Piyush Kumar Singh · NR Layer-1 & NTN
Standards-grounded analysis of 5G NR, NTN and wireless systems.
NR5G connects public specifications and research literature to mathematical derivations, numerical examples and implementation constraints. The emphasis is on work that can be inspected, challenged and reproduced without proprietary modem information.
Public standards
Explicit assumptions
Numerical checks
Open code and data
First reproducible experiment
LEO state uncertainty → residual NTN timing and Doppler
A public Python model now turns the satellite-ephemeris discussion into an inspectable experiment: one declared 600 km pass, controlled error sweeps, complete CSV data, regenerated figures, 11 tests and explicit model limitations.
Reproducible experiment
Read the result and engineering interpretation
A 10 ms epoch error produces up to 0.436 µs residual service-link RTT and 5.360 Hz residual Doppler in the declared Hyderabad pass. See why those values change with geometry and what they do—and do not—prove.
Review the experiment →
Versioned code, data and tests
Reproduce or challenge every number
Inspect the configuration, coordinate transforms, orbit model, error injections, signed time series, summary tables, vector figures, test suite and CI workflow.
Open the simulator repository →
Featured NR NTN & Physical-Layer Work
Begin with the topics closest to modem and satellite-radio engineering. Each page identifies whether it is a standards analysis, technical derivation or research synthesis.
Standards-guided numerical analysis
SIB19, Epoch Time and Timing Advance
Follow a transparent NTN link from radio-frame epoch and Common TA through UE-specific delay prediction, random access and uplink arrival at the synchronization reference point.
Trace the timing numerically →
Numerical geometry analysis
LEO Orbits, Beams and Elevation
Connect orbital motion, elevation angle, slant range, delay, radial velocity and Doppler using explicit geometry and worked values.
Build the satellite geometry →
Technical derivation
OFDM Orthogonality and NR Numerology
Derive the SCS–symbol-duration relationship, reconstruct the 15 kHz timing grid and test a complete hypothetical 10 kHz design.
Derive the NR time-frequency grid →
Technical derivation
MIMO and NR Channel Estimation
Move from the channel matrix and capacity result to LS/LMMSE estimation, NR reference signals, channel aging and hardware-constrained spatial rank.
Build MIMO from first principles →
Engineering Foundations
Supporting material is added when it strengthens an implementation or research question rather than to create a broad telecom encyclopedia.
Standards analysis
NR over Non-Terrestrial Networks
Transparent payloads, ECEF state, range and range rate, GEO/LEO behavior, timing, Doppler and the assumptions NR changes for satellite access.
Build the NR NTN model →
Standards & certification analysis
Who Verifies a Commercial Modem?
Separate 3GPP conformance specifications from certification, regulation, operator acceptance and field behavior.
Follow the verification chain →
Topic collection
5G NR Engineering
Browse implementation-oriented physical-layer derivations and standards analyses in one place.
Explore 5G NR →
Weekly Signals & Wireless Industry Map
Dated, source-checked views of what is changing now: one tracks research and standards developments; the other maps the companies turning wireless ideas into products and networks.
Weekly primary-source review
NR5G Weekly Radar
Eight to twelve evidence-graded developments across 5G, 6G, NTN, RF, RAN, sensing, patents and commercialization, with reported gains separated from independent validation.
Read the latest issue and archive →
Curated industry landscape
Wireless Company Atlas
Forty-one companies across 22 countries, organized by geography, products, technical specialization, target markets and demonstrated maturity—not by current vacancies.
Explore the company landscape →
Research Syntheses
These pages connect peer-reviewed or institutional sources to engineering mechanisms and open questions. They are labelled as syntheses, not original research.
Peer-reviewed research synthesis
Inverse-Designed RFICs
How learned electromagnetic surrogates and reinforcement learning are changing RF and sub-THz circuit design from parameter tuning toward specification-driven synthesis.
See when AI starts solving Maxwell →
Engineering evidence review
RF Materials and Propagation
Permittivity, conductivity, loss, building penetration and conductive fabrics, grounded in propagation recommendations and measurement standards.
Explore RF materials →
Evidence before labels
The site now separates explanation from executable evidence.
NR5G distinguishes standards interpretation, mathematical derivation, literature synthesis and reproducible experimentation. The LEO pass study publishes code, configuration, full data, plots, tests and limitations; “original research” remains reserved for a defensible novel contribution with independent baselines.
Inspect the evidence →
About NR5G
NR5G is maintained by Piyush Kumar Singh, a software engineer focused on 5G NR Layer-1 modem development and NR-NTN. All published material is based on public standards, public research and independent derivations.
About the author, scope and validation method →