RF in Slow Motion: Sonifying a Wi-Fi 7 Packet
What would a 160 MHz OFDM waveform up in the 5 GHz U-NII band sound like if scaled to audio frequencies to keep the same wavelength (acoustic vs RF)?
Adaptive Beamforming is like Squeezing a Water Balloon
Think of adaptive beamforming as squeezing a water balloon, a simple analogy that reveals how combining multiple antennas creates focused gains and deep nulls. This post walks through the MVDR (Wiener-filter–based) solution, explains steering and scanning vectors, and shows how array geometry and known signal direction control what you can and cannot cancel. Practical tips highlight limits like the N-1 interferer rule.
5G NR QC-LDPC Encoding Algorithm
Lyons Zhang breaks down the 5G NR QC-LDPC encoding structure, emphasizing the circulant permutation matrices and why QC-LDPC suits simple hardware. The post defines the Q(P) and Q(-1) notation, summarizes BG1 and BG2 dimensions and selection rules, and shows how the parity-check matrix is partitioned for practical encoder implementations.
Polar Coding Notes: A Simple Proof
Lyons Zhang presents a compact, elementary derivation of channel polarization for binary-input discrete memoryless channels. The note leverages Mrs. Gerber's Lemma to bound conditional entropies and follows the Alsan-Telatar averaging argument to show mediocre channels vanish. The proof sidesteps martingale convergence and recovers the standard result that the fraction of good channels approaches the channel capacity.
Polar Coding Notes: Channel Combining and Channel Splitting
Lyons Zhang walks through the core algebra of polar coding, showing how channel combining builds the vector channel W_N from N copies of a binary-input DMC using the polar transform G_N = B_N F^{⊗n}. The notes then define channel splitting, derive the coordinate-channel transition probabilities from the chain rule, and present the recursive formulas that let you compute W_{2N}^{(2i-1)} and W_{2N}^{(2i)} from W_N^{(i)}.
There and Back Again: Time of Flight Ranging between Two Wireless Nodes
Conventional timestamping seems too coarse for centimeter-level RF ranging, yet many products claim and deliver that precision. This post unpacks the fundamentals behind high-resolution wireless ranging, contrasting common RF approaches such as RSSI, ToA, PoA, TDoA, and AoA. It also explains how device timestamps and counter registers work, giving engineers a practical starting point for implementing or evaluating time-of-flight ranging systems.
A Beginner's Guide to OFDM
Orthogonal Frequency Division Multiplexing made modern high-speed wireless practical by turning one fast serial bitstream into many slow parallel streams carried on orthogonal sinusoids. This beginner guide explains, with minimal math, how the iDFT/DFT pair builds OFDM, how spectral slicing makes each subcarrier effectively flat so equalization reduces to simple divisions, and why a cyclic prefix prevents inter-symbol interference.
Minimum Shift Keying (MSK) - A Tutorial
How does MSK achieve both excellent spectral efficiency and a constant-envelope signal suitable for nonlinear amplifiers? This tutorial builds MSK step‑by‑step from binary FSK, shows the minimum frequency spacing and continuous‑phase construction, and then recasts MSK as an OQPSK (pseudo‑symbol) representation. It finishes by generalizing MSK into CP‑FSK and the wider CPM family so you can connect practical pulse shapes and modulation indices to performance.
Discrete-Time PLLs, Part 1: Basics
In this series of tutorials on discrete-time PLLs we will be focusing on Phase-Locked Loops that can be implemented in discrete-time signal proessors such as FPGAs, DSPs and of course, MATLAB.
GPS - some terminology!
Hi!
For my first post, I will share some information about GPS - Global Positioning System. I will delve one step deeper than a basic explanation of how a GPS system works and introduce some terminology.
GPS, like we all know is the system useful for identifying one's position, velocity, & time using signals from satellites (referred to as SV or space vehicle in literature). It uses the principle of trilateration (not triangulation which is misused frequently) for...
Minimum Shift Keying (MSK) - A Tutorial
How does MSK achieve both excellent spectral efficiency and a constant-envelope signal suitable for nonlinear amplifiers? This tutorial builds MSK step‑by‑step from binary FSK, shows the minimum frequency spacing and continuous‑phase construction, and then recasts MSK as an OQPSK (pseudo‑symbol) representation. It finishes by generalizing MSK into CP‑FSK and the wider CPM family so you can connect practical pulse shapes and modulation indices to performance.
A Beginner's Guide to OFDM
Orthogonal Frequency Division Multiplexing made modern high-speed wireless practical by turning one fast serial bitstream into many slow parallel streams carried on orthogonal sinusoids. This beginner guide explains, with minimal math, how the iDFT/DFT pair builds OFDM, how spectral slicing makes each subcarrier effectively flat so equalization reduces to simple divisions, and why a cyclic prefix prevents inter-symbol interference.
Handling Spectral Inversion in Baseband Processing
Spectral inversion often sneaks in during RF and IF mixing chains and can break downstream demodulation. Eric Jacobsen shows that at baseband you can correct inversion with three trivial, equivalent operations: invert Q, swap I and Q, or invert I, and he explains the math and geometric intuition behind each. The fixes work in modulators or demodulators and tolerate arbitrary phase offsets.
Understanding and Relating Eb/No, SNR, and other Power Efficiency Metrics
Eric Jacobsen untangles the common confusion around Eb/N0, SNR, Es/No and related power-efficiency metrics, showing when each metric applies and how to convert between them. He covers practical measurement techniques including spectrum-analyzer and slicer-based estimates, the impact of symbol rate, modulation order and FEC code rate, and offers simple sanity checks to catch common dB and factor-of-two errors. Engineers get a concise toolkit for accurate comparisons.
Frequency Dependence in Free Space Propagation
Free-space propagation of electromagnetic waves is essentially independent of frequency, a counterintuitive conclusion Eric Jacobsen demonstrates step by step. He shows the λ^2 factor in the Friis transmission equation comes from antenna effective area and gain, not from the space between antennas, explaining why dipoles favor lower bands while dishes improve with frequency. The post also reminds engineers that material penetration and atmospheric absorption remain genuine frequency dependent concerns.
Pulse Shaping in Single-Carrier Communication Systems
Eric Jacobsen clears up common confusion around pulse shaping in single-carrier communications, focusing on matched filtering, Nyquist filtering, and related terminology. He uses the NRZ rectangular pulse as a concrete example to show how the transmit spectrum becomes a sinc envelope when the bitstream has enough randomness, and he highlights how bit patterns and context-sensitive terms can change the observed behavior.
5G NR QC-LDPC Encoding Algorithm
Lyons Zhang breaks down the 5G NR QC-LDPC encoding structure, emphasizing the circulant permutation matrices and why QC-LDPC suits simple hardware. The post defines the Q(P) and Q(-1) notation, summarizes BG1 and BG2 dimensions and selection rules, and shows how the parity-check matrix is partitioned for practical encoder implementations.
Adaptive Beamforming is like Squeezing a Water Balloon
Think of adaptive beamforming as squeezing a water balloon, a simple analogy that reveals how combining multiple antennas creates focused gains and deep nulls. This post walks through the MVDR (Wiener-filter–based) solution, explains steering and scanning vectors, and shows how array geometry and known signal direction control what you can and cannot cancel. Practical tips highlight limits like the N-1 interferer rule.
Understanding Radio Frequency Distortion
Markus Nentwig breaks down how analog RF nonlinearities appear in a complex baseband model so you can simulate and predistort real transmitters. The article shows that even-order terms vanish in-band under narrowband assumptions, while odd-order products collapse to |BB(t)|^(n-1) BB(t) and do not depend on the carrier frequency. It also explains bandwidth scaling and includes a MATLAB example plus measured PA coefficients.
Polar Coding Notes: Channel Combining and Channel Splitting
Lyons Zhang walks through the core algebra of polar coding, showing how channel combining builds the vector channel W_N from N copies of a binary-input DMC using the polar transform G_N = B_N F^{⊗n}. The notes then define channel splitting, derive the coordinate-channel transition probabilities from the chain rule, and present the recursive formulas that let you compute W_{2N}^{(2i-1)} and W_{2N}^{(2i)} from W_N^{(i)}.
Minimum Shift Keying (MSK) - A Tutorial
How does MSK achieve both excellent spectral efficiency and a constant-envelope signal suitable for nonlinear amplifiers? This tutorial builds MSK step‑by‑step from binary FSK, shows the minimum frequency spacing and continuous‑phase construction, and then recasts MSK as an OQPSK (pseudo‑symbol) representation. It finishes by generalizing MSK into CP‑FSK and the wider CPM family so you can connect practical pulse shapes and modulation indices to performance.
Handling Spectral Inversion in Baseband Processing
Spectral inversion often sneaks in during RF and IF mixing chains and can break downstream demodulation. Eric Jacobsen shows that at baseband you can correct inversion with three trivial, equivalent operations: invert Q, swap I and Q, or invert I, and he explains the math and geometric intuition behind each. The fixes work in modulators or demodulators and tolerate arbitrary phase offsets.
Understanding and Relating Eb/No, SNR, and other Power Efficiency Metrics
Eric Jacobsen untangles the common confusion around Eb/N0, SNR, Es/No and related power-efficiency metrics, showing when each metric applies and how to convert between them. He covers practical measurement techniques including spectrum-analyzer and slicer-based estimates, the impact of symbol rate, modulation order and FEC code rate, and offers simple sanity checks to catch common dB and factor-of-two errors. Engineers get a concise toolkit for accurate comparisons.
A Beginner's Guide to OFDM
Orthogonal Frequency Division Multiplexing made modern high-speed wireless practical by turning one fast serial bitstream into many slow parallel streams carried on orthogonal sinusoids. This beginner guide explains, with minimal math, how the iDFT/DFT pair builds OFDM, how spectral slicing makes each subcarrier effectively flat so equalization reduces to simple divisions, and why a cyclic prefix prevents inter-symbol interference.
Pulse Shaping in Single-Carrier Communication Systems
Eric Jacobsen clears up common confusion around pulse shaping in single-carrier communications, focusing on matched filtering, Nyquist filtering, and related terminology. He uses the NRZ rectangular pulse as a concrete example to show how the transmit spectrum becomes a sinc envelope when the bitstream has enough randomness, and he highlights how bit patterns and context-sensitive terms can change the observed behavior.
Frequency Dependence in Free Space Propagation
Free-space propagation of electromagnetic waves is essentially independent of frequency, a counterintuitive conclusion Eric Jacobsen demonstrates step by step. He shows the λ^2 factor in the Friis transmission equation comes from antenna effective area and gain, not from the space between antennas, explaining why dipoles favor lower bands while dishes improve with frequency. The post also reminds engineers that material penetration and atmospheric absorption remain genuine frequency dependent concerns.
Discrete-Time PLLs, Part 1: Basics
In this series of tutorials on discrete-time PLLs we will be focusing on Phase-Locked Loops that can be implemented in discrete-time signal proessors such as FPGAs, DSPs and of course, MATLAB.
Understanding Radio Frequency Distortion
Markus Nentwig breaks down how analog RF nonlinearities appear in a complex baseband model so you can simulate and predistort real transmitters. The article shows that even-order terms vanish in-band under narrowband assumptions, while odd-order products collapse to |BB(t)|^(n-1) BB(t) and do not depend on the carrier frequency. It also explains bandwidth scaling and includes a MATLAB example plus measured PA coefficients.
Design of an anti-aliasing filter for a DAC
If you need a practical way to design an anti-aliasing filter for a DAC, this post delivers an Octave/Matlab script that numerically optimizes a Laplace-domain transfer function for linear phase and arbitrary magnitude. The routine models the DAC sample-and-hold sinc response, compensates group delay automatically, and can include an optional multiplierless FIR equalizer. An example shows a 5.4 dB objective improvement and reduced analog Q for easier implementation.
5G NR QC-LDPC Encoding Algorithm
Lyons Zhang breaks down the 5G NR QC-LDPC encoding structure, emphasizing the circulant permutation matrices and why QC-LDPC suits simple hardware. The post defines the Q(P) and Q(-1) notation, summarizes BG1 and BG2 dimensions and selection rules, and shows how the parity-check matrix is partitioned for practical encoder implementations.
