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.

Summary: 75 modules: 70 at A, 3 at B, 2 at C.

Foundations#

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

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

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

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)

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

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

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

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

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

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

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