Can NeRFs "See" without Cameras?
Authors: Chaitanya Amballa
Yu-Lin Wei
Sattwik Basu
Zhijian Yang
Mehmet Ergezer
Romit Roy Choudhury
Venue: NeurIPS 2025 poster ()
Keywords: NeRF
Indoor floorplan
Primary area: applications
TL;DR: Enabling NeRFs to "see" in wireless multipath settings.

Abstract: Neural Radiance Fields (NeRFs) have been remarkably successful at synthesizing novel views of 3D scenes by optimizing a volumetric scene function. This scene function models how optical rays bring color information from a 3D object to the camera pixels. Radio frequency (RF) or audio signals can also be viewed as a vehicle for delivering information about the environment to a sensor. However, unlike camera pixels, an RF/audio sensor receives a mixture of signals that contain many environmental reflections (also called “multipath”). Is it still possible to infer the environment using such multipath signals? We show that with redesign, NeRFs can be taught to learn from multipath signals, and thereby “see” the environment. As a grounding application, we aim to infer the indoor floorplan of a home from sparse WiFi measurements made at multiple locations inside the home. Although a difficult inverse problem, our implicitly learnt floorplans look promising, and enables forward applications, such as indoor signal prediction and basic ray tracing.

Can NeRFs "See" without Cameras?
Chaitanya Amballa' amballa2@illine edu
Sattwik Basu' sattwik2eillinois. edu
Yu-Lin Wei yul yullin1w2@1liimois
Zhijian Yang' yzhijian@amae com
Mehmet Ergezer mergezer@amazon. com
Romit Roy Choudhury croy@illinois. edu
University of Illinois Urbana-Champaiga
Amazon
Abstract
Neural Radiance Fields (NeRFs) have been remarkably successful at synthesizing novel views of 3D scenes by optimizing a volumetric scene function. This scene function models how optical rays bring color information from 3D object to the camera pixels. Radio frequency (RF) or audio signals can also be viewed as a vehicle for delivering information about the environment unlike camera pixels, an RF/audio sensor receives a mixture of signals that contain many environmental reflections (also called "multipath"). Is still possible to infer the environment using such multipath signals? We show that with redesign, NeRFs can be taught learn from multipath signals, and thereby "see" the environment. As a grounding application, we aim to infer the indoor floorplan of a home from sparse WiFi measurements made multiple locations inside the home. Although a difficult inverse problem, our implicitly learnt floorplans look promising, and enables forward applications, such as indoor signal prediction and basic ray tracing.
sensor. However,
Introduction
NeRFs 25 43 45 have delivered impressive results in solving inverse problems, resulting in 3D scene rendering. While NeRFs have mostly used pictures (from cameras LIDARs) to infer 3D scene, we ask if the core ideas can generalize to the case of wireless signals (such as RF or audio). Unlike camera pixels that receive line-of-sight (LoS) rays, wireless receiver (e.g.. WiFi antenna on smartphone) would receive a mixture of LoS and many reflections, called multipath. If the receiver moves, it receives sequence of N measurements. Using these N wireless measurements, is it possible to learn representation of the scene, such as the floorplan of the user's home? A vanilla NeRF understandably fails since it is not equipped handle multipath. This paper is focused on redesigning NeRFs so they can learn to image the environment, thereby solving the inverse problem from ambient wireless signals.
growing body of work 3. 26 wireless. While none have concentrated on imaging, NeRF2 47 and NeWRF (22 have augmented NeRFs to correctly synthesize WiFi signals at different locations inside an indoor space. However, correct synthesis is possible without necessarily learning the correct signal propagation models. We find that NeRFs with adequate model complexity can overfit a function to correctly predict signals at test locations, but this function does not embed the true behavior of multipath signal propagation. We re-design the NeRF's objective function so that it learns the environment through line-of-sight (LoS) paths and reflections. This teaches the NeRF an implicit representation the scene, which can then be utilized for various forward tasks, including WiFi signal prediction and ray tracing.
is investigating connections between NeRFs and
In model, EchoNeRF, each voxel is parameterized by its opacity 5 E [o, and orientation E [- x.. When trained perfectly, free-space air voxels should be transparent (Ō = 0), wall voxels should be opaque 1), and each opaque voxel's orientation should match its wall's orientation.
Equual contribution.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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As measurements, we use the received signal power. Thus. the imput to our EchoNeRF model is the transmitter (Tz) location, a sequence of known receiver (Rz) locations, and the signal power measured at each Re location. The output of EchoNeRF is an (implicitly learnt) floorplan of the indoor space. We expect to visualize the floorplan by plotting the learnt voxel opacities.
Voxelsc
[a]
[b)
(c)
(d)
Tx
Rx
Rx
Rx
Virtual 7x
Walls LoS rays
Tx
Figure 2: (a) Fitting signal power using virtual Tas. (b) Ideally, virtual Trs should be located on wall surfaces. (c) Sparse virtual Tæs learnt by NeWRF shown in black/gray dots. (d) Dense virtual Tas learnt by NeRF2. Neither correspond to the true (red) floorplan.
Figure 1: LoS and correct multi- path reflections.
Learning floorplans requires modeling the correct reflections (see Fig. I since these reflections help reveal where the walls are. However, without knowledge of the walls, the reflections are difficult to model, leading measurements is relatively sparse compared to the number of pixels measured in image-trained NeRFs. Finally, measured signals will have "blind spots", meaning that rays that bounced off certain regions of the walls may not have arrived at any of the Rx locations. This leaves gaps or holes in the floorplan and NeRF's interpolation through these gaps will produce error blur.
type of chicken and egg problem. Additionally, the number of wireless
EchoNeRF approaches this problem by modeling the received signal power as a combination of the LoS power and the power from first order reflections. The LoS model is inherited from classical NeRFs. The main departure from past work is in modeling the reflections. Since opaque voxels are unknown during training, the reflection surfaces are known; hence, the reflection power the Rx. is modeled as an aggregate over all plausible reflections. Given the planar structure of walls, the plausible set of reflections can be heavily pruned to reduce the optimization complexity, Reflections aggregated over this plausible set models the total (LoS reflection) power at a receiver Rx.
EchoNeRF trains to minimize the loss between the modeled and measured power across all Ra locations, and in the process, learns the voxel's opacities that best explain the measured dataset. Some regularization is necessary to cope with sparse measurements and to ensure smoothness of walls. Lastly, to handle some gradient imbalance issues, EchoNeRF freezes the LoS model once it converges, and uses this intermediate state partly supervise the reflection model.
To evaluate EchoNeRF, we train on 2.4 GHz WiFi signals from NVIDIA's Sionna simulator [4] with floorplans from the Zillow's Indoor Dataset (ZIND) (9. Results show consistent improvement over basclines in terms of the estimated floorplan's 's loU and Fl score. Qualitative results show visually legible floorplans without any post-processing. Applying forward functions the floorplan, EchoNeRF can predict the received signal power for new (T'x, Rr) locations (outperforming existing baselines). Lastly, basic ray tracing explains the predictions, offering interpretability to its results.
2 Related Work and Research Scope
Wireless (WiFi) channel prediction using NeRFs. NeWRF 22 and NeRF2 47 recent papers that have used NeRFs to predict the wireless channel impulse response (CIR) 40 at unknown locations inside a room. Drawing a parallel to optical NeRFs, a voxel's color in optics becomes voxel's transmit power in wireless. The voxel's density in optics remains the same in wireless, modeling how that voxel attenuates signals passing through NeRF2 and NeWRF assign transmit power and attenuation to each voxel such that they best explain the measured CIR. The authors explain that voxels assigned non-zero transmit power will be called virtual transmitters; these voxels represent the reflection points on the walls. However, many assignments are possible that fit the CIR training data, especially when the data is sparse. Fig. a) illustrates 2 possible assignments. While the predicted CIRs could achieve low error for all such assignments, only one of the assignments will model the true reflections, forcing the virtual transmitters to be located on the wall surfaces (Fig. 2(b)). We have plotted NeRF2 and NeWRF's assignment of voxel densities (see Fig. c.d) to confirm

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that the high accuracy in CIR prediction is not an outcome of correctly learning the wall layout. Our goal is to repair this important issue, i.e., assign voxel densities that obey the basic physies of wall reflections. Correct voxel assignment leads to the correct layouts, which then makes the (forward) CIR prediction easy.
Neural radiance fields for audio. Another active line of research focuses on predicting room impulse response (RIR) for audio 23 37 19 6.. Neural Acoustic Field (NAF) 23 extended the classical NeRF to train on RIR measurements in a room and predict the RIR (magnitude and phase) at new (Tx, Rx) locations. NAF identified the possibility of overfitting to the RIR and proposed to learn, jointly, the local geometric features of the environment (as spatial latents) and the NAF parameters. The spatial latents embed floorplan information but a decoder needs to be trained using the partial floorplan data. EchoNeRF requires no floorplan supervision, and secondly, relies entirely on signal power (less informative than RIR) to estimate the floorplan.
Follow up work are embracing more information about the surroundings (pictures 20
37
19
(24),
LIDAR scans [27]. meshes and optical NeRFs [6), boost RIR accuracy. Results are steadily improving, however, this sequence of ideas is unaligned with solving the core inverse problem. Our goal is to first invert the signal power to a floorplan, which can then enable CIR/RIR predictions.
Modeling reflections in optical NeRFs Optical NeRFs have tackled reflections
10
331 for
synthesizing glossy surfaces and mirrors, and for re-lighting [32 [3]] NeRFRen
12 proposes to
decompose a viewed image into a transmitted and a reflected component. Ref-NeRF on reflections through similar decomposition of the transmitted and reflected color, however, the reflected color is modeled as a function of the viewing angle and the surface-normal, resulting in
also focuses
accurate models of specular reflection. Recent proposals such as NeRF-Casting 422 and oRCA (8
have further improved the models of multipath for glossy and mirrored surfaces, and others [5] 46
have developed similar ideas, with the core insights centering around solving a two-component decomposition problem. EchoNeRF faces the challenge of not knowing the number of rays adding up from all possible directions in the environment. Hence, EchoNeRF must solve a many-component decomposition problem by leveraging the physics of multipath signal propagation.
In the context of LIDARs, PlatoNeRF [8] and NeTF [34] cope with unknown reflections, however, LIDARs have very high time resolution (due to high clock frequency). and is therefore able to assign the incoming rays to different time buckets. This temporal separation allows the NeRF to make separate measurements for different surfaces in the scene. Since EchoNeRF uses only signal power- single scalar measurement that contains a mixture of the LoS and all the reflections the inverse problem of recovering the voxel attributes from only the power is far more complex.
3 EchoNeRF Model
Setup and Overview. At a Rx location, we model the received signal power &b as
VoLoS + theff + +... + vires,
where thss is the power from the direct line-of-sight (LoS) path, and freef, the aggregate power from all tthh order reflections (i.c., all signal paths that underwent exactly k reflections before arriving at the Rx) F We assume M fixed transmitters and move the Rx to N known locations and measure vi at each of them. EchoNeRF accepts M x N measurements as input and outputs the 2D floor-plan F, a binary matrix of size L x L, where L denotes the maximum flcorplan length.
We train EchoNeRF on the measured data using our proposed objective function. This function only models the LoS and the first order reflections. We disregard the higher orders since they are very complex to model and contribute, on average, < 6% of the total power (see statisties in Appendix C The NeRF model we use is remarkably simple MIP designed to predict the density E [0. 1] and orientation w E [[ .r of specified voxel in the indoor scene. The orientation aids in modeling reflections. The proposed objective function parameterized by voxel attributes (5, w) and the (,', Ra)) locations - models an approximation of the received power &e at that Rx location. Minimizing La loss of this power across all Rx locations trains the MLP. Plotting out all the voxel densities in 2D gives us the estimated floorplan F.
"This model is a simplification since it ignores the signal phase in estimating the received power. Appendix B shows that with a moving wide-band receiver, like WiFi, the approximation may be tolerable for a sensing application like EchoNeRF.
3

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3.1 The LoS Model
Friss' equation [ from electromagnetics models the free-space received power as P. = K where a d is the distance of signal propagation, and K is a product of transmit-power, wavelength, and antenna-related constants MT We model this free-space (LoS) behavior in the NeRF framework through the following equation.
II (1-8,) 1OS K (f],,
d²
where K can be empirically measured, and d is the known distance between the (Tx, RE). The numerator includes the product of voxel densities over all voxels along the LoS ray from Tx to Rxr (with an abuse of notion, we write this as U; E LoS). This models occlusions. When the LoS path is completely free of any occlusions (i.e., 6; 0, Vi where {ile; LoS}). we expect the received power to only be attenuated by the pathloss factor de (in the denominator). Eq. | has a slight difference to classical NeRF's volumetric scene function. In our case, voxels along the ray do not contribute to the received power (whereas in NeRF, each voxel's color is aggregated to model the final pixel color at the image). other words, have modeled single transmitter Eq.
3.2 The Reflection Model
To model reflections, consider voxel Vi. Whether Uy reflects ray from the Ta towards Rer depends on (1) ny's density 6g and orientation wi, (2) the (Tx: Re)) locations, and (4) whether the path from Tx Vj. and from Uy to Rx are both occlusion-free Parameterized by these, Eq. | models thref (uz). which is the received power at Ræ due to the signal that reflected off voxel uj.
II
(x))
II
(1 61)
&e (Reie,
IE(e;:Tx>
(dT + doy.Rz)
Let us explain this equation briefly. The leading 6y ensures that voxel by is not a reflector when 6, O. The f(0, 3) term models the wave-surface interactions, i.e.. how signals get attenuated as a function of the incident angle 9 and how signals scatter as function of the offset angle 3 (which is the angle between the reflected ray and the direction of the Rx from v,). The next two product terms ensure that for the Rr to receive this reflection, the voxels along the 2 segments (T'x to v/ and vy to Rx) must be non-opaque; if any &g or 6, equals 1, that reflection path is blocked, producing no power contribution via this voxel U to the receiver Rx. Finally, the denominator is the squared distance from Tx to Uy, and from vy to Rx, modeling signal attenuation.
To compute the full reflection power, the natural question is: which voxels are contributing to the received power? Geometrically, any opaque voxel (Tx, Re) pair. This is because, for triangle formed by Tx, Vy. and Rr. the voxel orientation wy can be assigned direction that bisects the angle at Uy. For this wy, the reflected ray will perfectly arrive at the Rx. Thus, without the knowledge of orientation and density, the total first order reflection power the Rr should be modeled as the sum of reflections on all voxels. This makes the optimization problem excessively mnder-determinet.
be a plausible reflection point between any
x Larger K is needed when the We address this by modeling w discrete value-multiple of K environment has complex surface orientations; however, most floorplans exhibit perpendicular walls 48 S II] and K = is adequate. Once wy becomes discrete, the voxels that can produce plausible reflections become far fewer out of many plausible reflections from voxels with Wj 135 Eq. sums up the power from all reflections that occur the plausible set:
call this the "plausible set" V. Fig. 3 visualizes V and shows 3
Drefi
Σ
(3)
Thus, the final modeled power specific Rx location becomes & vLLos + treft.

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Stage
PLOO
135'
Tx
00000
Eq-(1)
V
Vj
((g)))
800%
(x,
0000
MLP
(8, w)
Tx, Rx locations
stagges (ip), :bLOS)
45'
Copy weights
90'
1l
stage
Stage 2
ViOs
Dreef
3
(2)
Rx
Tx, Rxr locations
Estagez (V. PLOSs Prers)
Figure 3: Colored stripes define the man- ifold from which reflections are plausible between (Tx, Rr). Voxels located on the manifold form the plausible set V. Dashed lines show plausible reflections.
Figure EchoNeRF's two-stage training approach: In Stage 1, the LoS model is trained using known Rr lo- cations and signal power. This provides warm-start to the reflection model in Stage 2 which refines the learned voxel densities and orientation.
3.3 Gradient Issues during Training
Training against a L2 loss, L. = || 1tr 11 did not generate legible floorplans. We found that the d' Los dominated the loss term, drowning the reflection model's influence learning. At high level, the gradient of the LoS model (Eq. [ w.r.t. 6 has fewer terms in the numerator's 's product, and smaller d² in the denominator. The reflection model's gradient w.r.t. d; has many more terms since the reflection path is much longer; the denominator is also larger. Since (1 6,) < 1, their products force the gradient decrease geometrically with more terms, causing the reflection gradient to be much smaller compared to LoS. We formalize this explanation below by considering the LoS and reflection losses individually"
L = VLOS- LLoss
Cres = [ures Vies
Consider the gradient of LLOS w.r.t the density of Uz.
V8,LLos 2(0LOs vLas)
Σ
V V/ Los
(n ig LoStw)
where
V V
(() Los d(n)²
K
II
(1 - 6,)
(4)
JELog(n) jæi
where LoS(") the n-th LoS path passing through voxel 04.
The gradient of Lref has a nearly identical expression with the only difference being many more
product terms and that V ( depends on where o; is present in the n-th set of reflection path voxels (denoted by (n)())), For example,
(n).Tz V Fref
C
II
(1-8,) 6,)
II
(1 (1- 6k)
(5)
(m)
((m)
jti
8(m) (()) (0.3)
C
(m) TTTan
(m)
'Here, si denotes ground signal power 'For the case of explanation, use vi.ss and wier to denote the ground truth LoS and reflection powers. respectively. We do not need to know these terms practice.

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here Va, (x) denotes the gradient when is between Tx to the reflection point v. Pref
Finally, since the modeled power approximates the measured power, the residual error will remain non-zero even if the floorplan accurately learnt. As result, the optimization is biased towards voxels of higher gradients, i.e., voxels on the LoS path, suppressing the importance of reflections. To address this, we train EchoNeRF in 2 stages.
3.4 Multi-stage Training
Stage 1: We first use the LoS model against the measured ground truth power 15 (see Fig. 4 This converges quickly because the network easily learns the transparent voxels (6=0) located along LoS paths. For LoS paths that are occluded, the network incorrectly learns excessive opaque voxels between the (Tx, Rx), but this does not affect the LoS error since the path is anyway occluded. Hence, the outcome crude floorplan but near-perfect LoS power estimate LLSS We utilize this Los in stage (discussed soon).
As Stage training progresses, some opaque voxels emerge, offering crude contours of some walls. We estimate voxel's spatial gradient, Vo,, and use it to supervise the orientation w; of that voxel. The intuition is that a voxel's ' orientation needed to model reflections in Stage 2 - is essentially determined by the local surface around that voxel. The gradient Vo, offers an opportunity for weak supervision. Thus, the loss for Stage 1 is:
Lstagel |10b" 1 112 L+
where L+= A1 Σ
Voj w + X2Zree
with '1, A2 > 0 being tunable hyperparameters. The regularization term Greg will be discussed soon. Finally, the near-perfect estimate LoS power, denoted wross is also carried over to Stage 2 to ensure the reflection model is penalized when it veers away from this LoS estimate.
Stage focuses on training the reflection model using the following loss function.
| VLos| |05 VLas Uref 1 +
Estage2
The first term in the RHS ensures that the Stage I's LoS estimate is honored in Stage 2. The second term subtracts Stage I's LoS power from the measured power, (v1* LLOs); this models the total power only due to reflections. Our (first order) reflection model thre is trained to match this aggregate power (L2 loss). The supervision orientation and the regularization terms are the same as in Stage
Regularization: Floorplans demonstrate significant local similarity in orientation, hence we penalize differences orientation among neighbors, using regularization (Eq. ( similar Total
Variation (31.. This can be achieved without additional computational cost to the neural network by directly utilizing voxel orientations obtained from each ray.
Greg
W - Wm. 1
(8)
(n
no
Here n, is the number voxels queried from the plausible set and n, is the number of voxels along the each ray.
4 Experiments
Floorplan and Wireless Simulation Dataset. Floorplans are drawn from the Zillow Indoor Dataset each floorplan, we use the A algorithm [3] to generate a walking trajectory that traverses all rooms. We use the NVIDIA Sionna RT [5
9.
14
ray tracer for radio propagation modeling to
compute the ground truth signal power (also known as received signal strength index (RSSI). We randomly place A Txs, one in each room, denoted as Tm. To simulate omnidirectional transmissions

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at 2.4GHz from each Tx location, we shoot 10? rays into the given floorplan. For receiver locations, we sample the user trajectory at fixed time interval to obtain . Rr locations, denoted R, Sionna accounts for specular reflections and refraction when these rays interact with walls in the specified floor plan; we use the default materials for the walls. As with most WiFi simulators, Sionna does not model signal penetration through walls this means that a 7x and Rx located on opposite sides of wall will not receive any RSSI. Overall, we gather M x RSSI measurements (Tmy Ray 2m..) that serve input to EchoNeRF.
Baselines used for comparison are:
1. NeRF2 47: Models WiFi reflections via virtual transmitters to predict channel impulse response (CIR).
2. Heatmap Segmentation 21 Interpolates CIR across the whole floorplan and applies an image segmentation algorithm (on the interpolated RSSI heatmap) isolate each room. Essentially, the algorithm identifies the contours of sharp RSSI change since such contours are likely to correspond to walls. Implementation details are included the Appendix E.4
3. MLP: Trains an MLP network directly estimate the RSSI based on Tx and Rx locations.
4. EchoNeRF LoS: Reports EchoNeRF's result considering only LoS path (ablation study).
Metrics. We evaluate using 3 metrics:
(A) Wall Intersection over Union (Wall IoU): This metric measures the degree to which the predicted walls and the true walls superimpose each other in the 2D floorplan. The following equation defines the metric:
Wall_ IOU WPOWP" WPUWP
where WP denotes the set of predicted wall pixels and WP denotes the true wall pixels. This is harsh metric given wall pixels are small fraction of the total floorplan; if predicted wall even offset by one pixel from the true wall, the Wall_Iol IoU drops significantly. IoU (30] has often been defined in terms of room pixels (instead of wall pixels); this is an overestimate in our opinion, since predicting even empty floorplan results in an impressively high IoU.
(B) F1 score [35] Defined F1 2xPxR, where P is the precision and R is the recall of the P4K
bitmap. P and R are defined based on wall pixels, similar as above.
(C) RSSI Prediction Error (RPE): We split all Rz locations into training and test set. RPE reports the average median RSSI error over all the test locations across floorplans.
4.1 Overall Summarized Results
2000 receiver locations
1000 receiver locations
Method
Wall_ f
Fl Score t
RPE $
Wall_loU f
Fl Score
RPE
MLP
1.03
0.65
Heatmap Seg.
0.12 + 0.03
0.21 + 0.05
1.32
0.09 + 0.02
0.16 + 0.04
1.46
NeRF2
0.14 + 0.02
0.24 0.03
4.36
0.12 + 0.02
0.21 0.04
4.2
EchoNeRF Los
0.27 + 0.07
0.42 - 0.10
0.10
9.12
0.25
0.04
0.39 + 0.06
10.86
EchoNeRF
0.38 0.06
0.55 + 0.06
3.56
0.32 + 0.06
0.48 + 0.05
4.32
Table Performance Results for Wall_loU, Score, and RPE
Table reports comparative results between EchoNeRF and baselines, averaged over 20 different experiments, using all metrics. The number of measurements are sparse (N = 2000 and N = 1000), given that apartment sizes in our dataset are more than 250, 000 pixels. Mean and standard deviation are reported in the table. EchoNeRF outperforms all models in terms of Wall_Iol and F1 Score. Compared to EchoNeRF LoS, EchoNeRF demonstrates visible improvements, highlighting the advantage of modeling reflections. The absolute Wall IoU values are understandably low because the metric penalizes small errors.
NeRF2 is unable to predict the floor plan (opaque voxels) well and only able to achieve better RPE than EchoNeRF LoS. EchoNeRF outperforms both EchoNeRF_ and NeRF2. Interestingly. MLP incurs a lower RPE than NeRF2 suggesting that RSSI is amenable to interpolation, and NeRF2's implicit representation may not be an advantage for this interpolation task.
7

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Ground Truth
Heatmap Seg.
NeRF2
EchoNeRF LoS
EchoNeRF
Figure 5: Qualitative comparison of ground truth floorplans against baselines. In the first row, red stars denote Tx locations and light gray dots denote Rx measurement locations. The bottom two rows show floorplans learnt by EchoNeRF LaoSS LoS (i.e., Stage 1) and EchoNeRF (i.e., Stage 2) with sharper walls and boundaries. More visualizations available at https:: //cc:///cccceeeeee www.hheeff..thuu...t...ee io/
4.2 Qualitative Results: Visual floorplans, RSSI heatmap, and basic ray tracing
Visual floorplans. Figure presents visualization from all baselines and a comparison with our LoS-only model (as ablation). All the floorplans use 2000 receiver locations. We make following observations. (1) Heatmap Segmentation leverages the difference of RSSI on opposite sides of a wall, however, reflections pollute this pattern, especially at larger distances between T'r and Rx. Further, signals leak through open doors, injecting emrors in the room boundaries. (2) NeRF2 performs poorly since its MLP learns one among many possible assignments of virtual transmitters to fit the RSSI training data. The virtual transmitters hardly correlate to the walls of the environment. (3) EchoNeRF LoS can infer the position inner walls. However, these walls are thick and slanted because while EchoNeRF LoS identify occlusions between (Tx, Rx) pair, it cannot tell the shape and pattern of these occlusions. Crucially, EchoNeRR LoS also cannot infer the boundary walls since receivers located outside the house. (4) EchoNeRF outperforms the baselines, sharpens the inner walls compared to EchoNeRF LoS, and constructs the boundary walls well.
Shortcomings:
Recall that some parts of the floorplan are in the "blind spots" of our dataset since no reflection arrives from those parts to any of our sparse Rx locations (e.g., see bottom left corner of the 1x floorplan; no signals reflect off this region to arrive at any of the Rz locations). Hence, EchoNeRF is unable to construct the bottom of the left wall this floorplan. Finally, note that areas outside the floorplan (e.g., the regions the right of 6th floorplan) cannot be estimated correctly since no measurements are available from those regions (hence, those voxels do not influence the gradients).
RSSI prediction. Figure visualizes and compares predicted RSSI. The top row shows predictions new Rx locations with the Tw held at the trained location; the bottom row shows predictions when

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EchoNeRF
NeRF2
MLP
Figure Heatmaps highlighting EchoNeRF's ability to learn signal propagation. (Top row) Inferred RSSI heatmaps with Tz (red star) used training. (Bottom row) new Tx (green star) degrades NeRF2 and MLP while EchoNeRF shows accurate predictions.
Figure 7: (a) Tracing re- flections on the learnt floorplan. (b) True re- flections from Sionna.
both Ta and Ræ are moved to new locations. Two key observations emerge: (1) EchoNeRF is limited by Sionna's ss inability to simulate through-wall signal penetration; NeRF2 has access to an expensive license for through-wall wall simulation and shows better predictions inside the rooms. However, in areas that EchoNeRE can "see" (e.g., corridors in the top row), the awareness of reflecting surfaces leads significantly better predictions. (2) When the Tx location differs from that used in training, EchoNeRF's s improvement over NeRF2 is significant. This is the core advantage of first solving the inverse problem and then leveraging it for the (forward) RSSI prediction.
Learning reflected rays. For a given (Tx, Rx) pair, we examine the points the plausible set that contribute to the reflections. Fig. compares the ray-tracing results from the NVIDIA Sionna simulator (we pick only first order reflections). EchoNeRF captures many of the correct reflections. Of course, some
incorrect a false positive occurs in the bottom right room since segment is missing in our estimate; false negatives also occur in the top right room where again some parts of the wall are missing.
wall
4.3 Relaxing Assumptions Sensitivity Study
Transmitter's location. We assumed knowledge Tr locations, however, we relax this by applying maximum likelihood estimation observed RSSI power, v/* (sce Appendix On average, the estimated Tx location error 2.08 pixels in floorplans of sizes zs 512 x 512 pixels.
Receiver location error. Table shows
Error (m)
0
0.5
2
EchoNeRF's sensitivity to Rx location errors. We inject Gaussian noise (0,, o²I) I) to the Rr locations: implies a physical error of 1m. Wall_Iol IOU accuracy obviously drops with error but 0.5 meter of error is tolerable without destroying the floorplan structure. Advancements in WiFi positioning systems have demonstrated robust sub-meter error.
Wall_Iol
0.38
0.35
0.33
0.29
Table 2: Estimated Wall_ at various levels of injected noise
Effect of Furniture. Fig. 8 visualizes inferred floorplans when toy objects are scattered in open spaces (Rr locations remain N=2000). EchoNeRF is able to identify some of the object blobs but sharp- ening the small objects is challenging due more higher order reflections from furniture. Follow up work is needed, either in modeling nd order reflections by imposing stronger regularizations.
Figure 8: EchoNeRF's floorplan inference with furniture in conference (left) and apart- ment (right) layouts.

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Material
EchoNeRF LoSt
EchoNeRRF
SNR (dB)
EchoNeRR Lost
EchoNeRF1
Qualitative
Concrete
0.251
0.371
00
(no noise)
0.251
0.371
Legible
Glass
0.236
0.364
60
0.246
0.336
Legible
50
0.231
0.292
Legible
Brick
0.232
0.357
40
0.226
0.298
Legible
Marble
0.226
0.328
30
0.207
0.241
Missing walls
Wood
0.227
0.311
10
0.090
0.140
Illegible
Table 3: Sensitivity across materials.
Table 4: Noise robustness across SNR levels.
Material Sensitivity. Table 3 shows the mean Wall_Iol of EchoNeRF on five different materials averaged across six scenes (shown in Fig. (5) Materials with higher reflectivity, such as concrete and glass, yield better performance than absorptive materials like wood. This is because more reflections allow better performance for EchoNeRF'S reflection model.
Robustness to RSSI error. We added Gaussian noise to the RSSI measurements with mean equal to the noise floor (in dB) and a variance of 4 dB. We vary the noise floor levels ranging from 80 to 130 dB across the 6 floorplans shown in Fig. 5 The SNR at receiver is computed as the difference between the received signal power and the noise floor (c.g., a received power of dB with noise floor of dB results in SNR of 10 dB). We report the mean Wall_IoU for EchoNeRF_ LoS and EchoNeRF in Table 4 The performance drops with decreasing SNR; both EchoNeRF LoS and EchoNeRF's floorplans are still legible till 30 dB, but below that (when noise power becomes comparable to the signal power) they break down, leading to missing and illegible walls. Our results are conservative; when we report a specific SNR level (e.g., 40dB), it represents the highest SNR (best-case) among all receivers in that scenario, meaning other receivers experience even lower SNRs. In practice, WiFi SNR ranges from 30-60dB depending on the distance from the router, with close- fooe-iprx measurements often exceeding 50-60dB. For average real-world SNR conditions around 45dB, the corresponding best-case SNR would be 60+dB, which aligns with the top rows where EchoNeRF demonstrates strong performance.
5 Follow ups and Conclusion
Follow-ups. (1) The ability to model 2nd order reflections will boost EchoNeRF's accuracy, allowing it to sharpen the scene and decode smaller objects. For short range applications, such as non-intrusive medical imaging, 2nd and 3rd order reflections would be crucial. This remains an important direction for follow-on research. (2) Extending EchoNeRF to 3D floorplans is also of interest, and since is undesirable to increase the number of measurements, effective 3D priors, 2D-to-3D post-processing may be necessary. Such post-processing tools exist 77] but we have not applied them since our goal is improve NeRF's inherent inverse solver. (3) Expanding evaluations beyond ZInD, which contains largely unfurnished, rectangular rooms, to richer datasets such as HM3D 22) and MVL (36) would also be valuable: furniture and clutter can introduce significant multipath effects that complicate RF signal modeling, and additional research is needed to understand these effects. We defer this to future work, as our focus in this paper is not so much to understand the limits of RF-based NeRFs, but to establish the fcasibility of such frameworks. (4) Finally, EchoNeRF floorplans can offer valuable
spatial context to Neural RIR synthesizers like [47 [2 6 19 20 Synthesized RIR could in-turn aid EchoNeRF's s floorplan inference, forming the basis for an alternating optimization strategy. We leave these ideas follow-up research.
Conclusion. In summary, we re-design the NeRF framework so it can learn to "see" its environment by leveraging both line-of-sight (LoS) paths and multipath reflections. While such reflections bring to the sensor more information about the surroundings, their mixtures with the LoS path also complicates the core inverse problems. EchoNeRE takes step towards solving this inverse problem, but also leaves room for further research in neural wireless imaging and varies downstream applications.
Acknowledgments
We would like to thank Prof. Shenlong Wang for his guidance in the initial phase of this work. We also thank the anonymous reviewers for their valuable feedback. This work was partially supported by NSF #2008338, #1 #1909568, #2148583, and #MRI-201 8966. This work used DELTA at NCSA through allocation CIS230230 from the Advanced Cyberrifrrasrrucure Coordination Ecosystem: Services Support (ACCESS) program, which supported by U.S. National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296
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Appendix for Can NeRFs "See" without Cameras?
A Background on Channel Impulse Response
When a wireless signal propagates, it is typically influenced by multipath effects such as reflections and scattering, well as attenuation caused by the surrounding environment- collectivvvl referred to as the channel. The overall impact of these phenomena on the signal is characterized by linear model known as the Channel Impulse Response (CIR) 28
Mathematically, the CIR is expressed as a sum of scaled and delayed impulses as shown in Equ 9
htt)) Σ a 8(t (T));
where N is the number of multipath components, a, denotes the amplitude (attenuation factor) of the i-th path, de represents the phase shift the i-th path, and т; is the delay the i-th path.
For an input signal xxtt transmitted through the channel htt), the output signal measured at a Rx, y() obtained by the convolution:
v(() x(()== h(t)) + (().
(10)
where w()) represents zero-mean additive noise. For a simple two-path channel with line of sight (LoS) path and one reflected path, the CIR h(t) is given
h(t) at)(t) age T2).
(11)
The received signal (t) would then be:
(t) = ztt) * [a18(t) age
tb 6(t T2)] + w(()
(12)
B Modelling Wideband Multipath Signal Power
This section shows how received power in multipath scenarios can be approximated as sum of powers of LoS and all other multipaths. frequency domain, the received signal y(t) at a particular receiver can be expressed as
Y(K) - H(W)
(13)
Here, X(fx) and W(fi) represent the discrete Fourier transforms of the signal z(t) and the additive noise wt) at subcarrier frequency fo with k E {O.,,...,K) The channel can be written as (fx)) = Ele au exp(-j2x fieT)) where 1 E {1, L} is an index over separate multipaths. Here, aj and 7i represents the attenuation and phase of the 1-th multipath component at subcarrier We assume that the channel H(fx)) and the signal X ((fa) are independent.
The received power at each frequency l is given by thy (f())..
((()(()) 21
E[(H((())X((I) + +
(14)
-xx BIJ (1+) vowa
where vx.-- = (f&))()a)) and v'w ElI Next. Next.
14

---

E| E|H(J = -
E
OtN exp (-j27 (wT)
Σ mm0
an exp (j2n (j2T[(Tm) SkTm))
alkam exp 1- (1 Tmm)
E
1=0 m=0
E
aik
a exp (-j2mf (n Tm))
1=0
L
E
CIR
+
E (md exp (-j2ff (Tr Tm))
1=0
E
aik
We assume that channel gains between different multipaths 7, m with 1 * have vanishingly small correlation. Therefore, the total received power vi can be computed by summing all individual subcarrier powers.
VY
K
L
E
lawe?
+ tbwa
K
IE
[1bxa
lamd?
+ s/w
1=0 k=
Here, we separate out Σx= x Loo |2] LoLs to represent the LoS power over all subcarriers and k=
K
E
[xxxa lawe"
[2] Oreef
< 11 < L, to denote the power of I-th order reflections.
C
Approximating Channel with First-Order Reflections
EchoNeRF models the total received power the Rx as the combination of the LoS power EchoNeRF Los, and the contributions from all the first-order reflections. To validate the contri- bution of the achievable power from EchoNeRF when compared the total received power s), we evaluate the relative contributions of these signals to the total power using the NVIDIA Sionna simulator [5]. To this end, we compute the ratios of the LoS signal vr.os, LoS with the first order reflections thLoS + fieef: and LoS with the first two orders of reflections V1..s + dreff + threfa- These are compared to total received power s), which approximated as the sum of the LoS power and the power from the first ten reflections.
Fig shows path power contribution ratio from different paths in histogram. While the v'Los power alone only accounts for approximately 70% of the total received power and is more spread out, LLS + Preffi accounts to 95% of the total power, with reduced spread. Moreover, secondary reflections Frefz only contribute to less than 3% of the total power. Hence, EchoNeRF models the first-order reflections along with the lfne-of-sight.
'We use to denote complex conjugate
15

---

YLos
600
Vios + Wro
y
Frequency
Vlos + Wref Wref
400
300
200
100
0.5
0.6
Ratio Contributions
Figure 9: Histograms illustrating the contribution ratios from line-of-sight (LoS), LoS combined with first-order reflections, and LoS combined with first- and second-orde reflections. The orange graph highlights the significant contribution of first-order reflections the total power, supporting EchoNeRF'ss 's approach of modeling only the first reflection alongside the LoS power.
D Relaxing Tx Assumptions
We relax the assumption that Tx locations are known. Given the set of receiver locations (Rx; } and the signal powers { the goal is to estimate the transmitter location Tx (Txx, Txy). ). To achieve this, we apply a maximum likelihood estimate (MLE). Briefly, among all the measured signal powers (1/)) from given 7' identify the P strongest signal powers and their corresponding received locations. The rationale behind selecting the strongest powers that they are significantly influenced by the LoS component, allowing us model them effectively only using the Friss' equation M. We assume independence among the measurements since the received LoS power across locations, for given Tx location, are independent. So, the likelihood equation for all these measurements be written as:
p(11, 1/2
up Tx)
II ==1
p(u Tx)
We approximate that the ii is normally distributed with a mean modeled by the line-of-sight power de and variance o² where d, ||Tx- Rx,/| is the distance between Tx and Rx,, The likelihood
function for each observation ub; is thus given by:
(vi # )2
p( Tx)
V2T0²
exp
202
Maximizing log- likeliioldood L of (v1) ViE [I....,Pp
P
(
(wi K )2
log L(Tx) = Σ log
V2m22
exp
20
i=1
P log log(2
1
K
2
log (Tx)
1
202
d?
Minimizing the second term gives the optimal Tx* as:
K
2
Tx* argmin
Tx
Tx
Rx
16

---

We use Scipy's 'minimize' with the BFGS method to numerically solve for Tx". Fig 13 visualizes the ground truth and the estimated locations across floorplans. The estimated 7x positions closely match the ground truth, and we report the 7x location error to be 2.08 pixels. Fig TO, demonstrates the performance of EchoNeRF __o___Lo_____ and EchoNeRF using the estimated 7x locations for the 6 floorplans in Fig 13] Performance is comparable to that achieved with ground truth 7x locations, highlighting robustness.
Ground Truth
EchoNeRF LoS
EchoNeRF
Figure 10: Qualitative comaprison of EchoNeRF LoS and EchoNeRF when Tx locations unknown, and are estimated. The top row shows the ground truth floorplan, Rx locations along with the estimated Txs in blue. The second and third row displays the performance of EchoNeRF Los and EchoNeRF respectively. Despite the 7x locations being unknown, our methods accurately estimate them, leading performance comparable to the where 7x locations are known.
E
Details on Model Training
The signal power measured at the receiver is typically represented a logarithmic scale. RSSI values generally range from -50 dB to -120 dB, where higher value (e.g., -50 dB) corresponds to stronger signal. Fig iillutraates typical input to EchoNeRF where measurements have been collected from approximately 2000 Rxs positioned in the floorplan, with data gathered from five Txs.
E.1 Linear-Scale RSSI Loss:
For the training of EchoNeRF, optimize on the linear-scale RSSI values. Linear loss ensures that the receivers that capture stronger signals are given more importance during training. We partition our dataset into an 80-20 split, using 80% of the data for model training, including baselines.
For EchoNeRF's network, we employ a simple 8-layer MLP with a hidden dimension of 256 units. For each voxel uy. the outputs from the final layer passed through sigmoid activation obtain the opacity 5, and through a Gumbel softmax [6] layer to sample the output normal w from one of the possible K., orientations. This sampled orientation is then used in the subsequent stages of training, such as for calculating the direction of the reflected signal M. For the learnable baselines, such MLP and NeRF2, we adopt the same architecture as used in EchoNeRF.
E.2 Supervising Voxel Orientations
EchoNeRF leverages the spatial gradient of a voxel's opacity, Vo, to supervise its orientation during the multi-stage training process. To compute this gradient, evaluate the opacities of neighboring
17

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Figure 11: Observed signal power at the Rxs. The top left figure shows the positions of the Rxs and Txs, followed by the power the receivers from each of the five transmitters. The colormap ranges from red showing stronger signals to blue for weaker signals.
Tx 9
M
Rx
W
j
B
θ
Jj
Figure 12: An incoming ray from a transmitter Tx reflecting around voxel ny and arriving at receiver Rx. The incoming ray makes incident angle 0 with the normal wj the reflecting surface. The ray after reflection passes a receiver Rx at certain distance making an angle B3
voxels along each of the K,, directions and apply finite difference methods. We found that this approach yielded superior results compared to using the gradient available via autograd.
In general, the power from reflections depends not only the total distance traveled but also the angle at which the reflection occurs at the voxel uy and whether the reflected ray reaches the receiver (Rr). We model this behavior through and respectively which parameterize nonlinear function f. The incidence angle 0 measures the angle between the Tx and the orientation wy. and 3 denotes the angle Rx makes with the reflected ray M (see fig 12 Note that v3 E V, and if wj is correct,
g = O. The reflected ray M can be computed as shown Eqn 15
M = (uj Tx) 2 [( Tx)
(15)
Here Wj is unit vector.
E.3 Detailed network parameters
We assume the floorplan is unknown shape inside a 512 512 grid. For any ray or ray segment,
we uniformly sample = 64 voxels on it. We choose λ₁ = X = 0.01 for LoS training followed by
Å1 = A2 0.1 for training the EchoNeRF model. We find that discretized opacity values {0. 1} improve our LoS model. We use the straight-through estimator 4 to avoid the unavailability of the gradient at the discretization step. To help optimization and encourage sparsity of the number of reflections, we use only the top-k contributions (k=10) while training the reflection model. We use the ADAM optimizer [17] with 1.0 -4 learning rate. We train our models on NVIDIA A100 GPUs.
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Figure 13: Comparison of Ground truth Tx locations indicated in red in the first column with the estimated Tx locations shown in blue from starting from column two. The Rx positions used for the estimation are marked in green.
E.4 Heatmap Segmentation Implementation Details
The raw trajectory signal power values are first interpolated to obtain a heatmap that provides smoother representation of the input measurements. Of course, interpolating for regions without any data can lead to incorrect results, especially in larger unseen areas. A rule-based classifier is then applied for segmentation, using two criteria: (1) RSSI values above a threshold to identify potential room areas, and (2) smoothness of the RSSI signal, assessed through the second-ordes derivative, ensure continuity within rooms. The initial segmentation is refined using morphological operations (via dilation and erosion) with a 3x3 kernel smooth rough edges and eliminate small components. Overlapping regions are resolved by comparing gradient magnitudes, followed by additional morphological processing and connected component analysis to obtain the final, refined segmentation.
Code: We plan release code, data, and baselines In the meantime, Section provides sufficient details to allow readers to reproduce our results, especially since our network components simple MI.Ps.
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Evaluation on Additional Floorplans
Ground
Truth
Heatmap Seg.
NeRF2
3
EchoNeRF LoS
EchoNeRF
EchoNeRF
Signal
Predic- tion
Figure 14: Qualitative comparison of Ground Truth floorplans against those inferred by baselines Heatmap Segmentation and NeRF2. We note that while NeRF2 unable to predeit any reasonable floorplan, Heatmap Segmentation inniéntationn shape is limited the (convex hull of the) trajectory data (see bottom left of the second row, first column). Additionally, it fails to capture critical details, such as door openings. The 4th and 5th rows show floorplans by our proposed models EchoNeRF _LoS and EchoNeRF. EchoNeRF LoS captures the rough shape of the floorplan, especially the interior walls, while EchoNeRF further improves these walls by adjusting their thickness and accurately correcting their shape. EchoNeRF also correctly identifies the floorplan boundary, as evidenced in the last column, where the exact boundary is captured just from the reflections. To understand the signal propagation captured by EchoNeRF, we place one Tx in each floor plan randomly (that is not present training data) and evaluate the signal power discrete receivers. These Rxs are placed on a grid at equal intervals and the predicted signal power is converted into heatmap. The bottom row shows these inferred signal power heatmaps with the brightest point indicating the location (as the Rx closest to the Tx receives the highest power). EchoNeRF is not only able to predict the signals well across the floorplan, but also capture the propagation paths i.c., LoS signal and the first-order reflections. For instance, in the first column, the left portion of the center hall receives power only due to the wall reflection from the left wall.
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Ground Truth
Heatmap Seg.
NeRF2
EchoNeRF LoS
EchoNeRF
EchoNeRF
Signal
Predic-
tion
Figure 15: Additional qualitative comparisons of Ground Truth floorplans against those inferred by baselines Heatmap Segmentation and NeRF2. The 4th and 5th rows show floorplans by our proposed models EchoNeRF LoS and EchoNeRF with clearly identified walls and boundaries. The bottom row shows inferred signal power heatmaps demonstrating EchoNeRF's capability to learn accurate signal propagation.
G Societal Impact Statement
We acknowledge that NeRFs hold significant potential for positíve societal impact. Applications span AR/VR, medical imaging, airport security, and education, where accurate 3D reconstructions can greatly enhance functionality and understanding. However, our work EchoNeRF also introduces potential risks. In particular, the ability infer detailed spatial layouts from limited sensory input could be misused to access private sensitive floorplan information. We emphasize the importance of responsible use.
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The abstract and introduction accurately describe the proposed framework EchoNeRF teaching NeRFs to learn wireless reflections.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification:
Limitations are discussed in Section
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Reviews:
[{"review_id": "g0mvHNkiVm", "reviewer": "Reviewer_myAA", "summary": "The paper introduces EchoNeRF–a method for reconstructing floorplans from WiFi measurements. In contrast to prior works, EchoNeRF specifically targets reconstructing geometry rather than just WiFi signals. To achieve this, the method proposes two key ideas: (1) a multi-path model for WiFi signals that represents simulated signal as a sum of multi-bounce paths and (2) a floorplan representation which uses opacity and a discretized normal to describe walls. The multi-path signal is then simulated, for the first-and second bounce, using a two-stage algorithm which first recovers the line-of-sight paths before geometry with first-order reflections. In practice, the method recovers significantly more accurate floorplans than prior work and as a result also can simulate WiFi signals for new transmitter locations much more accurately.", "questions": "1. Do the authors have a sense of how this method would work in 3D where scenes exhibit some variation in the added Z dimension? Separately, have the authors thought about how 2D floorplans may be useful in reconstructing components of indoor scenes with visible light?\n\n1. Is there any reason to expect that parameterizing the occupancy with a signed distance function (SDF) as in [Wang et al. 2021, Yariv et al. 2021, Miller et al. 2024] would improve the quality of the reconstructed floorplans?\n\nreferences:\n```\n@article{wang2021neus,\n  title={NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction}, \n  author={Peng Wang and Lingjie Liu and Yuan Liu and Christian Theobalt and Taku Komura and Wenping Wang},\n  journal={NeurIPS},\n  year={2021}\n}\n@inproceedings{yariv2021volume,\n  title={Volume rendering of neural implicit surfaces},\n  author={Yariv, Lior and Gu, Jiatao and Kasten, Yoni and Lipman, Yaron},\n  booktitle={Thirty-Fifth Conference on Neural Information Processing Systems},\n  year={2021}\n}\n@InProceedings{Miller:VOS:2024,\n  author    = {Miller, Bailey and Chen, Hanyu and Lai, Alice and Gkioulekas, Ioannis},\n  title     = {Objects as Volumes: A Stochastic Geometry View of Opaque Solids},\n  booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},\n  month     = {June},\n  year      = {2024},\n  pages     = {87-97}\n}\n```", "limitations": "Yes.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "strengths:\n\n1. The paper develops a principled technique for reconstructing floorplans with WiFi signals and in the process makes an interesting observation that existing WiFi based NeRF methods really do not reconstruct the geometry in any sort of meaningful way. This is a similar to the series of papers a few years ago, e.g. NeuS [Wang et al. 2021] and VolSDF [Yariv et al. 2021], which demonstrated that NeRF was failing to capture high quality surfaces even though novel views were extremely high quality. In this case, the gap between the geometry recovered by EchoNeRF and methods like NeWR and NeRF2 is even more drastic.\n\n2. The paper has extensive discussion of both the design decisions, implementation, and the limitations of the method. This should make the paper and the method extremely useful to the broader NeurIPS community as it improves reproducibility and motivates future work.\nThe approach itself is very novel and provides a new framing of how to simulate WiFi with NeRF, both in terms of theory and practical approaches.\n\nweaknesses:\n1. A very minor point, it would have been great to have an example with real world data.\n\n\nreferences:\n```\n@article{wang2021neus,\n  title={NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction}, \n  author={Peng Wang and Lingjie Liu and Yuan Liu and Christian Theobalt and Taku Komura and Wenping Wang},\n  journal={NeurIPS},\n  year={2021}\n}\n@inproceedings{yariv2021volume,\n  title={Volume rendering of neural implicit surfaces},\n  author={Yariv, Lior and Gu, Jiatao and Kasten, Yoni and Lipman, Yaron},\n  booktitle={Thirty-Fifth Conference on Neural Information Processing Systems},\n  year={2021}\n}\n```", "was_revised": true, "final_justification": "The paper presents a novel and well-structured approach for reconstructing floor plans from WiFi measurements, introducing a principled multi-path signal model and a wall representation that jointly enable significant improvements over prior WiFi-based NeRF methods in both geometry recovery and signal simulation. The method is clearly motivated, thoroughly discussed, and experimentally validated. My questions about extending to 3D and the potential role of SDF parameterization were addressed in the rebuttal with concrete technical considerations and future plans. With these points clarified, I maintain my strong recommendation for acceptance.", "rebuttal": "We sincerely thank the reviewer for their constructive feedback. Below, we answer some concerns.\n\n---\n> **Q1. Do the authors have a sense of how this method would work in 3D where scenes exhibit some variation in the added Z dimension?**\n\nYes, we have pondered on this question and see two possible approaches to extend to 3D:\n\n(1) Re-compute the reflection manifolds in 3D, i.e., given the Tx and Rx locations, find which voxels will produce valid reflections. In 2D, these manifolds were curved lines on the 2D plane (as shown in Fig. 3), however, in 3D, the manifolds will become curved lines in the 3D space. Importantly, the number of voxels on these manifolds do not grow excessively, since the 2D manifolds are essentially projections of the 3D manifolds. Hence, we expect the optimization to remain stable.\n\n(2) A more engineering approach could be as follows. When the Tx and Rx are at a similar height $h$, hardly any reflections occur on the vertical walls from higher or lower than $h.$  Hence, we only need to estimate the ceiling and the floor, since the vertical walls can be extended upward and downward from a 2D floorplan. Since ceilings and floors are both horizontal ($90^\\circ$ orientation), we can only add a vertical $90^\\circ$ manifold in our optimization to model the reflections from the ceiling and floor. Knowing the ceiling and floor heights, and the 2D floorplan, a closed 3D floorplan can be created using existing 3D software.\n\nIn follow-up work, we plan to attempt idea #1 first and fall back, if necessary, on idea #2.\n\n---\n> **Q2. Separately, Have the authors thought about how 2D floorplans may be useful in reconstructing components of indoor scenes with visible light?**\n\nYes, there is indeed a lot of room for innovation in multi-modal fusion. We focussed only on RF in this paper to understand where EchoNeRF alone can get us. However, once the RF mode matures, we see 2 immediate tracks for fusion: \n\n1. Camera helping RF: When cameras can be partially used to view parts of the environment (e.g., kitchen and living room but not the bedroom or bathroom), they can offer valuable initialization to EchoNeRF. This can boost EchoNeRF’s accuracy. Cameras may even be adaptively used to selectively repair parts of the floorplan that exhibit higher uncertainty. \n2. RF helping cameras: RF can assist cameras by reducing the number of measurements needed to infer the full scene. This is possible because RF signals can see through walls, which obviates the need for the user to walk to all corners of the house. EchoNeRF can also be used as a second information stream to add robustness to vision-based imaging.\n\n---\n> **Q3. Is there any reason to expect that parameterizing the occupancy with a signed distance function (SDF) as in [Wang et al. 2021, Yariv et al. 2021, Miller et al. 2024] would improve the quality of the reconstructed floorplans?**\n\nThanks for bringing SDF into our chain of thought. SDF is indeed useful for predicting  surface occupancy and may improve the smoothness of walls if we replace opacity with SDFs, as proposed in Wang et al. 2021. However, the wall orientation estimates may be less stable while SDFs are being trained. We found empirically (and as also observed in several papers [1,2]), that the orientations inferred from opacities are noisy during the learning process. That said, we would like to revisit the potential benefits of plugging SDFs into our now-stable EchoNeRF pipeline.\n\n[1] Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains\n\n[2] Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields\n\n\n---\n> **Q4. Minor weakness: A very minor point, it would have been great to have an example with real world data.**\n\nWe want to thank you for recognizing that this problem is hard even in simulation. When we started this project, we were envisioning demos of EchoNeRF in the same spirit as camera-based NeRFs. This paper falls short and we acknowledge EchoNeRF has a simulation-to-real gap. However, the core inverse problem with RF proved to be hard (in our opinion) even in a simulation setting; we realized the hardness as we iterated through many failures before finally solving it.\n\nOur next step is to add the necessary pieces to EchoNeRF so it can function in real scenarios. These pieces include, but are not limited to, fusing with RGB, audio, LIDAR or other sensors; using channel impulse responses (CIR) to extract more information from each measurement; leveraging multiple frequencies in WiFi/6G signals; using floorplan priors; and even post-processing on the final results. These should help in narrowing the sim2real gap."}, {"review_id": "9RweBfXtec", "reviewer": "Reviewer_zf7b", "summary": "This paper addresses the problem of floor plan estimation from *multipath* signals (e.g., radio frequency (RF) signals such as WiFi or audio). The paper proposes a novel and interesting approach, **EchoNeRF**, by redefining Neural Radiance Fields (NeRF) to learn, implicitly, the environment structure through many line-of-sight (LoS) paths of multiple reflection RF measures. This manuscript presents a compelling evidence of the efficacy to predict floor plan geometries solely from RF signals.", "questions": "Q1: Did the authors consider to evaluate EchoNeRF in environments with walls exhibiting different RF absorption and reflection properties. For example, brick, wood, concrete, and glass windows? If so, how do the reconstruction results differ across such diverse environments?\n\nQ2: Since multipath signals arise not only from walls but also from ceilings and floors, can the proposed EchoNeRF reconstruct full 3D room geometry, including floor and ceiling. If so, I suggest you to add those experiments to enhance your novelty and the discussion for future works.\n\nQ3: I recommend that the authors expand the discussion in Section 5 to address the challenges associated with multiple receivers (RX) and transmitters (TX). open challenges in complementing previous solution that uses RGB cameras or depth/lidar sensors (multimodal approaches), and open concerns related to data privacy.\n\nQ4: Fig. 3 requires significant improvement. In its current form, it is really difficult to interpret and does not effectively convey the intended information. For instance, the purple shadow (representing the manifold of reflexions at $\\omega$=45$^\\circ$) present incident and reflected lines that is not at $\\omega=45^\\circ$ in the illustration. Can you elaborate on this?\n\nQ5: In L154-L157, the paper stands that $\\omega_j = [{1,..,K_\\omega}]$ with $K_\\omega=4$, However, in L158 and Fig.3  $\\omega$=45$^\\circ$. can you elaborate on this? Is this related to the number of reflations of the signal and the shape of the room?\nif so, how this affect more complex room shapes? What happens if $\\omega$ is overestimated, e.g 64? what about underestimated e.g. 1?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "# Strengths\n* The paper is well-written and organized. The manuscript stands clearly the motivation, challenges, and implications of the proposed solution. It also present a clear description of details and assumption towards the modification of NeRF-like pipeline for RF signals.\n* The benchmarks and baselines are suitable for the task and relevant for evaluations. \n* The idea behind the proposed **EchoNeRF** is novel and it sounds feasible and valid. Although, the floor plan estimation results significantly differ from other solutions that use cameras or direct geometry sensors, the quality of the estimated geometry are impressive. \n\n# Weaknesses\n\n* One minor weakness in the presented manuscript is the lack of experiments using real RF signal like UWB sensors or RF IC-boards, which are relatively easy to use and inexpensive. \n\n* One major weakness in the presented manuscript is that the evaluation is limited to the ZinD dataset [9], which primarily contains sparsely furnished and geometrically simple rectangular rooms. Expanding the experiments to include more complex datasets such as MVL-dataset or HM3D may enhance the discussion of the limitations of the proposed **EchoNeRF**.\n> Solarte, B., Wu, C. H., Jhang, J. C., Lee, J., Tsai, Y. H., & Sun, M. (2024, September). Self-training Room Layout Estimation via Geometry-Aware Ray-Casting. In European Conference on Computer Vision (pp. 253-269). Cham: Springer Nature Switzerland.\n\n  > Ramakrishnan, S. K., Gokaslan, A., Wijmans, E., Maksymets, O., Clegg, A., Turner, J., ... & Batra, D. (2021). Habitat-matterport 3d dataset (hm3d): 1000 large-scale 3d environments for embodied ai. NeurIPS 2022", "was_revised": true, "final_justification": "The authors addressed my main concerns, however evaluations on more complex scenes that challenges the limits of the proposed solution are still missing. Nevertheless, I sincerely considered that the idea presented in this manuscript is significantly novel, and it has the quality needed for NeurIPS standard. Thus, I keep my rating of borderline accept.", "rebuttal": "We sincerely thank the reviewer for their constructive feedback. Below, we answer some concerns.\n\n---\n> **Q1. One major weakness in the presented manuscript is that the evaluation is limited to the ZinD dataset [9], which primarily contains sparsely furnished and geometrically simple rectangular rooms. Expanding the experiments to include more complex datasets such as MVL-dataset or HM3D may enhance the discussion of the limitations of the proposed EchoNeRF.**\n\nThank you for pointing to those datasets. Yes, greater floorplan complexity (complex wall patterns, furniture, clutter) will all help to bring out the deficiencies in EchoNeRF. The goal with this work was not so much to understand the limits of RF based NeRFs, but to establish the feasibility of such frameworks. Given that past work could hardly infer any geometry, our goal was to explore if NeRFs can be taught RF reflections, and if that training can converge to a reasonable floorplan. Frankly, and perhaps naively, we have been surprised at how much NeRFs could infer even when the measurements are just signal power (not channel impulse responses (CIR)). We believe there are many untapped opportunities that can be pursued in follow-up work to close the sim2real gap. Examples of such opportunities are: using priors, fusion with other modalities such as camera or audio, utilizing multiple RF frequencies, using CIR measurements, etc. \n\n---\n> **Q2. Did the authors consider to evaluate EchoNeRF in environments with walls exhibiting different RF absorption and reflection properties. For example, brick, wood, concrete, and glass windows? If so, how do the reconstruction results differ across such diverse environments?**\n\nWe ran some experiments this week to observe the sensitivity to materials: we tested for 5 materials across the 6 floorplans shown in Fig 5. We report the mean IoU for EchoNeRF_LoS and EchoNeRF below:\n\n| Material  | EchoNeRF_LoS IoU (&uarr;) | EchoNeRF IoU (&uarr;)|\n|:---------:|:----------------:|:------------:|\n| Concrete  | 0.251            | 0.371        |\n| Glass     | 0.236            | 0.364        |\n| Brick     | 0.232            | 0.357        |\n| Marble    | 0.226            | 0.328        |\n| Wood      | 0.227            | 0.311        |\n\nMaterials with higher reflectivity, such as concrete and glass, yield better performance than absorptive materials like wood. This is because more reflections allow better performance for EchoNeRF’s reflection model.\n\n---\n> **Q3. Since multipath signals arise not only from walls but also from ceilings and floors, can the proposed EchoNeRF reconstruct full 3D room geometry, including floor and ceiling. If so, I suggest you to add those experiments to enhance your novelty and the discussion for future works.**\n\nThanks. We have pondered on this question and see two possible approaches to extend to 3D:\n\n(1) Re-compute the reflection manifolds in 3D, i.e., given the Tx and Rx locations, find which voxels will produce valid reflections. In 2D, these manifolds were curved lines on the 2D plane (as shown in Fig. 3), however, in 3D, the manifolds will become curved lines in the 3D space. Importantly, the number of voxels on these manifolds do not grow excessively, since the 2D manifolds are essentially projections of the 3D manifolds. Hence, we expect the optimization to remain stable.\n\n(2) A more engineering approach could be as follows. When the Tx and Rx are at a similar height $h$, hardly any reflections occur on the vertical walls from higher or lower than $h.$  Hence, we only need to estimate the ceiling and the floor, since the vertical walls can be extended upward and downward from a 2D floorplan. Since ceilings and floors are both horizontal ($90^\\circ$ orientation), we can only add a vertical $90^\\circ$ manifold in our optimization to model the reflections from the ceiling and floor. Knowing the ceiling and floor heights, and the 2D floorplan, a closed 3D floorplan can be created using existing 3D software.\n\nWe plan to add this discussion to the future work section of the revised version. In follow-up work, we plan to attempt idea #1 first and fall back, if necessary, on idea #2.\n\n\n---\n> **Q4. Fig. 3 requires significant improvement. In its current form, it is really difficult to interpret and does not effectively convey the intended information. For instance, the purple shadow (representing the manifold of reflexions at=45) present incident and reflected lines that is not at in the illustration. Can you elaborate on this?**\n\nWe now see how this figure can be confusing; we will redraw it in the revised version. Let us try to explain briefly what the purple curve, labeled $45^\\circ$, means. \n\nSay a voxel has an orientation of $45^\\circ$ with respect to a horizontal X axis. For a given Tx and Rx, at what location should we place this voxel so that the signal from the Tx would reflect on this voxel and reach the Rx? Observe that only certain locations will satisfy this requirement. The locus of all these locations is the purple line.\n\n---\n> **Q5. In L154-L157, the paper stands that $\\omega_j$ = [1, … K] with $K_\\omega$ = 4.. However, in L158 and Fig.3, $\\omega_j =45^{\\circ}$. can you elaborate on this? Is this related to the number of reflations of the signal and the shape of the room? if so, how this affect more complex room shapes? What happens if $K_\\omega$  is overestimated, e.g 64? what about underestimated e.g. 1?**\n\nThat was a typo and thank you for catching it. $K_\\omega$ denotes the number of possible discrete orientations for wall voxels, where orientation $\\omega$ is in $[0, 180)$. When $K_\\omega = 4$, we can write $\\omega_j = j\\frac{180}{K_\\omega}$. \n\nIn such settings, walls that are oriented at $0^\\circ$, $45^\\circ$, $90^\\circ$, and $135^\\circ$ will be searched for by the EchoNeRF model. Higher values of $K_\\omega$ will benefit the estimation of floorplans with more complex wall structures, while lower $K_\\omega$ will need more investigation, an item for our future work.\n\n---\n> **Q6. I recommend that the authors expand the discussion in Section 5 to address the challenges associated with multiple receivers (RX) and transmitters (TX). open challenges in complementing previous solution that uses RGB cameras or depth/lidar sensors (multimodal approaches), and open concerns related to data privacy.**\n\nThanks for the thoughtful suggestion. We were unable to discuss several of these open questions due to the lack of space in the submission draft. If accepted, we will create space to discuss the open challenges to help facilitate follow-up research after EchoNeRF."}, {"review_id": "EGjjPgh87D", "reviewer": "Reviewer_ybbR", "summary": "This paper proposes a method to learn wall layouts from radio-frequency (RF) measurements of multiple transmitters (Txs) placed throughout the scene and emitting concurrently. The key to the approach is to learn a NeRF (MLP-based) that learns a mapping of locations to opacity and orientation such that the RF power is accurately reconstructed. The authors demonstrate through simulated results that this analysis-by-synthesis approach enables interpretable room layout reconstructions (with the assumption that any voxel orientation is at either 0, 45, 90, or 135 degrees, since walls tend to be perpendicular).", "questions": "I enjoyed the paper and it's well written, but the first two weaknesses listed above make it difficult to recommend for acceptance in its current form. Thus, adding real-world results and sufficient discussion to past work would help mitigate my concerns.\n\nA few other smaller comments:\n\n- L154 The nomenclature for wj is confusing - if wj is an angle, why is the set of discrete values = (1, 2, 3, …) instead of (45, 90, 135, …)? It did not become clear that these values should be multiplied by 45 degrees until later in the text.\n\n- While there is more thorough background on RF in the appendix, a brief background section in text would be very helpful for a broad audience like NeurIPS. This could briefly describe at a high level questions, such as how do we interpret the data? Is there a temporal dimension or is it just an intensity image? Do RF signals reflect like optical signals (scatters on diffuse objects, reflects in one direction on specular objects)?\n\n- In training stage 1, is there any way to filter out pixels that correspond to occlusions and only supervise other pixels?\n\n- An ablation with varying numbers of discretized voxel orientations would be informative (increasing K_w)\n\n- This paper calls itself a NeRF based method but there is no notion of *radiance* in the formulation - seems like more of a neural implicit representation (NIR). The authors may consider revising their terminology or motivating why they call this method a NeRF.\n\n- It would be helpful if the Fig 5 caption was a bit more descriptive (e.g. mention how the reader can interpret the red stars and lightly colored lines in the first row)\n\n- Why is voxel orientation used as an output of the NIR rather than using more traditional neural SDF approaches that represent scene geometry and can easily be used to compute reflected ray directions?", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n1. The paper's proposed _EchoNeRF_ model seems reasonable, novel, and effective (at least in simulation). In particular, I was impressed the model is able to handle multiple transmitters simultaneously (akin to multiplexed imaging), since this would result in measurements mixing together, making it much more difficult to separate power for each Tx such that geometry can be learned. This is a hard problem and may be relevant in domains beyond RF.\n\n2. I found the ablations and comparison between EchoNeRF and EchoNeRF_LOS helpful and informative. In particular, it was interesting to see what happens when furniture is in the scene. \n\n3. The paper is very well written and the techniques, for the most part, are well explained. The figures are clean and informative.\n\n**Weaknesses**\n1. The paper lacks any real-world validation, making it difficult to assess its practicality. This issue is exacerbated by a lack of comprehensive analysis or even discussion of the impact of real-world noise (aside from noise in receiver location in Sec 4.3 and mentioning the use of additive noise in the background on modelling in the appendix). \n\n2. The paper claims on L22 that \"optical NeRF understandably fails since it is not equipped to handle multipath\", which is a misleading generalization, and subsequently misses several works related to optical multipath NeRF that should be cited and/or discussed. Some of the multipath NeRF from lidar literature is similar to this work, but isn't discussed. In particular, PlatoNeRF [1] models first-order reflections from multiple \"virtual Txs\" and uses a similar two-stage training approach (however, it does not model multiple Txs at once as in this work). A more comprehensive list of papers that should be cited/discussed is below.\n\n3. One of the main advantages of modeling reflections is stated to be occlusion-awareness (L128-129), but this occlusion-awareness is minimally ablated. it's discussed on L263-266, but it's unclear to me why EchoNeRF_LOS cannot see the outer walls as the Txs (red stars) are directly adjacent to them - maybe if the Rx location was shown in the GT, it would become more clear.\n\n4. The authors discuss NeWRF, but don't offer quantitative comparison. Fig 1 is helpful and clearly shows this method isn't adequate for reconstruction (so this point is fairly minor), but it would be helpful to at least show qual. results on one of the same scenes as EchoNeRF for apples to apples comparison.\n\nMultipath modeling with LiDAR:\n\n[1] PlatoNeRF. https://doi.org/10.1109/CVPR52733.2024.01380. (models first-order reflections with NeRF)\n\n[2] Non-Line-of-Sight Imaging via Neural Transient Fields. https://doi.org/10.1109/TPAMI.2021.3076062 (models second-order reflections with NeRF)\n\nMultipath modeling with RGB:\n\n[3] NeRF-Casting. https://doi.org/10.1145/3680528.3687585\n\n[4] oRCA. https://doi.org/10.1109/CVPR52729.2023.01990", "was_revised": true, "final_justification": "Although the paper is missing real-world evaluation, the rebuttal mitigated my main concerns. Based on the rebuttal, I would like to increase my rating to **borderline accept**. I encourage the authors to reword L22 to say \"vanilla NeRF\" rather than \"optical NeRF\" to be more clear, add the missing related works, and add the new ablation on noise to the supplementary materials in the next revision.", "rebuttal": "We sincerely thank the reviewer for their constructive feedback. Below, we answer some concerns.\n\n---\n> **Q1. The paper lacks any real-world validation, making it difficult to assess its practicality. This issue is exacerbated by a lack of comprehensive analysis or even discussion of the impact of real-world noise (aside from noise in receiver location in Sec 4.3 and mentioning the use of additive noise in the background on modeling in the appendix).**\n\nWe acknowledge that EchoNeRF has a considerable simulation-to-real gap. However, even in simulations, this still proved to be a challenging problem (in our opinion), mainly due to the core inverse problem that needed to be solved under unknown number of multipath reflections, sparse signal measurements, and each measurement being a scalar (because RF signal power is a scalar). \n\nWe believe this paper has finally solved this inverse problem, arguably the most critical piece in the whole RF-NeRF puzzle. While this does not deliver a practical end-to-end system, the current version of EchoNeRF gives us (and others) a platform to build on with follow-up ideas. These ideas include, but are not limited to, fusing with RGB, audio, LIDAR or other sensors (as suggested by several reviewers); using channel impulse responses (CIR) to extract more information from each measurement; leveraging multiple frequencies in WiFi/6G signals; using floorplan priors; and even post-processing on the final results. These should all help in closing the sim2real gap.\n\nRegarding real-world noise, we have run new experiments this week where noise is added at the receiver. We report graceful degradation in EchoNeRF with increasing noise levels, shown below:\n\nSpecifically, we added Gaussian noise to the RSSI measurements with a mean equal to the noise floor (in dB) and a variance of 4 dB. We tested five noise floor levels ranging from -80 dB to -130 dB across the 6 floorplans shown in Fig 5. The SNR at a receiver is computed as the difference between the received signal power and the noise floor (e.g., a received power of -70 dB with a noise floor of -80 dB results in an SNR of 10 dB). Our typical RSSI measurements ranges from -60dB (strong) to -130dB (weak). We report the mean IoU below:  \n\n\n| SNR (in dB)    | EchoNeRF_LoS IoU (&uarr;) | EchoNeRF IoU (&uarr;) | Qualitative   |\n|:----------------:|:------------------:|:--------------:|:---------------:|\n| ⁡inf﻿ (no noise) | 0.251            | 0.371        | Legible       |\n| 60             | 0.246            | 0.336        | Legible       |\n| 50             | 0.231            | 0.292        | Legible       |\n| 40             | 0.226            | 0.298        | Legible       |\n| 30             | 0.207            | 0.241        | Missing walls |\n| 10             | 0.09             | 0.14         | Illegible     |\n\nAs expected, the performance drops with decreasing SNR; both EchoNeRF_LoS and EchoNeRF’s floorplans are still legible till 30dB, but below that (when noise power becomes comparable to the signal power) both EchoNeRF_LOS and EchoNeRF break down. This is expected. \n\n---\n> **Q2. The paper claims on L22 that \"optical NeRF understandably fails since it is not equipped to handle multipath\", which is a misleading generalization, and subsequently misses several works related to optical multipath NeRF that should be cited and/or discussed. Some of the multipath NeRF from lidar literature is similar to this work, but isn't discussed. In particular, PlatoNeRF [1] models first-order reflections from multiple \"virtual Txs\" and uses a similar two-stage training approach (however, it does not model multiple Txs at once as in this work). A more comprehensive list of papers that should be cited/discussed is below.**\n\nIn L22, we were referring to vanilla NeRFs which do not model multipath. In L95-L100, we discussed how follow-up work have modeled multipath as a 2-component decomposition problem, while EchoNeRF must handle a $K$-component decomposition, where $K$ is unknown.  \n\nThanks for pointing us to the papers. We will surely cite them in our revised version but the ideas from these papers don’t apply directly to ours. Specifically, the RGB based reflection-aware NeRFs (e.g., NeRFCasting and ORCa) are still focussed on efficiently solving the 2-component decomposition, typically for rendering glossy surfaces or mirrors. \n\nThe other line of work using LIDARS (e.g., PlatoNeRF, NLOS imaging) are coping with many unknown reflections, however, LIDARs have very high time resolution (very high clock frequency), and is therefore able to receive the incoming rays in different time buckets. This temporal separation allows the NeRF to make separate measurements for different surfaces in the scene.\n\nSince we use only signal power in EchoNeRF, we only have one single scalar measurement (named RSSI) that contains a mixture of the LoS and all the $K$ reflections. This makes our inverse problem even more complex.\n\n---\n> **Q3. One of the main advantages of modeling reflections is stated to be occlusion-awareness (L128-129), but this occlusion-awareness is minimally ablated. it's discussed on L263-266, but it's unclear to me why EchoNeRF_LOS cannot see the outer walls as the Txs (red stars) are directly adjacent to them - maybe if the Rx location was shown in the GT, it would become more clear**\n\nWe understand the confusion and let us briefly clarify it here. We will explain better in the revised version of the paper.\n\nIn row 1 of Fig. 5 , the red stars denote the Tx locations, and the light gray dots denote the Rx locations (i.e., where measurements are made). Row 4 of the same figure shows the results from the EchoNeRF_LOS model. The outer walls are not detected in row 4 because there are no Rx location, hence no measurements, from outside the home; the gray dots in row 1 are all inside the home floorplan. However, when there are walls between a red Tx and a gray Rx inside the home, those occlusions show up in row 4 as inner walls.\n\nIn row 5, EchoNeRF “sees” the reflections from the outer walls, and hence the results in row 5 can bring the outer walls as well.\n\nWe hope this helps to clarify the situation.\n\n---\n> **Q4. The authors discuss NeWRF, but don't offer quantitative comparison. Fig 1 is helpful and clearly shows this method isn't adequate for reconstruction (so this point is fairly minor), but it would be helpful to at least show qual. results on one of the same scenes as EchoNeRF for apples to apples comparison.**\n\nWe understand that apples-to-apples comparison with NeWRF would be helpful, hence we have now run the following experiment for the 4th floorplan in Figure 5. We placed 500 receivers (Rx), spread across the floorplan, and one transmitter (Tx) located at the center. Results from training NeWRF using their official codebase do not show any floorplan. Instead, the learnt geometry has somewhat similar behavior as that of Fig 2(c), where black dots are scattered inside and outside the actual floorplan at virtual Tx locations, but not aligned with walls of the house. \n\nThis is not surprising. As authors of the NeWRF paper themselves acknowledged, their neural model fits the signal measurements well but does not solve the core inverse problem to learn the physics of signal propagation (which is in turn important to predict the floorplan).\n\nWe will include this qualitative comparison in our revised manuscript.\n\n---\n> **Q5. It would be helpful if the Fig 5 caption was a bit more descriptive (e.g. mention how the reader can interpret the red stars and lightly colored lines in the first row**\n\nOf course. We realized this as we responded to Q3 above.\n\n---\n> **Q6. L154 The nomenclature for $\\omega_j$ is confusing - if $\\omega_j$ is an angle, why is the set of discrete values = (1, 2, 3, …) instead of (45, 90, 135, …)? It did not become clear that these values should be multiplied by $45^\\circ$ until later in the text.**\n\nYes, we were sloppy here. We will make this precise.\n\n---\n> **Q7. Why is voxel orientation used as an output of the NIR rather than using more traditional neural SDF approaches that represent scene geometry and can easily be used to compute reflected ray directions?**\n\nDuring the optimization, one can indeed calculate the voxel’s orientation using the voxel opacities. However we found empirically (and as also observed in several papers [1,2]), the orientations inferred from opacities, or via SDF, are noisy during the learning process. These intermediate noisy orientations destabilizes EchoNeRF’s ability to learn the reflections. This is the motivation to explicitly model the orientations per voxel. \n\n[1] Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains\n\n[2] Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields\n\n---\n> **Q8. A brief background section on RF in text would be very helpful for a broad audience like NeurIPS. This could briefly describe at a high level questions, such as how do we interpret the data? Is there a temporal dimension or is it just an intensity image?**\n\nThanks for this suggestion; it makes sense to add a brief review for the wider audience. We will add a background section in the revised version.\n\n---\n> **Q9. In training stage 1, is there any way to filter out pixels that correspond to occlusions and only supervise other pixels?**\n\nWe understand your intuition, however, please note an occluding pixel can be located anywhere along the line joining the Tx and the Rx. For all these possible locations, the received LoS power will be the same, hence the LoS model (in stage 1) does not have a way to pin down the correct occluding pixel. To address this, the second stage training is helping to correctly position the occluding pixel, by optimizing for the occlusion pixel that best explains the reflections. This is why filtering out the occluding pixels is not suitable. This motivates the need for the 2-stage training."}, {"review_id": "A4WH4mTkKt", "reviewer": "Reviewer_fth9", "summary": "EchoNeRF demonstrates that a NeRF-style volumetric model can recover the and predict the 3D indoor structure using only sparse RF power measurements. By introducing the virtual transmitters that can cast power RF beams through a voxel grid and learning per‐voxel reflectivity and density to match line-of-sight and single-bounce multipath signals, the method reconstructs floorplans and accurately forecasts unseen transmitter without any optical inputs. Also, this work clarify the limitation of single stage training - LoS model dominate the training due to the gradient issue and correspondently propose the two-stage training strategies. This work opens the door to camera-free mapping and localization driven by RF multipath.", "questions": "1. The voxel grid and discrete normal angles also impose coarse spatial and angular resolution, and iterating over every voxel (even with orientation pruning) can become expensive as scene size grows. Please clarify the impact of voxel grid density and normal angles discretion. \n\n2. Please provide more details of selection strategies of voxel for the reflection.\n\n3. More ablation study should be included, eg. 1) with and without reflection model and 2) only one stage training versus two-stages training.", "limitations": "1. EchoNeRF models only line-of-sight and first-bounce reflections (≤6 % of total RF power), ignoring higher-order multipath that can dominate in cluttered or non-planar scenes.\n\n2. Its voxel grid and discrete normal sampling yield coarse spatial/angular resolution, and—even with orientation pruning—iterating over all voxels becomes costly as scene size grows.\n\n3. The paper lacks a thorough ablation study isolating the reflection model and comparing single-stage versus two-stage training.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper’s simple yet effective free-space LoS model and its natural extension to first-bounce reflections are well justified.\n\n2. Discretizing voxel orientations offers a clear, efficient way to handle multiple reflections.\n\n3. The two-stage training schedule successfully addresses gradient instability in single-stage methods.\n\nWeakness:\n1. The motivation is vague - what practical, efficiency and cost advantages do RF signals offer over camera-based 3D reconstruction?\n\n2.  The voxel-selection strategy for reflections needs more details. Summing reflected power by iterating over every voxel scale poorly as the voxel count grows. Although the authors accelerate this with discrete orientation angles, further implementation are needed.\n\n3. Lack of ablation study. Experiments isolating the reflection model's impact and comparing single-stage versus two-stage training are needed. \n\n4. Proposed method only models line-of-sight plus first-bounce reflections - which only account for less than 6 % of total RF power - so it ignores high-order multipath that can be substantial in cluttered or non-planar environment.\n\nOverall, the paper is well written and demonstrates a competitive improvement compared to other methods. However, I have several concerns - outlined in the weakness section. Although there are some limitations, the paper still has several commendable aspects. I would vote for a borderline accept, but I may adjust my score depending on the authors' rebuttal and the other reviewers' feedback.", "was_revised": true, "final_justification": "The authors' rebuttal addressed most of my concerns. Based on the feedback from other reviewers, it is evident that this paper is of decent quality, despite some flaws. Therefore, I maintain my original score: borderline accept.", "rebuttal": "We sincerely thank the reviewer for their constructive feedback. Below, we answer some concerns.\n\n---\n> **Q1. The motivation is vague - what practical, efficiency and cost advantages do RF signals offer over camera-based 3D reconstruction?**\n\nWe think there are a number of advantages, and based on your comment, we realize we should add them to the introduction of the paper:\n\n1. Privacy: Using cameras to infer floorplans raise privacy concerns inside homes and offices. Apple’s ARKit (which uses the phone camera or LIDAR to perform localization and mapping at homes) have received pushback from customers. Amazon Alexa has not adopted vision techniques due to privacy. RF based methods learn only the geometry of the environment, without “seeing” the details in rooms. Several companies have expressed enthusiasm to us for RF based imaging solutions.\n2. See through: Extensions of EchoNeRF may be able to do X-ray vision, i.e., infer objects inside an opaque box using RF measurements from outside the box. This can have applications in medical imaging, airport security, or military applications (where a team of soldiers may want to infer the floorplan and people inside an enemy building).\n3. Fewer measurements: The RF modality can serve as an assistance to cameras to reduce the number of measurements. For instance, cameras may be used to image the lobbies and corridors of a hotel, while the RF modality can sense the rooms and un-visited areas. This  lowers the overhead of visiting every location with the camera. \n\nLastly, we are curious about what can be achieved with RF-based NeRFs and perhaps more applications would emerge once such capabilities have matured.\n\n---\n> **Q2. The voxel-selection strategy for reflections needs more details. Summing reflected power by iterating over every voxel scale poorly as the voxel count grows. Although the authors accelerate this with discrete orientation angles, further implementation are needed.**\n\nThanks for understanding our paper correctly and asking this question. We make 2 observations:\n\n1. For each discrete orientation, the manifold of reflection is sparse even in 3D. As a result, the number of optimization variables do not grow too fast. For instance, let’s consider all voxels at $90^\\circ$ orientation, i.e., their surface normal is perpendicular to the horizontal floor. Now, say a Tx and Rx are on the floor and we want to identify which of the $90^\\circ$ voxels above the floor will result in a valid reflection from the Tx to the Rx. For this case, observe that the manifold is the vertical line bisecting Tx and Rx; only voxels on this vertical line are candidates for reflection. Similar manifolds will exist for other discrete orientations.\n2. Yes, even if the manifolds are thin/sparse, they may still add up when number of discrete orientations grow. However, observe that we only consider voxels with high opacities ($\\approx 1$), since they are the ones likely to reflect. Voxels that are transparent are ignored, implying that we are discarding many voxels even on the manifolds. This also helps the optimization.\n\n\n---\n> **Q3. Lack of ablation study. Experiments isolating the reflection model's impact and comparing single-stage versus two-stage training are needed.**\n\nPerhaps this confusion arises from not explaining Fig. 5 in detail.\nObserve that row 4 in Fig. 5 is the output of the LoS model, and row 5 shows the improvements with the reflection model. Row 4 is also the result from the 1st stage of our model (where the LoS model dominates), while row 5 is after completing the full 2-stage training.\n\nIf you are curious about training the whole EchoNeRF model in a single stage, we tried that but the one-stage training did not converge and led to poor results. This prompted us to move to the 2-stage solution.\n\n---\n> **Q4. Proposed method only models line-of-sight plus first-bounce reflections - which only account for less than 6% of total RF power - so it ignores high-order multipath that can be substantial in cluttered or non-planar environment.**\n\nWe should have been clearer here. It’s actually the opposite. The line of sight (LoS) and the first-bounce together makes up 94% of the total power (and 6% is the contribution from all higher order reflections). The reason for this is that higher order reflections travel longer distances and get absorbed by multiple surfaces; hence their power attenuates significantly by the time they reach the receiver.\n\n---\n> **Q5. More ablation study should be included, eg. 1) with and without reflection model and 2) only one stage training versus two-stages training.**\n\nPlease see response to question 3."}]

Author rebuttal:

Meta-review: The paper received positive reviews with scores of 4, 4, 4, 5. Reviewers emphasized the novelty of extending NeRFs to RF multipath signals (myAA, zf7b, ybbR, fth9), the principled two-stage training and reflection modeling (myAA, fth9), the clarity of presentation (zf7b, ybbR), and the strong improvements over prior RF-based NeRF approaches (myAA, ybbR). Concerns about real-world validation, dataset diversity, related work coverage, and ablation details were largely mitigated by additional experiments and clarifications in the rebuttal.

After thoroughly reviewing the paper, the reviews, and the authors’ rebuttal, the AC concurs with the reviewers’ overall positive consensus and therefore recommends the paper for **acceptance**.

For the camera-ready version, the authors should ensure all discussions from the rebuttal are incorporated into the main paper and supplementary materials. The specific changes that need to be implemented are:

**1. Real-world validation and motivation (ybbR, zf7b, fth9)**: Integrate the new noise robustness and material sensitivity experiments, clarify expected SNR ranges, and expand the discussion on practical advantages of RF over camera-based methods (privacy, see-through capability, reduced measurement requirements) .

**2. Related work positioning  (ybbR)**: Add missing citations to multipath NeRF literature (e.g., PlatoNeRF, NeRF-Casting, oRCA) and refine terminology (“vanilla NeRF”).

**3. Experimental clarity (zf7b, fth9)**: Acknowledge the limitations of ZinD, point to HM3D/MVL as future directions, and highlight the role of two-stage training and reflection modeling in the ablations .

**4. Presentation improvements (ybbR, zf7b)**: Revise unclear figures (e.g., Fig. 3 and Fig. 5) and ensure new results from the rebuttal are properly integrated.
Decision: Accept (poster)