V.wb: wideband DMT on a bare pair: technical details¶

This is the technical companion to V.wb: wideband on a bare pair, the plain-English overview. Start there; this page keeps the full detail: the code's names, the Recommendations' clauses, the numbers and the test lists.

AT+MS=VWB (or AT+MS=200) runs D-Modem's own wideband mode. On a line sampled at 48000 Hz or more it is the default, and the only mode the core will run there.

It is meant for a bare copper pair between two D-Modems: a dry pair, an alarm or leased circuit, or a pair of your own in a building or between buildings. The line hardware is pico-serial's WB stick (SPEC-WB.md in pico-serial: a codec at 96 kHz, a wideband transformer, protection), or any codec that samples the pair at 48000 Hz or more.

Both ends are D-Modem, so the modulation follows no Recommendation. It is not ADSL: it does not talk to a carrier's DSLAM, and it does not need megahertz of band.

The code is in two files:

• dsp/vwb.cpp: the modem itself, VwbModem;
• dsp/dp_vwb.cpp: the pump the core runs, DP_VWB. It refuses to start below 48000 Hz.

V.42 (LAPM) and V.44 run on top, as on any other call.

The signal¶

The signal is discrete multitone (DMT, the same idea as OFDM) in frequency-division duplex: many narrow tones, each with its own QAM, and each direction on its own part of the band.

• The tones are 187.5 Hz apart at every rate, and there are 173.9 symbols a second.
• The band is the WB stick's. Its transformer and DC block cut below about 2.7 kHz. Its codec's ADC passes up to 37 kHz at 96 kHz, and only 21 kHz at 192 kHz. So 96000 Hz is the stick's rate, and 192000 Hz is kept for tests and for other hardware.
• The caller sends on the lower part of the band and the answerer on the upper part, with a guard of 4 tones between them. The split is chosen at training, so that both ways get about the same rate.
• Each tone carries 0 to 12 bits. Its QAM has ceil(b/2) bits on I and floor(b/2) on Q, Gray coded on each axis, at unit power. Each tone also has a fine gain within ±2.5 dB.
• In data, each band has 8 pilot tones, which carry the sync symbol's point. They keep the receiver's timing.

Timing and the two clocks¶

Each receiver resamples its input onto the far end's clock, with a 32-tap Kaiser windowed sinc at 256 phases (VwbInterp).

A type 2 timing loop drives the resampler. Its error is the slope of the pilots' phase errors across the band (or of every tone's, while the sync symbols are on). The loop changes only the resampler's rate, never its phase in steps. So a correction never puts a step into a symbol, and the receiver's own echo stays clean.

The answerer is loop timed:

1. It sends on the caller's clock: its transmitter goes through the same mapping as its receiver.
2. It lines its symbols up with the caller's as they reach its own receiver. It measures the delay of its own echo while it sends its full-band sync.

Its echo therefore lands on the same symbol boundaries as what it receives, and in its own band it is orthogonal to the far signal. At the caller, the two are apart by twice the pair's delay. The caller measures that offset (its own echo's delay comes from its full-band sync). The plan then moves the answerer's symbols by half of it, so that at both ends the echo is the same few samples ahead.

The FFT window starts half the cyclic prefix (20 samples at 96 kHz) before the prefix's end. That leaves 20 samples for the pair's dispersion and 20 for the echo's offset.

The hybrid's leak of each side's own signal (10 to 20 dB down on the stick, -15 dB in the tests) therefore costs nothing measurable. The clock offset is tracked whatever it is. The tests run ±100 ppm (the stick's crystals are within ±50 ppm), and the receivers report the offset they track.

The start-up¶

The timeline is from vwb_test's logs at 96 kHz:

• the probe is heard after 35 ms;
• both full-band syncs are done after 2.1 s;
• the plan is made after 2.8 s;
• data runs both ways after 5.0 s.

The echo's tail. Each side hears its own full-band sync through the hybrid, delayed by as much as the host's buffers and the pair take. A USB or ALSA line holds tens of milliseconds each way (dmodemd's USB line sends its samples about 50 ms ahead). If that echo were taken for the far end's sync, the receiver would lock onto it.

So each side looks for the far end's next sync only 32 symbols (184 ms) after its own has ended:

• the answerer, for the caller's full-band sync;
• the caller, for the answerer's sync on its message band. That sync is 80 symbols long (48, plus those 32), so that it is still there to be found and trained on.

The message channel is QPSK on the lowest 30% of the tones (the caller's) and the highest 30% (the answerer's), at least 16 tones each, with 4 pilots each. The plan's split always falls between these two bands. So while one side has switched to the plan and the other has not, neither side's echo lands on tones it receives.

• Each bit goes on 2 tones (the caller's) or 4 (the answerer's). The receiver adds the copies, each weighed by its tone's measured SNR.
• A frame is a type octet, a length (2 octets), the payload and a CRC-32. It is whitened by a PRBS (x^15 + x^14 + 1); a frame of zeros would otherwise peak and clip. It fills a whole number of symbols, the same number for every frame of one direction.
• Frames repeat until the far end answers them.
• The answerer's SNR frame is one octet a tone (dB × 2).
• The caller's plan frame holds:
• the split (as an offset from the band's first tone);
• the guard;
• the answerer's shift (2 octets);
• a code for each tone: its bits, 15 for a pilot, 0 unused;
• each tone's gain (128 + 0.1 dB steps).

The plan:

1. Each tone's bits are the most whose SNR need is met with a 4 dB margin. A b-bit QAM needs q²P/2, with q = 4.75 and P the constellation's power at unit spacing.
2. The split is the one that maximizes the slower direction's bits.
3. Each band gets 8 pilots, each on the best tone near its place.
4. Gains equalize the margins within ±2.5 dB, and the band's power is kept.

Data¶

1. The core's octets go through the self-synchronizing scrambler 1 + x^-18 + x^-23 (V.34's GPC, bits.h).
2. Then RS(255,239) (rs.cpp: 8 octets corrected in each codeword).
3. Then a block interleaver of D codewords. D is as many codewords as 30 ms of the line hold, from 1 to 8: 2 at 150 kbit/s.
4. The bits go onto the tones in tone order, least significant first.

The reported rate is the octets' rate: the bits of a symbol, times 239/255, times 173.9.

The interleaver is shallow on purpose. V.42's window (15 frames of 128 octets) waits a round trip for its acknowledgement, and a deeper interleaver's delay cut LAPM to 53 kbit/s on a 149 kbit/s pump in the tests. At D = 2 it gets 138 kbit/s.

The receiver follows the channel on its decisions (LMS, 0.01) and on the pilots. It retrains (the start-up again; ATI11 counts it, and the core keeps the call) when:

• the pilots are lost for 8 symbols;
• half of the last 32 codewords fail;
• a start-up phase times out.

If there is no data again within S7 seconds, the pump gives up (NO CARRIER).

Leased lines: AT&L1¶

A bare pair has no exchange: no dial tone, no ringing, no hook. At 48000 Hz and above the core treats the line as one without an exchange, with or without AT&L1:

• it never runs call progress;
• ATD (with any number, or none) starts the data pump as the caller at once;
• ATA starts it as the answerer, which waits for the caller's probe for S7 seconds.

AT&L1 (S47=1, the leased line setting; the voice band's leased lines are in leased.md) adds the behaviour of a permanent connection:

• ATS0=1 (any S0 but 0) answers with no ring as soon as the modem is idle. Each time a call ends, it waits for the caller's probe again.
• When the line ends a call (NO CARRIER: no data again within S7), the modem starts it again by itself 2 s later. The caller dials again, and the answerer waits for the probe again.

ATH, dropping DTR, ATZ or AT&L0 stop this until the next command line, so that a command can be typed between the attempts.

Rates measured in simulation¶

Both ends run on the simulated pair of dsp/test/vwb_line.cpp at 96 kHz:

• the cable is 24 AWG with a loss of k·sqrt(f)·length (k = 0.025 dB/km/sqrt(Hz), about 8 dB/km at 100 kHz), its skin-effect phase, and 5 µs/km of delay;
• each end's transformer is a high pass at 2.7 kHz;
• white noise at the receivers;
• -15 dB of each side's own signal at its receiver (the hybrid);
• the answerer's clock 100 ppm fast (resampled to and from the line);
• about 5.3 ms of latency each way (the two sides' converters and buffers), in blocks of at most 5 ms.

All rates are octets after RS, each way, both ways at once. Every case ran with no bit error.

148656 bit/s is the most there is at 96 kHz: 76 data tones a way at 12 bits. More would need tones above 36 kHz (the stick's ADC passes 37 kHz) or more bits a tone. That is about 300 kbit/s both ways together, as SPEC-WB expected.

Other results:

• Through V.42. Under libdmodem (vwb_call_test), 400 kB each way at once, byte for byte, went at 138558 bit/s each way through V.42 on the 148656 bit/s pump.
• Through a host's buffers. With each end's samples 4672 ahead and in 20 ms frames, as dmodemd's USB line has them (vwb_call_test's HostLatency), the call connects as before; V.42 then carries 83 kbit/s each way (LAPM's window waits a longer round trip). dmodemd itself runs the call between two fake WB sticks on this pair in real time (frontend/dmodemd/test/pico_wb_test.py, hardware.md).
• Dropout. A 0.5 s cut of the pair costs one retrain. The data goes on after it, and LAPM sends again what was lost.
• CPU. One end takes about 1.5% of one x86 core at 96 kHz.

Left to do¶

• Bit swapping in a call (a tone's bits moved as its noise changes).
• Trellis coding.
• V.42's extended windows, which a long interleaver, and a host's buffers, would need.
• A real pair, and a real WB stick (dmodemd's --usb drives it: hardware.md).