Geometry-Aided Channel Deduction with Partial Channel Estimates and Uncalibrated Digital Twin

Hongning Ruan; Zhaoyang Zhang; Zirui Chen; Ziqing Xing; Zhaohui Yang; Mérouane Debbah

eess.SPSep 29, 2026

Geometry-Aided Channel Deduction with Partial Channel Estimates and Uncalibrated Digital Twin

Authors: Hongning Ruan, Zhaoyang Zhang, Zirui Chen, Ziqing Xing, Zhaohui Yang, Mérouane Debbah

Organizations: College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China · Zhejiang Provincial Laboratory of Multi-Modal Communication Networks and Intelligent Information Processing, Hangzhou 310027, China · Institute of Fundamental and Transdisciplinary Research, Zhejiang University, Hangzhou 310058, China · Research Institute for Digital Future, Khalifa University, 127788 Abu Dhabi, UAE

Abstract

The acquisition of high-dimensional channel state information (CSI) in wireless MIMO-OFDM communications usually requires high pilot overhead, or relies on accurate and complete positional or environmental information. In this paper, we propose a geometry-aided channel deduction (GCD) approach, which utilizes an uncalibrated digital twin (DT) with only approximate environmental geometry and positions to assist the channel acquisition. The key rationale behind is that, even imprecise geometric information, which can be easily obtained in advance through radio sensing technologies or existing geographic databases, provides certain structural features about the current channel; meanwhile, the coarse instantaneous channel estimates using only a small amount of pilots provide dedicated information that aligns with the channel structure and further compensates for the geometry inaccuracy and other channel unknowns. To this end, we first extract geometric features from the DT, which contain only simple structural information of the channel. Then we propose random prompt augmentation, a novel method to generate an appropriate prompt that converts geometric multi-path structure into a CSI-like representation while suppressing the disturbance of other unknown channel parameters. The prompt is then fused with the pilot-based instantaneous channel estimate via a channel deduction network. To further enhance the network's versatility, we incorporate pilot configurations into the existing learning architecture to support variable pilot patterns. Comprehensive experiments validate the superiority of the proposed method, which demonstrates high channel acquisition quality, low pilot overhead, and strong robustness. Furthermore, the structural prompt also serves as scenario-related context, enabling our approach to generalize well in new scenarios.

Figures & tables

Category	Auxiliary information	Low pilot overhead	Robustness to inaccurate information	No error propagation	Cross-scenario generalization capability	Low data collection cost	Related works
Pilot-based channel estimation (pilot only)	None		✓	✓	✓	✓	[ 9 , 10 , 11 , 12 , 13 , 14 , 15 ]
Pilot-free channel prediction (auxiliary information only)	Past channels	✓			✓	✓	[ 16 , 17 ]
	Position	✓		✓		✓	[ 18 , 19 ]
	Real-time sensing	✓		✓	✓		[ 20 ]
	Radio environment	✓		✓			[ 21 , 22 , 23 , 24 , 25 , 26 ]
Hybrid channel acquisition (pilot & auxiliary information)	Past channels	✓	✓		✓	✓	[ 27 ]

TABLE I : Comparison of relevant works on channel acquisition.

Fig. 1 : Overview of the proposed channel acquisition framework.

Fig. 2 : (a) Detailed diagram of the proposed framework. (b) Comparison of the original pre-mapping module in [ 27 ] and the proposed pre-mapping module.

Fig. 3 : Specific structures of the modules used in the channel deduction network. The plus sign “+” denotes residual connection, and “C” denotes concatenation.

Fig. 4 : Satellite images of the four cities.

Fig. 5 : Environmental maps of the 12 scenarios.

Setting	Interval	Start
FRFS	$R_{\rm t}=4$	$S_{\rm t}=1$
FRFS	$R_{\rm c}=16$	$S_{\rm c}=1$
FRVS	$R_{\rm t}=4$	$S_{\rm t}\in\{1,2,\cdots,R_{\rm t}\}$
FRVS	$R_{\rm c}=16$	$S_{\rm c}\in\{1,2,\cdots,R_{\rm c}\}$
VRVS	$R_{\rm t}\in\{2,4,8\}$	$S_{\rm t}\in\{1,2,\cdots,R_{\rm t}\}$
VRVS	$R_{\rm c}\in\{4,8,16,32,64\}$	$S_{\rm c}\in\{1,2,\cdots,R_{\rm c}\}$

TABLE II : Different settings of pilot patterns.

Scheme	Network Module	Paremeter settings
(m)GCDNet	(m)CMixer	$K=3$ , $N_{\rm t}^{\prime}=N_{\rm t}$ , $N_{\rm c}^{\prime}=N_{\rm c}$
(m)GCDNet	Transformer Encoder	$L=6$ , $D=512$
(m)PCMixer	CMixer	$\widetilde{K}=8$ , $N_{\rm t}^{\prime}=N_{\rm t}$ , $N_{\rm c}^{\prime}=N_{\rm c}$
(m)PCMixer	ResMLP	$\widetilde{L}=6$ , $D=512$
(m)CMixer	-	$\widetilde{K}=8$ , $N_{\rm t}^{\prime}=N_{\rm t}$ , $N_{\rm c}^{\prime}=N_{\rm c}$

TABLE III : Settings of network structure parameters.

Scheme	Mask-free		Mask-enhanced
Scheme	Parameters	FLOPs	Parameters	FLOPs
(m)GCDNet	21.85 M	610.76 M	24.73 M	708.48 M
(m)PCMixer	15.33 M	182.38 M	21.56 M	194.83 M
(m)CMixer	4.51 M	152.84 M	10.69 M	362.21 M
(m)PCMixer-L	43.27 M	1.25 G	55.72 M	1.27 G
(m)CMixer-L	17.44 M	1.16 G	40.32 M	2.69 G

TABLE IV : Number of parameters and FLOPs of networks in different schemes, evaluated under

R_{\rm t}=4

R_{\rm c}=16

Fig. 6 : NMSE performance with networks trained under different pilot pattern settings. In the box plots, the boxes extend from the first quartile (Q1) to the third quartile (Q3) with a line at the median, and the whiskers extend from the 10th percentile to the 90th percentile. (a) NMSE box plot of mask-free schemes. (b) NMSE box plot of mask-enhanced schemes. (c) Median NMSE of mask-enhanced schemes under different noise conditions.

Scheme	FRFS				FRVS				VRVS
	NMSE (dB)		$\rho$		NMSE (dB)		$\rho$		NMSE (dB)		$\rho$
	Mean	Median	Mean	Median	Mean	Median	Mean	Median	Mean	Median	Mean	Median
mGCDNet	-8.60	-14.45	0.9412	0.9854	-9.95	-17.46	0.9614	0.9940	-9.69	-16.37	0.9602	0.9924
mPCMixer	-11.98	-16.65	0.9712	0.9903	-9.29	-14.68	0.9550	0.9876	-7.53	-12.01	0.9359	0.9801
mCMixer	-1.17	-1.47	0.6001	0.7424	-6.18	-12.24	0.9034	0.9805	-6.77	-12.45	0.9061	0.9825
mPCMixer-L	-12.97	-18.47	0.9782	0.9944	-8.85	-13.67	0.9518	0.9857	-6.44	-9.67	0.9264	0.9700

TABLE V : NMSE and

\rho

performance with networks trained under different pilot pattern settings.

Fig. 7 : NMSE performance under different pilot intervals. (a) Median NMSE under various groups of $(R_{\rm t},R_{\rm c})$ . (b)-(d) Cumulative probability distribution of NMSE with $(R_{\rm t},R_{\rm c})\in\{(8,64),(4,16),(2,4)\}$ . (e)-(g) Median NMSE under different noise conditions with $(R_{\rm t},R_{\rm c})\in\{(8,64),(4,16),(2,4)\}$ .

Scheme	$R_{\rm t}=8$ , $R_{\rm c}=64$				$R_{\rm t}=4$ , $R_{\rm c}=16$				$R_{\rm t}=2$ , $R_{\rm c}=4$
	NMSE (dB)		$\rho$		NMSE (dB)		$\rho$		NMSE (dB)		$\rho$
	Mean	Median	Mean	Median	Mean	Median	Mean	Median	Mean	Median	Mean	Median
mGCDNet	-7.70	-12.90	0.9437	0.9857	-9.69	-16.37	0.9602	0.9924	-10.43	-17.36	0.9643	0.9938
mPCMixer	-5.59	-9.18	0.9143	0.9694	-7.53	-12.01	0.9359	0.9801	-8.48	-12.79	0.9424	0.9819
mCMixer	-1.91	-4.28	0.6987	0.8982	-6.77	-12.45	0.9061	0.9825	-9.47	-14.82	0.9492	0.9890
DMPS	-0.01	-0.01	0.2418	0.1584	-0.12	-0.12	0.3619	0.3499	-1.32	-7.87	0.6611	0.9518

TABLE VI : NMSE and

\rho

performance under various pilot intervals.

Fig. 8 : Impact of prompt length (i.e., the number of neighboring samples) and position error. (a) Median NMSE under different numbers of neighboring samples. (b) Median NMSE under different scales of user position errors.

Fig. 9 : NMSE performance in multi-scenario learning. (a) NMSE box plots in learned scenarios. (b) NMSE box plots in unseen scenarios without additional training.

Scenario	Scheme	NMSE (dB)		$\rho$
Scenario	Scheme	Mean	Median	Mean	Median
San Francisco BS 1	mGCDNet	-11.48	-19.08	0.9678	0.9955
	mPCMixer	-9.59	-15.61	0.9515	0.9908
	mCMixer	-5.29	-12.84	0.8505	0.9820
Singapore BS 1	mGCDNet	-8.28	-13.64	0.9298	0.9859
	mPCMixer	0.31	0.09	0.1828	0.0944

TABLE VII : NMSE and

\rho

performance in two example scenarios.

Fig. 10 : AAR performance under different BS transmit power values. (a) Mean AAR in a learned scenario. (b) Mean AAR in an unseen scenario.

Fig. 11 : Experiments on non-ideal environmental geometry. (a) Example cases of the environmental map. (b) NMSE box plot of mGCDNet in various cases.

Fig. 12 : NMSE performance of mGCDNet under BS/user position errors and imperfect ray tracing results, where the median NMSE and quartiles are presented. (a)-(b) NMSE under different scales of user/BS position errors. (c) NMSE under different limits of path number. (d) NMSE under different limits of path depths.

Fig. 13 : NMSE performance after finetuning in the new scenario Singapore BS 1. (a) NMSE in the new scenario. (b) NMSE in a previous scenario.

Scenario		Frequency	Bandwidth	BS antenna
San Francisco	BS 1	5 GHz	40 MHz	$1\times 16$	Short dipole
	BS 2	3.5 GHz	20 MHz	$1\times 16$	Short dipole
	BS 3	5 GHz	20 MHz	$4\times 4$	$\lambda/2$ dipole
Shanghai	BS 1	6.7 GHz	50 MHz	$2\times 8$	Isotropic
	BS 2	2.4 GHz	20 MHz	$2\times 8$	TR 38.901
	BS 3	5.9 GHz	46 MHz	$4\times 4$	TR 38.901

TABLE VIII : System configurations of different scenarios.

Fig. 14 : NMSE performance in multi-scenario learning. (a) NMSE box plots in learned scenarios. (b) NMSE box plots in unseen scenarios without additional training.

Scenario	Scheme	NMSE (dB)		$\rho$
Scenario	Scheme	Mean	Median	Mean	Median
San Francisco BS 1	mGCDNet	-9.75	-16.30	0.9568	0.9924
	mPCMixer	-7.70	-14.05	0.9291	0.9876
	mCMixer	-5.44	-11.49	0.8576	0.9772
Singapore BS 1	mGCDNet	-8.14	-11.74	0.9399	0.9815
	mPCMixer	0.50	0.12	0.1579	0.1030

TABLE IX : NMSE and

\rho

performance in three example scenarios.

Fig. 15 : Experiments on ASU Campus. (a) Satellite image of the scenario. (b) Mean AAR under different BS transmit power values.

Fig. 16 : Single-scenario learning performance of schemes with different prompt designs. (a) Cumulative probability distribution of NMSE. (b) Median NMSE under different prompt lengths.

Fig. 17 : NMSE performance of schemes with different prompt designs in multi-scenario learning. (a) NMSE box plots in learned scenarios. (b) NMSE box plots in unseen scenarios without additional training.

Fig. 18 : Impact of prompt length on NMSE performance of schemes with different prompt designs. (a) Median NMSE in a learned scenario. (b) Median NMSE in an unseen scenario.

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