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Multi-feed Plane Wave Generator for Compact OTA Multi-Target Emulation With Joint Angle-Delay-Doppler Control

Le Yu, Guangming Dong, Chunhui Li, Wei Fan

arXiv:2609.39180v1eess.SP

TL;DR

OTA target emulation must reproduce a prescribed wavefront across the DUT aperture, while single-feed CATRs offer one direction and multiprobe angular synthesis still requires far-field illumination. This paper combines channel-emulated target signals with PWG-synthesized directions through a multi-input APM; at 1.6 m, experiments demonstrated target-parameter errors within the reported bounds.

  • Problem

    OTA angle emulation needs a prescribed wavefront across the DUT aperture, while conventional single-feed CATRs provide one direction and multiprobe synthesis still requires far-field spacing.

    Source: §I · p. 1

  • Method

    A channel emulator controls target delay, Doppler, and echo coefficient, while a multi-input APM maps independent target-signal paths to PWG excitation vectors that synthesize incident directions over a shared test zone.

    Source: §I · p. 2

  • Results

    At 1.6 m versus the DUT's 7.2 m Fraunhofer distance, experiments showed angular deviations within 1°, interpolated delay errors within 2.4 ns, and velocity errors within 0.15 m/s.

    Source: §IV · p. 8

  • Takeaways & Limitations

    The results demonstrate the feasibility of compact multi-target and multi-angle OTA sensing evaluation for large-aperture phased-array DUTs.

    Source: §IV · p. 8

    The usable angular range is constrained by finite PWG aperture, and the number of simultaneously emulated directions is limited by the PWG-side APM's independent input ports.

    Source: §IV · p. 8

Abstract

from arXiv · show

Over-the-air (OTA) radar target emulation is an important method for evaluating the sensing capabilities of integrated sensing and communication (ISAC) and radar devices. Conventional single-feed compact antenna test ranges (CATRs) are generally limited to a single target direction, while multi-feed angular-synthesis methods commonly used in radar testing still require far-field illumination over the device-under-test (DUT) aperture. To overcome these limitations, this paper proposes a radar target OTA emulation framework based on multi-feed plane wave generator (PWG). The key capability is the simultaneous emulation of spatially close targets from different directions with joint angle--range--Doppler control. Target range is emulated through the corresponding delay, while Doppler and the complex echo coefficient are controlled by a channel emulator. Meanwhile, a multi-input amplitude and phase matrix (APM) maps each independent target-signal path to a dedicated PWG excitation vector that synthesizes the corresponding incident plane wave over the same test zone. This enables multiple target directions to be reproduced as local plane waves at a test distance substantially shorter than the conventional far-field requirement. The framework is experimentally validated at 3~GHz using a real $1\times11$ phased-array DUT. The PWG--DUT separation is 1.6~m, substantially shorter than the 7.2~m Fraunhofer distance of the DUT. At this separation, the synthesized $0^{\circ}$ and $10^{\circ}$ incident waves each exhibit an amplitude peak-to-peak error of 1.0~dB. Across two four-target angle--delay cases and one two-target angle--velocity case, the estimated target parameters show angular deviations within $1^{\circ}$, interpolated delay errors within 2.4~ns, and velocity errors within 0.15~m/s.

I. INTRODUCTION

Accurate OTA angle-of-arrival emulation requires a prescribed wavefront across the DUT aperture, but existing radiated approaches face limits in angular flexibility or compact spacing. The paper proposes using a PWG with multi-input signal mapping to emulate multiple target directions over a shared test zone at shorter-than-far-field distance.

I. INTRODUCTION

  • Nearby radiators can create wavefront curvature and nonuniform DUT-aperture illumination, distorting receive-beam response and angle estimation.Accurate OTA emulation therefore needs an incident field approximating the desired far-field wavefront over the aperture.Source: §I · p. 1
  • Mechanical repositioning changes the incident direction but becomes cumbersome for multiple targets and limits the rate of angular variation.Conductive emulation controls delay, Doppler, and attenuation but bypasses the antenna aperture and free-space propagation path.Source: §I · p. 1
  • Electronic multi-antenna and multiprobe methods synthesize angular states, but still require far-field illumination for large-aperture DUTs.Thus, angular synthesis alone does not resolve compact-distance testing.Source: §I · p. 1
  • Single-feed CATRs provide one direction at a time, while multi-angle CATR configurations add cost and complexity and restrict available directions by feed or reflector count.PWGs synthesize local plane waves, but simultaneous emulation of independent target signals from different directions over one test zone remains insufficiently investigated.Source: §I · p. 2
  • The proposed framework controls delay, Doppler, and echo coefficient with a channel emulator and synthesizes target directions with PWG incident wavefronts.A multi-input APM assigns each independent signal path a dedicated PWG excitation vector, reproducing directions over the same test zone at less than conventional far-field distance.Source: §I · p. 2
  • The paper evaluates the method at 3 GHz using a real 1×11 phased-array DUT, measuring synthesized-field quality and estimated target-parameter deviations.The listed contributions also include a measured PWG transfer matrix and multi-input APM for mapping paths to calibrated spatial stimuli over a common test zone.Source: §I · p. 2

II. PWG-BASED TARGET-FIELD SYNTHESIS

The framework represents each target by its signal and spatial state, then groups targets with the same AoA into angular-state signals. Each angular-state signal is assigned to a PWG input path for plane-wave synthesis over the DUT aperture.

II. PWG-BASED TARGET-FIELD SYNTHESIS

  • Each target is characterized by AoA, round-trip delay, radial velocity, and complex echo coefficient, and targets sharing an AoA are grouped into an angular-state signal.Targets with the same direction can retain different delays, velocities, and echo coefficients within the grouped signal.Source: §II · p. 2
  • Each angular-state signal is assigned to an independently controlled PWG input path, whose excitation vector synthesizes its desired incident wave over the DUT aperture.Multiple angular-state paths can be activated simultaneously.Source: §II · p. 2

A. Reference Target-State Model and Angular-State Mapping

The target-state model specifies each target's direction, delay, velocity, and complex echo coefficient. Targets are grouped by AoA, with their responses combined into an angular-state signal for assignment to a PWG input path.

A. Reference Target-State Model and Angular-State Mapping

  • Each target's AoA, round-trip delay, radial velocity, and complex echo coefficient define its target state.The coefficient's magnitude and phase specify target-response magnitude and initial phase.Source: A. Reference Target-State Model and… · p. 2
  • The channel emulator realizes the Doppler term by varying its complex channel-coefficient phase according to the prescribed radial velocity.The frequency-domain target response uses swept frequency and center frequency.Source: A. Reference Target-State Model and… · p. 2
  • Targets with the same prescribed AoA are grouped into an angular-state signal, even when their delays, velocities, and echo coefficients differ.The responses of targets sharing a direction are combined before assignment to a PWG input path.Source: A. Reference Target-State Model and… · p. 2
  • Each distinct AoA is assigned one independently controlled PWG input path, limiting the number of angular states to available input paths.For example, two targets at each of two angles form two combined angular-state signals.Source: A. Reference Target-State Model and… · p. 2

B. Transfer-Matrix-Based Plane-Wave Synthesis

The PWG constructs the desired plane wave for each angular state, then combines independently controlled paths to emulate multiple targets while retaining their programmed signal properties.

B. Transfer-Matrix-Based Plane-Wave Synthesis

  • Each angular state is represented by a desired plane-wave vector over the test-zone sampling points, using its prescribed angle and the points’ positions.The plane-wave vector is defined from the propagation direction and sampling-point positions.Source: B. Transfer-Matrix-Based Plane-Wave… · p. 2, Figure 1 · p. 3
  • A continuous PWG excitation vector is obtained for each angular state, then scaled and quantized for the available APM amplitude and phase states.The excitation is constrained by a total-energy limit; the pseudoinverse solution is the unconstrained minimum-norm least-squares solution.Source: B. Transfer-Matrix-Based Plane-Wave… · p. 3
  • Amplitude and phase peak-to-peak errors are evaluated over the sampling points covering the required DUT aperture.Each angular state is characterized independently before simultaneous multi-angle emulation.Source: B. Transfer-Matrix-Based Plane-Wave… · p. 3
  • Under linear, coherent superposition, independently controlled paths preserve each input’s programmed delay, velocity, and echo coefficient while mapping it to its corresponding synthesized wavefront.The paths are activated simultaneously after individual angular-state field quality is confirmed.Source: B. Transfer-Matrix-Based Plane-Wave… · p. 3

A. Experimental System and Linearity Characterization

The system connects channel-emulator target signals through independently controlled PWG paths to a phased-array DUT and measures its combined response. The 100-path responses agree closely from 2.8 to 3.2 GHz, and 3 GHz is selected for subsequent measurements.

A. Experimental System and Linearity Characterization

  • The channel emulator’s two outputs feed separate PWG-side APM inputs, while the DUT-side APM applies calibrated receive weights and sends the combined response to the VNA.Each active APM-output–PWG-element pair is one PWG excitation path.Source: A. Experimental System and Linearity… · p. 3, Figure 2 · p. 4
  • The transmit setup uses 100 APM channels to drive a 10 × 10 PWG subarray, while a DUT-side APM combines the 11 outputs of a real phased-array DUT.The 10 × 10 subarray uses every other element of the physical 20 × 20 PWG; the DUT aperture is 0.6 m.Source: A. Experimental System and Linearity… · p. 3, Table I · p. 4
  • At 3 GHz, the PWG–DUT separation is 1.6 m, compared with the DUT’s 7.2 m Fraunhofer distance.The system uses frequency-swept acquisition for angle–delay measurements and repeated single-frequency acquisition for angle–velocity measurements.Source: A. Experimental System and Linearity… · p. 4, Figure 3 · p. 4
  • The linearity check compared a postprocessed prediction from individual excitation-path measurements with the measured response when all 100 paths operated simultaneously.The probe was fixed at the test-zone center during the frequency sweep.Source: A. Experimental System and Linearity… · p. 4
  • From 2.8 to 3.2 GHz, predicted and measured amplitude and phase responses nearly coincide, supporting stable linear and coherent synthesis; 3 GHz was selected for subsequent measurements.Below approximately 2.6 GHz, the measurement shows appreciable discrepancies, suggesting additional open-laboratory interference.Source: Figure 4 · p. 4, A. Experimental System and Linearity… · pp. 4–5

B. Spatial-Field Characterization and DUT Calibration

The measured transfer matrix is used to synthesize and characterize fields for desired angles, then the DUT’s receive paths are calibrated for subsequent measurements.

B. Spatial-Field Characterization and DUT Calibration

  • The transfer matrix is identified from 168,100 complex-response measurements across a 41 × 41 grid and 100 active PWG paths, requiring approximately 16 hours.The measured matrix is used to obtain a continuous PWG excitation vector for each desired AoA; each subsequent characterization scan takes approximately one hour.Source: B. Spatial-Field Characterization and… · p. 5
  • Within the marked test zone, amplitude PPEs are 1.0, 1.0, and 1.1 dB for (0°, 0°), (10°, 0°), and (5°, 5°), respectively.The measurements characterize fields synthesized using the measured transfer matrix.Source: B. Spatial-Field Characterization and… · p. 5
  • The 11 DUT receive paths are calibrated from measured complex responses, using the lowest-power element as the reference and applying relative amplitude and phase coefficients in later measurements.The reference choice allows higher-power paths to be equalized by attenuation alone.Source: B. Spatial-Field Characterization and… · p. 5

C. DUT Measurement and Target-Parameter Estimation

The calibrated DUT receive beam is stepped through commanded angles, and its complex responses are transformed over swept frequency or slow time to form target maps.

C. DUT Measurement and Target-Parameter Estimation

  • Target-parameter deviations are calculated relative to programmed AoA, delay, and velocity values, not as absolute measurement accuracy or uncertainty.The DUT receive beam is steered over commanded azimuth angles, and the VNA records the combined complex response at each beam state.Source: C. DUT Measurement and… · p. 5
  • The DUT receive-beamformer output links each angular-state signal to the element-response vector and the receive weights applied across DUT elements.The calibrated and quantized receive weights are loaded successively to sample the response over the beam-steering angle.Source: C. DUT Measurement and… · p. 5
  • Frequency-windowed responses are transformed into angle–delay maps for static targets, while slow-time Fourier transforms produce angle–Doppler maps for dynamic targets.The maps display normalized powers; the velocity mapping converts Doppler frequency to radial velocity.Source: C. DUT Measurement and… · p. 5
  • The spatial-field characterization presents amplitude and phase for three incidence directions, while the measured complex responses of 11 DUT elements are used to calibrate receive paths.The figures show the PWG fields at (0°, 0°), (10°, 0°), and (5°, 5°), and the DUT element responses at 3 GHz.Source: Figure 5 · p. 6, Figure 6 · p. 6

D. Angle–Delay Target Measurement

The angle–delay tests evaluate two four-target scenes with different degrees of target separation. The measured estimates stay close to their programmed angles and delays in both cases.

D. Angle–Delay Target Measurement

  • The two cases each use four equal-nominal-power targets at 0° or 10°; Case I shares angles or delays across targets, whereas Case II provides greater separation in both dimensions.The usable bandwidth is 80 MHz, corresponding to a nominal delay resolution of 12.5 ns.Source: D. Angle–Delay Target Measurement · p. 6
  • Case I delay deviations are no larger than 2.1 ns and angular deviations at most 1°; in Case II, all estimated angles match programmed states and delay deviations remain within 2.4 ns.Case II’s delay deviations are small relative to the 12.5 ns nominal resolution.Source: D. Angle–Delay Target Measurement · pp. 6–7, Figure 7 · p. 7, Table II · p. 7
  • Case I peak shifts are mainly associated with the DUT’s finite angular resolution and interactions between closely spaced target responses.Equal nominal target powers need not yield equal estimated peak powers, and relative peak powers should not be interpreted as CE echo-coefficient accuracy.Source: D. Angle–Delay Target Measurement · pp. 6–7

E. Angle–Velocity Target Measurement

The angle–velocity experiment uses two programmed moving targets and estimates both angles and velocities from the measured response. The estimates are close to their programmed values.

E. Angle–Velocity Target Measurement

  • Two equal-nominal-power targets are programmed at (0°, 5 m/s) and (10°, 10 m/s), and the DUT beam is scanned from −40° to 40° in 2° steps.The CE generates Doppler signatures through time-varying complex channel coefficients; synchronized acquisition yields 2001 complex samples over 1 s on an equivalent 2 kHz slow-time grid.Source: E. Angle–Velocity Target Measurement · p. 7
  • The two targets are estimated at their programmed angles, with velocities of 5.09 and 10.15 m/s and absolute deviations of 0.09 and 0.15 m/s.The small relative-power difference indicates that the two CE–PA–APM–PWG paths are sufficiently balanced in this experiment.Source: E. Angle–Velocity Target Measurement · p. 7

IV. CONCLUSION

The paper separates target-signal generation from spatial-wavefront synthesis to emulate multiple target directions as local plane waves over a DUT aperture at sub-far-field distances. Experiments demonstrate compact multi-target, multi-angle evaluation, while the current system and validation remain limited in angular scope and target-angle dynamics.

IV. CONCLUSION

  • Independent signal paths control delay, Doppler, and echo coefficients, while a multi-input APM maps them to PWG excitation vectors for distinct local plane-wave directions.This permits multiple target directions over the same DUT aperture at distances shorter than the conventional far-field requirement.Source: §IV · p. 8
  • At 3 GHz, a 1 × 11 DUT tested 1.6 m away versus its 7.2 m Fraunhofer distance yielded angular deviations within 1°, delay errors within 2.4 ns, and velocity errors within 0.15 m/s.Synthesized incident fields had amplitude PPEs of 1.0–1.1 dB and phase PPEs of 6.4°–12.2°.Source: §IV · p. 8
  • The system targets spatially close targets in a limited angular sector, with field-synthesis quality declining away from broadside and simultaneous directions limited by APM input ports.The finite PWG aperture constrains usable angular range.Source: §IV · p. 8
  • Experiments tested only fixed target AoAs; dynamic-angle emulation through excitation-vector updates remains unvalidated.Future work will assess dynamic-angle emulation and more accurate calibration and finer amplitude and phase control.Source: §IV · p. 8
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