OFDM, explained by DVB-T

Speaker notes

Chapter 2 followed one carrier, DVB-S, from bits to the dish and back. This chapter keeps almost the whole chain and changes one thing: the single carrier becomes 6817 carriers. That is OFDM.

DVB-T is a good teacher for OFDM. Every step is written down in one public standard (ETSI EN 300 744), the numbers are round enough to work out by hand, and it is the same idea as under 4G, 5G and Wi-Fi.

At the end: what DVB-T2 changed, and how the same OFDM is scaled for DAB, Wi-Fi and 5G.

Speaker notes

The map for the whole chapter, as in chapter 2: the transmitter on top, the receiver below.

Grey: the steps of chapter 2, unchanged. DVB-T uses the same scrambler, the same Reed-Solomon code (204, 188), the same interleaver with 12 branches and the same convolutional code with the same puncturing as DVB-S.

Blue: the bits become points. DVB-T adds an inner interleaver and offers QPSK, 16-QAM and 64-QAM, where DVB-S has only QPSK.

Orange: OFDM, the subject of this chapter. The points are placed on carriers with pilots between them, one IFFT turns them into a signal, and a guard interval goes in front of every symbol. The receiver drops the guard, runs an FFT and uses the pilots to undo what the air did.

The map comes back before every part, with the steps of that part in green.

Speaker notes

A satellite dish sees one path: straight up. A roof antenna sees the transmitter, and also the hills, the buildings and, in a network, other transmitters on the same channel. That is why DVB-T could not simply reuse the DVB-S modulation.

Speaker notes

Radio travels about 300 m per microsecond: 1 km of extra path is 3.3 µs of delay.

In the drawing: a reflection off the flats, 1.5 km longer, arrives 5 µs late; one off a hill, 6 km longer, 20 µs late. These are examples; real echoes over land range from fractions of a microsecond to tens of microseconds, and much longer in a single-frequency network (part 07).

Indoors the echoes are a thousand times shorter, tens of nanoseconds. The idea is the same, only the scale changes.

Speaker notes

Chapter 1 gave the rule: the bandwidth is roughly the symbol rate. 1 symbol per T needs about 1/T; 4 symbols per T need about 4/T.

So one carrier that fills a TV channel of 7.61 MHz with roll-off 0.35, as DVB-S would, sends about 5.6 million symbols per second: each symbol lasts 0.18 µs.

OFDM uses the same width differently: it cuts it into many narrow carriers, each changing slowly. 4 carriers at 1 symbol per T carry the same 4 symbols per T in about the same 4/T. DVB-T uses 6817 of them, each sending one symbol per 896 µs.

The next slide puts numbers on what that means for an echo.

Speaker notes

A single carrier: the echo of 20 µs overlaps 113 later symbols. The receiver would need an equaliser that undoes 113 symbols of mixing, and keeps up as the echoes change.

OFDM: the same echo is 2 % of a symbol. The next parts show how the guard interval removes even that, and how the receiver undoes the rest with one multiplication per carrier.

0.18 µs: 7.61 MHz / 1.35 is 5.64 million symbols per second.

Speaker notes

A sine that runs for ever has a single line as its spectrum. Switch it on for a time T only, and the line widens into a sinc: a peak at the sine's frequency, with zeros every 1/T on both sides.

Row by row: 5 periods in T gives a peak at 5/T. 6 periods in the same T peaks 1/T further, at 6/T, exactly where the first sinc is zero. 7 periods: again 1/T further.

Bottom row: the sum of the three sines is what is sent. Its spectrum is the sum of the three sincs. At 5/T, 6/T and 7/T only one sinc is not zero, so the receiver reads each sine's amplitude back without any trace of the others.

That is the whole trick of OFDM: the carriers are sines that fit a whole number of periods in one symbol time T, 1/T apart. In DVB-T 8k, T = 896 µs, so the carriers are 1116 Hz apart.

Speaker notes

This is the "orthogonal" in OFDM. The receiver reads every carrier at its centre, where every neighbour crosses zero.

It only works when the receiver's frequency is exact: a few per cent of 1116 Hz off, and the neighbours are no longer zero there. Part 06 shows how much that hurts, and how a receiver gets it right.

Compare chapter 2: DVB-S keeps its neighbours apart with a filter and 35 % extra bandwidth (the roll-off). OFDM lets its carriers overlap and needs no gap at all between them.

Speaker notes

The top is calculated: the sum of 6817 sinc² shapes, with guard 1/4. The sum is flat across the channel; the small ripple at the top is the drawing's resolution. Of 8 MHz, 7.61 MHz is used; the rest keeps distance to the neighbouring channels.

At the edges the spectrum falls by 30 dB within a few carriers. The slow tails beyond are the sinc tails of the outer carriers; a real transmitter filters them to meet the channel mask.

DVB-T has two modes. 8k: 8192-point FFT, 6817 carriers, 1116 Hz apart, symbols of 896 µs. 2k: 2048-point FFT, 1705 carriers, 4464 Hz apart, symbols of 224 µs. 8k copes with longer echoes and suits large networks; 2k copes better with movement. In 7 and 6 MHz channels all times scale up by 8/7 and 8/6.

Speaker notes

6817 oscillators, each with its own amplitude and phase, would be impossible to build. Chapter 1 gave the shortcut: adding up sines is the inverse Fourier transform. Put one I/Q point on each carrier, run one inverse FFT, and out comes the sum of all of them as samples in time.

DVB-T uses an IFFT of 8192 points. 6817 of them carry data, pilots and TPS; the other 1375, at the edges, stay zero: that is the gap to the neighbouring channels.

The output is 8192 samples in 896 µs: 9.14 million samples per second (64/7 MHz, which is 8192 × 1116 Hz). A DAC and an I/Q mixer move them to the channel, as in chapter 1.

The signal on the right looks like noise: thousands of carriers with random phases add up that way. Now and then they line up into a peak far above the average. The transmitter's amplifier must handle those peaks without clipping, so it runs well below its maximum: the opposite of the satellite in chapter 2.

The receiver does the reverse with one FFT: from 8192 samples back to one point per carrier.

Speaker notes

Step 1 and 2 are in the frequency domain: one point per carrier. Step 3 crosses to the time domain. Steps 4 and 5 work on samples.

Of the 6817 carriers, 6048 carry data in every symbol. The rest are pilots (part 04) and 68 TPS carriers that tell the receiver the settings.

68 symbols make a frame, 4 frames a superframe. The pilot pattern and the TPS follow that frame.

The receiver does the same steps backwards: down-convert, drop the guard, FFT, undo the channel with the pilots, read the QAM points.

Speaker notes

Without a guard, the echo of symbol 1 would run into the start of symbol 2. With a guard, the receiver waits until the latest echo of symbol 1 has passed, and listens for exactly 896 µs. In that window every path, the direct one and every echo, holds one symbol only.

The drawing is to scale: 8k mode, guard 1/4. The echo of 20 µs is barely visible; the second mast at 150 µs still fits.

Why a copy and not silence? The next slide.

Speaker notes

Every carrier makes a whole number of periods in T (that is what spacing 1/T means). The end of the symbol therefore connects perfectly to its start. A copy of the end in front just lets each sine run a little longer, and the sum of all carriers runs on just as smoothly.

The receiver throws the guard away and listens for exactly T. A late echo then still shows whole periods of every carrier in the window, only shifted in phase. A phase shift per carrier is what the equaliser undoes (part 04). So the carriers stay orthogonal and nothing leaks between them.

Silence instead of a copy would cut each sine short inside the window when an echo arrives late, and the carriers would leak into each other.

The bottom row shows why the carriers must fit: a sine with 5.5 periods gets a jump at the guard, and a jump needs new frequencies.

The price is time: the guard carries no new data. 1/32 of the symbol costs 3 %, 1/4 costs 20 % of the bit rate.

Speaker notes

The four guard intervals of EN 300 744, as a fraction of the symbol time.

Extra path: how much longer an echo may travel than the first signal, for 8k mode, at 300 m per µs. In 2k mode a quarter of that.

Bit rate: 64-QAM, code rate 2/3, 8 MHz; the same in 2k and 8k. 6048 carriers × 6 bits × 2/3 × 188/204, divided by the symbol time with its guard.

The operator picks it: a single transmitter can live with 1/32; a large single-frequency network, where the next mast is an echo tens of km away, needs 1/4 or 1/8.

Speaker notes

Echoes add up or cancel per frequency: some carriers arrive strong, others weak, each turned by its own angle. QAM puts information in amplitude and phase, so the receiver must know that change per carrier. Pilots tell it.

Speaker notes

Drawn from the positions in EN 300 744, 8k mode: the first 60 of 6817 carriers, 8 symbols.

Scattered pilots (blue): on every 12th carrier, moved 3 carriers on in each next symbol. After 4 symbols, every 3rd carrier has been measured. The receiver uses them for the channel.

Continual pilots (black): 177 carriers that are a pilot in every symbol, at fixed, irregular positions. The receiver uses them to lock its frequency and to find which carrier is which.

TPS (light blue): 68 carriers with the settings, next slides.

Pilots are sent 2.5 dB stronger than the data (amplitude 4/3), with a value both sides know from a fixed pseudo-random sequence.

Speaker notes

At each pilot the receiver divides what arrived by what it knows was sent: that is the channel there, a gain and a phase. Between the pilots it interpolates, first over time (4 symbols, so every 3rd carrier has a value), then over frequency.

The drawing is calculated: one echo half as strong, 20 µs late. The channel then repeats every 1 / 20 µs = 50 kHz, about every 45 carriers. Pilots every 3rd carrier follow it easily.

How long an echo can the pilots follow? Measuring every 3rd carrier means samples 3 × 1116 Hz apart, which follow echoes up to 1 / 3348 Hz = 299 µs. The longest guard is 224 µs: the pilot pattern was chosen to cover it.

This is the step a single carrier could not do simply. Here each carrier is so narrow that the channel is flat across it, and one division undoes it.

Speaker notes

In chapter 2 the DVB-S receiver had to find the code rate by trying. A DVB-T receiver is told: TPS (Transmission Parameter Signalling) carries the settings.

One TPS bit per symbol, so one frame of 68 symbols carries 68 bits: a sync word, the constellation, the hierarchy, the code rates, the guard interval, the mode, the frame number, a cell ID, and a BCH code to protect it.

The bit is sent as a change of phase from one symbol to the next (DBPSK), so the receiver can read it before it has measured the channel.

With the TPS read, the receiver knows how to demap and decode everything else.

Speaker notes

Chapter 2: a satellite uses QPSK because its amplifier runs near saturation, where only the phase survives. A DVB-T transmitter must keep its amplifier linear anyway, for the peaks of the OFDM signal. So amplitude can carry information too, and DVB-T offers 16-QAM and 64-QAM.

C/N: what EN 300 744 gives for quasi error-free reception in a Gaussian channel, rate 2/3. In a channel with echoes it needs more: 64-QAM 2/3 needs 19.3 dB when there is no direct path (Rayleigh).

DVB-T also allows hierarchical modulation: a robust QPSK stream inside the 64-QAM points, for mobile reception, and a second stream in the fine detail for roof antennas. Few networks use it.

Speaker notes

An echo makes fades: a few neighbouring carriers come in weak. Without interleaving, those would be neighbouring bits for the Viterbi decoder: a burst, the one thing it repairs worst (chapter 2).

So DVB-T mixes twice. A bit interleaver spreads the bits of each point over different points, in blocks of 126. A symbol interleaver then spreads the points over all 6048 data carriers of a symbol, with a pseudo-random pattern.

The receiver undoes the mixing. The carriers lost in a fade become scattered points, and their bits scattered bits: what the Viterbi decoder handles best.

The demapper also tells the decoder how sure it is about each bit (soft bits), and the equaliser knows which carriers were weak. A good receiver uses that: a bit from a faded carrier counts for little.

The drawing is an illustration with 48 carriers and a simple pattern; the real permutation is in EN 300 744.

Speaker notes

The whole calculation: 6048 × 6 bits × 2/3 × 188/204 / 924 µs = 24.1 Mbit/s.

64-QAM, rate 2/3, guard 1/32 is a typical setting for roof antennas. The highest DVB-T rate, 64-QAM, 7/8, guard 1/32, gives 31.7 Mbit/s; the lowest, QPSK, 1/2, guard 1/4, 5.0 Mbit/s.

Compare DVB-S in chapter 2: 38 Mbit/s in a transponder of about 37 MHz. DVB-T carries 24 in 8 MHz: three times as many bits per hertz, because the signal on the ground is much stronger.

Speaker notes

Chapter 2 had this list for DVB-S. For OFDM it changes, because the FFT only works with the right start and the right frequency.

1. Symbols: the receiver compares the signal with itself 896 µs later (next slide). The guard is a copy, so the two match where a guard is. That also tells 2k from 8k, and the guard length.

2. Fine frequency: the phase of that same match shows how far off the receiver is, within ± half a carrier spacing.

3. Whole carriers: the tuner can be off by several carriers. After the FFT, the continual pilots sit on known, irregular positions; the receiver shifts until they line up.

4. TPS: with frequency and timing locked, it reads the settings from the TPS carriers, once it has found the frame sync word in them.

5. Channel: then the scattered pilots, the equaliser, the demapper, and the decoders of chapter 2.

Speaker notes

An OFDM signal looks like noise, so there is nothing to see in it directly. But the guard is a copy: the samples of each guard come back exactly one symbol time later.

The receiver multiplies each sample by the conjugate of the one 896 µs later and adds that up over the length of the guard. Where the window sits on a guard, the products all point the same way and add up to a peak. Elsewhere they are random and cancel.

The phase of the peak is extra: if the receiver's frequency is off, the copy has turned by a known angle in 896 µs. That angle gives the frequency error within ± half a carrier spacing.

Calculated with 64 carriers, guard 1/4, QPSK, at 10 dB signal over noise: even there the peaks stand out.

Speaker notes

If the receiver's frequency is off, it no longer reads each carrier at its centre, where the neighbours are zero. Each carrier then picks up a little of all the others: inter-carrier interference. It looks like noise.

Calculated: 256 carriers, 64-QAM, no noise. 2 % of the spacing gives a modulation error ratio (MER) of 29 dB; 6 % gives 20 dB. 64-QAM at rate 2/3 needs 16.5 dB, so at 6 % there is little room left for real noise.

The scale: 22 Hz at 600 MHz is 0.04 ppm. A tuner's oscillator is never that good, so the receiver measures the error (previous slide and the continual pilots) and corrects it in the samples before the FFT.

The common turn of all points is taken out in the drawing, as a receiver does with the continual pilots; what is left is the leak between carriers.

Compare chapter 2: a frequency error in QPSK makes the constellation turn. In OFDM it also makes the carriers leak, which no later step can undo.

Speaker notes

In analogue TV, neighbouring transmitters needed different channels, or they interfered. With OFDM, a second mast sending exactly the same signal at exactly the same moment is, for the receiver, one more echo. As long as it arrives within the guard, it adds signal instead of interfering.

The example: masts 40 km apart, a receiver 10 km from A and 30 km from B. The signals take 33 and 100 µs: 67 µs apart, well inside a guard of 224 µs.

Every mast must send the same bits in the same symbol at the same instant. Each mast locks to GPS for time and frequency, and a marker in the transport stream (the mega-frame initialisation packet, ETSI TS 101 191) tells every mast which packet goes out when.

Speaker notes

Saves channels: the spectrum for TV is limited, and an SFN covers a whole area on one channel.

Fills the gaps: a gap filler in a valley or a tunnel repeats the signal on the same channel.

The same idea indoors: a distributed antenna system sends one operator's signal from many antennas in a building. To a phone, the antennas are echoes of each other, inside the cyclic prefix of 4G or 5G. That is the subject of the deck on OFDM and active DAS.

Beyond the guard: an echo that arrives later than the guard smears into the next symbol and acts as interference. Network planners choose the guard and the mast distances together.

Speaker notes

The green steps are the ones DVB-T2 changes. As DVB-S2 did for satellite (chapter 2), DVB-T2 keeps the idea and replaces the parts.

Speaker notes

DVB-T dates from 1997, DVB-T2 from 2008.

Error correction: the LDPC and BCH codes of DVB-S2, a few dB closer to the Shannon limit (chapter 2).

Modulation: up to 256-QAM, and rotated constellations: each point is turned so that its I and its Q each carry all its bits, and I and Q are sent on different carriers. When a fade takes one, the other still says which point it was.

More carriers: 32k mode has 27 841 carriers 279 Hz apart, symbols of 3.6 ms. With a guard in µs as long as before, that is a smaller fraction of the symbol, so less is lost to guards.

Pilots: 8 patterns, so the operator picks the density that fits the guard, instead of one pattern for all.

Capacity: the DVB Project gives 30 % or more over DVB-T, in the same channel and at the same coverage; how much depends on the settings compared.

Speaker notes

One idea, one rule: the guard must be longer than the echoes, and to keep the guard a small part of the symbol, the symbol must be long, so the carriers close together.

Broadcasting over a country (DAB, DVB-T) needs guards of hundreds of µs, so symbols of a millisecond and carriers about 1 kHz apart. A Wi-Fi network in a building needs less than a µs, so it can use short symbols and widely spaced carriers, which cope better with movement and frequency errors.

4G and 5G sit in between: cells of kilometres, and phones that move.

Echoes up to: the guard in µs times 300 m. Sources: ETSI EN 300 401 (DAB), EN 300 744 (DVB-T), 3GPP TS 36.211 and 38.211 (normal cyclic prefix), IEEE 802.11.