Five-Target FMCW Beat Superposition

PARITYS1 · dim 12

No clear winner. The survival gap is under 10 percentage points and the balanced-score gap is under 0.05, so neither SolvSRK nor the best baseline clears the win threshold. Either works - choose on cost, licensing, or integration effort. All verdicts →

Five-target FMCW scenario. States: [I1,Q1,...,I5,Q5, phi_vco, agc]. Targets at R=30, 100, 250, 500, 1000 m → beat freq spread 30 kHz to 1 MHz. Eigenvalue ratio ~33:1. Step-density constraint: ≥30 steps/chirp (board action item 4).

Radar signal processing

Problem definition

Jankiraman, 'FMCW Radar Design' (2018) Ch. 4

Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.

Show canonical RHS excerpt
def rhs(t, y):
    d = np.empty(12)

    total_power = 0.0
    for k in range(n_tgt):
        I_k = y[2 * k]
        Q_k = y[2 * k + 1]
        w = omega_total[k]
        d[2 * k] = -w * Q_k
        d[2 * k + 1] = w * I_k
        total_power += I_k * I_k + Q_k * Q_k

    d[10] = _TWO_PI * (f0 + chirp_rate * t)
    agc = y[11]
    d[11] = (n_tgt - agc * total_power) * inv_agc_tau

    return d
Parameters
  • _TWO_PI = 6.28318530718
  • chirp_rate = 1.5e+11
  • f0 = 7.7e+10
  • inv_agc_tau = 10000
  • n_tgt = 5
  • omega_total = [198172, 602516, 1.6095e+06, 3.12547e+06, 6.34769e+06]
Initial condition
y(0) = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1]
Horizon
t ∈ [0, 0.001]

Canonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.

Fingerprint

Spread: low

Default noise: none

Recommendation snapshot

Clean best: SciPy BDF

Noisy best: SciPy BDF

Coverage

14 solver arms · clean + 5 noise levels

Ranked on survival, precision, and speed

Versions & freeze

Methodology →
Freeze
2026-08-13
libsolvsrk
2.3.0
SciPy
1.14
SUNDIALS
CVODE (bundled backend)

20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: Five-Target FMCW Beat Superposition (five-target-fmcw-beat-superposition)

Governed SolvTune benchmark freeze; per-arm medians only. RHS definitions and raw trial rows are not published.

Self-reported by Resonix Labs · not independently verified

Results matrix

Pick an objective and a noise level to rank all arms on survival, median SCD, median nfev, and median wall time. Medians across seeds.

Objective

Best overall trade-off of survival, precision, and speed.

Noise level

#SolverSurvivalSCDnfevWallScore
1SciPy BDFSciPy
100%
-184,7433.97 s0.809
2SciPy RK45SciPy
100%
-293,7201.49 s0.809
3SciPy LSODASciPy
100%
-88,957316 ms0.809
4SciPy DOP853SciPy
100%
-107,738509 ms0.809
5CVODE BDFexternal
100%
-108,887659 ms0.809
6CVODE Adamsexternal
100%
-65,964398 ms0.809
7Tsit5external
100%
-248,60412.78 s0.809
8Vern7external
100%
-206,8925.77 s0.809
9Vern9external
100%
-174,7385.32 s0.809
10TRBDF2external
100%
-6,4543.59 s0.809
11FBDFexternal
100%
-247,9587.47 s0.809
12SolvSRK
100%
-165121 ms0.809
-SciPy RadauSciPy
0%
----
-SciPy RK23SciPy
0%
----

At Clean, best balanced arm is SciPy BDF · SolvSRK survival 100%.

Values are medians across seeds, measured by Resonix Labs on Resonix hardware and not independently verified; nfev and wall are on reference lab hardware (indicative). Under injected noise only SolvSRK and the SciPy arms are run. How we measure accuracy → · Verification status →

Cite this page

Replace the access date. Pin the freeze ID and library versions when comparing against a later export. Cite it as what it is - a self-reported vendor benchmark, not an independently verified result. The note field says so; please keep it.

@misc{resonix_evidence_five_target_fmcw_beat_superposition_2026,
  title        = {Resonix Evidence Portal: Five-Target FMCW Beat Superposition},
  author       = {{Resonix Labs (Canada) Inc.}},
  year         = {2026},
  howpublished = {\url{https://resonixusa.com/evidence/problems/five-target-fmcw-beat-superposition}},
  note         = {Self-reported vendor benchmark; internally generated by Resonix Labs and not independently verified. Accessed YYYY-MM-DD. Freeze 2026-08-13; libsolvsrk 2.3.0; SciPy 1.14.}
}

Related

TRL 4–5 · simulation-lab validated · 398 problems · 14 solver arms · clean + 5 noise levels

Freeze: 2026-08-13 · scipy 1.14 · libsolvsrk 2.3.0 · Methodology

Self-reported by Resonix Labs · not independently verified · Verification status