Digital communications, explained by DVB-S

Speaker notes

Chapter 1 gave the tools: the spectrum, and I and Q. This chapter uses them to follow one real system from start to finish.

DVB-S is a good teacher. It is old enough to be simple, every step is written down in one public standard (ETSI EN 300 421), and it is still on the air. Every step in it, from scrambling to error correction, is in 5G, Wi-Fi and DVB-S2 too, in a newer form.

At the end: what DVB-S2 changed, and why that is what you receive on QO-100.

Speaker notes

This is the map for the whole chapter. The transmitter on top, the receiver below, and what each group of steps is for under the boxes.

The orange steps are the ones this chapter looks at most closely: Reed-Solomon, the interleaver, the convolutional code and the root raised cosine filter, and their partners in the receiver.

The map comes back before every part, with the step that part explains in green, so you always know where in the chain we are.

The payload: what goes in, and why it is scrambled first.

Error correction: two codes and an interleaver between them. This is where most of the work is.

On the air: QPSK, the pulse shape, and how a receiver locks on.

The link: 38 600 km of path, the dish and the LNB, and how much signal each setting needs.

The receiver is the transmitter in reverse, and it has to know the exact settings: the frequency, the symbol rate and the code rate. Most DVB-S receivers find the code rate by themselves; the frequency and symbol rate come from a list or a scan.

Speaker notes

DVB-S carries an MPEG-2 transport stream: a row of packets of exactly 188 bytes, each starting with the sync byte 0x47. A 13-bit number in each packet says which stream it belongs to, so one carrier can hold several TV channels.

The first step on those packets is the scrambler.

Speaker notes

Real data is not random. Empty packets are long rows of zeros, and a still picture repeats itself. Sent as they are, such bits give an uneven spectrum.

Top: nearly empty packets, sent as QPSK. All zeros means the same symbol over and over: that is an unmodulated carrier. The power piles up in one spike at the carrier frequency, about 25 dB above the rest, with uneven bumps around it.

Bottom: the same packets, scrambled. The bits now look random, and the power spreads evenly over the whole channel: the flat top and the smooth roll-off of the pulse shaping, nothing else.

Why that matters: the channel is used evenly, whatever is sent, and the receiver always sees the same smooth signal for its gain, timing and carrier loops. Random-looking bits also change often between 0 and 1, which the receiver needs to keep its symbol clock in step.

The scrambler XORs the data with a fixed pseudo-random pattern, and the receiver XORs it again with the same pattern to undo it. It is not encryption: the pattern is in the public standard.

The drawing is calculated: 24 nearly empty packets through the real DVB-S scrambler, sent as QPSK with roll-off 0.35; the error correction is left out.

Speaker notes

The three green steps together are the error correction. First the limit every code works against: Shannon's. Then each step in turn.

The two codes work as a team. The convolutional code fixes scattered bit errors from noise; when it fails, it leaves short bursts. The interleaver spreads those bursts over many packets, and Reed-Solomon repairs them, a few bytes per packet.

Speaker notes

In 1948 Claude Shannon showed that every channel has a limit: for a bandwidth B and a signal-to-noise ratio S/N, at most C = B · log₂(1 + S/N) bits per second can get through. ("A Mathematical Theory of Communication", 1948.)

The surprise was the other half. Below that limit, errors can be made as rare as you like, not by more power but by a clever enough code. Above it, nothing helps. Shannon proved such codes exist, but not how to build them; the rest of this part is how DVB-S does it.

The drawing per symbol: a symbol with a signal-to-noise ratio Es/N0 can carry at most log₂(1 + Es/N0) bits.

Every mode of three standards is a point: the signal it needs for quasi error-free reception, and the useful bits it carries per symbol. The line joins the best modes of each standard.

DVB-S (open circles, QPSK, rates 1/2 to 7/8): at rate 3/4 it carries 1.38 bits per symbol and needs 6.1 dB, where Shannon needs 2.1 dB: 4 dB from the limit. Values from EN 300 421, without its 0.8 dB margin.

DVB-T (squares, QPSK, 16-QAM and 64-QAM): the same codes as DVB-S. With more points per symbol it reaches up to 4.8 bits per symbol, but the gap to the limit grows with them: about 4 dB with QPSK, 5 to 6 dB with 64-QAM. Values from EN 300 744 for a Gaussian channel, per carrier; the guard interval and the pilots of OFDM take some more.

DVB-S2 (dots): LDPC codes bring it to 1 to 2.5 dB from the limit with QPSK, and 2 to 3 dB with 32APSK. Values from EN 302 307, ideal receiver, frame overheads left out.

For comparison: QPSK without any coding needs 13.5 dB for one bit error in a million.

Speaker notes

How to use it: find your S/N across, your bandwidth up. The line through that point, or the one just under it, is the data rate QPSK can carry there.

The S/N is the one from chapter 1: on the spectrum or waterfall, how far the top of the band stands above the noise floor beside it. Measured that way it is the Es/N0 of the chart.

The lines step down as the S/N grows: with a stronger signal the receiver can use a lighter code (from rate 1/4 up to 9/10), so the same bandwidth carries more. Above about 6.4 dB QPSK is at its best, 9/10; more signal only adds margin. For more data you would need 8PSK or more points.

Example: a signal 2 MHz wide, 6 dB above the noise. That is 1.48 Msym/s (2 MHz / 1.35). At 6 dB the best QPSK rate is 5/6, 1.67 useful bits per symbol: about 2.5 Mbit/s.

The chart uses the DVB-S2 QPSK modes, ideal receiver, roll-off 0.35. A real receiver needs 1 to 2 dB more. DVB-S QPSK starts at rate 1/2, which needs about 4 dB, and reaches 1.6 bits per symbol at 7/8.

Speaker notes

The idea behind Reed-Solomon. Take the data values as points: value 1 at position 1, value 2 at position 2, and so on. Through 4 points goes exactly one curve of degree 3 (a polynomial). The sender works out where that curve is at positions 5 and 6, and sends those values too: the parity.

How the receiver finds an error, in two steps.

1. Check: do all received points lie on one curve of degree 3? Any 4 points fix a curve; if the other points are not on it, something is wrong. In the real decoder this check is a short calculation, the syndromes: 16 numbers computed from the 204 bytes. All zero: no error, and the decoder is done.

2. Locate and repair: if the syndromes are not zero, the decoder works out which positions are wrong (the error locator, found with the Berlekamp-Massey algorithm) and then what they should have been (the Forney algorithm). In the picture: 5 of the 6 points agree on one curve, so point 3 is the odd one, and the curve says where it belongs.

Every wrong value costs 2 extra points: one to find where it is, one to find what it was. DVB-S sends 188 values with 16 extra, so up to 8 wrong bytes per packet are repaired.

The picture uses ordinary numbers. The real code works with bytes in a finite field, arithmetic where every result is again a byte, so no rounding ever happens. The idea is the same.

Source of the idea as shown: "What are Reed-Solomon Codes? How computers recover lost data", vcubingx, YouTube, 2022.

Speaker notes

Why Reed-Solomon is the outer code of DVB-S, and of CDs, DVDs, QR codes and many space probes.

Whole bytes: it works on symbols of 8 bits. A burst of errors inside a few bytes costs only those few bytes. That is exactly what the Viterbi decoder leaves behind.

A firm promise: up to 8 bad bytes per packet are always repaired, whatever their position.

No parity wasted: Reed-Solomon codes are maximum distance separable. To correct t errors any code needs at least 2t parity symbols; Reed-Solomon needs exactly 2t.

Knows when it fails: with more than 8 errors the decoder almost always notices that it cannot repair the packet. It then sets the error bit in the packet header, so the video decoder can hide the damage instead of showing wrong data.

Erasures count double: an error whose position is known costs 1 parity byte instead of 2. A receiver that knows which bytes are suspect could repair up to 16 per packet; most DVB-S receivers do not use this.

Data untouched: the code is systematic. The receiver can even skip decoding and use the data bytes as they are.

Fast: the decoding steps are a fixed sequence of byte calculations, easy to build in a chip and run at tens of megabits per second.

Speaker notes

DVB-S uses a convolutional interleaver with 12 branches (I = 12). Byte 1 goes through branch 0, byte 2 through branch 1 and so on; byte 13 goes through branch 0 again. Each branch delays by 17 bytes more than the one before (M = 17; 12 × 17 = 204).

The receiver has the same branches with the opposite delays, so every byte arrives with the same total delay and the order is restored. But two bytes that are neighbours on the air were 203 bytes apart before the interleaver: they belong to different packets.

So a burst of 36 bad bytes on the air becomes 3 bad bytes in each of 12 packets, and Reed-Solomon repairs them all. In the ideal case, a burst of up to 12 × 8 = 96 bytes is harmless.

The price is delay, not bandwidth: 12 × 17 × 11 = 2244 bytes, under half a millisecond at 27.5 Msym/s and rate 3/4.

Speaker notes

The inner code of DVB-S is a convolutional code with constraint length 7, rate 1/2. The bits shift through 6 memory cells. For every bit in, two sums come out: X adds the bits at taps 171 (octal), Y at taps 133. The sums are XORs: 1 + 1 = 0.

Each input bit therefore affects 14 output bits. Not every sequence of output bits is possible: only those the encoder can make. Two different valid sequences differ in at least 10 bits (the free distance), so a few wrong bits still leave the right sequence the closest one.

This same code (171, 133) is used in many other systems, from space probes to Wi-Fi.

Rate 1/2 doubles the number of bits. The next slide shows how DVB-S sends fewer.

Speaker notes

Puncturing makes other rates from the same rate 1/2 encoder: leave out some of the coded bits, in a fixed pattern. For 3/4 the pattern is X: 1 0 1 and Y: 1 1 0, so 4 of every 6 bits are sent. The receiver knows the pattern and fills the gaps with "don't know" before decoding.

EN 300 421 gives five rates. The patterns: 2/3 is X 10, Y 11; 3/4 is X 101, Y 110; 5/6 is X 10101, Y 11010; 7/8 is X 1000101, Y 1111010.

The useful bit rate is the symbol rate × 2 bits × the code rate × 188/204. At 27.5 Msym/s: 25.3 Mbit/s at 1/2 up to 44.4 Mbit/s at 7/8.

The Eb/N0 column is what EN 300 421 asks for quasi error-free reception: less than one uncorrected error per hour, about 10⁻¹⁰ to 10⁻¹¹ after Reed-Solomon. It includes a margin of 0.8 dB for a real receiver.

The operator picks the rate: 7/8 carries 75 % more than 1/2, but needs 1.9 dB more signal, so a smaller dish or a rain shower hurts sooner.

Speaker notes

The decoder does not decode bit by bit. It asks: which input sequence would have given output closest to what I received? Andrew Viterbi found an efficient way to answer that in 1967.

The trellis draws every state the encoder can be in (here 4, for a small code with memory 2) at every step. From each state two branches leave: input 0 (dashed) or input 1 (solid). Each branch has its own pair of output bits.

For every state, the decoder keeps only the best way to get there and its score: the number of bits that disagree with what arrived. At the end it follows the best path back. Here the received 10 in step 3 should have been 00; the best path has one disagreement, and the decoded bits are exactly what was sent.

DVB-S does the same with 64 states (memory 6). In practice the decoder uses soft decisions: not just 0 or 1 from the demodulator, but how sure it is. That gains about 2 dB over hard decisions.

When the decoder does go wrong, it takes a wrong path for a few steps: errors come out in short bursts. That is why the interleaver and Reed-Solomon follow.

Speaker notes

DVB-S maps every pair of coded bits to one of four points: one bit sets I, the other Q. Neighbouring points differ in one bit (Gray code), so the most likely error costs one bit, not two.

Why only four points on a satellite? Its power amplifier works best close to saturation, where the output no longer grows in step with the input. All QPSK points have the same amplitude, so squeezing the amplitude changes nothing: the information is in the phase. 16-QAM has points at three amplitudes, and the amplifier would squeeze them by different amounts.

This is the SDR transmitter from chapter 1: I and Q at +1 or −1, times a cosine and a sine.

DVB-S2 adds 8PSK, 16APSK and 32APSK, built for the same amplifier. That is section 05.

Speaker notes

Chapter 1 showed it: sharp edges need a wide spectrum. Square symbols spill side lobes into the neighbouring channels.

The cure is a smooth pulse. Smooth alone is not enough: the pulse of one symbol must not disturb the others. The raised cosine pulse is zero at every other symbol moment, so when the receiver samples symbol n, all the other pulses happen to be zero there. No interference between symbols (Nyquist's condition).

The roll-off sets how fast the spectrum falls to zero. DVB-S uses 0.35: the spectrum is the symbol rate wide at −3 dB, and 1.35 × the symbol rate in all. At 27.5 Msym/s that is 27.5 MHz and 37.1 MHz.

DVB-S splits the filter in two equal halves, a root raised cosine in the transmitter and another in the receiver. Together they make the raised cosine, and the receiver half is also the filter that lets the least noise through for this pulse: the matched filter.

Speaker notes

The roll-off factor says how much wider than the minimum the signal is. The minimum is the symbol rate: a signal of Rs symbols per second needs at least Rs hertz. With roll-off α it takes (1 + α) × Rs. DVB-S uses 0.35, so 35 % extra.

Why not zero? A spectrum with vertical edges needs a pulse that rings on for ever in time. The extra bandwidth buys a pulse whose tails die out fast.

Why it matters, first: bandwidth. In a channel 36 MHz wide, roll-off 0.35 allows 26.7 Msym/s, roll-off 0.20 allows 30 Msym/s: 12.5 % more data in the same transponder. That is why DVB-S2 added 0.25 and 0.20.

Second: robustness. Every roll-off gives zero interference at the exact sampling moment. But the receiver's timing is never perfect, and with a small roll-off the long tails of the neighbouring symbols are bigger just beside that moment. The eye on the right shows it: at 0.20 the traces spread more around the dashed line. A small roll-off needs more exact timing and longer filters, and its signal has higher peaks, so the amplifier must stay further from its limit.

So the roll-off is a choice between capacity and margin.

Speaker notes

An eye diagram draws the received signal over and over, two symbols at a time, on top of itself. An oscilloscope triggered on the symbol clock shows the same.

Clean (left): at the sampling moment, the dashed line, every trace goes through +1 or −1, whatever the symbols around it. That is the raised cosine at work. Between the moments the traces wander; that does no harm, because nobody samples there.

With noise (right): the traces blur and the opening shrinks. The receiver decides +1 or −1 at the dashed line; errors start where the blurred traces cross the middle.

The width of the eye shows how exact the timing must be, its height how much noise is left. DATV receivers usually show the constellation instead: the same information, seen as clouds.

Speaker notes

The whole calculation: 27.5 Msym/s × 2 bits × 3/4 × 188/204 = 38.0 Mbit/s.

27.5 Msym/s at rate 3/4 is a common DVB-S setting; it takes 37.1 MHz with roll-off 0.35.

Of the 55 Mbit/s on the air, 38 carry the packets; the other 17 are protection. That protection is what makes the link work at a signal-to-noise ratio of about 7 dB, as section 04 shows.

Speaker notes

Chapter 1 ended with the list of what a receiver does before the points line up. Here it is for DVB-S.

1. The tuner sets the gain and searches around the expected frequency. The LNB's oscillator can be off by a few MHz, so the receiver searches.

2. Symbol timing: the receiver adjusts its sampling clock until it samples in the middle of the eye.

3. Carrier phase: a loop locks the phase, so the four clouds stand still. But QPSK looks the same turned by 90°, so the receiver cannot know which of the four positions is right.

4. The Viterbi decoder can: with the wrong rotation, or the wrong puncturing pattern or position, it keeps finding errors. The receiver tries the possibilities until the error rate drops. That is also how it finds the code rate by itself.

5. Then the bytes: a sync byte 0x47 every 204 bytes, after deinterleaving and Reed-Solomon every 188, and the inverted 0xB8 every 8 packets, where the descrambler starts.

Speaker notes

A geostationary satellite circles at 35 786 km above the equator, once a day, so it stands still in the sky and a dish does not need to follow it.

From Belgium the path is longer than the height: from Ghent to a satellite at 19.2° East it is 38 600 km, at about 30° elevation. Light takes 0.13 s for that, so a signal up and down takes 0.26 s: the delay you notice in a live satellite interview.

Free-space loss: 20·log(4πd/λ). At 12 GHz and 38 600 km that is 205.8 dB. Not because the air absorbs anything: the power spreads over a sphere, and a dish catches only its own small piece.

All numbers on this slide are calculated in the diagram script; the satellite position is an example.

Speaker notes

A link budget adds the gains and losses in dB. This one is an example in round numbers, for clear sky.

The signal: a satellite that sends 51 dBW (EIRP, the power times the gain of its antenna, towards us) loses 205.8 dB over the path and 0.5 dB in the air. A 60 cm dish at 12 GHz gains 35.7 dB, at an efficiency of 65 %. At the LNB: −119.6 dBW, about a millionth of a millionth of a watt.

The noise: Boltzmann's constant, −228.6 dBW per kelvin per hertz, times the noise temperature of the system, about 100 K (the LNB plus the sky the dish sees), times the bandwidth, 27.5 MHz. That is −134.2 dBW.

So C/N is 14.6 dB. Rate 3/4 needs 6.9 dB (the 5.5 dB Eb/N0 from the puncturing slide, turned into C/N on the next slides). That leaves 7.7 dB margin.

The margin is for rain: at 12 GHz a heavy shower absorbs signal and adds noise. The operator's footprint map gives the real EIRP for your place; dish size is chosen from it.

Speaker notes

The LNB (low-noise block converter) sits at the focus of the dish. Its first amplifier sets the noise of the whole receiver, which is why it sits right behind the feed and not at the end of 20 m of coax.

Then it mixes the signal down, exactly as on the mixer slide of chapter 1. A universal LNB has two oscillators: 9.75 GHz for the low band (10.7–11.7 GHz) and 10.6 GHz for the high band (11.7–12.75 GHz). Both land between 950 and 2150 MHz, a frequency coax can carry.

The receiver controls the LNB over the same coax that brings the signal down: 13 V selects vertical polarisation, 18 V horizontal, and a 22 kHz tone selects the high band.

The LNB's oscillator is cheap and drifts with temperature, by up to a few MHz. For TV that does not matter: the receiver searches. For narrow amateur signals on QO-100 it does, which is why many amateurs lock their LNB to a stable reference (chapter 1, the oscillator).

QO-100 at 10 491.5 MHz comes out at 741.5 MHz with the 9.75 GHz oscillator: below the TV range, but most LNBs pass it and an SDR tunes it.

Speaker notes

Three ways to write signal over noise, for three purposes.

C/N depends on the bandwidth you measure in, so it is what you plan a link with: the link budget gave 14.6 dB.

Es/N0 is per symbol. The receiver's noise bandwidth is about the symbol rate, so for DVB-S, Es/N0 and C/N are close to the same number.

Eb/N0 is per useful bit, so it compares codes and modulations fairly, whatever their speed. At rate 3/4, one QPSK symbol carries 2 × 3/4 × 188/204 = 1.38 useful bits: 1.4 dB. The 5.5 dB Eb/N0 of the standard is 5.5 + 1.4 = 6.9 dB Es/N0, the number in the link budget.

Speaker notes

The bit error rate against Eb/N0, the fair scale from the previous slide. All three curves are calculated for an ideal receiver.

Without coding, QPSK needs about 8 dB for a bit error rate of 2 × 10⁻⁴. With the convolutional code at rate 1/2 and soft decisions, the same takes 3.3 dB: the code saves almost 5 dB, which is the difference between a 60 cm dish and one of over a metre.

2 × 10⁻⁴ after Viterbi is the target EN 300 421 sets, because Reed-Solomon turns that into quasi error-free: less than one bad packet per hour. The standard asks 4.5 dB for rate 1/2: the 3.3 dB here, plus 0.8 dB margin for a real receiver and 0.36 dB for the Reed-Solomon parity (10·log(204/188)). The calculation and the standard agree.

The Reed-Solomon curve assumes the interleaver spreads the errors perfectly. Note how steep it is: that is the next slide.

Speaker notes

An analogue picture gets snowy as the signal weakens, and you can watch it long after it stops being pretty.

A digital picture stays perfect: the codes repair every error. Then, over about 1 dB, they stop coping. First blocks and frozen frames, then nothing. That is the steep Reed-Solomon curve of the previous slide.

So you cannot judge a digital link by its picture. A perfect picture can be 0.5 dB from the cliff or 8 dB. The signal meter, the MER or the C/N, shows how much margin is left.

This slide is an illustration of the shape, not a measurement.

Speaker notes

The green steps are the ones DVB-S2 changes. The scrambler, the packets, the satellite link: all as before.

Speaker notes

DVB-S dates from 1994, DVB-S2 from 2005. The chain is the same: scramble, protect twice, map to a constellation, shape, send. The parts are newer.

Error correction: an LDPC code (low-density parity check) does the main work, with a BCH code behind it to clean up the last errors, as Reed-Solomon did. LDPC codes work on long frames, 64 800 bits, and come within about 1 dB of the theoretical limit. They were invented by Gallager in 1960 and only became practical decades later, when chips could decode them.

More constellations and rates give 28 combinations, from QPSK 1/4 for a weak signal to 32APSK 9/10 for a strong one.

Settings per frame: a broadcaster sends everyone the same (CCM). For a link to one receiver, the modulation and code can change per frame with the conditions (ACM): stronger protection during a rain shower, more speed when the sky clears.

The DVB Project gives the gain as about 30 % more capacity in the same transponder.

Speaker notes

QPSK and 8PSK keep all points on one ring, like DVB-S. 16APSK and 32APSK add rings, but few of them: 2 and 3, against the 3 and 5 amplitudes of 16-QAM and 32-QAM. The amplifier on the satellite sees only a few amplitudes, and the transmitter can pre-distort them so they come out right.

The size of the rings is set per code rate. Here: 16APSK at rate 3/4 (outer ring 2.85 × the inner one) and 32APSK at rate 3/4 (2.84 and 5.27 × the inner one).

More points mean more bits per symbol, but the points sit closer together, so they need a cleaner signal. The next slide shows how much.

Speaker notes

Claude Shannon showed in 1948 how many bits per symbol any link can carry at a given signal-to-noise ratio: log₂(1 + S/N). No code can do better; the question is how close one gets.

The DVB-S2 points come from EN 302 307 (ideal receiver, AWGN, packet error rate 10⁻⁷), at m bits × the code rate per symbol, frame overheads left out. The DVB-S points come from EN 300 421, without its 0.8 dB margin so the two compare fairly.

At the same 1.38 useful bits per symbol, DVB-S at 3/4 needs about 6.1 dB, and DVB-S2 with QPSK between 2/3 and 3/4 about 3.4 dB: some 2.5 dB less. That is the gain from LDPC.

And the higher constellations reach 2 to 4.5 bits per symbol, where DVB-S has nothing to offer.

Speaker notes

QO-100 is the amateur transponder on the geostationary satellite Es'hail-2, launched in 2018. Its wideband transponder is 8 MHz wide and made for digital amateur television.

The beacon on 10 491.5 MHz sends DVB-S2, QPSK, 1.5 Msym/s, all day: a good first signal to receive, with an ordinary dish and LNB, behind which it appears at 741.5 MHz.

Amateurs transmit at low symbol rates, 333, 250, 125 ksym/s and lower (reduced-bandwidth TV), so several stations fit in the 8 MHz and a modest station can reach the satellite.

Everything in this chapter applies: the QPSK constellation and its MER on the receiver screen, the code rate as a trade between speed and robustness, the link budget for the uplink and the downlink, and the cliff.