Adaptive Multi-Rate (AMR)
Study Guide

Speech coding for mobile & VoIP | Communication Engineering Essentials
🎓 Undergraduate Level
📡 3GPP TS 26.071
⚡ ACELP + DTX
📱 GSM / UMTS / LTE

Adaptive Multi-Rate (AMR) is a speech audio codec standard optimized for mobile communications (GSM, WCDMA) and VoIP. It was developed by the European Telecommunications Standards Institute (ETSI) and adopted by 3GPP. The key innovation: multiple bit rates (from 4.75 kbit/s up to 12.2 kbit/s) and the ability to switch dynamically based on radio channel conditions and network load.

💡 Core idea: When channel quality is good, use a higher bitrate for better speech quality. When interference is high or cell edge, switch to a lower bitrate → robust error protection & capacity gains.

AMR is widely used in GSM (AMR-FR/AMR-HR), UMTS, LTE (VoLTE) and many IP-based telephony systems. It operates on 20 ms frames (160 samples at 8 kHz sampling) and uses Algebraic Code-Excited Linear Prediction (ACELP) as the core coding algorithm.

AMR defines 8 source codec bit rates for the narrowband version (AMR-NB). The most common modes are:

AMR Mode IndexBit Rate (kbit/s)Description / Use case
04.75Very low bitrate – maximum robustness, baseline quality
15.15Low rate, increased error resilience
25.90Good trade-off for poor channels
36.70Standard for half-rate channels
47.40Widely used for AMR-HR/FR
57.95Enhanced performance
610.2Near toll quality
712.2Highest bitrate (GSM EFR equivalent) – best speech quality

AMR also supports wideband (AMR-WB) (G.722.2) with 9 modes from 6.6 kbit/s to 23.85 kbit/s, offering improved speech clarity (50–7000 Hz). In this guide, focus remains on NB fundamentals, which are essential for undergrad comms.

📈 Adaptation logic

Network side (BSC/RNC) measures RxQual, C/I, BLER. Based on thresholds, the AMR mode is renegotiated in-band using codec mode request (CMR). Adaptation granularity: every 20–40 ms possible.

🛡️ Link adaptation gain

Compared to fixed-rate codecs, AMR offers 2–4 dB gain in coverage and capacity. Operators can increase voice capacity by ~30–50% using lower bitrates under congestion.

AMR is based on Algebraic Code-Excited Linear Prediction (ACELP). At the heart lies the analysis-by-synthesis principle: the encoder minimizes perceptual weighted error between original and synthesized speech.

  • Linear Prediction (LP) filter – models spectral envelope (short-term correlation). LP coefficients are quantized using LSF (Line Spectral Frequencies).
  • Adaptive codebook (pitch) – models long-term periodicity (voiced speech).
  • Fixed (algebraic) codebook – models innovation/residual signal. Uses structured algebraic pulses (positions & signs) for low complexity.
  • Perceptual weighting filter – exploits masking properties of human hearing, shaping quantization noise.
🧮 Key formula concept: Synthesized speech \( s'(n) \) = LP synthesis filter \( 1/A(z) \) excited by \( e(n) = \text{(adaptive contribution)} + \text{(fixed codebook contribution)} \). AMR encoder searches for best pitch delay, gains, and algebraic pulse positions to minimize error.

For undergraduates: ACELP achieves high perceptual quality at low bitrates (4.75–12.2 kbps) by exploiting speech specific structure and using sparse algebraic codebooks. Complexity is moderate, making it suitable for real-time DSP/ARM cores.

AMR encodes speech in 20 ms frames (160 samples). Each frame yields a set of class A, B, C bits according to error sensitivity. Class A bits are most critical and receive strongest channel coding.

  • Class A bits – if errors occur, speech degradation is severe. Protected by convolutional codes & CRC.
  • Class B bits – moderate importance.
  • Class C bits – least sensitive, may be left with less protection.

Discontinuous Transmission (DTX): During silence periods (pause), AMR switches to Silence Descriptor (SID) frames, transmitting comfort noise parameters every 8 frames (160 ms). This saves battery and reduces interference by ~50% during conversation.

Frame TypeDescriptionTypical Size (bits)
Speech framesActive speech, 8 modes (4.75–12.2 kbps)95–244 bits per 20ms
SID_FIRST / SID_UPDATEComfort noise parameter update~39 bits
NO_DATA (DTX)No transmission, receiver generates comfort noise0 (null)
Bad Frame Indication (BFI)Error concealment at decoder—

In-band signaling: CMR (Codec Mode Request) allows the receiver to suggest mode change, improving link adaptation without higher layer messaging.

In cellular systems (GSM, UMTS), AMR speech frames are protected by unequal error protection (UEP) based on bit-sensitivity. For GSM, each AMR frame is mapped onto a radio block using:

  • Convolutional coding (rate 1/2 or rate 1/3) tailored for each mode.
  • Cyclic Redundancy Check (CRC) on Class A bits.
  • Interleaving to combat fading bursts.

📶 Example: AMR 12.2 kbps

Class A = 81 bits, Class B = 103 bits, Class C = 60 bits. Total source bits = 244 bits/20ms. After adding CRC (8 bits) and tail bits, rate-matched to 456 bits per GSM burst.

⚠️ Error concealment

At decoder, bad frames are detected (CRC or energy). Concealment repeats previous parameters, mutes gradually, avoids annoying artifacts. AMR gracefully degrades quality even at high FER (up to 5% FER is tolerable).

For VoLTE (LTE), AMR rides over RTP/UDP/IP with robust header compression (RoHC) and relies on PDCP retransmissions, but adaptive bitrate still used to manage cell capacity.

AMR-WB (G.722.2) provides superior speech quality (50 Hz – 7 kHz) compared to narrowband (300–3400 Hz). It uses 16 kHz sampling and 9 source rates from 6.6 kbit/s to 23.85 kbit/s. Core improvements:

  • Extended bandwidth doubles speech clarity, consonants, and naturalness.
  • Improved noise shaping and inter-frame prediction.
  • Widely deployed as “HD Voice” in UMTS/LTE and VoIP.
📌 Exam tip: AMR-NB → narrowband (8 kHz sampling, 4.75–12.2 kbps). AMR-WB → wideband (16 kHz sampling, 6.6–23.85 kbps). Both use ACELP but WB features improved perceptual weighting.

Backward compatibility is ensured through transcoding, but end-to-end AMR-WB provides rich audio for modern communication.

Where is AMR used?

  • GSM: AMR-FR (Full Rate) and AMR-HR (Half Rate) replace older FR/EFR codecs.
  • UMTS/HSPA: AMR-NB and AMR-WB mandatory for circuit-switched voice.
  • VoLTE / IMS: AMR-WB preferred, AMR-NB fallback.
  • VoIP & WebRTC: AMR payload format (RFC 4867) for RTP streaming.

📖 Key points for exams

✔️ AMR mode adaptation: 8 rates (NB)
✔️ ACELP = LP filter + pitch + algebraic codebook
✔️ DTX + comfort noise reduces interference
✔️ Unequal error protection (Class A/B/C)
✔️ Frame length: 20 ms, 160 samples (8 kHz)
✔️ In-band CMR for link adaptation

🧪 Common numerical

If AMR 12.2 kbps active speech, and DTX reduces transmission during 50% silence, average bitrate ≈ 6.1 kbps + SID overhead. Estimate spectral efficiency gains.

📚 Further reading: 3GPP TS 26.071 (AMR speech codec), TS 26.201 (AMR-WB), ITU-T G.722.2.

🔑 Terminology

ACELP: Algebraic Code Excited Linear Prediction
CMR: Codec Mode Request (in-band signaling)
DTX: Discontinuous Transmission
SID: Silence Insertion Descriptor
UEP: Unequal Error Protection
MOS: Mean Opinion Score (AMR-NB 12.2 ≈ 4.1, 4.75 ≈ 3.5)
VAD: Voice Activity Detection

✏️ Self-check questions

  1. Why does AMR use multiple bitrates? How does adaptation improve network capacity?
  2. Explain the difference between AMR-NB and AMR-WB (sampling, bitrates, audio bandwidth).
  3. Describe the role of algebraic codebook in ACELP.
  4. What is the purpose of DTX and comfort noise generation?
  5. How does unequal error protection work in AMR over GSM?

📌 Check answers: refer to sections above & 3GPP specs.

🧠 Final insight: AMR represents a perfect blend of source coding (ACELP), channel-aware adaptation, and system-level resource optimization. Understanding AMR gives deep insight into modern digital cellular architecture.