Denys Inhul

ch1: the radar landscape

date: May 17 2026

1. The big picture

A radar allows us to learn information about our environment by using EM waves to interact with that enviornment. One of the marvelous things is that speed of light is insanely large relative to the scales we are all used to. a EM wave at $3 \cdot 10^8$ m/s can travel 100km back and forth in sub 0.7ms. That’s how you can detect planes and rockets hundreds of km away near-”instantly”.

Another core property of EM wave is its frequency, and insane dynamic range we get of kilometere long wavelengths to sub-mm wavelengths. Different bands and magnitudes of frequencies interact with the envrionment (atmosphere, objects, space, etc.) in different ways, allowing us to gather rich information. Lower frequencies can penetrate dense materials like walls and concrete, some bands can refleect off of diferent layers of atmosphere, some allow us to capture high precision sub-mm movements and location, some bands experience specific interactions with water and ice allowing us to detect those separately from everything else.

Generally one can capture all this EM signal by having a receiver (RX) that reads and transcodes EM waves into a signal. Working with the analog representation of such signals is still a pretty critical process in the pipeline, but I will mostly ignore that and focus on digital processing of raw signals digitized with an ADC (analog-to-digital converter).

In the abundnace of EM signals and some kind of structure of those signals, one could make a passive radar that simply listenes to external signals and reconstructs a picture of reality from that.

But, if you can also have the transmitter (TX) under you control, you have a lot more levers of understanding the reality. Having transmitted waveform with extremely precise timing information is extremely useful when receiveing and comparing the RX waveform signal. You can imagine as if you’re probing the world with a 300,000 km/s electro magentic stick and seeing what you feel. You can learn objects’ positions, velocities, material, size, and other characteristic by choosing the transmitted waveform, antena gemoetry and post-processing applied, although it’s worth saying that learning all of those characteristics to arbitrary precision and accuracy is extremely hard and sometimes is even impossible.

2. Information we get

With TX under your control, you choose the waveform: how amplitude, frequency, and phase evolve over time, and where the antenna points. RX measures the same four properties on whatever comes back. Every radar observable is some comparison between the wave you sent out and the wave that returned. The richness of that comparison grows with how long you watch (more samples in time), how many antennas you have (more samples in space), and which polarizations you record.

Distance

Whatever timing feature you stamp onto the wave (a pulse edge, a chirp ramp, a coded sequence) comes back delayed by the round-trip travel time $\tau$:

Factor of two for the round trip. Without a timing feature you cannot extract range at all, which is why a pure CW tone gives speed but not distance: the return looks identical to the transmission up to an unknown phase, so there is nothing to compare against. Range resolution is set by the waveform’s bandwidth $B$: the narrower the timing feature, the more precisely you can locate its echo. It works out to $\Delta r = c / (2B)$. A gigahertz of bandwidth buys you about 15 cm of range resolution; a megahertz buys 150 m.

Speed

A moving target Doppler-shifts the carrier frequency:

Round trip shows up as a factor of two again. The sign of $\Delta f$ tells you whether the target is approaching or receding. This is the cheapest observable in radar: a tone, a mixer, and a low-pass filter, no clever waveform required. Police speed guns, automatic doors, and dollar-store motion sensors all live here. Distance and speed live on different parts of the same wave (timing features vs carrier frequency), so a waveform that carries both can extract them at once. That’s the trick chirp-based and pulse-Doppler radars exploit.

Signature

The strength and character of the return tell you about the object itself. The simplest cut is radar cross-section $\sigma$, a single scalar capturing how much energy the object scatters back. Two-way path loss is characterized by:

Doubling target range cuts received power by 16. This is why long-range surveillance radars need huge apertures or huge transmit power, and why stealth aircraft are designed to drive $\sigma$ down by orders of magnitude through shape and absorber materials.

Beyond a single number, the return has structure. Different materials and shapes scatter different frequencies differently, so sweeping the carrier reveals frequency-dependent reflectivity. Different polarizations are scattered differently too: smooth surfaces preserve polarization, vegetation depolarizes, edges and wires have signature responses. With dual-polarized TX and RX you record a full $2 \times 2$ scattering matrix per resolution cell, which is how weather radar tells rain from hail and SAR tells forest from bare ground.

Direction

There are two ways to know where a return came from. You can point a narrow beam in one direction at a time, either mechanically (a rotating dish) or electronically (a phased array, where you offset the phase of many small elements so their wavefronts add constructively in a chosen direction). Beamwidth scales as $\theta \approx \lambda / D$: bigger aperture or shorter wavelength gives a tighter beam.

Or you can listen on many antennas at once and compare phases between them. A wave arriving at angle $\theta$ hits adjacent receivers a tiny bit out of phase:

Inverting this gives the angle. The number of independent angles you can resolve is bounded by the number of elements.

Fine motion

If the radar is phase-coherent, it knows the phase of every return relative to its own local oscillator. Across many pulses, the phase of a fixed range bin tracks the target’s range change to a tiny fraction of a wavelength. A full $2\pi$ of phase corresponds to $\lambda/2$ of displacement (round trip again). At 24 GHz, $\lambda/2 \approx 6$ mm, so a single degree of phase resolves about 17 μm of motion.

This is what lets radar see motion much finer than its own range resolution. The bulk range bin might be a meter wide, but micrometer-scale changes within that bin show up as phase drift across pulses. From this one trick you get heartbeat and breathing through walls (the subject of chapter 2), structural vibration monitoring, InSAR ground deformation maps from orbit, and micro-Doppler signatures of rotating propellers and walking gaits.

3. The architecture zoo

The transmitted waveform is what most distinguishes one radar from another. Below are the main configurations:

Pulsed

Transmit a short RF burst, then listen during silence. Round-trip delay gives range directly. Velocity needs many pulses processed together. Close targets are blinded by the TX pulse. Used in long-range surveillance, weather radar, and ground-penetrating radar.

CW Doppler

Transmit a constant tone. Look at the frequency offset of the return. Measures velocity directly with no signal processing math. Cannot measure range, because no time reference exists in the waveform. Used in police speed guns, automotive blind-spot detectors, and motion sensors like the HB100 and RCWL-0516.

FMCW

Transmit a chirp whose frequency sweeps linearly. Mix the return against a copy of the transmitted signal. The mixer output is a tone whose frequency is proportional to the round-trip delay, hence to target range. Recovers both range and velocity with cheap hardware running at low instantaneous transmit power. Standard in automotive 77 GHz, mmWave presence sensors, drone altimeters, and almost every homebuilt radar.

PMCW

Like FMCW, but instead of sweeping the carrier in frequency, you modulate it in phase with a pseudo-random code (a PN sequence, m-sequence, or Gold code). The receiver correlates the return against the same code; range comes from the correlation peak, velocity from phase evolution across many code repetitions. The big advantage over FMCW is mutual interference: with each radar using a different code, neighboring units look like uncorrelated noise to one another. The cost is higher ADC sample rates and more digital compute. Showing up in newer automotive 77 GHz radars from Uhnder and several Tier-1 suppliers.

Stepped frequency

Like FMCW but with discrete frequency steps instead of a continuous sweep. Slower to acquire a full sweep, but each frequency can be calibrated independently. Used in ground-penetrating radar and some imaging systems.

Pulse-Doppler

Coherent pulse train. Range from each pulse, velocity from phase evolution across pulses (slow-time FFT). The dominant architecture in modern military and weather radar.

SAR (synthetic aperture)

Move the antenna along a known path and coherently combine returns. The travel path becomes a synthetic aperture much wider than any physical antenna. Cross-range resolution becomes independent of physical antenna size, set instead by total path length. Used in satellite Earth observation (Sentinel-1, Biomass), reconnaissance, and drone-mounted imaging.

Passive (bistatic)

Give up TX entirely and listen for reflections of signals that other systems are already broadcasting: FM/DAB radio, DVB-T television, GSM/LTE cells, GPS, Starlink, even the Sun. A reference channel captures the direct path from the illuminator; a surveillance channel captures the reflected path off the target; cross-correlating the two recovers bistatic range and Doppler. No transmit power means no emission license, no spectrum allocation, and you are very hard to detect yourself. The price is messy waveforms you do not control and coverage that depends on which illuminators happen to be lit. Used in air surveillance (Silent Sentry, Cassidian), space-object tracking, and meteor-trail detection.

Polarimetric

TX and RX in two orthogonal polarizations. Records the full 2x2 scattering matrix per cell. Separates rain from snow from hail; classifies forest from ground from water.

note: phased array is not a separate architecture but a beamforming choice. Many small antennas with controlled phase offsets steer the beam electronically with no moving parts. Compatible with any waveform above. Treated in detail in Chapter 6.

4. Frequency bands and their tradeoffs

Every radar lives in a frequency band, and every band is a tradeoff. Lower frequencies penetrate walls and weather but need large antennas and give poor angular resolution. Higher frequencies get tiny antennas and tight beams but get absorbed by water, oxygen, and human bodies.

Three independent things scale with frequency:

• Antenna size. Resonant elements scale with $\lambda = c/f$. At 30 MHz, $\lambda/2 = 5$ m. At 77 GHz, $\lambda/2 \approx 2$ mm.
• Beamwidth. For a fixed aperture $D$, beamwidth $\theta \approx \lambda/D$. Higher $f$ at the same physical aperture gives a tighter beam.
• Loss in matter. Water vapor peaks near 22 GHz, oxygen near 60 GHz, dielectric losses in walls rise roughly as $f^{1.5}$ to $f^2$ in the mmWave range.

Higher frequency does not just mean a smaller antenna. It also means more atmospheric loss, less wall penetration, and tighter manufacturing tolerances. A 77 GHz patch antenna can detune from a fingerprint on its surface. The tradeoff is between aperture-for-resolution at high frequencies and penetration-and-robustness at low frequencies.

5. Capability matrix

Which architecture gives you which observable, at what difficulty.

Practically only a handful of these are realistic to build in a garage or a small lab. CW Doppler is by far the easiest: a $10 HB100 module and an Arduino get you a working motion sensor in an afternoon. FMCW is the actual workhorse for serious homebuilt work; TI eval boards in the AWR/IWR series run around $200-400 and give you a full 77 GHz radar with MIMO and several RX channels, and almost every interesting homebrew radar project you’ve come across online is one of these. Stepped-frequency setups are also reachable if you have a half-decent VNA lying around. Pulsed and passive radars are doable but a much bigger software lift: pulsed needs fast switching and a fast ADC, while passive needs a pair of SDRs and a lot of signal-processing competence. SAR is right at the edge of what’s feasible (a drone-mounted FMCW board with a good IMU and GPS will get you something halfway). PMCW and pulse-Doppler are essentially out of reach for hobbyists; the silicon is either custom or not sold to retail, and the processing complexity makes them institutional in practice.

next: ch2: heartbeat through a wall →