GMSK filters data with a Gaussian filter before MSK modulation, achieving a compact spectrum and constant envelope for efficient nonlinear amplification, as in GSM. ## Answer #### Generation of PSK In binary **Phase Shift Keying** the carrier phase is $0$ for bit 1 and $\pi$ for bit 0: $$ s(t)=\pm\sqrt{\frac{2E_b}{T_b}}\cos 2\pi f_ct,\quad 0\le t\le T_b $$ ```text data -->[polar NRZ encoder]--> b(t)=+-1 -->(X)--> BPSK ^ sqrt(2/Tb) cos 2pi fc t ``` The polar NRZ data multiplies the carrier in a product (balanced) modulator. When $b(t)$ changes sign, the output phase jumps by $180^\circ$. ```text data: 1 0 1 PSK : /\/\/\ \/\/\/ /\/\/\ ``` #### Detection of PSK (coherent) ```text x(t)-->(X)-->[integrate 0..Tb]--x-->[decision x>0 ? 1 : 0] ^ carrier recovery (squaring loop / Costas loop) ``` 1. The receiver regenerates a carrier exactly in phase with the transmitted one (e.g. square the signal, extract $2f_c$ with a PLL, divide by 2). 2. The product $x(t)\cos\omega_ct$ is integrated over the bit, giving $x=\pm\sqrt{E_b}$ + noise. 3. A zero-threshold decision device outputs 1 for $x>0$ and 0 for $x<0$. Signal space: two antipodal points $\pm\sqrt{E_b}$ on $\phi_1$; $P_e=\tfrac12\text{erfc}\sqrt{E_b/N_0}$. Envelope detection is impossible because the envelope is constant. #### GMSK **Gaussian Minimum Shift Keying** is MSK in which the NRZ data is first passed through a **Gaussian low-pass filter** before it frequency-modulates the carrier with $h=0.5$. ```text NRZ data ->[Gaussian LPF, BT]->[FM mod, h=0.5]-> GMSK ``` - The filter smooths the sharp transitions, so the phase changes gradually and the spectrum becomes very compact. - The product $BT$ (filter 3-dB bandwidth × bit period) sets the trade-off; GSM uses $BT=0.3$. - Some intersymbol interference is introduced, but it is small for $BT\ge0.3$. **Advantages:** narrow main lobe and very low sidelobes (less adjacent-channel interference), constant envelope so efficient class-C power amplifiers can be used (long battery life), and simple non-coherent or coherent detection. These are why GSM uses GMSK (DECT and Bluetooth use the closely related Gaussian FSK, GFSK). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is BPSK generated? A. Unipolar data gates the carrier B. Polar NRZ data multiplies the carrier in a balanced modulator C. Data frequency-modulates a VCO D. Two carriers are summed Answer: B. Each sign change of b(t) causes a 180-degree phase jump. (Key point: PSK generation) 2. How is the carrier recovered for coherent PSK detection? A. Pass the signal through an envelope detector B. Use a low-pass filter on the received signal C. Square the signal, extract 2fc with a PLL, then divide by 2 (squaring or Costas loop) D. Delay the signal by Tb Answer: C. PSK has no carrier component, so a squaring or Costas loop regenerates it. (Key point: Carrier recovery) 3. How is GMSK made? A. MSK output is filtered by a Gaussian BPF B. Data is Gaussian filtered then used for PSK C. Data is squared before MSK D. NRZ data passes through a Gaussian LPF before frequency modulating with h = 0.5 Answer: D. Gaussian filtering smooths the transitions of the MSK modulating signal. (Key point: GMSK construction) 4. Why is GMSK used in GSM? A. Compact spectrum with low sidelobes and constant envelope allowing efficient class-C amplifiers B. It has zero ISI C. It has a larger main lobe than MSK D. It needs linear amplifiers Answer: A. Smooth phase transitions reduce adjacent-channel interference, and constant envelope saves battery. 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