--- title: "GSM signal processing (speech to radio)" subject: "Wireless Communication" chapter: 8 key: "semester_7/wireless_communication:gsm-signal-processing" source: https://www.bctengineer.com/q/semester_7/wireless_communication/gsm-signal-processing site: BCT Engineering --- # GSM signal processing (speech to radio) Wireless Communication · Chapter 8: Wireless Systems and Standards - Asked in: 2081 Baisakh, 8 marks; 2071 Bhadra, 8 marks (asked 2 times) - Video: [GSM Speech Coding, Authentication and Security](https://www.youtube.com/watch?v=wcUGMsCxxso) — WIT Solapur - Professional Learning Community - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/gsm-signal-processing - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-8 ## Question What are the basic signal processing operations to be performed to convert a speech signal into a radio signal and back in GSM? Explain with necessary figures. ## Short answer The transmitter chain is A/D (8 kHz, 13-bit), RPE-LTP speech coding to 13 kbps, channel coding to 22.8 kbps, interleaving over 8 bursts, A5 ciphering, burst formatting, and GMSK modulation. The receiver reverses these steps with equalization, de-interleaving, channel decoding, and speech decoding. ## Answer In GSM, speech goes through a chain of digital operations that compress it, protect it against errors, secure it and fit it into TDMA bursts before GMSK modulation. The receiver reverses the chain. ```text TRANSMITTER speech->[A/D 8kHz,13bit]->[Speech coder RPE-LTP] ->[Channel coder]->[Interleaver]->[Ciphering A5] ->[Burst formatting]->[GMSK mod]->[Freq hop/RF] | channel RECEIVER | speech<-[D/A]<-[Speech decoder]<-[Channel decoder] <-[De-interleaver]<-[Deciphering]<-[Burst disassembly]<-[Equalizer+GMSK demod]<-[RF] ``` #### 1. Speech coding - Speech is sampled at 8 kHz, 13 bits (104 kbps). - The **RPE-LTP** (Regular Pulse Excited – Long Term Prediction) coder compresses each 20 ms block into **260 bits** → **13 kbps**. - Bits are graded by importance: Class Ia (50 bits), Class Ib (132 bits), Class II (78 bits). #### 2. Channel coding - Class Ia: 3 parity (CRC) bits added for error detection. - Class Ia + parity + Class Ib + 4 tail bits = 189 bits → **rate 1/2 convolutional code (K = 5)** → 378 bits. - Class II (78 bits) sent uncoded. - Total = 378 + 78 = **456 bits per 20 ms = 22.8 kbps**. #### 3. Interleaving - The 456 bits are split into **8 blocks of 57 bits** and spread diagonally over **8 consecutive bursts** (each burst carries halves from two speech frames). A burst lost in a deep fade only damages 1/8 of a frame, which the decoder can correct. #### 4. Ciphering - Data is XORed with a key stream from the **A5** algorithm using the session key **Kc** (from A8 and the SIM's Ki), giving privacy over the air. #### 5. Burst formatting - Each 114-bit pair (2 × 57) gets 3+3 tail bits, 2 stealing flags, 26-bit training sequence and 8.25 guard bits → **156.25-bit normal burst**, sent in one time slot (576.9 µs). #### 6. Modulation - **GMSK with BT = 0.3** at 270.833 kbps; constant envelope allows efficient non-linear amplifiers; 200 kHz channel. - Optional **slow frequency hopping** (217 hops/s) adds diversity. #### Receiver side 1. RF reception and down-conversion. 2. **Adaptive equalizer** (Viterbi/MLSE) uses the 26-bit training sequence to undo multipath ISI; GMSK demodulation. 3. Burst disassembly, **deciphering** with the same A5/Kc. 4. **De-interleaving** of 8 bursts. 5. **Channel decoding** (Viterbi decoder) and CRC check; a bad frame is replaced by extrapolation of the previous one. 6. **Speech decoding** (RPE-LTP) and D/A conversion back to audio. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The RPE-LTP coder compresses each 20 ms speech block into how many bits? A. 456 bits (22.8 kbps) B. 260 bits (13 kbps) C. 104 bits D. 189 bits Answer: B. RPE-LTP gives 260 bits per 20 ms = 13 kbps; 456 bits is after channel coding. (Key point: Speech coder output) 2. How does channel coding get from 260 bits to 456 bits per 20 ms? A. Class Ia + Ib + parity + tail (189 bits) is rate-1/2 coded to 378, plus 78 uncoded Class II bits B. All 260 bits are rate-1/2 coded to 520 and then punctured to 456 C. Only Class II is coded; Class I is sent raw D. Repetition of 260 bits by 1.75 times Answer: A. 378 + 78 = 456 bits; the least important Class II bits are sent uncoded. (Key point: Channel coding) 3. Why are the 456 bits interleaved over 8 bursts? A. So a burst lost in a deep fade damages only 1/8 of a frame, which the decoder can correct B. To encrypt the data C. To reduce the bit rate D. To add the training sequence Answer: A. Interleaving spreads burst errors so the channel decoder faces scattered errors it can fix. (Key point: Interleaving purpose) 4. At the receiver, what does the adaptive equalizer use to undo multipath ISI? A. The stealing flags B. The tail bits only C. The A5 key stream D. The 26-bit training sequence Answer: D. The known training sequence in the burst lets the Viterbi/MLSE equalizer estimate the channel. (Key point: Equalizer role) ## Related in Wireless Communication - [Characteristics of speech signal](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-characteristics) — Wireless Communication, chapter 6 - [Waveform/voice coding and GSM codec](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Awaveform-voice-coding-gsm-codec) — Wireless Communication, chapter 6 - [Speech characteristics and linear predictive coder](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-lpc) — Wireless Communication, chapter 6, asked 5× - [Need for speech coding; vocoder concept](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-coding-need-vocoder) — Wireless Communication, chapter 6, asked 2× - [Formant vocoder and speech characteristics](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aformant-vocoder-speech) — Wireless Communication, chapter 6 - [Speech characteristics; formant and channel vocoder](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspeech-formant-channel-vocoder) — Wireless Communication, chapter 6 ## Related in other subjects - [Discrete vs continuous signal; convert (25.25)₁₀](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Adiscrete-continuous-convert-25-25) — Digital Logic, chapter 1 - [Stack definition and basic operations](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Astack-operations-algorithms) — Data Structure and Algorithm, chapter 2 - [Data structure and basic operations](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Adata-structure-basic-operations) — Data Structure and Algorithm, chapter 1 - [Linked list and its basic operations](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Alinked-list-and-operations) — Data Structure and Algorithm, chapter 4