Lab059: establish limits of preamble-only carrier estimation

PROJECT_LOG.md

@@ -2535,3 +2535,49 @@ variation неустойчива. TX control BER 0/0; AWGN control при оди
 Следующий этап: отдельно согласовать полностью офлайн-проверку исправленного preamble-only
 CFO/carrier estimator на сохранённых Lab056, Lab054 и контролях, без payload truth в
 оценивателе и без запуска Lab059 автоматически.
+
+# Запись 053
+
+## Дата
+
+11 сентября 2026 года
+
+## Тема
+
+Lab059 — пределы восстановления несущей только по 1280-символьной преамбуле
+
+## Выполнено
+
+Lab058 зафиксирована отдельным коммитом
+82f17499ace5e655991240348401b9700c7c3349 с согласованным сообщением; push не
+выполнялся. Затем проведён только офлайн-анализ сохранённых Lab056, Lab054 и
+Lab047. Оборудование не опрашивалось, аппаратных команд не было, RF TX=0.
+
+До альтернатив сохранён точный P0 baseline. Активная ветвь корректно учитывает
+BPSK², знак, единицы и reference time, но использует только две точки по 512
+символов и отбрасывает последние 256 символов преамбулы. На Lab056 B ошибка P0
+относительно whole-burst reference составила +4,7307/+4,7608 Гц, средняя SER
+52,4169%. P3 с устойчивым наклоном фазы по всей squared-преамбуле дал
+−0,1249/+0,3917 Гц и SER 3,6170%, близко к диагностическим 3,4959%.
+
+Независимая проверка первой реализации выявила зависимость P1–P3 от RAW
+полезной части через глобальное удаление DC. Исправленный расчёт ограничивает
+DC и FIR-опору P1/P3 полной преамбулой, а P2 — только TRAIN; отдельный тест
+меняет RAW после преамбулы и подтверждает неизменность новых оценок. P0 сохранён
+дословно со штатной обработкой как исторический baseline.
+
+Две удачные реализации P3 не признаны доказательством устойчивости. Monte Carlo
+с300 реализациями для каждой из17 CFO, двух скоростей и трёх заранее заданных
+уровней EVM дал на500ксимв/с/EVM0,84535 вероятность |ошибки|≤0,5Гц только
+5,86/10,47/3,67/9,61% для P0/P1/P2/P3. Лучший RMSE P1 равен3,728Гц;
+AWGN CRLB sanity check даёт3,598Гц. Lab047 сохранён36/36 для всех методов;
+Lab054 остался0/16 HEADER/FEC/CRC/packet у всех методов, исторически NOT_A.
+
+Вывод PREAMBLE_ONLY_INSUFFICIENT: P3 полезен как начальная оценка, но при
+наблюдаемом качестве B требуется carrier tracking через burst. Следующий один
+этап рекомендуется сделать офлайн: decision-directed tracking без payload truth
+и без изменения формата. Физический предел B около3,50% ошибок остаётся.
+
+Созданы постановка, отчёт, baseline, CSV/JSON и пять графиков Lab059. Исходные
+IQ повторно хешированы до/после и не изменились. Lab059 не коммитировалась,
+push не выполнялся. Следующий этап: STOP; Lab060 автоматически не начинать.

data/processed/lab059/real_results.csv

@@ -0,0 +1,225 @@
+dataset,label,frame,symbol_rate,method,timing_samples,frequency_hz,diagnostic_reference_hz,frequency_error_hz,estimation_symbols,estimation_duration_seconds,phase_drift_to_burst_end_degrees,preamble_errors,validation_errors,validation_symbols,validation_phase_rmse_rad,header_raw_errors,header_voted_errors,HEADER_ACCEPTED,FEC_STARTED,CRC_PASS,PACKET_OUTPUT,symbol_errors,symbols,symbol_error_rate,evm_rms,matched_residual_db
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data/processed/lab059/summary.json

@@ -0,0 +1,823 @@
+{
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+  "verdict": "PREAMBLE_ONLY_INSUFFICIENT",
+  "main_reason": "ни один preamble-only метод не обеспечивает устойчивую ошибку менее 0,5 Гц на качестве B",
+  "recommended_next_single_step": "проверить decision-directed carrier tracking through burst",
+  "future_options": {
+    "decision_directed": "первый кандидат: не меняет формат и не знает payload truth",
+    "costas_loop": "альтернатива для слежения по всему burst; требует настройки полосы петли",
+    "periodic_pilots": "наиболее явная опора, но требует изменения формата и overhead"
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+  "lab054_historical_result": "NOT_A, 0/16",
+  "lab059_commit": "NOT_PERFORMED",
+  "push": "NOT_PERFORMED",
+  "integrity": {
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data/processed/lab059/synthetic_results.csv

@@ -0,0 +1,25 @@
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+20000,LAB058_B_EVM,0.84535,P2,5100,17,0.0008314817399338177,0.48833634165135953,0.32478059797899206,0.9640636741241208,1.2526697998533654,0.0,0.4025490196078431,0.6947058823529412,0.9596078431372549,0.74862814469735
+20000,LAB058_B_EVM,0.84535,P3,5100,17,-0.005590240158082864,0.5201396504062407,0.11894627555568146,0.3430226441253915,0.4786715240391113,0.002156862745098039,0.8507843137254902,0.9915686274509804,0.9974509803921568,0.7428826884058787
+500000,LAB058_A_EVM,0.31739,P0,5100,17,-0.028324835474221908,2.253141535486236,1.4962503201559325,4.448489433622006,5.709437492053499,0.27725490196078434,0.08725490196078431,0.1676470588235294,0.34784313725490196,0.231339425193028
+500000,LAB058_A_EVM,0.31739,P1,5100,17,0.05429497252499488,1.3758457866823075,0.9250930671491767,2.7024857819222334,3.5664388844212724,0.07941176470588235,0.14901960784313725,0.28019607843137256,0.54,0.2311393421976552
+500000,LAB058_A_EVM,0.31739,P2,5100,17,0.06565713877478316,4.581561184769926,3.0883642545236056,8.953835433400844,11.96456273215203,0.5976470588235294,0.039411764705882354,0.08509803921568627,0.17450980392156862,0.2345544161089221
+500000,LAB058_A_EVM,0.31739,P3,5100,17,0.058842766466235895,1.4134247608333887,0.9614089281004776,2.7679878506095847,3.6337112005617693,0.0888235294117647,0.1411764705882353,0.2747058823529412,0.5180392156862745,0.23115195125818536
+500000,INTERMEDIATE_EVM,0.55,P0,5100,17,-0.03875761089802868,4.131625501040117,2.9042927999066057,7.9528339390408584,10.52341079713349,0.5666666666666667,0.05019607843137255,0.09411764705882353,0.1935294117647059,0.4421333889963128
+500000,INTERMEDIATE_EVM,0.55,P1,5100,17,0.06423845186681068,2.3913290252749078,1.6065121427546019,4.649532259708706,6.192878068670655,0.3092156862745098,0.08431372549019608,0.16607843137254902,0.32372549019607844,0.441761357535385
+500000,INTERMEDIATE_EVM,0.55,P2,5100,17,0.02004625787745806,7.921237841542093,5.269438855163791,15.620242877196675,20.258593678746344,0.756078431372549,0.02372549019607843,0.05274509803921568,0.10549019607843137,0.4472161493685728
+500000,INTERMEDIATE_EVM,0.55,P3,5100,17,0.04886503438637983,2.549592162835184,1.7274887723017696,5.021571593956331,6.353311747517625,0.3415686274509804,0.08686274509803922,0.16294117647058823,0.31019607843137254,0.4418171712060747
+500000,LAB058_B_EVM,0.84535,P0,5100,17,-0.018449630005399873,6.8080438723195575,4.64257978395003,13.265150787635067,17.80453591229988,0.7207843137254902,0.03058823529411765,0.058627450980392154,0.11607843137254902,0.7431007414530082
+500000,LAB058_B_EVM,0.84535,P1,5100,17,0.05043041270946037,3.727888844043392,2.4981252391550526,7.436680937825983,9.894508393786168,0.5098039215686274,0.05235294117647059,0.10470588235294118,0.21274509803921568,0.7424981320951237
+500000,LAB058_B_EVM,0.84535,P2,5100,17,0.07780133250091027,12.264121666056068,8.25551126333268,23.708553996717562,31.583472778910384,0.8311764705882353,0.01647058823529412,0.03666666666666667,0.07196078431372549,0.7498501168809314
+500000,LAB058_B_EVM,0.84535,P3,5100,17,0.049138012426324186,7.089259568773472,2.934776228989742,8.527851599718817,11.382887324913723,0.5794117647058824,0.049019607843137254,0.09607843137254903,0.18254901960784314,0.7429492477214338

docs/LABS_INDEX.md

@@ -495,3 +495,26 @@
   [JSON](../data/processed/lab058/summary.json),
   [CSV](../data/processed/lab058/segment_metrics.csv),
   [H(f)](../data/processed/lab058/channel_transfer.png). STOP; push не выполнялся.
+
+## Lab059 — пределы carrier recovery по одной преамбуле
+
+- **Запись 053; только сохранённые IQ, RF TX=0.** P0 baseline записан до P1–P3
+  и численно воспроизвёл Lab057/Lab058. Активный P0 использует два блока BPSK²
+  по512 символов; ошибки B1/B2 +4,7307/+4,7608Гц дают SER52,4169%.
+- **Лучший реальный результат P3:** после ограничения RAW-обработки только
+  преамбулой ошибки −0,1249/+0,3917Гц, средняя SER B 3,6170% против
+  whole-burst diagnostic3,4959%. A не ухудшена.
+- **Предел устойчивости:** на synthetic500K/EVM0,84535 P1 имеет лучший RMSE
+  3,728Гц, а P3 попадает в ±0,5Гц лишь в9,61% из5100 испытаний. AWGN CRLB
+  sanity check3,598Гц. Две реальные реализации недостаточны для устойчивого PASS.
+- **Контроли:** Lab04736/36 у P0–P3; Lab0540/16 HEADER/FEC/CRC/packet у всех,
+  исторический `NOT_A, 0/16` сохранён. Независимо найденная RAW/DC-утечка
+  P1–P3 исправлена и закрыта регрессионным тестом; исходные IQ не изменились.
+- **Вердикт:** `PREAMBLE_ONLY_INSUFFICIENT`. Следующий один кандидат — полностью
+  офлайн decision-directed carrier tracking через burst без payload truth и
+  изменения packet format. Физический предел B около3,50% SER остаётся.
+- [Постановка](lab059_current_state.md), [отчёт](lab059_offline_result.md),
+  [JSON](../data/processed/lab059/summary.json),
+  [real CSV](../data/processed/lab059/real_results.csv),
+  [synthetic CSV](../data/processed/lab059/synthetic_results.csv). STOP;
+  Lab059 не коммитировалась, push не выполнялся, Lab060 не создана.

docs/lab059_current_state.md

@@ -0,0 +1,78 @@
+# Lab059 — границы и заранее зафиксированный план
+
+## Цель
+
+Lab059 проверяет только по сохранённым данным, достаточно ли 1280-символьной
+преамбулы для оценки остаточного частотного сдвига на весь burst длительностью
+около 0,2048 с. Штатный приёмник, формат пакета, преамбула, RRC, FEC и CRC не
+изменяются. Оборудование не опрашивается, аппаратные команды не выполняются,
+RF TX = 0.
+
+Исходный HEAD после отдельной фиксации Lab058:
+`82f17499ace5e655991240348401b9700c7c3349`.
+
+## Зафиксированные методы
+
+- **P0 CURRENT.** Дословно воспроизводится активная ветвь штатного приёмника:
+  первые 1024 символа возводятся в квадрат, делятся на два блока по 512,
+  частота определяется по разности фаз центров блоков с делением на `4*pi`.
+  Последние 256 символов преамбулы в оценке частоты не участвуют.
+- **P1 FULL PREAMBLE PHASE SLOPE.** Известные BPSK-знаки удаляются на всей
+  преамбуле. Фазы когерентных 20-символьных блоков аппроксимируются линейной
+  моделью с заранее заданными Huber-весами.
+- **P2 SPLIT PREAMBLE.** TRAIN заранее фиксирован как индексы 32…607,
+  VALIDATION — 672…1247. Между ними оставлен разрыв 64 символа; по 32 символа
+  у начала и конца преамбулы не используются. Частота и фаза оцениваются только
+  по TRAIN, а VALIDATION проверяет экстраполяцию без переоценки.
+- **P3 SQUARED FULL PREAMBLE.** Все 1280 символов возводятся в квадрат,
+  фаза 20-символьных блоков аппроксимируется той же устойчивой моделью,
+  частотный наклон делится на два из-за удвоения фазы BPSK.
+
+P0 сохраняет точную активную ветвь, включая штатное удаление среднего DC по
+всему переданному в неё фрагменту: это часть воспроизводимого baseline, а не
+новое решение. Для P1 и P3 удаление DC и RRC-фильтрация ограничены RAW-опорой
+полной преамбулы; для P2 — RAW-опорой только TRAIN. Поэтому полезная часть RAW
+не влияет на вход новых оценивателей. Все методы получают Fs, Rs, RRC,
+номинальную несущую и уже найденное начало кандидата. Для изоляции carrier
+recovery timing остаётся штатным P0 и не подбирается отдельно по методу.
+Начальная фаза относится к `t=0`; центр символа `k` расположен в
+`(k+0.5)/Rs`.
+
+Header, payload, magic, FEC и CRC не участвуют в оценке. Известные переданные
+биты подключаются только после заморозки параметров для подсчёта ошибок, EVM и
+matched/residual. Диагностическая оценка по всему burst служит только внешней
+справочной величиной после расчёта preamble-only оценки.
+
+## Baseline и реальные данные
+
+До сравнения P1–P3 программа отдельно сохраняет P0 baseline для Lab056
+A1/B1/A2/B2, 16 кадров Lab054 и 36 ранее принятых кадров Lab047. Lab047 служит
+положительным контролем. Исторический результат Lab054 остаётся `NOT_A, 0/16`.
+Сохранённые raw-файлы открываются только для чтения; их SHA-256 проверяются до и
+после расчёта.
+
+## Synthetic Monte Carlo
+
+Фиксированные частоты: `0, ±0.25, ±0.5, ±1, ±2, ±5, ±10, ±20, ±100 Гц`.
+Проверяются 20 и 500 ксимв/с, Fs = 8 Мвыб/с, действующие RRC и преамбула 1280
+символов. Чистые точки решения формируются реальным TX/RX RRC-трактом, после
+чего добавляется воспроизводимый комплексный гауссов шум на символьном выходе.
+Уровни EVM заранее фиксированы: 0,317390 (качество A Lab058), 0,55 и 0,845350
+(среднее физическое качество B Lab058). Последний уровень не подгоняется по
+исходу оценивателя.
+
+Для каждой комбинации используются 300 реализаций и фиксированная схема seed.
+Катастрофическая ошибка заранее определена как `|frequency error| > 1/(2T)`,
+то есть фазовый уход более 180° за `T = 0,2048 с`; порог равен 2,44140625 Гц.
+Публикуются bias, RMSE, median/P95/P99 абсолютной ошибки, катастрофическая доля
+и вероятности ошибки не более 0,25/0,5/1,0 Гц.
+
+## Критерий вывода
+
+`PREAMBLE_ONLY_SUFFICIENT` требует одновременно приблизить Lab056 B к
+диагностическому результату, устойчиво пройти Monte Carlo, не ухудшить Lab056 A
+и сохранить положительный контроль Lab047. Нестабильная субгерцовая точность
+даёт `PREAMBLE_ONLY_MARGINAL`; принципиально недостаточная стабильность на
+качестве B даёт `PREAMBLE_ONLY_INSUFFICIENT`.
+
+Lab059 не коммитируется. Push не выполняется. Lab060 автоматически не создаётся.

docs/lab059_offline_result.md

@@ -0,0 +1,187 @@
+# Lab059 — пределы восстановления несущей только по преамбуле
+
+## Что произошло простыми словами
+
+У штатного приёмника есть только 2,56 мс известной преамбулы, чтобы предсказать
+фазу несущей на весь burst длительностью около 204,8 мс. Для ограничения ухода
+фазы 30 градусами ошибка частоты должна быть не больше 0,4069 Гц. Штатная
+двухблочная оценка на B1/B2 ошиблась примерно на +4,73/+4,76 Гц и поэтому
+повернула решения почти на полный оборот к концу burst.
+
+Один из новых диагностических методов, P3, оказался очень удачным именно на
+двух сохранённых B-сегментах: ошибки составили −0,125 и +0,392 Гц, а средняя
+доля ошибочных символов упала с 52,4169% до 3,6170%. Это почти совпало с
+диагностически достижимыми 3,4959% Lab058. Однако это две реализации, и они не
+доказывают устойчивость. В 5100 синтетических испытаниях качества B P3 попадал
+в ±0,5 Гц только в 9,61% случаев; лучший по RMSE метод P1 имел RMSE 3,728 Гц и
+попадал в ±0,5 Гц в 10,47% случаев.
+
+Следовательно, текущая реализация P0 действительно слаба, и P3 может дать
+хорошую начальную оценку. Одновременно 1280 символов при 500 ксимв/с и
+наблюдаемом качестве B не дают надёжной субгерцовой точности сами по себе.
+Для устойчивого результата требуется сопровождать фазу или частоту в ходе
+самого пакета. Это задаёт следующий программный эксперимент. Физический предел B,
+установленный Lab058 — около 3,50% ошибочных символов даже при диагностическом
+выравнивании — остаётся отдельной задачей.
+
+## Границы и целостность
+
+Lab059 выполнялась только офлайн. HackRF Plus не опрашивался, аппаратные команды
+и передачи не запускались, RF TX = 0. Прочитаны сохранённые Lab056, Lab054 и
+Lab047. Размеры и SHA-256 пяти исходных IQ-файлов проверены до и после расчёта;
+совпадение полное. Исторический результат Lab054 не изменён: `NOT_A, 0/16`.
+
+P0 baseline физически записан в `baseline_p0.json` до вычисления P1–P3. Он
+воспроизвёл Lab057 для Lab054: максимальное расхождение CFO равно
+`1,42e-13 Гц`, ошибки преамбулы `7767/7767`, HEADER/CRC `0/0`. Для четырёх
+сегментов Lab056 различия P0 с Lab058 по CFO, BER и EVM находятся на уровне
+округления floating point.
+
+Независимая проверка обнаружила, что первая реализация P1–P3 удаляла DC по
+всему burst до выделения преамбулы. Из-за этого RAW полезной части менял вход
+оценивателя, хотя правильные payload-биты ему не передавались. Исправленный
+вариант ограничивает DC и FIR-опору P1/P3 полной преамбулой, а P2 — только
+TRAIN. Отдельный тест изменяет RAW после преамбулы и подтверждает неизменность
+P1–P3. P0 намеренно оставлен точным baseline со штатной глобальной обработкой.
+
+## Требуемая точность
+
+Использовано `delta_f_max = phase_limit / (360*T)`, где `T = 0,2048 с`.
+
+| Допустимый уход фазы | Максимальная ошибка частоты |
+|---:|---:|
+| 15° | 0,203451 Гц |
+| 30° | 0,406901 Гц |
+| 45° | 0,610352 Гц |
+| 60° | 0,813802 Гц |
+| 90° | 1,220703 Гц |
+
+Порог 0,4069 Гц — инженерная цель для 30°, а не новый обязательный порог
+протокола. Катастрофическая ошибка Monte Carlo заранее определена как больше
+2,441406 Гц, что соответствует уходу более 180° за burst.
+
+## Аудит штатной математики P0
+
+Активный код получает точки после номинального переноса 50 кГц, RRC-фильтра и
+штатного timing. Он возводит BPSK в квадрат, усредняет символы `[0,512)` и
+`[512,1024)`, затем берёт разность фаз. Центры находятся в моментах `256/Rs` и
+`768/Rs`, расстояние равно `512/Rs`. Формула имеет вид
+`delta_phase / (4*pi*(512/Rs))`; `4*pi` правильно учитывает удвоение фазы после
+BPSK². Компенсация использует отрицательный знак, gain относится к `t=0`, центр
+символа k — к `(k+0.5)/Rs`. Повторной компенсации не обнаружено.
+
+Для 500 ксимв/с однозначный диапазон P0 равен ±244,140625 Гц, поэтому +4,7 Гц
+не является алиасом. Главный практический недостаток — две фазовые точки без
+избыточности; последние 256 символов преамбулы не участвуют в частотной оценке.
+Для 20 ксимв/с диапазон P0 всего ±9,765625 Гц, поэтому synthetic ±20 и ±100 Гц
+преднамеренно показывают алиас и увеличивают сводный RMSE P0.
+
+## Методы
+
+| Метод | Использованные символы | Оценка | Проверка |
+|---|---:|---|---|
+| P0 CURRENT | 1024 | два блока BPSK² по 512 | P2 VALIDATION только как диагностика |
+| P1 FULL PHASE SLOPE | 1280 | Huber-fit фаз 64 despread-блоков по 20 | фиксированная преамбула |
+| P2 SPLIT | 576 TRAIN | Huber-fit 36 despread-блоков по 16 | 576 VALIDATION без переоценки |
+| P3 SQUARED FULL | 1280 | Huber-fit фаз 64 BPSK²-блоков по 20, наклон /2 | фиксированная преамбула |
+
+P2 использует TRAIN 32…607 и VALIDATION 672…1247; разбиение зафиксировано до
+результата. Timing одинаков для P0–P3, чтобы эксперимент изолировал carrier
+recovery. P1/P3 получают RAW-опору только полной преамбулы, P2 — только TRAIN.
+Ни один новый оцениватель не получает header, magic, payload, JPEG, FEC или CRC.
+
+## Lab056 A/B
+
+Ошибки частоты ниже считаются относительно whole-burst diagnostic reference
+Lab058, подключённого только после заморозки preamble-only оценки.
+
+| Метод | B1 ошибка CFO | B2 ошибка CFO | Средняя \|ошибка\| | B1 SER | B2 SER | Средняя SER B |
+|---|---:|---:|---:|---:|---:|---:|
+| P0 | +4,730655 Гц | +4,760847 Гц | 4,745751 Гц | 52,5218% | 52,3121% | 52,4169% |
+| P1 | −3,318571 Гц | +2,179939 Гц | 2,749255 Гц | 61,2846% | 42,1677% | 51,7262% |
+| P2 | −19,977856 Гц | +46,721234 Гц | 33,349545 Гц | 49,7775% | 50,2294% | 50,0035% |
+| P3 | −0,124881 Гц | +0,391708 Гц | 0,258294 Гц | 3,3089% | 3,9250% | 3,6170% |
+
+P3 дал средние EVM 0,84378 и matched/residual +1,4944 дБ, практически совпав
+с физической диагностикой Lab058 (0,84535 и +1,46485 дБ). Разница его средней
+SER с нижней диагностической ссылкой составляет +0,1211 процентного пункта.
+
+Для A1/A2 все методы сохранили среднюю SER 0,01776%. P3 дал EVM 0,31283/0,32516
+и ошибки CFO −0,0171/+0,0935 Гц относительно diagnostic reference. P2 сильнее
+ухудшил EVM A2 до 0,41255, что дополнительно показывает слабость короткого TRAIN.
+
+![Ошибка CFO](../data/processed/lab059/frequency_error_by_method.png)
+
+![Фазовый уход](../data/processed/lab059/burst_phase_drift.png)
+
+![Ошибки символов B](../data/processed/lab059/lab056_b_symbol_errors.png)
+
+## Synthetic Monte Carlo
+
+Чистая преамбула получена действующим TX/RX RRC-трактом при Fs 8 Мвыб/с:
+400 отсчётов/символ и 4001 tap для 20 ксимв/с, 16 отсчётов/символ и 161 tap для
+500 ксимв/с. После этого на выходе выбора символов добавлен комплексный AWGN с
+заранее заданным EVM 0,317390, 0,55 или 0,845350. Поэтому тест учитывает реальный
+RRC и дискретизацию в чистой форме, но не моделирует цветной или
+частотно-селективный остаток реального OTA-тракта.
+
+Для каждой из 17 частот, каждого качества и каждой скорости выполнено 300
+реализаций. В строке качества B для 500 ксимв/с каждый метод имеет 5100 оценок.
+
+| Метод | Bias | RMSE | Median abs | P95 abs | P99 abs | Катастрофические | P(≤0,25 Гц) | P(≤0,5 Гц) | P(≤1 Гц) |
+|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|
+| P0 | −0,018 Гц | 6,808 Гц | 4,643 Гц | 13,265 Гц | 17,805 Гц | 72,08% | 3,06% | 5,86% | 11,61% |
+| P1 | +0,050 Гц | 3,728 Гц | 2,498 Гц | 7,437 Гц | 9,895 Гц | 50,98% | 5,24% | 10,47% | 21,27% |
+| P2 | +0,078 Гц | 12,264 Гц | 8,256 Гц | 23,709 Гц | 31,583 Гц | 83,12% | 1,65% | 3,67% | 7,20% |
+| P3 | +0,049 Гц | 7,089 Гц | 2,935 Гц | 8,528 Гц | 11,383 Гц | 57,94% | 4,90% | 9,61% | 18,25% |
+
+Модельная граница Крамера—Рао для известных символов, неизвестной постоянной
+фазы и комплексного AWGN равна
+`sqrt(6*EVM²*Rs² / ((2*pi)²*N*(N²−1)))`. При N=1280, Rs=500000 и
+EVM=0,845350 она даёт СКО не меньше примерно 3,598 Гц. P1 с RMSE 3,728 Гц
+близок к этому масштабу. Это model-dependent sanity check, а не утверждение,
+что реальный OTA-остаток является AWGN.
+
+При 20 ксимв/с P1 на том же EVM получил RMSE 0,1465 Гц и 99,92% попаданий в
+±0,5 Гц; длительность преамбулы там 64 мс. Разница показывает, что ограничение
+500 ксимв/с связано прежде всего с 25-кратно более коротким временем наблюдения,
+а не с ошибкой единиц или знака.
+
+![Распределение synthetic 500K](../data/processed/lab059/synthetic_500k_error_distribution.png)
+
+## Lab047 и Lab054
+
+Положительный контроль Lab047 не ухудшился: P0, P1, P2 и P3 каждый получили
+36/36 HEADER_ACCEPTED, 36/36 FEC_STARTED, 36/36 CRC_PASS и 36/36 PACKET_OUTPUT.
+Во всех методах суммарно осталось две ошибки преамбулы и ноль ошибок заголовка.
+
+Lab054 осталась отрицательной для всех методов:
+
+| Метод | Ошибки преамбулы, сумма | Raw header errors | Voted header errors | HEADER_ACCEPTED | FEC_STARTED | CRC_PASS | PACKET_OUTPUT |
+|---|---:|---:|---:|---:|---:|---:|---:|
+| P0 | 7767 | 946 | 283 | 0/16 | 0/16 | 0/16 | 0/16 |
+| P1 | 8264 | 1000 | 313 | 0/16 | 0/16 | 0/16 | 0/16 |
+| P2 | 8871 | 1085 | 348 | 0/16 | 0/16 | 0/16 | 0/16 |
+| P3 | 9020 | 1140 | 373 | 0/16 | 0/16 | 0/16 | 0/16 |
+
+Эти данные не превращают Lab054 в новый опыт и не меняют его исторический
+вердикт. Плохое физическое качество Lab054 не исправляется заменой одной
+оценки частоты.
+
+![Lab054](../data/processed/lab059/lab054_result_by_method.png)
+
+## Инженерный вывод
+
+`PREAMBLE_ONLY_INSUFFICIENT`.
+
+P3 показывает, что штатный P0 можно существенно улучшить на конкретной записи,
+но ни один preamble-only метод не обеспечивает устойчивую ошибку менее 0,5 Гц
+при качестве B. Следующий один шаг — полностью офлайн проверить
+decision-directed carrier tracking на протяжении burst, используя решения BPSK
+без знания правильного payload. Это сохраняет текущий формат пакета и позволяет
+использовать P3 как начальную оценку. Costas loop остаётся разумной альтернативой,
+но потребует отдельной настройки динамики петли. Periodic pilots дают явную опору,
+однако меняют формат и добавляют overhead, поэтому их логично рассматривать позже.
+
+Lab058 commit: `82f17499ace5e655991240348401b9700c7c3349`.
+Lab059 не коммитировалась. Push не выполнялся. RF TX = 0. Lab060 не создавалась.

tests/test_lab059_preamble_carrier_limits.py

@@ -0,0 +1,155 @@
+"""Проверки математики и информационных границ Lab059."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from experiments import lab059_preamble_carrier_limits as lab059
+
+
+@pytest.mark.parametrize("frequency_hz", [-100.0, -5.0, -0.25, 0.0, 0.5, 20.0])
+def test_phase_slope_conversion_sign_units_and_square_factor(frequency_hz):
+    ordinary = 2 * np.pi * frequency_hz
+    squared = 4 * np.pi * frequency_hz
+    assert lab059.phase_slope_to_hz(ordinary, squared_bpsk=False) == pytest.approx(frequency_hz)
+    assert lab059.phase_slope_to_hz(squared, squared_bpsk=True) == pytest.approx(frequency_hz)
+    if frequency_hz:
+        assert lab059.phase_slope_to_hz(squared, squared_bpsk=False) == pytest.approx(2 * frequency_hz)
+
+
+def test_phase_drift_and_frequency_limit_are_inverse():
+    for phase_limit in (15, 30, 45, 60, 90):
+        frequency = lab059.maximum_frequency_error_hz(
+            phase_limit, lab059.BURST_DURATION_SECONDS
+        )
+        assert lab059.phase_drift_degrees(
+            frequency, lab059.BURST_DURATION_SECONDS
+        ) == pytest.approx(phase_limit)
+    assert lab059.maximum_frequency_error_hz(30, 0.2048) == pytest.approx(0.4069010416666667)
+
+
+def test_awgn_crlb_scale_matches_rate_and_observed_b_quality():
+    slow = lab059.awgn_cfo_crlb_standard_deviation_hz(0.845350, 1280, 20_000)
+    fast = lab059.awgn_cfo_crlb_standard_deviation_hz(0.845350, 1280, 500_000)
+    assert fast / slow == pytest.approx(25.0)
+    assert fast == pytest.approx(3.5982182026)
+
+
+@pytest.mark.parametrize("symbol_rate", [20_000, 500_000])
+@pytest.mark.parametrize("method", lab059.METHODS)
+def test_clean_known_cfo_reference_time_and_compensation(symbol_rate, method):
+    frequency_hz = 7.25 if symbol_rate == 20_000 else -37.5
+    phase_at_zero = -0.73
+    indexes = np.arange(lab059.PREAMBLE_SYMBOLS)
+    times = (indexes + 0.5) / symbol_rate
+    symbols = lab059.lab057.EXPECTED * np.exp(
+        1j * (phase_at_zero + 2 * np.pi * frequency_hz * times)
+    )
+    estimate = lab059.estimate_carrier(symbols, symbol_rate, method)
+    assert estimate.frequency_hz == pytest.approx(frequency_hz, abs=1e-8)
+    assert np.angle(estimate.gain * np.exp(-1j * phase_at_zero)) == pytest.approx(0.0, abs=1e-10)
+    corrected = lab059.compensate(symbols, symbol_rate, estimate)
+    assert np.max(abs(corrected - lab059.lab057.EXPECTED)) < 1e-9
+
+
+def test_p0_matches_active_two_block_formula_and_ambiguity():
+    symbol_rate = 500_000
+    frequency_hz = 41.25
+    times = (np.arange(lab059.PREAMBLE_SYMBOLS) + 0.5) / symbol_rate
+    symbols = lab059.lab057.EXPECTED * np.exp(2j * np.pi * frequency_hz * times)
+    expected = lab059.lab057.squared_cfo_statistics(symbols, symbol_rate)
+    estimate = lab059.estimate_carrier(symbols, symbol_rate, "P0")
+    assert estimate.frequency_hz == pytest.approx(expected["cfo_hz"], abs=1e-12)
+    assert estimate.estimation_symbols == 1024
+    assert estimate.unambiguous_abs_hz == pytest.approx(symbol_rate / 2048)
+
+
+def test_p2_reference_time_is_global_burst_zero():
+    symbol_rate = 500_000
+    frequency_hz = -12.75
+    phase_at_zero = 1.12
+    times = (np.arange(lab059.PREAMBLE_SYMBOLS) + 0.5) / symbol_rate
+    symbols = lab059.lab057.EXPECTED * np.exp(
+        1j * (phase_at_zero + 2 * np.pi * frequency_hz * times)
+    )
+    estimate = lab059.estimate_carrier(symbols, symbol_rate, "P2")
+    assert estimate.frequency_hz == pytest.approx(frequency_hz, abs=1e-9)
+    assert np.angle(estimate.gain * np.exp(-1j * phase_at_zero)) == pytest.approx(0.0, abs=1e-10)
+    assert estimate.validation_errors == 0
+
+
+@pytest.mark.parametrize("method", lab059.METHODS)
+def test_payload_truth_cannot_change_carrier_estimate(method):
+    symbol_rate = 500_000
+    indexes = np.arange(4096)
+    expected = np.resize(lab059.lab057.EXPECTED, len(indexes))
+    values = expected * np.exp(1j * (0.4 + 2 * np.pi * 3.5 * (indexes + 0.5) / symbol_rate))
+    changed = values.copy()
+    random_generator = np.random.default_rng(5907)
+    changed[lab059.PREAMBLE_SYMBOLS:] = (
+        random_generator.normal(size=len(changed) - lab059.PREAMBLE_SYMBOLS)
+        + 1j * random_generator.normal(size=len(changed) - lab059.PREAMBLE_SYMBOLS)
+    ) * 100
+    first = lab059.estimate_from_burst(values, symbol_rate, method)
+    second = lab059.estimate_from_burst(changed, symbol_rate, method)
+    assert first == second
+
+
+def test_raw_payload_cannot_change_new_preamble_only_estimates():
+    symbol_rate = 500_000
+    values, _truth = lab059.lab057.synthetic_waveform(
+        symbol_rate, delay_symbols=0.0, cfo_hz=3.5, phase_rad=0.4, es_n0_db=None
+    )
+    frontend = lab059.lab057.Frontend(symbol_rate)
+    probe = values[: (4096 + 42) * frontend.samples_per_symbol]
+    stock = frontend.extract(probe, 4096)
+    matched = frontend.filter(probe)
+    symbols = lab059._extract_symbols(
+        matched, frontend.nominal, stock.timing_offset_samples,
+        4096, frontend.samples_per_symbol,
+    )
+    changed = probe.copy()
+    payload_start = (
+        frontend.nominal + stock.timing_offset_samples
+        + lab059.PREAMBLE_SYMBOLS * frontend.samples_per_symbol
+    )
+    changed[payload_start + len(frontend.taps):] += 10 + 7j
+    first = lab059.real_carrier_estimates(
+        probe, frontend, stock.timing_offset_samples, symbols, symbol_rate, ("P1", "P2", "P3")
+    )
+    second = lab059.real_carrier_estimates(
+        changed, frontend, stock.timing_offset_samples, symbols, symbol_rate, ("P1", "P2", "P3")
+    )
+    assert first == second
+
+
+def test_phase_extrapolation_uses_one_compensation_only():
+    symbol_rate = 500_000
+    count = 102_400
+    frequency_hz = 4.7
+    phase = 0.8
+    indexes = np.arange(count)
+    expected = np.resize(lab059.lab057.EXPECTED, count)
+    symbols = expected * np.exp(1j * (phase + 2 * np.pi * frequency_hz * (indexes + 0.5) / symbol_rate))
+    estimate = lab059.estimate_from_burst(symbols, symbol_rate, "P1")
+    corrected = lab059.compensate(symbols, symbol_rate, estimate)
+    assert np.max(abs(corrected - expected)) < 1e-8
+
+
+def test_fixed_split_is_disjoint_and_not_result_dependent():
+    assert len(lab059.P2_TRAIN) == len(lab059.P2_VALIDATION) == 576
+    assert lab059.P2_TRAIN[0] == 32 and lab059.P2_TRAIN[-1] == 607
+    assert lab059.P2_VALIDATION[0] == 672 and lab059.P2_VALIDATION[-1] == 1247
+    assert set(lab059.P2_TRAIN).isdisjoint(lab059.P2_VALIDATION)
+
+
+def test_partial_baseline_summary_does_not_create_nan_for_unrun_methods():
+    row = {
+        "dataset": "Lab056", "label": "B1", "method": "P0",
+        "frequency_error_hz": 1.0, "symbol_error_rate": 0.5,
+        "evm_rms": 1.0, "matched_residual_db": 0.0,
+    }
+    summary = lab059.summarize_real([row])
+    assert set(summary["Lab056"]) == {"P0"}
+    assert summary["Lab054"] == {} and summary["Lab047"] == {}