# LIMITATIONS — E4-H160

## 1. Nothing was measured

Every number comes from a model. The model is standard (Gaussian main lobe, white noise, single
target, first grating order), but it is a model. **No experimental confirmation is claimed.**

## 2. The Monte-Carlo did not attain the bound, and I did not fix it

RMSE/CRB ≈ 0.75 (T3). A correct bound cannot be beaten, so there is a normalization error somewhere —
most likely in how the complex-noise variance enters `J`, possibly a factor of 2 from treating real
and imaginary parts separately. I report the discrepancy rather than adjusting a constant until the
number looks right, because the adjustment would be unverifiable without an independent derivation.

**Consequence:** the *relative* comparisons in T2 remain valid (all bounds computed the same way), but
the absolute statement "an estimator can reach this precision" is untested.

## 3. The extended-target model is a crude idealisation

I modelled an extended target as `A(f) = 1` — always partly illuminated. A real extended target
produces a *superposition* of echoes from different angles, so the received signal is a sum of
delayed copies, and the reconstruction problem becomes a deconvolution over the target's angular
profile. That is harder than the single-delay problem solved here, and it could partially restore a
limit for certain geometries (e.g. a target whose illuminated fraction saturates).

**This is the most important open question in the project**, because it is exactly the regime where
M2's refutation of the "fundamental" claim is strongest.

## 4. Prior art unverified

The Ghent paper on swept-source FMCW LiDAR with dispersive OPA beam steering was identified by search
but **not retrieved**. If it contains the target-dependence or the super-B_eff behaviour, this
project's only candidate novelty disappears and the result is a rediscovery.

## 5. Single architecture

Uniform array, first order, monostatic, one polarisation, no turbulence, no speckle, no target
scintillation. A different architecture (e.g. phase-steered with a fixed grating) changes `dθ/dλ` but
not the structure; a **non-uniform** array or a **two-dimensional** array changes the illumination
envelope shape and would change the constants, though not the saturation argument.

## 6. SNR held fixed at the peak

The bound scales as `1/√SNR`, and SNR here is defined at the peak of `|A|²`. A system with fixed total
power rather than fixed peak intensity would redistribute SNR across the band and shift the
super-B_eff penalty, possibly turning "mildly harmful" back into "neutral".

## 7. No absolute range accuracy analysis

Only precision (variance) was studied. Bias from the envelope's asymmetry, from target motion, or from
dispersion in the target's reflectivity is out of scope and could dominate in practice.

## 8. What would overturn the main conclusion

A demonstration that an extended target cannot in fact be reconstructed better than `c/(2B_eff)` —
i.e. that the superposition of echoes re-imposes an envelope limit. That is a calculation, not an
experiment, and it is the next thing to do.