CityDeploy-Bench: Benchmarking Physics-Grounded Spatial Set Planning for Multi-Transmitter Network Deployment

Chenyang Yuan; Xiaoyuan Cheng

cs.LGOct 8, 2026

CityDeploy-Bench: Benchmarking Physics-Grounded Spatial Set Planning for Multi-Transmitter Network Deployment

Authors: Chenyang Yuan, Xiaoyuan Cheng

Organizations: University of Sheffield · University College London

Abstract

Automating city-scale wireless deployment remains challenging under complex urban propagation and network-wide interference. We introduce \textbf{CityDeploy-Bench}, a benchmark that reframes multi-transmitter deployment as \emph{physics-grounded spatial set planning} under a unified ray-tracing verifier. The benchmark separates utility representation from planning dynamics, enabling controlled comparison between direct scalar rewards, relational models, and higher-order interaction structures across diverse planners. Our experiments reveal a clear transition in planning behavior as physical coupling grows. Deployment quality becomes increasingly dependent on whether the learned utility captures collective transmitter interactions, whereas stronger search alone cannot compensate for missing relational structure. This establishes multi-transmitter deployment as a coordination problem over physically interacting sets rather than a collection of independent spatial decisions. We release CityDeploy-Data and the benchmark framework as a reproducible testbed for research linking decision learning with physically grounded wireless network design.

Figures & tables

Figure 1: Trafalgar Square illustrates the central challenge of CityDeploy-Bench: effective multi-transmitter deployment requires coordinated decisions across the complete transmitter set under geometry-induced propagation and interference coupling.

Figure 2: Overview of CityDeploy-Bench. (1) Geographic regions are converted into physics-grounded urban scenes. (2) Scene semantics define feasible multi-transmitter deployments. (3) Sionna RT evaluates the complete active transmitter set, accounting for propagation, serving association, and interference. (4) Spatial set planning selects transmitter locations under scene-specific constraints to maximize joint service coverage.

Figure 3: CityDeploy-Data composition. (a) Representative $512\,\mathrm{m}$ urban morphologies. (b) Building and deployable-road fractions across all 60 scenes and three scene scales. (c) Distribution of 54,193 unique deployments by active TX count.

Figure 4: Marginal effect of adding one transmitter. We compare nested deployments $S$ and $S\cup\{p\}$ while retaining all existing TX positions. Left: change in path-loss coverage versus change in JM coverage across matched deployment pairs; density below the horizontal zero line shows cases where serving-link coverage improves while joint service deteriorates. Right: fraction of nested pairs with reduced JM coverage in each held-out scene. Across all 9,320 pairs, 42.44% exhibit a decrease in JM coverage after the additional TX is activated.

Figure 5: Planning quality and random-seed stability. Mean simulator-verified JM coverage is plotted against the mean within-condition standard deviation over five random seeds. Each condition is defined by city, deployment scale, TX cardinality, and utility representation. Several stochastic planners occupy the high-quality, low-variance region, showing that stochastic search does not inherently imply unstable planning.

Utility	Setting	RT (s) $\downarrow$	JM (%) $\uparrow$	PL (%) $\uparrow$	TP (%) $\uparrow$	SINR (%) $\uparrow$	RSRP (%) $\uparrow$
Regressor	Zero-shot	64.82 $\pm$ 1.06	34.76 $\pm$ 3.31	43.28 $\pm$ 4.48	55.62 $\pm$ 4.37	41.54 $\pm$ 3.72	47.31 $\pm$ 4.16
	Few-shot	66.31 $\pm$ 1.42	38.21 $\pm$ 2.76	46.78 $\pm$ 3.71	59.08 $\pm$ 3.56	45.02 $\pm$ 3.08	50.82 $\pm$ 3.43
	Full-pool	66.76 $\pm$ 1.15	39.47 $\pm$ 2.28	48.06 $\pm$ 3.12	60.31 $\pm$ 2.98	46.34 $\pm$ 2.58	52.11 $\pm$ 2.87
Pairwise	Zero-shot	70.18 $\pm$ 1.11	37.64 $\pm$ 2.91	46.21 $\pm$ 4.02	58.46 $\pm$ 3.89	44.37 $\pm$ 3.31	50.18 $\pm$ 3.72
	Few-shot	71.82 $\pm$ 1.53	41.03 $\pm$ 2.38	49.66 $\pm$ 3.31	61.84 $\pm$ 3.17	47.86 $\pm$ 2.74	53.64 $\pm$ 3.03
	Full-pool	72.31 $\pm$ 1.22	42.36 $\pm$ 1.94	50.94 $\pm$ 2.76	63.08 $\pm$ 2.63	49.21 $\pm$ 2.28	54.91 $\pm$ 2.52

Table 2: Target-scene adaptation in a challenging Paris deployment with 12 TXs. We compare zero-shot transfer, few-shot adaptation, and full-pool adaptation for utility models with increasing relational structure. Results are reported as mean

\pm

std. Adaptation consistently improves simulator-verified service, while higher-order relational modeling retains an advantage across all three regimes.

Appendix figures & tables30 assets

Supplementary material from the paper’s appendix.

Appendix

Scene side	Scenes	Master size	Masters/scene	Subsets per master
$128\,\mathrm{m}$	12	2	180	$N=1:2;\ N=2:1$
$256\,\mathrm{m}$	18	4	90	$N=2:6;\ N=3:4;\ N=4:1$
$512\,\mathrm{m}$	30	9	60	$N=5,6,7,8:4\text{ each};\ N=9:1$
Total	60		5,580 families	54,900 memberships

Appendix

Table 3: Deployment family construction. Counts describe the completed dataset. Memberships count appearances in families before deduplication. The final generation uses three blocks of the base master schedule.

Split	Groups	Scenes	$128\,\mathrm{m}$	$256\,\mathrm{m}$	$512\,\mathrm{m}$	Deployments
Training	36	42	8	12	22	38,162
Validation	9	9	2	3	4	8,019
Test	9	9	2	3	4	8,012
Total	54	60	12	18	30	54,193

Appendix

Table 4: Dataset partition. Size columns report numbers of scenes; deployment counts refer to unique records after deduplication.

Quantity	Value
Carrier frequency; system bandwidth $W$	$3.65\,\mathrm{GHz}$ ; $20\,\mathrm{MHz}$
TX power $P_{\mathrm{tx,dBm}}$ ; TX/RX heights	$24\,\mathrm{dBm}$ ; $10/1.5\,\mathrm{m}$
TX/RX antenna	Single element, isotropic, vertical polarization
Receiver noise figure $F_{\mathrm{NF}}$	$7\,\mathrm{dB}$
Subcarrier spacing; resource blocks	$30\,\mathrm{kHz}$ ; 51
Subcarriers per block; SSB power offset $\Delta_{\mathrm{SSB}}$	12; $0\,\mathrm{dB}$

Appendix

Table 5: Fixed radio profile used to construct service labels. Transmit power is per TX; the receiver noise figure is included in the thermal-noise calculation.

Service map	Condition	Interpretation
Path loss	$\mathrm{PL}\leq 106\,\mathrm{dB}$	Serving-link attenuation
SS-RSRP	$\mathrm{SS\text{-}RSRP}\geq-110\,\mathrm{dBm}$	Reference-signal power proxy
SINR	$\mathrm{SINR}\geq 5\,\mathrm{dB}$	Interference and noise tolerance
Effective throughput	$T_{\mathrm{eff}}\geq 10\,\mathrm{Mbps}$	Rate under the fixed resource share

Appendix

Table 6: Service conditions defining

\bm{\tau}

. These are per-cell radio requirements; a target JM coverage is a separate deployment-level requirement.

Component	Reward	IN	NRI	HPEM
Convolution channels	32/64/96	32/64/48	32/64/48	32/64/48
Kernel sizes	5/3/3	5/3/3	5/3/3	5/3/3
Strides	2/2/2	2/2/1	2/2/1	2/2/1
GroupNorm groups	4/8/8	8/8/8	8/8/8	8/8/8
Local / global scene width	96/96	48/96	48/96	48/128
TX embedding width	128	128	128	192

Appendix

Table 7: Saved base-model architectures. Parameter counts include auxiliary heads. IN and NRI share the scene encoder structure but have different relation modules.

Setting	HPEM	Reward / IN / NRI
Learning rate	$3\times 10^{-4}$	$10^{-4}$
Weight decay	$10^{-4}$	$10^{-5}$
Learning-rate schedule	Cosine, period 100, minimum 0	Plateau, factor 0.5, patience 5, minimum $10^{-6}$
Early-stopping patience	Disabled	15 epochs
Checkpoint criterion	Strictly lower total validation loss	Validation MSE improvement $>10^{-5}$
Sampling unit	Family membership	Unique deployment

Appendix

Table 8: Training settings from the saved base runs. HPEM uses a different selection loss and sample weighting from the other predictors.

Planner	Default configuration
Diffusion	100 steps; $M=10$ ; $\beta=1$ ; $\sigma:0.35\rightarrow 0.005$ ; antithetic noise; reflection; deterministic final step
SMC	100 temperatures; $\beta=1$ ; $a=1$ ; $\kappa=0.5$ ; one mutation per temperature; $s:0.45\rightarrow 0.08$
NUTS	50 warmup and 50 retained iterations per chain; $\beta=1$ ; initial step size 0.15; target acceptance 0.8; maximum depth 7; divergence threshold 1,000
BR-SNIS	100 rounds; 32 new uniform proposals per chain and round; $\beta=1$
Greedy	256 candidate locations; one coordinate-replacement round; scoring batches of at most 4,096 deployments
PSO	100 steps; inertia $0.9\rightarrow 0.4$ ; cognitive/social coefficients 1.49618; velocity limit 0.2; global topology

Appendix

Table 9: Reference implementation defaults.

d=2N

is the coordinate dimension. SMC-Gaussian and SMC-Langevin share the annealing settings; only their mutation kernels differ.

Panel of Figure 6 — Figure 6: Urban scene examples in London. Each row covers a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region and shows real-world imagery, the semantic overlay, the building mask, and the TX-deployable mask, from left to right.

Panel of Figure 7 — Figure 7: Urban scene examples in New York. Each row covers a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region and shows real-world imagery, the semantic overlay, the building mask, and the TX-deployable mask, from left to right. The Times Square example shows its southern portion.

Panel of Figure 8 — Figure 8: Urban scene examples in Paris. Each row covers a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region and shows real-world imagery, the semantic overlay, the building mask, and the TX-deployable mask, from left to right. The pixelated patch in the second row is present in the source imagery.

Panel of Figure 9 — Figure 9: Urban scene examples in Shanghai. Each row covers a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region and shows real-world imagery, the semantic overlay, the building mask, and the TX-deployable mask, from left to right.

Panel of Figure 10 — Figure 10: Urban scene examples in Sydney. Each row covers a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region and shows real-world imagery, the semantic overlay, the building mask, and the TX-deployable mask, from left to right.

Panel of Figure 11 — Figure 11: Urban scene examples in Tokyo. Each row covers a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region and shows real-world imagery, the semantic overlay, the building mask, and the TX-deployable mask, from left to right.

Figure 12: Deployment layouts and radio maps for nine HPEM-guided sampling methods in London. The scene is london_01 , with $N_{\mathrm{TX}}=9$ over a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region. All rows use random seed $62$ . Results are individual Sionna-evaluated deployments.

Figure 13: Deployment layouts and radio maps for nine HPEM-guided sampling methods in New York. The scene is new_york_04 , with $N_{\mathrm{TX}}=9$ over a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region. All rows use random seed $62$ . Results are individual Sionna-evaluated deployments.

Figure 14: Deployment layouts and radio maps for nine HPEM-guided sampling methods in Paris. The scene is paris_05 , with $N_{\mathrm{TX}}=9$ over a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region. All rows use random seed $62$ . Results are individual Sionna-evaluated deployments.

Figure 15: Deployment layouts and radio maps for nine HPEM-guided sampling methods in Shanghai. The scene is shanghai_05 , with $N_{\mathrm{TX}}=9$ over a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region. All rows use random seed $62$ . Results are individual Sionna-evaluated deployments.

Figure 16: Deployment layouts and radio maps for nine HPEM-guided sampling methods in Sydney. The scene is sydney_01 , with $N_{\mathrm{TX}}=9$ over a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region. All rows use random seed $62$ . Results are individual Sionna-evaluated deployments.

Figure 17: Deployment layouts and radio maps for nine HPEM-guided sampling methods in Tokyo. The scene is tokyo_03 , with $N_{\mathrm{TX}}=9$ over a $512\,\mathrm{m}\times 512\,\mathrm{m}$ region. All rows use random seed $42$ . Results are individual Sionna-evaluated deployments.

Method	Setting	RT (s) $\downarrow$	JM (%) $\uparrow$	PL (%) $\uparrow$	TP (%) $\uparrow$	SINR (%) $\uparrow$	RSRP (%) $\uparrow$
Diffusion	Zero-shot	21.84 $\pm$ 0.46	54.82 $\pm$ 2.71	63.48 $\pm$ 3.84	72.16 $\pm$ 3.62	60.74 $\pm$ 3.05	66.31 $\pm$ 3.51
	Few-shot	22.67 $\pm$ 0.71	58.06 $\pm$ 2.18	66.82 $\pm$ 3.13	75.41 $\pm$ 2.94	64.11 $\pm$ 2.56	69.72 $\pm$ 2.88
	In-distribution	22.91 $\pm$ 0.53	59.42 $\pm$ 1.82	68.15 $\pm$ 2.67	76.58 $\pm$ 2.46	65.47 $\pm$ 2.17	71.03 $\pm$ 2.39
Pairwise	Zero-shot	24.16 $\pm$ 0.51	57.31 $\pm$ 2.32	65.92 $\pm$ 3.31	74.86 $\pm$ 3.08	63.41 $\pm$ 2.73	68.87 $\pm$ 3.02
	Few-shot	24.88 $\pm$ 0.76	60.68 $\pm$ 1.86	69.28 $\pm$ 2.72	78.12 $\pm$ 2.53	66.82 $\pm$ 2.21	72.16 $\pm$ 2.48
	In-distribution	25.14 $\pm$ 0.57	61.96 $\pm$ 1.54	70.46 $\pm$ 2.28	79.26 $\pm$ 2.08	68.13 $\pm$ 1.88	73.42 $\pm$ 2.05

Appendix

Table 16: Cross-city planning performance under different adaptation regimes in Sydney scene with 4 TXs. We compare zero-shot transfer, few-shot target-city adaptation, and in-distribution evaluation for different relational energy models. Results are reported as mean

\pm

std. Few-shot adaptation substantially narrows the cross-city generalization gap, while in-distribution evaluation provides the strongest overall performance. Higher-order relational modeling consistently improves joint and per-metric coverage at the cost of moderately increased inference time.

Method	Setting	RT (s) $\downarrow$	JM (%) $\uparrow$	PL (%) $\uparrow$	TP (%) $\uparrow$	SINR (%) $\uparrow$	RSRP (%) $\uparrow$
Diffusion	Zero-shot	32.46 $\pm$ 0.68	46.24 $\pm$ 3.08	56.31 $\pm$ 4.22	65.42 $\pm$ 4.01	52.18 $\pm$ 3.47	58.76 $\pm$ 3.91
	Few-shot	33.52 $\pm$ 0.94	49.76 $\pm$ 2.51	59.87 $\pm$ 3.48	68.91 $\pm$ 3.27	55.72 $\pm$ 2.91	62.28 $\pm$ 3.21
	In-distribution	33.86 $\pm$ 0.72	51.04 $\pm$ 2.08	61.16 $\pm$ 2.94	70.13 $\pm$ 2.76	57.08 $\pm$ 2.46	63.61 $\pm$ 2.72
Pairwise	Zero-shot	35.74 $\pm$ 0.73	49.38 $\pm$ 2.67	59.42 $\pm$ 3.76	68.71 $\pm$ 3.51	55.26 $\pm$ 3.08	61.84 $\pm$ 3.42
	Few-shot	36.81 $\pm$ 1.02	52.63 $\pm$ 2.16	62.73 $\pm$ 3.07	71.86 $\pm$ 2.84	58.61 $\pm$ 2.54	65.16 $\pm$ 2.86
	In-distribution	37.18 $\pm$ 0.78	53.84 $\pm$ 1.79	63.96 $\pm$ 2.58	72.98 $\pm$ 2.37	59.87 $\pm$ 2.13	66.42 $\pm$ 2.39

Appendix

Table 17: Cross-city planning performance under different adaptation regimes in Tokyo scene with 6 TXs. We compare zero-shot transfer, few-shot target-city adaptation, and in-distribution evaluation for different relational energy models. Results are reported as mean

\pm

std. As scene complexity increases, absolute joint coverage decreases and the cross-city transfer gap becomes more pronounced. Few-shot adaptation recovers a substantial portion of this gap, while higher-order relational modeling provides consistent gains across adaptation regimes.

Method	Setting	RT (s) $\downarrow$	JM (%) $\uparrow$	PL (%) $\uparrow$	TP (%) $\uparrow$	SINR (%) $\uparrow$	RSRP (%) $\uparrow$
Diffusion	Zero-shot	64.82 $\pm$ 1.06	34.76 $\pm$ 3.31	43.28 $\pm$ 4.48	55.62 $\pm$ 4.37	41.54 $\pm$ 3.72	47.31 $\pm$ 4.16
	Few-shot	66.31 $\pm$ 1.42	38.21 $\pm$ 2.76	46.78 $\pm$ 3.71	59.08 $\pm$ 3.56	45.02 $\pm$ 3.08	50.82 $\pm$ 3.43
	In-distribution	66.76 $\pm$ 1.15	39.47 $\pm$ 2.28	48.06 $\pm$ 3.12	60.31 $\pm$ 2.98	46.34 $\pm$ 2.58	52.11 $\pm$ 2.87
Pairwise	Zero-shot	70.18 $\pm$ 1.11	37.64 $\pm$ 2.91	46.21 $\pm$ 4.02	58.46 $\pm$ 3.89	44.37 $\pm$ 3.31	50.18 $\pm$ 3.72
	Few-shot	71.82 $\pm$ 1.53	41.03 $\pm$ 2.38	49.66 $\pm$ 3.31	61.84 $\pm$ 3.17	47.86 $\pm$ 2.74	53.64 $\pm$ 3.03
	In-distribution	72.31 $\pm$ 1.22	42.36 $\pm$ 1.94	50.94 $\pm$ 2.76	63.08 $\pm$ 2.63	49.21 $\pm$ 2.28	54.91 $\pm$ 2.52

Appendix

Table 18: Cross-city planning performance under different adaptation regimes in Paris scene with 12 TXs. We compare zero-shot transfer, few-shot target-city adaptation, and in-distribution evaluation for different relational energy models. Results are reported as mean

\pm

std. The high-complexity setting exhibits the largest transfer gap and the lowest absolute joint coverage. Few-shot adaptation nevertheless recovers most of the performance lost under zero-shot transfer, and higher-order relational modeling remains beneficial across all three adaptation regimes.

Target JM (%)	Method	Setting	Req. TXs $\downarrow$	SR (%) $\uparrow$	Best JM (%) $\uparrow$	RT (s) $\downarrow$
45	Diffusion	Zero-shot	6.42 $\pm$ 0.79	83.33	46.58 $\pm$ 1.72	61.84 $\pm$ 7.48
		Few-shot	5.58 $\pm$ 0.67	91.67	48.31 $\pm$ 1.36	63.12 $\pm$ 7.86
		In-distribution	5.17 $\pm$ 0.58	100.00	49.26 $\pm$ 1.12	63.76 $\pm$ 7.31
	Pairwise	Zero-shot	5.83 $\pm$ 0.72	91.67	48.02 $\pm$ 1.49	68.31 $\pm$ 8.12
		Few-shot	5.00 $\pm$ 0.60	100.00	49.86 $\pm$ 1.21	69.74 $\pm$ 8.46
		In-distribution	4.67 $\pm$ 0.49	100.00	50.78 $\pm$ 0.98	70.28 $\pm$ 7.92

Appendix

Table 19: Cross-city target-coverage planning under different adaptation regimes in New York scene. We compare zero-shot transfer, few-shot target-city adaptation, and in-distribution evaluation for increasingly expressive relational energy models. Results are reported as mean

\pm

std over 12 independent trials. Higher target joint coverage requires more TXs and longer planning time. Few-shot adaptation substantially reduces the cross-city transfer gap, while in-distribution evaluation achieves the strongest overall performance.

Target JM (%)	Method	Setting	Req. TXs $\downarrow$	SR (%) $\uparrow$	Best JM (%) $\uparrow$	RT (s) $\downarrow$
35	Diffusion	Zero-shot	7.17 $\pm$ 0.72	75.00	35.92 $\pm$ 1.69	72.16 $\pm$ 8.84
		Few-shot	6.25 $\pm$ 0.62	91.67	37.68 $\pm$ 1.38	73.72 $\pm$ 9.18
		In-distribution	5.83 $\pm$ 0.58	100.00	38.62 $\pm$ 1.15	74.35 $\pm$ 8.57
	Pairwise	Zero-shot	6.50 $\pm$ 0.67	83.33	37.21 $\pm$ 1.51	79.64 $\pm$ 9.36
		Few-shot	5.58 $\pm$ 0.51	100.00	39.17 $\pm$ 1.22	81.26 $\pm$ 9.74
		In-distribution	5.17 $\pm$ 0.39	100.00	40.08 $\pm$ 1.01	81.91 $\pm$ 9.02

Appendix

Table 20: Cross-city target-coverage planning under different adaptation regimes in London scene. We compare zero-shot transfer, few-shot target-city adaptation, and in-distribution evaluation for increasingly expressive relational energy models. Results are reported as mean

\pm

std over 12 independent trials. Compared with the easy scene, higher deployment complexity leads to lower success rates and a larger number of required TXs, particularly at aggressive coverage targets.

Target JM (%)	Method	Setting	Req. TXs $\downarrow$	SR (%) $\uparrow$	Best JM (%) $\uparrow$	RT (s) $\downarrow$
25	Diffusion	Zero-shot	7.92 $\pm$ 0.79	66.67	25.84 $\pm$ 1.78	89.73 $\pm$ 10.86
		Few-shot	6.92 $\pm$ 0.67	83.33	27.62 $\pm$ 1.43	91.64 $\pm$ 11.24
		In-distribution	6.42 $\pm$ 0.51	91.67	28.51 $\pm$ 1.19	92.48 $\pm$ 10.52
	Pairwise	Zero-shot	7.25 $\pm$ 0.75	75.00	27.14 $\pm$ 1.59	98.16 $\pm$ 11.73
		Few-shot	6.25 $\pm$ 0.62	91.67	29.04 $\pm$ 1.23	100.27 $\pm$ 12.14
		In-distribution	5.83 $\pm$ 0.58	100.00	30.02 $\pm$ 1.01	101.14 $\pm$ 11.32

Appendix

Table 21: Cross-city target-coverage planning under different adaptation regimes in Shanghai scene. We compare zero-shot transfer, few-shot target-city adaptation, and in-distribution evaluation for increasingly expressive relational energy models. Results are reported as mean

\pm

std over 12 independent trials. The high-complexity scene exhibits the largest transfer gap and the strongest degradation in success rate at demanding target coverage levels. Few-shot adaptation recovers a substantial fraction of the lost performance, while higher-order relational models remain consistently advantageous.

Hidden	Hyper	Runtime (s)	Joint (%)	Pathloss (%)	Throughput (%)	SINR (%)	RSRP (%)
64	128	$1.08\pm 0.13$	$20.58\pm 3.48$	$20.91\pm 3.32$	$34.83\pm 5.00$	$33.61\pm 5.20$	$29.70\pm 4.39$
128	128	$1.08\pm 0.14$	$19.75\pm 3.81$	$20.03\pm 3.79$	$33.36\pm 4.27$	$32.21\pm 4.27$	$28.59\pm 3.88$
256	64	$1.09\pm 0.11$	$\mathbf{17.52\pm 1.69}$	$\mathbf{18.58\pm 2.28}$	$\mathbf{27.70\pm 1.75}$	$\mathbf{25.88\pm 1.84}$	$\mathbf{24.22\pm 1.77}$
256	128	$1.09\pm 0.10$	$18.55\pm 2.92$	$19.51\pm 2.55$	$29.76\pm 4.28$	$28.14\pm 5.02$	$25.80\pm 3.52$
256	256	$1.05\pm 0.09$	$19.05\pm 2.83$	$19.58\pm 2.26$	$31.07\pm 3.83$	$29.70\pm 4.60$	$26.48\pm 3.29$

Appendix

Table 22: Potential-model capacity ablation. Coverage prediction errors under different hidden and hypernetwork dimensions. Values are reported as mean

\pm

standard deviation; lower prediction error is better.

Inference Budget		Maximum Interaction Order
Particles	Steps	Unary	Pairwise	3rd-Order	4th-Order
10	20	38.90	40.15	41.47	42.82
	40	39.62	40.91	42.28	43.67
	60	40.18	41.52	42.94	44.40
	80	40.52	41.89	43.35	44.84
	100	40.68	42.08	43.55	45.06

Appendix

Table 23: Interaction order and inference-budget ablation. Simulator-verified JM coverage (%) under different maximum interaction orders, particle populations, and sampling steps. All settings use the same planning protocol on the New York scene with

N=3

TXs.

Figure 18: Service trade-offs under increasing TX cardinality. Each point aggregates six cities, nine planners, four utility representations, and five random seeds. Additional TXs improve serving-link coverage, while the resulting SINR and JM behavior depends on the balance between coverage gain and co-channel interference at each deployment scale.

Figure 19: Sensitivity of planning quality to utility representation. Each cell reports the mean change in simulator-verified JM coverage (percentage points) when HPEM is replaced by the pooled Regressor, IN, or NRI under the same planner. Results are averaged over five random seeds. Positive values favor the alternative representation; negative values favor HPEM.

Figure 20: Quality–efficiency trade-off across planning methods. The horizontal axis reports median planning time on a logarithmic scale and the vertical axis reports mean simulator-verified JM coverage. Results aggregate six cities, four utility representations, and five random seeds for representative deployment regimes. Dashed curves connect the empirical Pareto-optimal methods.

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Learning Coverage- and Power-Optimal Transmitter Placement from City Maps: A Comparative Study of Direct and Indirect Neural Approaches

Çağkan Yapar

Wireless Communications Multi-Objective Optimization

Open paper AskPDF arXiv

Optimal wireless transmitter placement is a central task in radio-network planning, and exhaustive search becomes prohibitively expensive at scale. This paper studies the single-transmitter setting under a learned propagation model, enabling exhaustive per-pixel assessment at scale in a regime where measurement-based labeling is infeasible and ray-tracing-based labeling is computationally out of reach. We introduce a dataset of 167525 urban scenarios (RadioMapSeer-Deployment) with dual ground-truth labels for coverage-optimal and power-optimal transmitter locations. Benchmark analysis reveals an asymmetric coverage-power trade-off: coverage-optimal placement sacrifices 13.86% of received-power, whereas power-optimal placement sacrifices 5.50% of coverage; the best balanced placement lies at

\bar{d}=2.60

from the ideal point (100%,100%). We evaluate two learning formulations: indirect heatmap-based models predicting received-power radio maps, and direct score-map models predicting the objective landscape over feasible transmitter locations. Within the heatmap family, discriminative models deliver one-shot predictions 1350-2400

\times

faster than exhaustive search, while diffusion models additionally support multi-sample inference that improves single-objective performance and, by reusing the same sample pool under a balanced criterion, recovers strong balanced placements without explicit multi-objective training. Dual score-map strategies combining power and coverage score-maps match the exhaustive balanced optimum (

\bar{d}=2.60

) and remain close to it across smaller candidate budgets, at 14-22

\times

speedups including the cost of evaluating shortlisted candidates. Dual score-map methods are strongest overall, whereas heatmap formulations remain attractive for their physically meaningful intermediate maps and, in the diffusion setting, for inference-time search.

Abstract

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