MIMO Radar Angle-of-Arrival Estimation for Automotive Targets

The problem

Range and Doppler alone cannot tell whether a target is in the ego lane or the next one; azimuth angle is needed, and automotive radars get it from small antenna arrays. MIMO increases the effective aperture by combining transmitters and receivers into a virtual array, but angle resolution is still limited, and super-resolution methods are sensitive to noise, snapshot count and calibration errors.

Objectives

• Design a TDM-MIMO array and its virtual aperture.
• Simulate multi-target returns through the full range–Doppler–angle chain.
• Implement FFT, MVDR and MUSIC angle estimation.
• Measure accuracy, resolution and computational cost.
• Study the effect of SNR, snapshots, motion and calibration errors.

What you need

Key concepts

Virtual array

With Nt transmitters and Nr receivers spaced appropriately, the combined channels behave like an Nt×Nr element array, increasing angular resolution.

TDM-MIMO

Transmitters take turns, chirp by chirp, so receivers can tell which transmitter each echo came from. Target motion between turns causes a phase error that must be compensated.

MVDR

Minimum variance distortionless response beamforming adapts weights to suppress interference while keeping unit gain in the look direction, giving sharper peaks than FFT.

MUSIC

A subspace method that splits the covariance matrix into signal and noise subspaces and finds angles where steering vectors are orthogonal to the noise subspace, giving high resolution.

Step-by-step guide

1. 1

   Set angular requirements

   Define requirements for a forward radar: azimuth field of view ±60 degrees, accuracy within a degree near boresight and the ability to separate two cars side by side at 50 m, which sets the needed resolution. Choose a configuration, for example 3 transmitters and 4 receivers giving a 12-element virtual uniform linear array at half-wavelength spacing. Compute the theoretical FFT beamwidth and compare with the requirement.

   Checkpoint: A requirements table and a virtual array layout with the theoretical resolution.

2. 2

   Build the signal model

   Reuse or build an FMCW range–Doppler simulation and extend it to multiple channels. For each chirp, the active transmitter and each receiver produce a beat signal whose phase depends on the element positions and target angle through the steering vector. Simulate targets at chosen ranges, speeds and angles with noise. Store the data cube as samples by chirps by virtual channels.

   Checkpoint: A data cube whose range–Doppler maps show targets in the right cells on every channel.

3. 3

   Detect and extract snapshots

   Form range–Doppler maps per channel, sum their magnitudes non-coherently and detect targets with CA-CFAR. For each detected cell, extract the complex values across the virtual channels as the angle snapshot. For subspace methods, gather multiple snapshots from neighbouring cells or several frames and form a sample covariance matrix, recording how many snapshots are used. Note that single-snapshot covariance estimates are rank-one, which is why snapshot count strongly affects subspace methods and must be reported with every result.

   Checkpoint: Snapshot vectors extracted for every detection and a covariance matrix for MVDR and MUSIC.

4. 4

   Compensate TDM motion

   Because transmitters fire in turn, a moving target's phase changes between transmitter slots, which shifts the estimated angle. Compute the expected phase shift from the estimated Doppler and the slot time and remove it from the channels of later transmitters. Show the angle error with and without compensation for a fast-closing target, so the need for this step is demonstrated.

   Checkpoint: Angle error for a moving target reduced after compensation, shown in a plot.

5. 5

   Implement FFT beamforming

   Apply a window across the virtual channels and take a zero-padded FFT to produce an angle spectrum, converting bins to angles with the arcsine relationship. Pick peaks and refine with interpolation. Compare with phased.BeamscanEstimator. Measure accuracy for single targets across the field of view and note the loss of accuracy towards large angles. Compare the measured beamwidth with the theoretical value from the first step and explain any difference due to windowing.

   Checkpoint: Single-target angle RMSE across the field of view for FFT beamforming.

6. 6

   Implement MVDR and MUSIC

   Implement MVDR using the inverse covariance with diagonal loading, and MUSIC using eigendecomposition with the number of sources from the detection stage or estimated with an information criterion. Validate against phased.MVDREstimator and phased.MUSICEstimator. Plot angle spectra for two close targets to show the sharper peaks compared with FFT. Choose the diagonal loading level on a validation set of simulated cases and keep it fixed afterwards. Record the number of operations and the runtime of each method per detection, because eigendecomposition and matrix inversion grow quickly with array size and affect embedded feasibility.

   Checkpoint: Spectra from all three methods for the same two-target case, with matching toolbox results.

7. 7

   Measure resolution and accuracy

   In Monte Carlo runs, place two equal targets at the same range and speed with angular separation decreasing from several beamwidths to a fraction of one. For each method compute the probability of resolving both targets and their angle RMSE. Repeat over SNR values and snapshot counts. Compare RMSE with the Cramér–Rao bound for a single target to show how close each method gets.

   Checkpoint: Resolution probability and RMSE curves against separation, SNR and snapshots, with the CRB.

8. 8

   Test calibration errors and coherent targets

   Add random gain and phase errors across virtual channels and mutual coupling effects, then measure how each method degrades. Test coherent sources, such as two reflections from one vehicle, where MUSIC fails without spatial smoothing; implement forward–backward or spatial smoothing and measure the recovery. Report computation time per detection for each method. Express calibration errors in degrees of phase and decibels of gain so the results can be compared with typical hardware tolerances.

   Checkpoint: Degradation curves for calibration error, results with spatial smoothing and timing per method.

9. 9

   Apply to a traffic scenario

   Build a scenario with two vehicles side by side ahead and a guardrail, either in the Driving Scenario Designer exported to target positions or as scripted trajectories. Run the full chain and plot estimated target positions in a bird's-eye view for each angle method. Assess whether the lane assignment of each vehicle is correct over time. Compute the lateral position error at several ranges, since a small angle error grows into a larger lateral error at distance.

   Checkpoint: Bird's-eye plots of estimated positions with lane assignment accuracy per method.

10. 10

    Write the thesis chapter

    Present the array design, signal model, TDM compensation, the three estimators, Monte Carlo results, calibration and coherence studies and the scenario test. Recommend which method suits which conditions on an embedded radar processor, considering accuracy and cost. State the simulation limits: ideal point scatterers, simple coupling model and no multipath from the road. Add a summary table that lists, for each method, its accuracy, resolution, robustness and cost, so the trade-offs can be compared at a glance.

    Checkpoint: A chapter with all figures reproducible from released scripts.

Testing & validation

• Angle RMSE against the Cramér–Rao bound across SNR and field of view.
• Probability of resolving two close targets by method.
• Degradation under gain and phase errors and coherent sources.
• Computation time per detection and lane assignment accuracy in a scenario.

Expected results

A complete MIMO radar angle-estimation simulation with TDM motion compensation, quantitative comparison of FFT, MVDR and MUSIC on accuracy, resolution, robustness and cost, and a traffic scenario demonstration.

Take it further

• Add elevation with a 2-D virtual array.
• Implement compressive-sensing angle estimation and compare.
• Estimate and correct array calibration errors online.
• Feed angle estimates to a tracker and measure lateral position accuracy.

Viva and review questions

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