V.90 analogue modem: technical details¶

This is the technical companion to V.90 and V.92: the analogue modem, 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.

The open DSP has V.90 as the digital modem (see V.90): the end of the call on the 8000 Hz G.711 network. This page is about the other end, the analogue modem: a softmodem on a telephone line (dmodemd -a, see hardware) calling an ISP's V.90 server.

Terms¶

• PCM: the digital modem's G.711 codes, which reach the analogue modem as voltages on its line.
• Ucode: a PCM code number from 0 to 127.
• UINFO: the Ucode of TRN1d's two points, which the analogue modem chooses in INFO1a.
• DIL (digital impairment learning): a sequence of codes, chosen by the analogue modem, that shows it what the network does to each code.
• Data frame interval: one of the 6 symbol positions of a data frame. Robbed bits and some pads affect only some intervals.
• T: one symbol period. T/2: half of one.
• mse: mean square error. rms: root mean square, here on a 16-bit scale.
• NLMS: normalised least mean squares, an adaptive filter update.

Stages¶

The work went in stages, each with its tests:

When it is used¶

The analogue modem's mode is chosen in V34Pump::start() (dp_v34.cpp):

• At 9600 Hz, with +MS set to V.90 or V.92 (V.92 is the default), the modem offers V.90 as the analogue modem. DSP_V90A=0 leaves PCM out (the call is then V.34).
• With V.92, it also asks for PCM upstream wherever the digital modem offers it. DSP_V92A_UP=0 leaves out PCM upstream alone.
• At 8000 Hz (-r 8000), V.90 as the analogue modem needs DSP_V90A=1; otherwise such a line runs V.34. See 8000 Hz lines.
• It is not offered when V.8 is used only to reach a low-speed modulation.
• V.91 is between two digital modems, so on an analogue line it is always V.34: the core turns +MS=V91 into V.34 there.

A dmodemd -a line is an analogue line at either rate. The line tells the core so through Host::analog_line(), and the core tells the pump through dp_runtime_set_analog(). A 9600 Hz line is always taken as analogue.

Phases 1 and 2 (stage A)¶

In dp_v34.cpp, with AT+MS=90 or 92 on an analogue line (see above):

V.8¶

• CM and JM carry PCM in the modulation octet, and the PCM modem availability octet with the analogue modem's bit (V8_PCM_ANALOGUE).
• A JM keeps that bit only when the CM had the digital modem's bit, just as the digital modem's JM keeps its own bit only for an analogue modem.
• The PSTN access octet's "digital connection" bit belongs to the digital modem alone.
• V.90 is agreed (v90a_on) when the other end's CM or JM has the digital modem's bit (v8_v90a()).

The roles¶

From phase 2 on, the analogue modem is the V.34 answer modem, whichever side called (9.2.2/V.90).

• When it answers, it is that already.
• When it calls, as an analogue modem calls an ISP, it becomes the answer modem at the end of V.8, 75 ms after CJ. From CJ on, its control channel sends at 2400 Hz and listens at 1200 Hz (the digital modem's INFO0d may come at once). The tone detectors, including the retrain's, are mirrored, and the answerer's phase 2 (P2A_*) begins with INFO0a.

This is the digital modem's swap the other way round: the digital modem becomes the call modem.

INFO0a and INFO0d¶

• INFO0a is V.34's INFO0 (Table 8/V.90): our symbol rates and carriers, with bits 26 and 27 clear.
• INFO0d (Table 7/V.90) is 13 bits longer than INFO0: 58 bits to the end of its CRC, which is at bit 42. It carries the digital modem's phase 2 power, its maximum power and where it measures it, the network's law (bit 39) and whether it takes 3429 baud upstream (bit 40).
• The receiver looks for frames of INFO0d's length:
• while it waits for INFO0 (info0_rx_len());
• for the INFO0d repeats of phase 2's recovery;
• when it tells INFO1d from the INFO0d before it.
• The law in INFO0d becomes ours (alaw): it is what the PCM receiver will decode.

Probing and INFO1d¶

Probing is V.34's: L1 and L2 both ways. INFO1d (Table 9/V.90) is INFO1c: for each symbol rate, the carrier, the pre-emphasis and the most the digital modem can receive from us.

INFO1a¶

INFO1a (Table 10/V.90, make_info1a_v90()) asks for V.90 with 6 in bits 37:39 (the digital modem's 8000 symbols a second).

• Bits 34:36 hold the upstream symbol rate that v90a_choose() picks. Of 3000, 3200 and 3429 baud (3429 only if INFO0d allows it), it takes the one for which INFO1d gives the most, on the carrier INFO1d asks for if our INFO0a has it.
• If INFO1d offers none of them, we send V.34's INFO1a instead (choose_bauds()), and the call goes on as V.34 with us as its answer modem (9.2.2.1.9/V.90).
• UINFO (bits 25:31) is the loudest Ucode within INFO0d's maximum power, and at least 67. 0 dBm0 is 3.17 dB below the sine at µ-law's overload point (3.14 dB for A-law). So INFO0d's −12 dBm0 (what our digital modem sends) gives UINFO 79 (−12.3 dBm0; −12.0 for A-law). The analogue modems in the interop tests ask for 77 to 79 with the same INFO0d.

Then phase 3 follows.

Phase 3 (stages B and C)¶

This is dp_v34.cpp's P3V_* states and v90a.cpp's PCM receiver (V90Rx).

What we send¶

v90a_start() sets up V.34's transmitter at the upstream symbol rate, on the carrier INFO1d asked for, with the answer modem's scrambler (GPA). The sequence is:

1. 70 ms of silence.
2. S for 128 T, then S-bar for 16 T.
3. PP, then TRN for 2048 T. (At least 512 T are needed: the digital modem trains on PP and TRN.)
4. Ja, again and again (V34_TX_JA). Ja is the DIL descriptor (V90Dil::build(), the inverse of the digital modem's parse()), sent as MP is: differentially on 4 points, scrambled.
5. Ja stops at the digital modem's Sd-bar, then silence. If Sd-bar has not come within 3 s of Ja's start, we retrain.
6. S once Jd is in, until Jd'; then S-bar for 16 T.
7. Silence while the DIL comes in.
8. S for 128 T and S-bar for 16 T, which end the DIL (9.3.2.10/V.90: within 5 s).

The receiver's input¶

The receiver works on the line at 16000 Hz, two samples per PCM symbol.

• V90Rx::line() takes the pump's 9600 Hz samples through V90Interp: a Blackman-windowed sinc over 128 samples, cut at 4800 Hz (the line's Nyquist frequency), tabulated at 256 phases between two samples and interpolated linearly between those.
• On an 8000 Hz line it takes the line's own samples (from process()), through the same interpolator at a step of 0.5 sample.
• The interpolator's output time moves with the timing loop (below).

Why 16000 Hz: the PCM signal fills the band up to 4000 Hz and beyond it (netsim's codec is a raised cosine with a roll-off of 0.15, up to 4600 Hz). Sampled at 8000 Hz, the band above 4000 Hz folds onto itself, and half a symbol away from the symbols' instants it cancels near 4000 Hz. A T-spaced equaliser then falls from 90 to 21 dB, and nothing brings it back. At 16000 Hz nothing folds, and a T/2 equaliser handles any delay (86 to 88 dB at every phase, offline, on a raised cosine line).

Finding Sd¶

Sd is looked for on every other sample (8000 Hz), since Sd repeats every 6 symbols at any phase.

• Over 24 samples, the line resembles itself 6 samples earlier and its negative 3 samples earlier (the pattern +W +0 +W −W −0 −W). This must hold for 96 samples.
• At Sd's reversal, the lag-6 correlation over 24 samples dips to about 0.5 (the 6 samples after it against the 6 before), at any phase.
• Within that dip, the receiver takes the 6 samples whose lag-6 correlation is most negative: −1 on the symbols' instants, −0.25 a third of a symbol off, where the reversal spreads.
• That gives symbol 0 of S-bar d, which is data frame interval 0, at sample b (16 kHz). TRN1d starts 48 symbols later.

The equaliser¶

• 128 taps at 16000 Hz (T/2, spanning 64 symbols). Symbol k's sample, b + 2k, sits at the middle tap.
• TRN1d's signs are known (GPC on ones, from zero). So:
• its first 96 symbols centre the delay (b moves to the best correlation, either polarity, since a line may reverse it);
• the next 1020 symbols give the normal equations, solved by Cholesky decomposition;
• after that, NLMS (step 0.005) on TRN1d's signs up to its minimum length of 2040 T, and on the decisions after it.

UINFO's level at each position¶

The receiver keeps a target level for each position, symbol k mod 6 (tlev). From the solution on, the targets are each position's recent mean magnitude, scaled so that the loudest equals UINFO's level.

This is needed for robbed bits. A robbed bit takes UINFO's least significant bit in its interval (Ucode 79 comes out as 78, a step lower). With one level for all six positions, the equaliser was trained to a target it could not reach one symbol in six: 38 dB where the clean line gives 77, and UINFO's spread (the noise CP is designed on) came out at 13 instead of 0.5. An equaliser that is the same for all six positions cannot give one of them a level of its own, so whatever it gives there is the line's, and the targets follow it. Ri uses the same targets.

The timing loop¶

timing() runs from the equaliser's solution on.

• Error signal: the equaliser's error times its slope, (a − y)(y(+1) − y(−1)), using its output one sample either side, divided by the recent power of the targets (the DIL's codes and the data's are up to 64 times UINFO's).
• Loop: it moves the interpolator's output time with a phase term (0.02) and a frequency term (2e−5), which follows the codec's clock.
• Clock fit: from symbol 2000 to 6000, the phase it has moved is fitted to a straight line. Its slope gives the clock's offset to about 0.1 ppm, where the frequency term alone is off by 1 or 2 ppm. The loop then runs on the fitted value, with gains of 0.004 and 2e−7: the loop's jitter would otherwise cost the dense constellations their margin.
• Second solution: then the equaliser is solved again, on the locked timing. (The first solution spans a drifting clock: 29 dB at 100 ppm.) UINFO's spread over 512 symbols is then taken as the noise (see Phase 4).
• Only then do we send our S, ending Jd. (We may wait 5 s for it, 9.3.2.7/V.90; once Jd is in, the code sends S at the latest 4 s into the wait, and retrains if Jd has not come in 4.5 s.) The receiver is ready about 1.1 s into TRN1d.
• Through the DIL, the loop runs on the frequency alone: the DIL's levels are what it is measuring, so there is nothing to steer by. From Ri on it follows the error again: Ri's signs, TRN2d's known symbols, then the decisions.

Jd and Jd'¶

Each decision's sign is decoded differentially, passed through the GPC descrambler (which synchronises itself, so TRN1d's bits before Jd do no harm), and shifted into a 72-bit window. A Jd frame is taken when its sync, start bits, CRC and fill bits are all right (V90Jd: the rates, the constellations of CP, E and SCR, and the look-ahead). Jd' is 8 zeros where the next frame's sync would be.

The DIL we ask for¶

v90a_start() asks for this DIL (DSP_V90A_DIL=0 asks for none: N is 0, and the digital modem goes to phase 4 after Jd'):

• all 128 Ucodes, loudest first;
• 36 symbols each (H = 5: six in each data frame interval);
• every symbol a training symbol (TP = 1, no reference symbols);
• the sign pattern SP is 12 long, its second half the opposite of its first, so each interval has three of each sign in a segment.

A round is 4608 symbols (0.58 s), and two rounds are measured. The DIL starts 12 symbols after Jd' (5 after its 8th symbol, where the receiver recognises it), in data frame interval 0.

The equaliser is held still during the DIL, because the levels are not known yet (a pad changes them). Each symbol's value times its sign goes into its interval's and Ucode's sums (dil_add()).

What the DIL shows¶

V90Rx::dil_analyse() works out, for stage D's constellations:

• Levels and noise: each Ucode's level in each interval (dil_level) and its noise. The DIL's noise is the median of those (about 1 on a 16-bit scale on netsim's quiet line). The data mode's noise is a different measure: the equaliser's mse on random signs.
• Unusable Ucodes: a Ucode is unusable where its noise is more than 4 times the DIL's noise plus 0.2% of its level. This catches the loudest codes, which clip at the analogue modem's codec (from about Ucode 112 on netsim's line). The loudest come first in a round, so that what they spill over the equaliser's span falls on the others that clip. (When Ucode 0 came first, as the round started, it had a noise of 280.)
• Robbed bits: an interval is taken as robbed when either:
• two neighbouring Ucodes (2m and 2m + 1, or 2m + 1 and 2m + 2, depending on the law's octet) come out alike in 7 out of 10 of the pairs that the noise can tell apart; or
• behind a pad (which moves the codes first), the interval tells fewer than 3/4 as many levels apart as the best interval.
• The pad: the equaliser, trained on UINFO through the pad, takes the pad's loss away; but the codes that were requantised lower show in the shape of the levels. Of 0 to 9 dB in 0.5 dB steps, the pad is the one whose levels (re-encoded, scaled as UINFO's) best fit the measured ones. The fit uses the levels at 10 times the noise and above, in the intervals that are not robbed.
• Distinct levels: the number of levels each interval tells apart (3 times the noise apart):

Failures¶

A failure in phase 3 retrains (stage F, below): no Sd-bar, no Jd or no Jd' (9.3.2.4, 9.3.2.7/V.90), or no DIL. After the last S-bar, phase 4 follows.

Results on netsim¶

netsim's NET_PAD and NET_RBS put pads and robbed bits on the codes going to the analogue modem (see testing). What the DIL found with them:

• 0, 3 and 6 dB pads (µ-law and A-law) found as 0.0, 3.0 and 6.0 dB, on a quiet line or with NET_FLOOR=100 to 300;
• one, two and three robbed intervals, alone and behind a 6 dB pad, and with the noise at 100 (where a robbed bit matters less: the robbed interval tells 31 levels apart against the others' 43).

The equaliser on netsim's quiet line (mse relative to the two points' power): 77 dB at TRN1d, at any phase of the codec's samples (NET_PHASE) and with its clock 50 to 200 ppm off the network's (NET_PPM).

The DIL's noise is 0.4 to 1.0 in all of them. Before the T/2 receiver, the figure was 75 dB at 8000 Hz on the network's clock and phase only (32 to 36 dB with dsp_util's converter, whatever the taps).

The echo canceller¶

The echo canceller (V34Echo, the V.34 answerer's) has a near part of 256 taps at 9600 Hz and a far part found at the round-trip delay, adapted by NLMS. It takes our own echo off the line before V90Rx::line(): our S during Jd, S-bar, phase 4's CPt, SCR, CP and E, and the upstream data to come.

• It trains while S, S-bar, PP, TRN and Ja go out and the digital modem is silent, until the digital modem's Sd (ec_schedule()). Then it stays as it is.
• For the PCM receiver, NLMS takes away too little in that time: about 33 dB of an echo 10 dB down, which leaves a noise of 12 against the 0.5 of a quiet line. So what it trained on is stored, and at the end the near part is solved by least squares (V34Echo::ls_solve(): the normal equations built from their first row, each next row the one before moved on by a sample, solved by Cholesky). That gives 47 to 51 dB, and is kept when it does better than NLMS.
• If it takes away less than 6 dB (no echo), it stays off.

DSP_TEST_ECHO gives a modem its own echo in the tests (see testing).

Not done yet¶

MD, and SCR during the DIL, are not done.

The DIL's sign pattern repeats with each segment, so what the equaliser leaves of the neighbouring symbols adds the same way each time. Some intervals' levels come out up to 0.3% high or low. TRN2d's random symbols put that right: each interval's gain on them, fitted over TRN2d's second half, scales the levels used for MP, Ed and CP.

Phase 3: the procedure and the receiver, as planned¶

This section is the original plan for phase 3 (9.3.2/V.90, the analogue modem). It explains why the receiver is built the way the previous section describes.

The procedure¶

• Out: 70 ms of silence, S (128 T), S-bar (16 T), MD if INFO1a asked for one (we do not), PP, TRN (at least 512 T, 4 points), then Ja (8.3.1, Table 12/V.90: the DIL descriptor) until the digital modem's Sd turns to S-bar d, then silence. The plan was to retrain if that had not happened within 1500 ms; the code waits 3 s from the start of Ja (P3V_JA). This is V.34's answerer phase 3 at the upstream symbol rate, with Ja in place of J (ptx as P3A_* has it), and the echo canceller trained on it as in V.34.
• In: the digital modem's Sd, S-bar d, TRN1d (its two points, with signs from the scrambled ones; the equaliser trains on its first 2040 T), and Jd (Table 13/V.90: the rates it can send, the constellation sizes). Then S from us (within 5 s), the digital modem's Jd' and the DIL our Ja asked for, and S-bar from us after Jd' (9.3.2.5 to 9.3.2.8/V.90).

What the PCM receiver needs¶

The PCM receiver is the new part. The digital modem's codewords become voltages at the network's 8000 Hz clock, and travel through the analogue loop to our codec. Our codec runs at 9600 Hz (the converter's rate, or the codec's own on an ALSA line: 8000 or 9600 Hz) on a clock of its own. The receiver needs:

• Timing locked to the network's clock. The data pump at 9600 Hz gives 6/5 samples per PCM symbol. That calls for a fractionally spaced equaliser at T/2 or finer, a timing estimate (from the drift of the centre of mass of the equaliser's taps, or from a timing error detector on TRN1d's two points), and an interpolator. An ALSA codec's clock runs free, so this is needed on real hardware at 8000 Hz too.
• An equaliser trained on TRN1d (known after its first symbols: the points are ±UINFO's level, the signs the scrambled ones), then decision-directed on Jd, which also uses 2 points. Its output is the linear value of the codeword sent, before the decision.
• An echo canceller for our own upstream signal while the downstream comes in (V.34's, with the reference at 9600 Hz). In phase 3 the digital modem sends TRN1d while we are silent or sending TRN, so the canceller trains on TRN.
• Detection of Sd and S-bar d for the frame alignment (8.4.4/V.90: the six-symbol pattern +W, +0, +W, −W, −0, −W of Ucodes UINFO + 16 and 0). Sd's first symbol is in data frame interval 0.

What the DIL is for¶

The DIL (8.4.1/V.90; Ja's descriptor, Table 12/V.90, says what it is) is the digital modem's codes in a pattern we ask for: each Ucode we name, repeated, in each of the 6 frame positions. From the equaliser's output for each code, position by position, the receiver finds:

• the level of each Ucode as it arrives (the network's pads change it: a 3 or 6 dB digital loss maps Ucodes onto others);
• robbed-bit signalling: in some positions the least significant bit is lost, so odd and even codes arrive at the same level, as on T1 lines;
• the noise at each, which sets the distances the constellations can afford.

Phase 4 (stage D)¶

Phase 4 (9.4.2/V.90) uses dp_v34.cpp's P4V_* states, v90a.cpp's constellation design and the PCM receiver's phase 4.

The constellations¶

CPt's constellations are designed at the end of phase 3 (v90a_phase4()), and CP's once TRN2d has shown the noise (v90a_cp_design()). Both use what the PCM receiver found:

• Levels: each Ucode's level in each frame interval (V90Rx::levels()). These are the DIL's levels, for the usable Ucodes; without a DIL, the law's linear values. For CP they are scaled by the gain TRN2d showed in each interval.
• Noise: the larger of:
• V90Rx::noise(): UINFO's spread about each interval's own mean, over 512 symbols before our S. The signs are random, so this includes the data mode's intersymbol interference; and because each interval has its own mean, a robbed bit does not count as noise. If the DIL's noise is larger, that is used instead.
• TRN2d's noise, measured with our SCR and its echo going out.
• Power limit: the most power INFO0d allows (Table 15/V.90, by its maximum power field). The power is Table 15's formula, each label's count over the 2^K values of the modulus encoder (V90Con::power()), on the transmitter's linear values.
• Other parameters: Sr = 0 (no spectral shaping), ld = 0, and every upstream rate from 4800 to 33600 bit/s enabled.

CPt (v90a_design_cpt()): 4 points in each interval, with D = 18 (K = 12, drn = 10, 24000 bit/s). The points are the Ucodes nearest L, 3L, 5L and 7L (with the signs, 8 levels evenly apart). L starts at 1 dB below the power limit and is lowered until the power is within it.

CP (v90a_design_cp()):

1. In each interval, the first point is the lowest level at least half the spacing up; each next point is at least the spacing above the last. The spacing is 10 times the noise (about one symbol error in 10^6).
2. K is the most the points can carry, up to 36 (D = 42, 56000 bit/s), and only a rate that Jd allows (from 28000 bit/s, K = 15, up).
3. Then the largest point of the interval whose largest point is loudest is dropped, again and again, until the power is within the limit and within 3 dB of CPt's (8.5.2/V.90).
4. Intervals with the same points share a constellation.

If there is no CP even at 28000 bit/s, the modem retrains, to V.34 (stage F, below).

What we send¶

1. CPt (V90Cp::build(), the inverse of the digital modem's parse()) right after phase 3's last S-bar, from a cleared scrambler and differential encoder. It is sent as MP is, again and again (V34_TX_CP: a frame to follow the current one, or E, takes over at its end).
2. On Ri-bar: SCR (ones, sent as CP is, a frame of 2 bits) after the CPt frame going out, while TRN2d's known part comes in (about 300 ms; 4000 ms at most, 9.4.2.2/V.90).
3. Then CP.
4. On MP, once a whole CP is out: CP' after the CP frame going out.
5. Once a whole CP' is out and MP' or Ed is in: E (20 ones), then B1 and the data mode's upstream (v90a_data_setup()).

What we receive¶

V90Rx::phase4():

• Ri: the equaliser follows the decisions on Ri. Ri is 8 frames of
• • • − − − of UINFO in a row (frame interval 0 first); its reversal is a frame mostly the opposite. TRN2d starts 24 symbols after it.
• Data frames from there: each value goes to the nearest level of its interval's constellation (CPt's). The labels give the modulus encoder's R (interval 0 least significant), the signs are decoded differentially, and all D bits go through the GPC descrambler (5.4/V.90 the other way, Sr = 0).
• TRN2d: its first 340 frames are known. A copy of the digital modem's encoder (V90Enc on our CPt, with Ucode + 1 as the linear values) gives the symbols, which train the equaliser and count its errors. After them, the decisions are used.
• MP and MP' come from the bits (V90Mp, Table 16/V.90: 86 bits, or 188 with the precoder's coefficients).
• Ed is the 2 frames of zeros after the last frame of an MP' sequence.
• B1d follows on CP's constellations, from a cleared descrambler and signs: 48 frames of ones, its bit errors counted.

With B1d in and our E out (P4V_E), the modem reports CONNECT and goes to the data mode (V90A_DATA, below).

Results on netsim¶

A fix found on the way¶

V.34's S-bar after an S of odd length used to restart its alternation from the beginning, so it was S turned by 90 degrees rather than reversed, and the digital modem never saw it. Our S before Jd' lasts as long as Jd' takes, so its length can be odd. S-bar now carries on S's alternation (V34Tx::s_odd).

Tests¶

Run with ctest -R open_v90a (label open). In each, the open modem at 9600 Hz is the analogue modem and the open digital modem (open8) is on the simulated network. Each is a data call: lines of text go both ways and are checked. open_v90a_ulaw (200000 octets), and open_v90a_ppm_fast, open_v90a_echo_answers and open_v90a_dil_rbs (100000 octets) also send bulk data (BULK).

Data mode (stage E)¶

The data mode is dp_v34.cpp's V90A_DATA state and V90Rx::frame() on con_data, CP's constellations.

Downstream¶

Downstream is 5.4/V.90 the other way round, with Sr = 0:

• Each of a frame's six values goes to the nearest level of its interval's constellation. The labels give the modulus decoder's R (K bits), the signs are decoded differentially, and all D bits go through the GPC descrambler, continuing from where B1d left it.
• The bits wait in V90Rx's queue (take(), 1024 bits) for the pump, which hands them to the core (CoreBits) a sample at a time.
• The equaliser and the timing loop follow the decisions, as in phase 4. Each point's level also follows its own decisions (LEV_MU, 0.01), because the DIL's levels, even scaled by TRN2d's gain, are a little off for some codes.
• The rate is CP's: (drn + 20) × 8000 / 6 bit/s.

Upstream¶

v90a_data_setup() starts V.34's data mode at INFO1a's symbol rate, from E on. The rate is the highest that both our CP's rate mask and the digital modem's MP allow (its maximum, rate_max). It uses MP's trellis code (16, 32 or 64 states), its precoder's coefficients, and its expanded constellation and nonlinear encoder bits.

CONNECT¶

CONNECT comes once B1d is in and our E is out. The log says "V.90 connect / (analogue modem)". The call's statistics are kept as for V.90, then V.42 and V.44 run as with V.34.

Carrier loss and logging¶

If the downstream's power stays below a thousandth of UINFO's for the pump's carrier loss time, the call ends. Each second, the log gives the downstream's error (rms, 16-bit scale), its signal-to-error ratio, the timing offset and the phase. Retrains and renegotiations are stage F, below.

No DC removal¶

The core normally takes the line's DC out (dcr_process() in Modem::process()). It does not when the pump reports that it takes exact PCM codes (dp_runtime_pcm()), as V.91 and V.92's PCM upstream do. The PCM receiver reports so from phase 3 on.

The reason: the codes' DC is part of their signal. The DC remover's estimate is a whole number that steps every block, and it came through as an offset of up to 10 on every value, which no equaliser could undo. In data mode that made the error wander from 0.5 to 9 rms over seconds, and V.42 frames failed. Without it, on netsim's quiet line, the error stays at 0.5 rms (78 dB) through a 200000-octet transfer.

On by default¶

V.90 as the analogue modem is the 9600 Hz modem's default (v90a in V34Pump::start(); see When it is used). The core keeps V.90 and V.92 on an analogue line. Against a modem that is not a V.90 digital modem, V.8 agrees on V.34 as before.

8000 Hz lines¶

On an analogue line at 8000 Hz (dmodemd -a -r 8000), the core reports the line as analogue with dp_runtime_set_analog(); otherwise an 8000 Hz line would be taken for the digital modem's network.

• The PCM receiver takes the line's samples from process() as they are, through V90Interp at 0.5 sample per output. (The pump's 8000 to 9600 Hz converter cuts below 4000 Hz, which would remove part of the PCM signal.)
• The echo canceller runs on those samples at 8000 Hz, on what we send at the same time. DSP_TEST_ECHO works there too.

The codec's samples have the band above 4000 Hz folded onto the band below it:

• On the network's symbols (phase 0), the samples are the codes themselves.
• A quarter of a sample off, an equaliser undoes the folding: 66 dB at TRN1d where 9600 Hz gives 77; 56000 bit/s, with CP's points 17 apart where they are 8 at 9600 Hz.
• Half a sample off, the folded part cancels what it lands on, near 4000 Hz, and no equaliser brings it back (21 dB at best, offline with 128 taps): no constellation.

A codec whose clock is not the network's drifts through every phase, and through the bad one every 1.25 s at 100 ppm. So V.90 at 8000 Hz only holds with the codec on the network's clock, and it is only used with DSP_V90A=1.

In the tests, netsim's NET_ANALOG=a (or b) with NET=8000:8000 makes modem A (or B) such a modem, and MODEM_ANALOG=<name> tells half_open that its line is analogue.

Retrains and rate renegotiations (stage F)¶

This is 9.5.2 and 9.6.2/V.90, tested against our digital modem's side of them (9.5.1, 9.6.1).

The digital modem's renegotiation¶

Figure 8/V.90:

1. In data mode, V90Rx::rd_frame() looks for Rd: + + + − − − (either polarity) of each interval's loudest point (label 0 or 1), 8 frames in a row. From then on no bits go to the core (circuit 104 is clamped).
2. On Rd-bar, 24 symbols on, phase 4's frames start again (reneg_frames()): CPt's constellations, a cleared descrambler and signs.
3. TRN2d is optional in a renegotiation, so it is not taken as known. The equaliser is trained on the decisions, and their error over frames 170 to 339 is the noise the new CP is designed on (phase 3's measure no longer counts).
4. The pump (v90a_reneg()) sends S for 128 T and S-bar for 16 T (V90A_RN_S, V90A_RN_SBAR), then phase 4's SCR, CP (designed again), CP', E and B1, and the data at the new rates. The log says "V.90 renegotiated / (analogue modem)"; there is no new CONNECT.

Ours¶

Figure 9/V.90: we send S and S-bar while the data still comes in; the digital modem answers our S-bar with Rd, and the rest is as above.

We start a renegotiation (v90a_reneg_ours()) when, after the first 2 s of data:

• the downstream's error is 2.5 times the noise CP was designed for (8 dB worse) for a second; or
• it is under half of that noise for 20 s, while a faster CP is still possible (D below 42).

DSP_V90A_RENEG=<ms>[a|c] starts one in a test, and the DTE can ask for one with ATO3. If no Ed arrives within 5000 ms plus 2 round trips of our S-bar, we retrain.

Not used: CPs (a silent period, to train the echo canceller again) and cleardown (9.7, a CP with drn = 0). The canceller does not track, and a hang-up ends the call without a cleardown.

Retrains¶

Retrains are 9.5.2/V.90.

• The digital modem's: its tone B, detected by rt_tone() on the PCM receiver's line in phases 3 and 4, in data mode and in renegotiations. We send 70 ms of silence, then our tone A, and run phase 2 again as the V.34 answerer. retrain() takes the PCM receiver off first, and gives the core its DC removal back.
• Ours (v90a_fail()): every failure of phases 3 and 4 (no Sd-bar, Jd, Jd', DIL, Ri-bar, TRN2d, MP, MP' or B1d) and a renegotiation that times out. ATO1 (the DTE) and DSP_V34_RETRAIN=<ms>[a|c] (a test, on either modem) also start one.
• Falling back to V.34: with no constellations or upstream rate to use, or from the third retrain on, phase 2's INFO1a asks for V.34 (the log says "V.34 this time"). So a line that PCM cannot use connects at V.34. After four retrains the call ends.
• Back in data after a retrain, the log says "V.90 retrained"; there is no new CONNECT.

Tests¶

V.92 (stage G)¶

With +MS=92 (the default; DSP_V92A=0 gives V.90 only), our INFO0a says V.92 (bit 26, Table 16/V.92; no short phase 2), and the digital modem's INFO0d says so too (bit 27). INFO0d has its two V.92 bits the other way round from INFO0a, which Info0::parse_d() takes into account. The log says "INFO0d V.92: V.92 as the analogue modem" (v92a_on).

The call is V.90's (PCM down, V.34 up: our INFO1a is V.90's), plus V.92's modem-on-hold (9.10/V.92; the digital modem's side is in V.92).

Our modem-on-hold request¶

Started by AT+PMHR=<s> in online command mode, or by DSP_V92_MOH_REQ=<ms>[:<s>] in a test:

1. We leave data mode as for a retrain, send our tone A, then MHreq.
2. On its MHack (with its T1), we go silent for s seconds (within T1).
3. Meanwhile it sends ANSam, and we take the call back: its ANSam for 200 ms, V.8 as the call modem (CM), phases 2 to 4. The log says "V.90 back from hold" and the data goes on (no new CONNECT).
4. On its MHnack instead: we send MHfrr, it sends ANSam, and the rest is the same.

Its modem-on-hold request¶

MHreq after its tone B:

1. Our retrain's tone A holds back its reversal for 1 s on a V.92 call (a retrain's reversal would come before MHreq, about 600 ms after the tone).
2. We answer MHack (with our T1, AT+PMHT) or MHnack.
3. We go on hold on its silence or tone.
4. We send ANSam (with the V.21 receiver on CM's channel, since we were the call's caller), and answer its CM: phase 1 as the answer modem, then phases 2 to 4.

The requester's way back, its CM to the held modem's ANSam, is now the digital modem's as well. Before, it sent ANSam itself after the hold, against 9.10.2.1/V.92. (The modems behind netsim's stand-in and the original library hang up during the hold, so this never showed.)

Tests: open_v92a_moh (ours, 5 s on hold, with a 50 s stream of data across it) and open_v92a_moh_theirs (the digital modem's).

V.92 PCM upstream, phase 3 (stage G2)¶

Where an INFO1d offers PCM upstream (its bit 70, Table 17/V.92: the 3429 baud low carrier bit), our INFO1a is Table 18's (make_info1a_v92()): a precoder and prefilter of p1 and z2 with the fewest coefficients (192 in all, 128 each), no MD, UINFO, and 6 for both symbol rates. Phase 3 then follows 9.5.2/V.92.

The PAM transmitter¶

V92ATx (dsp/v92a.cpp) sends PAM symbols (pulse amplitude modulation) at 8000 a second, one per sample of the network's codec.

• Each symbol is a sinc pulse cut at 4000 Hz (Blackman-windowed, 16 symbols either side) on our 9600 Hz line, so that where the codec samples one symbol the others are at their zeros.
• Its clock is the network's, as the PCM receiver's timing loop measures it (V90Rx::ppm(), once that runs on TRN1d). Until then (Ru, the first TRN1u and Ja) it runs free; by the end of the second TRN1u it is within one symbol at 100 ppm.
• LU is about our V.34 signal's power (V92A_LU, 3000 on the line).
• The symbols are made 16 ahead of the line, so the pump waits for E1u's last pulse to go out (e1u_sent()).

The sequence¶

Where the lengths are fixed, the transmitter moves itself on:

1. 70 ms of silence.
2. Ru for 384 T, Ru-bar for 24 T.
3. TRN1u for 2040 T (GPA on ones, from zero).
4. Ja: 24 ones, then the DIL descriptor of Table 20 (V.90's, plus the rate mask with every rate from 24000 to 48000 bit/s), scrambled and differentially encoded. It runs until the PCM receiver's Sd-bar, and ends at a 12-bit boundary.
5. Silence while TRN1d trains the receiver.
6. Su for 144 T once Jd is in, then Su-bar for 24.5 T (half a symbol later from then on).
7. Su until Jp, ending at 12 symbols. (V90Rx reads Jd's bit 47 for Jp, and Jp's fraction in bits 18:33.)
8. Su-bar for 24 T plus Jp's fraction (the digital modem's 0.5 makes the half symbol a whole one).
9. The second TRN1u (the data frames count from its first symbol) while the DIL is measured.
10. CPt: 24 ones, then V.90's CPt constellations in Table 23's form (v92_cpt_build()), until Ri, ending at the end of a CPt.
11. E1u (12 zeros).

The receiver and failures¶

• The receiver is V.90's: Sd, TRN1d, Jd; then Jp' (12 zeros, as Jd') after the Jp; the DIL; Ri.
• Failures (no Sd-bar, Jd, Jp, Jp', DIL or Ri in time, and those in phase 4 below) retrain, with V.90 for the rest of the call (v92a_noup). The digital modem, once PCM upstream has failed before data, also leaves bit 70 out of its INFO1d after that.

Fixes this needed¶

• Our digital modem's E1u detector: CPt's fill to the end of the data frame may be all zeros together with the CRC's last bit (when that is 0), which it took for E1u. E1u is now only a frame that starts after the last CPt's end.
• The PCM receiver's Sd-bar detector: after a hold, an echo of ours over Sd makes its lag-6 correlation dip a little before the reversal (to 0.49, where a reversal goes to −1.4). A dip that never goes below −0.2 is now not taken as Sd-bar, and the next one is taken. V.90 had the same dip, but there Sd comes later, past it.

V.92 PCM upstream, phase 4 and data mode (stage G3)¶

This follows 9.6.2/V.92, after E1u.

What we send¶

• TRN2u on 4 points (Table 28: the sign bit scrambled and differentially encoded, then the magnitude bit, 1/√5 or 3/√5 of LU), from a cleared scrambler. It runs until SUVd is in (or for 12000 T), once TRN2d has shown the noise that CP's design needs, and ends at a 12-symbol boundary.
• SUVu (Table 27, v92_suvu_build()), again and again, each the pump's next sequence (v92a_next_seq()).
• One CPu (Table 23 with type 1: V.90's CP constellations, v92_cpu_build()) once SUVd is in, sent again if no acknowledgement comes within 100 ms plus a round trip.
• All sent acknowledged once CPd is in.
• Each sequence is filled to 12 symbols (24 bits).
• E2u after the current sequence, once one of ours with the acknowledgement has gone out whole and SUVd', CPd' or Ed is in (and the CPd is one we can take: its moduli enough for its bits, its classes within its points). E2u is a symbol longer if CPd's bit 29 says so. Then B1u and the data.

What we receive¶

The receiver reads V.92's sequences in the place of V.90's MP:

• SUVd (51 bits to the end of its CRC), or CPd (Table 30: its length from its parts, v92_cpd_length(), V92Cpd::parse());
• their acknowledge bits, for Ed (2 frames of zeros after the acknowledged one), as MP' had them;
• B1d on CPu's constellations.

The upstream data mode¶

The data mode is 6.4/V.92, in V92ATx::data_symbol():

1. Each data frame's K = 2 (drn + 17) bits are scrambled (GPA, from zero at B1u).
2. Modulus encoder (6.4.1): the sign of R above (M − 1)/2 is coded differentially, and R is turned over when the last one was 1; then K0 to K11 come from R by the 12 moduli. R is held in 4 words (the moduli's product is up to 2^96).
3. Point choice: of each Ki's class, the point (CPd's linear values, the negative ones mirrored) that keeps the precoder's output smallest. On a trellis frame's 4th symbol, the point's parity makes the frame's sum match V.34's Y0 (the encoder state's low bit). The trellis codes are V.34's 16, 32 or 64 state codes, one step per trellis frame of 4 symbols.
4. Precoder: x = u + z1 * u + p1 * x (Q0.15 and Q1.14).
5. Prefilter: v = z2 * x + p2 * v.
6. Gain: LU × G × v on the line (8.8.3: G scales v to a mean square of 1, which is the power LU stands for).

CONNECT¶

CONNECT comes once B1d is in and B1u has gone out. The log says "V.92 connect / (analogue modem)". The downstream is V.90's data mode, with its retrains and modem-on-hold, both of which now come back with PCM upstream. PCM upstream's renegotiation and fast parameter exchange are stage G5, below.

Results on netsim¶

Against our digital modem on netsim's line:

A 1.5 MB transfer took 5 minutes, with no slip to design for (our clock is the network's) and no renegotiation.

Our digital modem's E2u detector had the same weakness as its E1u one: an acknowledged SUVu's fill, with its CRC's last 3 bits zero, is a frame of zeros. E2u is now only taken after the last sequence's end.

Tests¶

V.92 quick connect (stage G4)¶

Short phase 1¶

Calling (9.2.1.1/V.92), once ANSam has lasted 1 s:

1. QC1a on V.21(L) (Table 2: twice ten ones, 0101010101 and the frame 0 0 0 P W 0 X Y Z 1). P is 0, because our V.42 always runs its detection phase; UQTS is 79 (WXYZ = 1010). Then CM.
2. The digital modem's QCA1d (on V.21(H), where the JM receiver listens; the QC frame parser takes either kind, with bits 21 and 22 saying which) ends CM at once.
3. Silence until its ANSpcm. (QTS and QTS-bar before it are not looked for: our PCM receiver finds Sd in phase 3 as before.) V.8's ANSam 2100 Hz detector is used, for 50 ms.
4. TONEq (980 Hz, V.21(L)'s mark) until ANSpcm ends (at least 50 ms), then 75 ms of silence, and phase 2 as after V.8 for V.90, with us as the analogue modem.

If no ANSpcm arrives within 2 s, we send CM again and run V.8. A digital modem that does not answer QC1a sends JM to our CM as usual.

QC1a is sent on every call (with a fixed UQTS), not only after an earlier call; it is left out on a return from hold and in a retrain.

Short phase 2¶

Short phase 2 is 9.4.2/V.92. Our INFO0a's bit 27 asks for it when we go for PCM upstream (not in a retrain, and not after a failed PCM upstream). If the digital modem's INFO0d has bit 26 too:

1. its tone B reversal comes first (once it hears our tone A);
2. ours follows 40 ms after it, then 10 ms more of tone A;
3. then PCM upstream's INFO1a (Table 18). No INFO1d comes in short phase 2, so its bit 70 cannot offer PCM upstream; the digital modem asking for short phase 2 is taken as the offer.

If there is no tone B reversal within 2.5 s, we retrain (with a full phase 2).

Results¶

Against our digital modem, CONNECT comes:

The upstream is then 37333 bit/s: the network's samples land at another phase against our line's, and its prefilter design comes out one step lower than the 38666 after V.8.

Fixes¶

Two fixes on the digital modem's side:

• Its INFO0d asked for short phase 2 in a retrain, where it actually does the full one (and the return from hold went wrong on that).
• Our own flag for it is now cleared in a retrain (the INFO0 sequences are not sent again there).

Not done¶

Answering a digital modem's QC1d (9.2.3; ours never sends it), and V.8 bis' QC2a / CRe.

Tests¶

PCM upstream's renegotiation and fast parameter exchange (stage G5)¶

Rate renegotiation¶

Rate renegotiation is 9.8.2/V.92 (v92a_reneg()). It starts either:

• from the digital modem: its Rd and Rd-bar arrive at the PCM receiver (V.90's Rd: + + + − − − of the loudest points); or
• from us: on the downstream's error, as for V.90 (v90a_reneg_ours(); for margin we use a fast parameter exchange instead, below), on the DTE's ATO3, or with DSP_V90A_RENEG in a test.

Then:

1. Our Ru at the start of the next data frame (V92ATx::ru_req; the digital modem keeps counting its frames), then Ru-bar.
2. TRN2u, its differential encoder starting from Ru-bar's sign.
3. Phase 4's sequences again, on the receiver's renegotiation frames (TRN2d, SUVd, CPd, Ed, B1d), and a new CPu, E2u and B1u on the new CPd. The log says "V.92 renegotiated / (analogue modem)".

If no B1d arrives within 25 s (the digital modem's own limit), we retrain. Neither side asks for the silent period.

The digital modem's fast parameter exchange¶

This is 9.9.2.2/V.92.

1. Its Rf: + + − − + + and − − + + − − in turn on each interval's loudest point (V90Rx::rf_frame()). Then Rf-bar (the pattern one frame on, 4 frames).
2. Its SUVd and CPd in the data mode's modulation (from a cleared descrambler and signs) until Ed, then B1d.
3. Ours, from the next data frame on:
4. RM's 32 frames and RM''s 2 (Tables 25 and 26: their Ki go straight into the precoder, trellis coded);
5. then SUVu frames in the data mode (the scrambler and the modulus encoder's sign from zero; with a prefilter, the precoder and prefilter too, as the digital modem's prefilter receiver expects, following the original library);
6. a CPus after SUVd (Table 24: the downstream as it is, so the PCM receiver's constellations stay), acknowledged once CPd is in;
7. E2u (a frame of zeros);
8. FB1u's 48 frames of ones on the old parameters;
9. then B1u and the data on the new CPd, from zero. The log says "V.92 fast parameter exchange done".

The digital modem counts errors in FB1u and B1u:

• with its prefilter, about 100 in FB1u's 2688 bits, about as many as with the original library (154);
• with its plain precoder, none in either, since its receiver takes the restart at B1u the way this modem makes it (see V.92 PCM upstream: the trellis paths run to their end and then restart from state 0, the descrambler from zero, and the precoder's earlier outputs stay in the feedback). Before that fix, FB1u's last frames and B1u's first two or three often had tens of errors.

Our own fast parameter exchange¶

This is 9.9.2.1/V.92 (v92a_fpe(2)). We start one for margin (the downstream's error under half the noise CP was designed on for 20 s, with a faster CP possible; no training, unlike V.90's renegotiation for the same reason), or with DSP_V92A_FPE=<ms> in a test.

1. RM, RM' and SUVu go out as above, without waiting.
2. The PCM receiver's frames stay data until the digital modem's Rf (its answer to our RM'), so the start-up's SUVd and CPd events are cleared first (V90Rx::fpe_wait()).
3. After its SUVd we send a CPu (Table 23, not CPus) designed anew on the data mode's error (v90a_cp_design(2)). The receiver keeps it aside (V90Rx::data_cp_next()) and takes it up at the exchange's Ed: B1d and the data come on it, and the frames before Ed on the old constellations.
4. If its Rd arrives before then, its renegotiation takes over (9.9.2.1.2).

The downstream's errors still lead to a renegotiation, which has TRN2d to retrain on.

Before this was done, a digital modem's renegotiation or fast parameter exchange made us retrain to V.90. (The digital modem, with no RM a second after its Rf, renegotiated instead; the renegotiation alone already got through that.)

Tests¶

All send 150 kB each way.

open_v92a_dte_reneg has the DTE's ATO3 start ours, on a 25 s stream of data.

Testing¶

The only digital modem available is our own (open8): the closed modems in the interop tests are all analogue ones. There are two checks against that:

• The analogue modems' own phase 3 and 4 signals, from their calls to open8 (smartlink_v90_*, agere_v90_*, sm56_v90_*, ...), are a reference for ours: S, PP, TRN, Ja and CP can be compared side by side.
• The digital modem's receiver already reads theirs, so ours going through it the same way is a check of what we send.

netsim's analogue side (its noise, loss and echo) is what the receiver's equaliser is tested against. Its timing is tested with netsim's clock offset and phase between the network and the codec (NET_PPM, NET_PHASE; see open_v90a_ppm_fast and open_v90a_phase). Real lines through dmodemd -a have not been tried yet.