GSM signal processing (speech to radio)

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.

 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.