Maturity ======== For every module, the strongest evidence that it is right. The levels: - **A**: validated against an external reference (a published figure or table, a table of a standard reproduced verbatim, or the recorded output of a reference implementation: OptiCommPy 0.11, GNPy 3.0, AFF3CT v4.7.1); - **B**: against a closed form only; - **C**: self-consistency only (round trips, invariants); - **—**: not validated. The tests that give the evidence and the regimes not covered yet are listed module by module in `docs/MATURITY.md `_. .. generated by tools/maturity_table.py from validation/maturity.yaml: do not edit Summary: 75 modules: 70 at A, 3 at B, 2 at C. Foundations ----------- .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - Constellations, mapping, demapping and closed-form error rates - A - OptiCommPy outputs; closed forms of Proakis & Salehi * - Capacity and cutoff rate of CM and BICM - A - Caire, Taricco & Biglieri 1998 Figs. 4–7 * - Adaptive MQAM over fading (Rust only) - A - Goldsmith & Chua 1997 Figs. 3, 5, 10, Table II * - Sources (bits, PRBS, uniform and shaped symbols) - A - ITU-T O.150 Sec. 5 and Table 1, exact * - Differential PSK - A - Pawula, Rice & Roberts 1982 Sec. IV-A; closed forms of Proakis & Salehi * - Error rates with an imperfect channel estimate and over Jakes' fading - A - Chang & Su 2002 eqs. 31–53, Figs. 3–4 Coding and shaping ------------------ .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - Convolutional codes (Viterbi, BCJR) - A - AFF3CT; Yasuda et al. Table I * - Puncturing - A - Yasuda et al. Table I; patterns of IEEE 802.11 and EN 300 421 * - Turbo codes (LTE) - A - AFF3CT, K = 40 and 1024 * - LDPC codes - A - AFF3CT, PEG and DVB-S2 short code; Hu et al. 2005 * - Density evolution of LDPC ensembles (Rust only) - A - Richardson & Urbanke 2001 Tables I-II * - EXIT charts of parallel concatenated codes (Rust only) - A - ten Brink 2001 Tables II and IV * - Polar codes (SC, CA-SCL) - A - AFF3CT, SC and CA-SCL * - 5G NR channel codes: LDPC and polar with rate matching - A - Sionna vectors bit for bit; TS 38.212 tables * - Reed–Solomon codes - A - AFF3CT; Lin & Costello; ETSI EN 300 744, CCSDS 131.0-B * - BCH codes - A - AFF3CT; generators of EN 302 307-1 Table 6a * - CRC - A - CRC polynomials of TS 38.212 * - Scrambling, interleaving - C - balanced sequences, invertible permutations * - Finite-length bounds - A - Polyanskiy, Poor & Verdú 2010 Table I; the Shannon limits of BPSK; Costello & Forney 2007 * - Distribution matching and probabilistic amplitude shaping - A - Schulte & Böcherer 2016 Fig. 2; Böcherer et al. 2015 Tables VI–X Waveforms --------- .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - OFDM, channel estimation and gain correction - A - Cimini 1985 Figs. 3–7; Coleri et al. 2002 Sec. VI-B (with an oversampled comb) * - OFDM synchronisation (Schmidl–Cox, Moose, van de Beek) - A - Schmidl & Cox 1997, Moose 1994, van de Beek et al. 1997 * - PAPR: distribution and reduction - A - Ochiai & Imai 2001 eqs. (11), (27); Saul 2004 Figs. 8-9 (recursive clipping) * - Constant-envelope OFDM - A - Thompson et al. 2008 eq. (15); Guerreiro et al. 2016 Fig. 1; López Morales et al. 2022 Fig. 3; Pacheco & Hatzinakos 2006 Fig. 1 * - Chirp spread spectrum (LoRa modulation) - A - Chiani & Elzanaty 2019 Table I; Afisiadis et al. 2020 Figs. 2, 7; Vangelista 2017 Fig. 1 * - Continuous-phase modulation - A - Murota & Hirade 1981 Table I and Fig. 5; Sundberg 1986 Fig. 5; MSK of Proakis & Salehi * - FBMC/OQAM - A - Bouhadda et al. 2014 Table 1, Figs. 7, 10, 11; Nissel & Rupp 2017 eq. (17); Nissel, Schwarz & Rupp 2017 eqs. (13), (17), Figs. 5-8 * - UFMC - A - Vakilian et al. 2013 Fig. 3(b) * - OTFS and the delay–Doppler channel (Rust only) - A - Raviteja et al. 2019 Theorem 1 and its example; Hadani et al. 2017 Fig. 5 qualitatively MIMO ---- .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - MIMO detection - A - Yang & Hanzo 2015 Table X; MRC closed forms * - Message-passing detection of large MIMO (LAMA, OAMP) - A - Jeon et al. 2018 Table II; Ma & Ping 2017 eq. (42), Figs. 2–3 * - Space-time block codes - B - Tarokh et al. 1999 eqs. (39)–(40); MRC closed forms * - Capacity and precoding - A - Telatar 1999 Theorem 2, eqs. (13), (16)–(18), Figs. 1–4 * - MIMO channel estimation - A - Biguesh & Gershman 2006 Figs. 1–4, eqs. (12)–(59) * - Multi-user massive MIMO - A - Ngo, Larsson & Marzetta 2013 Props. 1–3, 5–7, Figs. 1 and 4 * - Downlink NOMA (Rust only) - A - Ding et al. 2014 Fig. 3 table, Fig. 1(a) Wireless channels ----------------- .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - Path loss (TR 38.901) - A - TR 38.901 Tables 7.4.1-1 and 7.4.2-1 against Sionna 2.2.0 * - AWGN - B - closed forms of the error rates * - Flat fading and antenna correlation - A - Loyka 2001 (exponential correlation, Fig. 1); BPSK over Rayleigh fading; MRC * - Tapped and clustered delay lines (TDL, CDL) - A - ITU-R M.1225 and 3GPP TR 38.901 tables, verbatim * - Reconfigurable intelligent surface - A - Basar et al. 2019 eqs. (14)–(18), Figs. 6–7 Optical ------- .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - Fibre: linear, split-step Fourier, Manakov, back-propagation - A - OptiCommPy and Optilux outputs; Häger & Pfister 2021 Figs. 5 and 8; Ip & Kahn 2008 Fig. 12 (in part) * - GN and EGN models - A - Carena et al. 2014 Fig. 1(a); GNPy outputs; Semrau, Killey & Bayvel 2019 Figs. 4a, 4b, 5 * - Raman amplification and ISRS - A - Bromage 2004 eqs. (3)–(5), Figs. 7–8; Hu et al. 2004 eq. (2); GNPy outputs; Semrau & Bayvel 2018 eq. (10) * - EDFA and PMD - A - the Maxwellian DGD of Foschini & Poole 1991 Fig. 3; the accumulated ASE * - Optical front ends (laser, modulators, photodiodes, coherent receiver) - A - OptiCommPy outputs * - Indoor optical wireless - A - Barry et al. 1993 Table II; Komine & Nakagawa 2004 Figs. 3–9 * - Free-space optics - A - Al-Habash et al. 2001 Figs. 3, 6–8 Hardware impairments -------------------- .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - Nonlinear amplifier driven by OFDM - A - Banelli & Cacopardi 2000 eqs. 7–31, Fig. 5; Bouhadda et al. 2014, Tables 2–3 * - Power amplifiers, IQ imbalance and digital predistortion - A - Ding et al. 2004 Fig. 4 (memory-polynomial predistortion) * - Phase noise, frequency and clock offsets - A - IEEE Std 1139-2022 Table B.2 (Allan variances of white FM) * - DAC and ADC - A - Max 1960 Table II; Bennett 1948; the exact error of a Gaussian input; IEEE Std 1241; Walden 1999 Receiver DSP ------------ .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - Filters and resampling - A - OptiCommPy outputs * - Carrier recovery - A - OptiCommPy outputs; Rife & Boorstyn 1974; Fatadin et al. 2009; Pfau et al. 2009 * - Clock recovery - A - OptiCommPy outputs * - Frame synchronisation - A - Massey 1972 Tables I–II (optimum rule) * - Adaptive equalisers - A - OptiCommPy outputs; Kikuchi's singularity * - Chromatic dispersion compensation - A - Eghbali et al. 2014 Table I, Figs. 5 and 9 * - Blind estimation: modulation recognition, M2M4 SNR, symbol rate - A - Pauluzzi & Beaulieu 2000 Figs. 9–10 (M2M4, CRB); exact cumulants of the alphabets Metrics and analysis -------------------- .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - Error rates, SNR and EVM - A - OptiCommPy outputs * - Information rates and shaping gains - A - Böcherer et al. 2015 Tables I, III; OptiCommPy outputs * - Receiver posteriors (``air`` metrics) - A - Alvarado et al. 2018 Remarks 4–5, eq. (35) * - Spectral metrics (PSD, ACLR, PAPR, CCDF) - C - a tone lands in its bin Systems and standards --------------------- .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - DVB-S - A - EN 300 421 Tables 2 and 3, Figures 2, 4 and 5 * - DVB-S2 - A - EN 302 307-1 Table 13 and the tables of the standard * - DVB-T - A - EN 300 744 Tables C.1 and A.1 (Gaussian within 0.12 dB) * - CCSDS 131.0-B-5 channel coding - A - Tables F-1, 3-1, 6-2, 7-1, 7-5, C-1 and Annex G, exact * - AIS - A - the CRC catalogue; pyais outputs; a simulated ship end to end * - FM broadcasting and RDS - A - BS.450 and NRSC-4 tables; a simulated station end to end * - LTE cell search and MIB - A - TS 36.211 Table 6.11.2.1-1 verbatim; a measured cell decoded * - 5G NR numerology, SSB, cell search and PDSCH DMRS - A - py3gpp outputs; Lin et al. 2019 * - 5G NR PDSCH - A - Sionna and py3gpp bit for bit; TS 38.101-4 test 1-2 (2 and 4 RX) within the requirements Simulation and specifications ----------------------------- .. list-table:: :header-rows: 1 :widths: 40 8 52 * - Module - Level - Strongest evidence * - Monte Carlo runner - A - Brown, Cai & DasGupta 2001: the intervals and their exact coverage; thread independence, stopping rules * - Specifications, verification and operating-point search - B - the search against the inverted closed forms * - Recordings (SigMF, raw IQ, NPY) - A - sigmf-python, the reference implementation, both ways .. end of the generated table