Table of Contents
- • Introduction
- • FMCW Radar Signal
- • The Radar Cube
- • Processing Chain Overview
- • Mapping the Processing Chain onto the S32R45
- • Range FFT
- • Doppler FFT
- • Non-Coherent Combining
- • CFAR Detection
- • Clustering (DBSCAN)
- • Angle Estimation (MUSIC DoA)
- • NXP Radar SDK Integration
- • Tools and Ecosystem
- • Conclusion
Introduction
In the previous articles of this series, we introduced the fundamentals of automotive radar in the Radar Overview and the hardware/software setup in Radar SW & HW Environment. Building on that foundation, this article follows the radar data on its journey through the complete processing chain — from digitized ADC samples to a final target list describing each object’s range, velocity, and angle.
The chain is modeled and prototyped in MATLAB® using Radar Toolbox™ and deployed on the NXP S32R45 radar processor through the NXP Model-Based Design Toolbox for RADAR. The key processing stages are distributed across the S32R45 Cortex-A53 cores, the SPT accelerator, the BBE32 DSP accelerator, and the LAX accelerator, using optimized kernels from the NXP Radar SDK.
FMCW Radar Signal
Frequency-Modulated Continuous Wave (FMCW) radar transmits a continuous chirp whose frequency increases linearly over time. The received echoes are mixed with the transmitted signal, producing a beat frequency (also called intermediate frequency, IF) proportional to the round-trip delay, which directly encodes target range.
Figure 1: FMCW Radar Transmit and Receive Chirp Diagram
The diagram plots frequency (vertical axis) against time (horizontal axis) and shows two piecewise-linear signals. The transmitted signal Tx (blue) rises linearly across the chirp, while the received signal Rx (orange) has the same shape but is delayed in time:
Tx(t) = ATx · cos( 2π fc t + 2π (fB / 2T) t² + φ0 )
Rx(t) = ARx · cos( 2π fc (t − td) + 2π (fB / 2T) (t − td)² + φ0 )
The relevant variables are summarized below:
| Symbol | Meaning |
|---|---|
| Tx(t) | Transmitted signal (blue curve) |
| Rx(t) | Received signal (orange curve) |
| td | Propagation delay between Tx and Rx |
| IF | Frequency difference between Tx and Rx during the chirp |
| T | Chirp (ramp) duration |
| fc | Chirp starting frequency |
| fB | Chirp bandwidth |
| R0 | Range of detected target |
| v | Velocity of detected target |
The three key physical intuitions of FMCW radar are:
- Range comes from the beat frequency, since the propagation delay td = 2(R0 + v·t)/c produces a frequency offset IF = (2 fB)/(T·c) · R0 during the linear ramp.
- Velocity comes from the phase evolution across successive chirps via the Doppler effect. A moving target introduces a Doppler frequency fv = (2 fc / c) · v. The chirps repeat at a fixed pulse repetition frequency (PRF), which must be high enough to capture this Doppler shift.
- Angle comes from the phase differences introduced across multiple receive antennas, enabling direction estimation and spatial separation of targets.
Chirp parameters are chosen according to sensing requirements: the chirp duration must exceed the round-trip time to the farthest target plus the additional time needed for mixing and signal formation.
The Radar Cube
After mixing and sampling, the acquired data is organized into a 3D structure called the radar cube, which is the input to the entire digital processing chain.
For a single antenna, each chirp produces a sequence of time samples (fast time) arranged into a column — one column per chirp. Stacking chirps side by side forms a 2D matrix (samples × chirps), and repeating this for every receive antenna and stacking along a third dimension produces the cube: samples × chirps × antennas.
Figure 2: The radar cube
Every subsequent stage operates on this cube, progressively collapsing its dimensions and transforming raw echoes into higher-level target information.
Processing Chain Overview
The FMCW processing chain converts the radar cube into a compact target list through a sequence of well-defined stages. Before looking at each block in detail, the table below provides a roadmap of the inputs and outputs at every step:
| Stage | Input | Output |
|---|---|---|
| Range FFT | Radar cube | Range cube |
| Doppler FFT | Range cube | Range–Doppler cube |
| Non-Coherent Combining | Range–Doppler cube | Range–Doppler map |
| CFAR Detection | Range–Doppler map | Detections |
| DBSCAN Clustering | Detections | Target clusters |
| MUSIC DoA | Clusters + antenna data | (range, velocity, angle) |
Figure 3: Processing Chain Overview
The process begins at the ADC, where analog signals are digitized. Range and Doppler FFTs extract distance and velocity, forming a range–Doppler representation. Data from multiple antennas is then combined to improve robustness, CFAR detects potential targets using adaptive thresholding, DBSCAN groups detections into individual targets, and MUSIC DoA estimates each target’s angle — converting raw samples into structured outputs of range, velocity, and angle.
Mapping the Processing Chain onto the S32R45
A key advantage of the NXP platform is that each stage of the chain is mapped onto the most suitable compute resource of the S32R45. The FFT-based stages and Non-Coherent Combining run on the SPT accelerator, the CFAR detection runs on the BBE32 DSP, the clustering runs on the Cortex-A53 cores, and the linear-algebra-heavy MUSIC estimation is offloaded to the LAX accelerator:
Figure 4: Radar processing chain hardware mapping
This mapping is what allows developers to prototype the entire chain in MATLAB and then deploy each stage to dedicated radar hardware without leaving the Model-Based Design environment.
Range FFT
The first stage operates on the radar cube by processing the fast-time samples within each chirp. For every antenna and chirp, the time-domain signal — containing superimposed beat frequencies from multiple targets — is transformed into the frequency domain using an FFT, separating the frequency components that each correspond to a distinct propagation delay, and therefore a specific range.
In this application, the radar front end does not perform in-phase and quadrature (I/Q) demodulation, so the acquired signal is purely real-valued. The resulting FFT spectrum is therefore symmetric, carrying redundant positive and negative frequency components. Since only the positive frequencies correspond to physically meaningful beat frequencies here, the negative-frequency half of the spectrum is discarded.
The radar cube is thus converted into a set of range profiles, where each sample index becomes a range bin. The output preserves the chirp and antenna dimensions but now contains complex values indexed by range — magnitudes indicating reflection strength, and phases retained for later processing.
Figure 5: Range FFT output
On the S32R45, this stage is executed on the SPT accelerator using the rangeFFT kernel provided by the NXP Radar SDK and exposed through the NXP Model-Based Design Toolbox for RADAR.
Doppler FFT
Building on the range-transformed data, the second stage processes the slow-time dimension by examining how the complex samples evolve across consecutive chirps. For a given range bin, a moving target produces a small phase difference between the corresponding Range FFT outputs of consecutive chirps. This progressive phase shift is a manifestation of the Doppler effect and encodes the target’s radial velocity. By analyzing these phase variations over time using a second FFT, the processing chain extracts the Doppler frequency components associated with motion.
This step converts the phase evolution observed across successive Range FFT outputs into velocity information, effectively mapping stationary and moving targets into different Doppler bins.
The output is a set of range–Doppler maps, one per antenna, where each cell represents a specific combination of distance and radial velocity and holds a complex value describing the target echo. The Doppler FFT output is shifted (typically via an FFT-shift operation) so that the zero-Doppler component is centered and negative Doppler frequencies appear first, giving a more intuitive velocity axis: negative values for targets moving in one direction, positive for the other.
Figure 6: Doppler FFT output
As with the Range FFT, this stage is accelerated on the SPT accelerator through the Radar SDK dopplerFFT kernel.
Non-Coherent Combining
At this point, each antenna provides its own range–Doppler map, differing mainly in phase due to the direction of arrival. These maps are combined across the antenna dimension, typically by computing magnitudes and aggregating them through averaging.
The input is a set of complex-valued maps; the output is a single range–Doppler magnitude matrix in which the antenna dimension has been collapsed. This suppresses uncorrelated noise and reinforces consistent target reflections, producing a cleaner, more robust representation well suited for detection.
Figure 7: Non-Coherent Combining output
This stage corresponds to the Non-Coherent Combining kernel (NonCohComb) of the NXP Radar SDK, executed on the SPT accelerator.
CFAR Detection
The combined range–Doppler magnitude matrix is then scanned to identify potential targets. Each cell is evaluated against a locally adaptive threshold derived from its surrounding neighborhood: nearby training cells estimate the noise level, while guard cells are excluded to avoid contaminating the estimate with the target’s own energy.
Through this process, the continuous-valued matrix becomes a discrete set of detections — cells whose magnitude significantly exceeds the estimated noise background. These are effectively points in range–velocity space representing likely target reflections.
CFAR runs on the BBE32 DSP accelerator.
Clustering (DBSCAN)
CFAR detections often include several neighboring points from the same physical target, as well as isolated points caused by noise. To organize them, DBSCAN clustering is applied in the range–velocity domain, grouping points based on spatial density.
Taking the detection coordinates as input, DBSCAN forms clusters where dense regions correspond to real targets, while sparse detections are discarded as noise. The output is a set of target clusters, each consolidating a single target’s range and velocity. This stage runs on the Cortex-A53 cores.
Angle Estimation (MUSIC DoA)
For each cluster, the detections are traced back to the complex per-antenna data from the range–Doppler stage. These per-antenna samples form vectors encoding the phase differences related to the direction of arrival. Combining multiple detections within a cluster, a covariance matrix is estimated to capture the spatial characteristics of the received signals.
An eigenvalue decomposition separates signal and noise subspaces, and criteria such as AIC determine the number of significant sources. The MUSIC algorithm then scans possible directions and identifies those that best match the signal subspace.
MUSIC has important practical limitations: the number of detectable signals must be strictly smaller than the number of antennas, otherwise the covariance matrix cannot be properly decomposed. It is also sensitive to low signal-to-noise ratio, correlated reflections, and array calibration errors — constraining its use in scenarios with many closely spaced targets or too few antenna elements.
On the S32R45, the MUSIC implementation is offloaded to the LAX accelerator through the NXP Model-Based Design Toolbox for RADAR, demonstrating how computationally intensive linear-algebra operations can be accelerated directly from MATLAB-generated code. The result is a direction-of-arrival estimate for each clustered target, completing its spatial characterization.
NXP Radar SDK Integration
The NXP S32R45 Radar SDK (RSDK 1.2.0) provides optimized radar processing kernels designed for the S32R45 radar processor. Through the NXP Model-Based Design Toolbox for RADAR, these kernels are callable directly from MATLAB and are automatically integrated into the generated application, so developers work at the algorithm level while the toolbox handles deployment to the accelerators.
In the processing chain presented in this article, the Radar SDK supplies optimized implementations for:
- Range FFT — SPT accelerator (
rangeFFT) - Doppler FFT — SPT accelerator (
dopplerFFT) - Non-Coherent Combining — SPT accelerator (
NonCohComb) - CFAR — BBE32 DSP accelerator
This lets developers prototype and validate the full chain in MATLAB while leveraging the S32R45 SPT, BBE32 DSP, and LAX hardware accelerators in the final deployed application, and it supports both standalone and Processor-in-the-Loop (PIL) execution.
Tools and Ecosystem
This processing chain brings together products from both MathWorks and NXP.
MathWorks
NXP
Conclusion
The FMCW radar processing chain transforms the raw radar cube into a compact set of target descriptors through a sequence of well-defined stages. Starting from time-domain samples, range and velocity are extracted with FFT operations, detections are found through adaptive thresholding and grouped into targets, and angle estimation leverages antenna diversity to determine direction. Each final target is characterized by the tuple (range, velocity, angle).
By mapping these stages onto the S32R45 Cortex-A53, SPT, BBE32 DSP, and LAX resources through the NXP Radar SDK and the NXP Model-Based Design Toolbox for RADAR, the entire chain can be prototyped in MATLAB and deployed to dedicated radar hardware within a single Model-Based Design workflow.
