Ferkans — Interactive Telecom Tutor

Why Satellite Broadcasting Uses APSK, Not QAM

DVB-S2 (ETSI EN 302 307, 2003) and its extension DVB-S2X (ETSI EN 302 307-2, 2014) are the satellite broadcasting and broadband-data standards used worldwide for television distribution, VSAT IP backhaul, and high-throughput satellite (HTS) data. The physical-layer design differs from 5G NR and Wi-Fi in two important ways, both of which trace back to the same root cause: a satellite amplifier is a non-linear, nearly-saturated travelling-wave tube (TWT).

Constellation = APSK, not QAM. QAM places points on a square grid, which produces a peak-to-average power ratio (PAPR) of about 2.6 dB for 16-QAM and 3.2 dB for 64-QAM. A TWT amplifier driven at 3 dB backoff wastes 3 dB of the satellite's radiated power; driving it harder saturates and introduces AM/AM and AM/PM distortion. APSK (Amplitude-and-Phase-Shift Keying) instead places points on a small number of concentric rings (usually 2-4). The PAPR is only 1-2 dB, and the ring structure is compatible with the AM/PM curve of the TWT.
Code structure = LDPC + BCH. DVB-S2 uses a long LDPC inner code (codelengths $N = 16200$ or $64800$ bits) concatenated with a short BCH outer code of rate $\sim 0.993$ . The BCH cleans up any error floor of the LDPC, bringing the final BER below $10^{-11}$ — satellite broadcasting demands quasi-error-free (QEF) reception.

Everything else is pure BICM-LDPC in the Caire-Taricco-Biglieri sense: a single binary code, a bit interleaver, and a (quasi-)Gray labelled mapper.

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Definition:
$(M_1, M_2, \ldots)$ -APSK Constellation

An $(M_1, M_2, \ldots, M_R)$ -APSK constellation is a constellation consisting of $R$ concentric rings, with $M_r$ points uniformly spaced in phase on ring $r$ of radius $\rho_r$ . The total size is $M = M_1 + M_2 + \cdots + M_R$ , and the spectral index is $L = \log_2 M$ label bits per symbol. The canonical DVB-S2 cases are:

16-APSK (DVB-S2): $(4, 12)$ — 4 points on an inner ring, 12 on an outer ring. $L = 4$ .
32-APSK (DVB-S2): $(4, 12, 16)$ — 3 rings. $L = 5$ .
64-APSK (DVB-S2X): $(4, 12, 20, 28)$ or related layouts.
128-APSK, 256-APSK (DVB-S2X): 5-ring or 6-ring layouts with per-rate-optimised radius vectors.

The ring radii $\rho_1 < \rho_2 < \cdots < \rho_R$ are free design parameters. Given the average energy constraint $\sum_r \frac{M_r}{M} \rho_r^2 = 1$ , they are chosen to maximise the BICM mutual information at the target code rate. The labelling is quasi-Gray: each ring uses a PSK Gray code for its angular portion, and the ring-selection bits are separated by the maximum possible label Hamming distance given the APSK geometry.

APSK differs from QAM precisely in the placement structure: QAM is a square grid maximising minimum Euclidean distance at fixed average energy; APSK is a ring structure maximising mutual information through a non-linear amplifier with a known AM/PM curve. On a linear AWGN channel QAM is marginally better (0.1-0.3 dB at the same rate); on a TWT-nonlinear channel APSK wins by 1-2 dB.

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DVB-S2/S2X APSK Constellations

The 16-, 32-, 64-, and 256-APSK constellations as specified in DVB-S2 and DVB-S2X. Each ring is a PSK sub-constellation; inter-ring radii $\rho_r$ are chosen per-code-rate in the standard (we show the values for code rate 3/4 in the annexes of EN 302 307). Notice how the ring structure clusters points — this is the PAPR-reducing property that makes APSK TWT-friendly. At 256-APSK the outer rings are densely populated because the ring count is capped (typically 5-6 rings) and the angular spacing must shrink.

Parameters

Constellation

Theorem: Optimal Ring-Ratio Design for 32-APSK

For a 32-APSK constellation $(4, 12, 16)$ with unit average energy, the BICM capacity is maximised at code rate $R$ by ring radii $(\rho_1, \rho_2, \rho_3)$ satisfying the ratio relations $\gamma_1 = \rho_2 / \rho_1, \qquad \gamma_2 = \rho_3 / \rho_1,$ where the optimal $(\gamma_1, \gamma_2)$ are found by numerically maximising $C_{\rm BICM}(\gamma_1, \gamma_2; \rho_1)$ subject to $\frac{4 + 12 \gamma_1^2 + 16 \gamma_2^2}{32} \rho_1^2 = 1$ . The DVB-S2 Annex A Table A.3 tabulates the solution for each code rate. For example, at $R = 3/4$ : $(\gamma_1, \gamma_2) \approx (2.84, 5.27)$ .

The geometry is: at low code rates (small $R$ ), noise dominates and the inner ring should be well separated from the outer rings — so $\gamma_1, \gamma_2$ are large. At high code rates (large $R$ ), the constellation should be "rounder", closer to a QAM, so the ratios shrink toward equal-radius PSK spacing. The tabulated values move from $\gamma_2 \approx 5.3$ at $R = 2/3$ down to $\gamma_2 \approx 4.3$ at $R = 9/10$ — a 20% contraction over the working rate range.

Show Hint

Write the BICM capacity as a function of $\rho_1, \rho_2, \rho_3$ via the mutual-information integral over per-bit channels.

Substitute the unit-energy constraint to reduce to two free variables $\gamma_1, \gamma_2$ .

Take partial derivatives and solve numerically at each target rate.

Proof

Step 1: Unit-energy parameterisation

Fix the inner ring radius $\rho_1$ and define $\rho_2 = \gamma_1 \rho_1$ , $\rho_3 = \gamma_2 \rho_1$ . The total energy is $\mathbb{E}|X|^2 = \frac{4 \rho_1^2 + 12 \rho_2^2 + 16 \rho_3^2}{32} = \rho_1^2 \cdot \frac{4 + 12\gamma_1^2 + 16 \gamma_2^2}{32}$ . Setting this to 1 gives $\rho_1^2 = 32/(4 + 12\gamma_1^2 + 16\gamma_2^2)$ .

Step 2: BICM capacity as function of ratios

With the labelling fixed (the quasi-Gray scheme of DVB-S2), the BICM capacity is $C_{\rm BICM}(\gamma_1, \gamma_2; \text{SNR}) = \sum_{\ell=0}^{4} I(Y; B_\ell),$ where each $I(Y; B_\ell)$ is a mutual-information integral evaluated numerically over the bit-channel. At given $\text{SNR}$ and the target $R$ , we maximise over $(\gamma_1, \gamma_2)$ .

Step 3: Rate-matching target

Design the $(\gamma_1, \gamma_2)$ pair so that $C_{\rm BICM} = L \cdot R = 5R$ at the target operating SNR (the SNR where BLER $= 10\%$ with the chosen LDPC code). This gives a family of $(\gamma_1, \gamma_2)$ parameterised by $R$ ; the ETSI Annex A table tabulates it.

Step 4: Example — $R = 3/4$

Target $C_{\rm BICM} = 5 \times 3/4 = 3.75$ bits/symbol, operating SNR $\approx 10.5$ dB. Numerical maximisation yields $(\gamma_1^\star, \gamma_2^\star) \approx (2.84, 5.27)$ , matching ETSI Annex A. $\blacksquare$

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Example: 32-APSK Ring Ratios for Rate 3/4

Compute the three ring radii $(\rho_1, \rho_2, \rho_3)$ of 32-APSK at rate $R = 3/4$ , with unit total average symbol energy, given the optimal ratios $\gamma_1 = 2.84, \gamma_2 = 5.27$ from the DVB-S2 Annex A table.

Solution

Unit energy constraint

$\rho_1^2 = \frac{32}{4 + 12\gamma_1^2 + 16\gamma_2^2} = \frac{32}{4 + 12 \cdot 8.07 + 16 \cdot 27.77} = \frac{32}{544.1} \approx 0.0588.$ $So$ \rho_1 \approx 0.2425$.

Middle and outer rings

$\rho_2 = \gamma_1 \rho_1 = 2.84 \times 0.2425 \approx 0.6887$ . $\rho_3 = \gamma_2 \rho_1 = 5.27 \times 0.2425 \approx 1.2782$ .

Verification

Average energy check: $\frac{4 \rho_1^2 + 12 \rho_2^2 + 16 \rho_3^2}{32} = \frac{4(0.0588) + 12(0.4743) + 16(1.6338)}{32} = \frac{0.2352 + 5.6919 + 26.141}{32} = \frac{32.067}{32} \approx 1.002.$ Small rounding error from quoted ratios; exact ratios give exactly 1.

Interpretation

The outer ring is at $\rho_3 = 1.28$ , the inner at $\rho_1 = 0.24$ — a factor $> 5$ between inner and outer radii. The TWT sees a relatively narrow amplitude range (most points are on the two outer rings, total weight $12 + 16 = 28$ out of 32), so the PAPR is $\rho_3^2 / \bar E = 1.63$ , i.e. 2.1 dB. Compare to 32-QAM which has PAPR 3.4 dB. $\blacksquare$

🚨Critical Engineering Note

ETSI EN 302 307: The DVB-S2/S2X Specification

EN 302 307-1 (DVB-S2) and its extension 302 307-2 (DVB-S2X) define the BICM chain for satellite broadcasting:

LDPC: 64800-bit "normal" frame or 16200-bit "short" frame; both quasi-cyclic with a specified base matrix.
BCH outer code: rate $\sim 0.993$ , corrects 8-12 bit errors per block. Cleans any LDPC error floor.
Modulations: QPSK, 8-PSK, 16-APSK, 32-APSK (DVB-S2 — 11 MODCOD codes). DVB-S2X extends with 64-, 128-, 256-APSK and an additional 10+ very-low-rate codes for 2% improved efficiency.
Code rates: 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9, 9/10 (DVB-S2); plus many in-between rates added in DVB-S2X.
Spectral efficiency range: 0.490 to 4.453 bits/symbol (DVB-S2); up to 5.90 with 256-APSK (DVB-S2X).

One MODCOD is one combination (modulation, code rate). DVB-S2 has 28 MODCODs; DVB-S2X adds 60+ more, including "very low SNR" codes for mobile satellite terminals operating below 0 dB Es/N0.

The standard fixes the physical-layer framing (BB frame, BICM frame, PL frame), pilot insertion pattern, scrambling sequences, and roll-off factors ( $\alpha \in \{0.20, 0.25, 0.35\}$ for the root- raised-cosine pulse shaping) in exquisite detail. Reading Section 5 and Annex A of the spec is the canonical preparation for implementing DVB-S2 — much like TS 38.212 + 38.214 for 5G NR.

Practical Constraints

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FEC frame size fixed at 16200 or 64800 bits
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BCH outer code mandatory — quasi-error-free BER $10^{-11}$
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Roll-off $\alpha \in \{0.20, 0.25, 0.35\}$
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Reference symbol energy normalisation $E_s = 1$

📋 Ref: ETSI EN 302 307-1 V1.4.1, ETSI EN 302 307-2 V1.1.1

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Historical Note: DVB-S2: The 2003 BICM Breakthrough for Satellites

2000-2003

DVB-S2 (standardised 2003) was the first mass-market wireless standard to ship capacity-approaching LDPC codes over BICM. The predecessor DVB-S (1995) used a rate-1/2 convolutional code concatenated with a shortened Reed-Solomon (204, 188) outer code — a classical turbo-era design that left a $\sim 2.5$ dB gap to Shannon.

The DVB-S2 design team (led by A. Morello, ETSI TM-SS, with strong academic input from EPFL and Eurecom) chose LDPC based on two observations: (i) Richardson and Urbanke's 2001 density-evolution results showed LDPC could close the gap to 0.8 dB at the long block lengths DVB allows, and (ii) quasi-cyclic LDPC made decoder ASICs tractable at the satellite receiver cost budget.

The choice of APSK over QAM was forced by the TWT. The Gaudenzi et al. 2006 paper (cited later in DVB-S2X) gave the theoretical justification: under a non-linear AM/AM-AM/PM model, a well-tuned APSK beats QAM by 1-2 dB of effective SNR at the cost of perhaps 0.1 dB on a purely linear AWGN channel.

This combination — LDPC + APSK + BICM — became the template that 5G NR inherited for terrestrial use. In the intervening 15 years, satellite broadcast was both the proof-of-concept and the training ground for modern BICM engineering.

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Common Mistake: APSK Labelling Is NOT Standard Gray

Mistake:

When implementing an APSK mapper, a common mistake is to use a naive "PSK-Gray-per-ring plus ring-index-Gray" labelling, assuming it is globally Gray in the BICM sense.

Correction:

APSK labellings cannot be globally Gray because the inter-ring nearest-neighbour pairs have $d_H \ne 1$ in general. The DVB-S2 spec uses a quasi-Gray labelling that minimises the average nearest-neighbour Hamming distance subject to the APSK geometry. The spec assigns specific bit-to-ring mappings in tables (Tables 11-14 of EN 302 307); implementations must copy these mappings exactly rather than deriving them from a Gray-code principle. Independent derivations often produce 0.3-0.5 dB worse BICM capacity.

Why This Matters: Satellite-5G Convergence: DVB-S2 Meets NR Non-Terrestrial Networks

3GPP Release 17 (2022) added non-terrestrial networks (NTN): 5G NR operating over LEO and GEO satellites. The NTN amendment required changes to NR timing, HARQ, and beam management, but kept the BICM chain unchanged — LDPC + QAM with MCS Table 2.

The interesting question is whether future NTN standards will adopt APSK from DVB-S2. Early prototypes use QAM because that matches the existing NR encoder/decoder hardware. But TWT amplifiers on LEO satellites still prefer ring-structured constellations; the argument has not yet been closed. A probable outcome is a hybrid: QAM for downlink (UE-friendly hardware) and low-order APSK for high-power gateway uplinks. The 2025+ NR Release 19 work item on NTN extensions is where this will be decided.

Quick Check

Which of the following is NOT a reason satellite systems prefer APSK over QAM?

Lower peak-to-average power ratio, allowing the TWT to operate closer to saturation

Compatibility with the AM/PM distortion curve of a non-linear amplifier

Strictly higher mutual information than QAM on a linear AWGN channel at the same $L$

The ring structure matches the ideal pre-distortion contour of the TWT

Correction:

Strictly higher mutual information than QAM on a linear AWGN channel at the same

L

On a linear AWGN channel, QAM is marginally better than APSK (0.1-0.3 dB at the same spectral efficiency). APSK's advantage appears only under the non-linear TWT model. The true reason for APSK is PAPR and AM/PM matching, not capacity.

APSK (Amplitude-and-Phase-Shift Keying)

A family of constellations with points arranged on concentric rings. Each ring is a PSK sub-constellation at a distinct radius. Used in DVB-S2/S2X (16-, 32-, 64-, 128-, 256-APSK) because the ring structure is robust to the AM/PM non-linearity of satellite TWT amplifiers and has lower PAPR than QAM.

MODCOD

A pair (modulation, code rate) specified in DVB-S2/S2X. DVB-S2 defines 28 MODCODs; DVB-S2X adds 60+ more. Every BB frame in a DVB-S2 transmission starts with a MODCOD header that the receiver uses to configure its demodulator and decoder.

Key Takeaway

DVB-S2/S2X is BICM with LDPC + BCH + APSK. The APSK constellation reduces PAPR for TWT-compatible operation; the BCH outer code cleans the LDPC error floor for quasi-error-free satellite broadcast. The ring radii are rate-dependent design parameters tabulated in ETSI Annex A — pure BICM-capacity optimisation. This was the first mass- market BICM-LDPC standard (2003) and the template for everything that followed.

DVB-S2/S2X: LDPC + APSK