A Deep Learning Framework for Evaluating the Over-the-Air Performance of the Antenna in Mobile Terminals

Abstract

This study introduces RTEEMF (Real-Time Evaluation Electromagnetic Field)-PhoneAnts, a novel Deep Learning (DL) framework for the efficient evaluation of mobile phone antenna performance, addressing the time-consuming nature of traditional full-wave numerical simulations. The DL model, built on convolutional neural networks, uses the Near-field Electromagnetic Field (NEMF) distribution of a mobile phone antenna in free space to predict the Effective Isotropic Radiated Power (EIRP), Total Radiated Power (TRP), and Specific Absorption Rate (SAR) across various configurations. By converting antenna features and internal mobile phone components into near-field EMF distributions within a Huygens’ box, the model simplifies its input. A dataset of 7000 mobile phone models was used for training and evaluation. The model’s accuracy is validated using the Wilcoxon Signed Rank Test (WSR) for SAR and TRP, and the Feature Selection Validation Method (FSV) for EIRP. The proposed model achieves remarkable computational efficiency, approximately 2000-fold faster than full-wave simulations, and demonstrates generalization capabilities for different antenna types, various frequencies, and antenna positions. This makes it a valuable tool for practical research and development (R&D), offering a promising alternative to traditional electromagnetic field simulations. The study is publicly available on GitHub for further development and customization. Engineers can customize the model using their own datasets.

1. Introduction

Rapid and accurate assessment of the radiation performance and electromagnetic safety of mobile phones is crucial for RF antenna development and optimization. Traditional assessment methods employ full-wave numerical simulations for each R&D scenario, adhering to CTIA and IEC/IEEE requirements for over-the-air (OTA) and SAR evaluation [1,2,3,4]. The simulations need to employ the detailed Computer-Aided Design (CAD) models of the mobile phones with a commercial software package running on accelerated hardware. In most cases, simulations were conducted to select the appropriate antenna based on its performance within the device.

Nevertheless, this approach presents several challenges. First, the repetitive simulation of mobile phones is a time-consuming task. Evaluating the performance per frequency band should cover eleven configurations, including seven configurations for OTA (phone in free space; and both left and right ears in “cheek”, “data” mode, and “talk” mode) and four configurations for SAR (both left and right ears in “cheek” and “tilt”). Among them, ten configurations integrate the models of mobile phones, head, and hand in the numerical experiments. The calculation volume commonly comprises 10 M–200 M voxels, depending on the uniform or heterogeneous discretization strategy. A single simulation could take dozens of minutes depending on the acceleration hardware. The total time required for simulating all the possible configurations/frequencies can be enormous. Second, the preparation of the simulation scenarios is very labor-consuming. The standard rigorously defines the relative positioning of the mobile phone with the hand and head phantoms. Each joint of the hand phantom must deform precisely to achieve a correct holding posture, preventing any overlap between the hand and the device [5]. The manipulation can take up to ten hours with a specialized operator.

The aforementioned analysis necessitates reducing the number of numerical simulations in R&D, and/or reducing computational complexity for the individual simulation [6,7]. In this context, surrogate modeling has been applied in estimating the S11 of the antenna [8]. The method entails the generation of training instances (simulated results) through sampling within the parameter space (of the antenna’s geometry). As such, the relationship between the antenna dimensions and the S11 of the antenna was statistically regressed by polynomial expressions. This may indicate that the performance of the antenna can be theoretically predicted using the established model, thus eliminating the need for numerical simulations. The disadvantage is the curse of dimensionality, which may demand a large number of simulations for regressing the surrogate model. With the widespread application of DL techniques across diverse fields [9], their role in antenna design, optimization, and performance evaluation has emerged as a primary research interest [10]. The S parameters and the OTA results of the individual antenna (without the handset) have been estimated accurately. These studies suggest that we could take a step further by estimating the performance of the antenna using the end-to-end approach, to save computation time while reducing the number of simulations.

In practice, as the structure, geometry, and material of the specific antenna vary significantly, it is difficult to combine this information as the input for the DL models. The principle of the equivalent source (Huygens’ box [11]) could be a feasible approach. In such a case, we calculate the electric and magnetic current distribution induced by the antenna on a closed surface using the full-wave algorithm. The reconstructed electric and magnetic currents are then used as equivalent sources for EIRP and SAR evaluation [12]. It is demonstrated that the accuracy depends on the spatial resolution of the Huygens’ box. Specifically, the relative error of the calculation is less than 1% when the spatial resolution is less than 1/30 of the wavelength [13]. Therefore, the inputs to the DL model can be standardized by converting the geometry of the antennas into electromagnetic field (EMF) distributions on a Huygens’ box.

In the study, we proposed a DL framework for estimating the performance of the antenna installed on a mobile terminal. The model examines the near-field EMF distribution of a mobile phone antenna in free space (FS) and predicts EIRP and SAR for various configurations. To demonstrate the generalization of the proposed model, six types of commonly used patch antenna models [14] are positioned within a 6.1-inch mobile phone for evaluation. The DL network is trained with the simulated data of EIRP, TRP, and SAR across various configurations, resulting in a dataset of 7000 samples. The consistency of the results from the DL model and the full-wave simulation is demonstrated in the work.

The key contributions of this study are:

• The proposed framework introduces a novel antenna performance prediction model, which can be used for preliminary assessment of SAR and EIRP while reducing the number of repetitive simulations with commercial software on the specialized computational platform;
• The study converts the features of the antenna and the internal components of the mobile phone into a near-field EMF distribution on the Huygens’ box, which simplifies the input of the DL model;
• A DL model based on the divide-and-conquer method [15] is proposed. It divides the estimation for SAR and EIRP into eight modules, reducing the training complexity and enhancing the convergence rate;
• The Wilcoxon Signed Rank (WSR) test [16] for assessing SAR and TRP accuracy is developed. The Feature Selection Validation (FSV) [17] method is employed to evaluate EIRP accuracy. These methods provide a comprehensive understanding of the performance of the antenna.

2. The Proposed Method

2.1. The Workflow of the Proposed Method

This study introduces an evaluation framework (RTEEMF-PhoneAnts) built upon convolutional neural networks. The operating frequency and Near Electromagnetic Field (NEMF) data of the mobile phone in FS serve as inputs for the model. Subsequently, the model predicts multiple performance metrics, including SAR, EIRP, and TRP for various configurations as required by [1,2,3,4]. The workflow is depicted in Figure 1.

Initially, an antenna database is developed, containing multiple patch antennas inserted into a simplified mobile phone model to simulate various of phone antenna configurations. Eleven configurations are established in accordance with [1,2,3,4]. Seven configurations are designated for EIRP and TRP evaluation, including:

• A phone in FS;
• A phone mounted in the “cheek” position on the head phantom (this includes the “cheek” position for both the left and right ears);
• PDA (Personal Digital Assistant) grip in “data” mode (for both the left and right hand);
• “Talk” mode (which includes configurations for the left and right head and hand).
• Additionally, four SAR evaluation configurations are created, including:
• The cheek (left and right) positions of the phone against the Specific Anthropomorphic Mannequin (SAM) phantom;
• Tilt (left and right) positions of the phone against the SAM phantom.

The positioning of the mobile phones relative to the SAM and hand phantoms strictly adheres to the requirements outlined in [1,2,3,4]. Subsequently, the Finite Difference Time Domain (FDTD) method is employed to evaluate the NEMF distribution for a phone in FS, as well as the EIRP, TRP, and SARs with a phone in these configurations. Following this, a dataset is generated containing the frequency, NEMF, EIRP, TRP, and SARs for use in model training and testing.

Secondly, a real-time antenna performance prediction model is developed and trained using the generated dataset. In this step, the mobile phone’s NEMF in FS serves as an input. Its distribution characteristics reflect the antenna’s radiation characteristics at the operating frequency as well as the influence of the mobile phone’s components on the antenna. The WSR test and FSV method are utilized to evaluate the model’s accuracy.

During practical R&D, the engineer simply calculates the NEMF for a new antenna in FS through numerical simulations. The NEMF and the operating frequency are input into the model, which then predicts the SARs for four configurations, and the EIRP and TRP for seven configurations. In this phase, there is no need to reconstruct simulation scenarios by precisely positioning the phone and manipulating the fingers as per [1,2,3,4], thereby further enhancing the evaluation efficiency.

2.2. RTEEMF-PhoneAnts Architecture

The proposed model (RTEEMF-PhoneAnts) for predicting mobile phone antenna performance is depicted in Figure 2.

The model uses the NEMF of the mobile phone in free space and the operating frequency as inputs. A feature vector is extracted from the NEMF through a max pooling layer, multiple convolutional layers, and shortcut connections. Subsequently, the frequency is appended to the feature vector. To reduce the complexity of model training and accelerate the convergence, the divide-and-conquer method is introduced to process the SAR and EIRP estimation for eight modules. Each of them is constructed by three fully connected layers.

In the SAR prediction module, the Whole-Body Average SARs (WBSARs), the averaged peak SAR in 1 g and 10 g (SAR-1g and SAR-10g) tissue for four distinct scenarios, are output. The length of the output vector for the SAR prediction module is 1 × 12. The EIRP for seven scenarios is predicted using the prediction modules. Specifically, the EIRP prediction module provides output vectors with a resolution of 5° for both elevation angle (θ) and azimuth angle (ϕ). Consequently, the output vector length for the EIRP prediction module is 2592. TRP is computed from EIRP by

$$\mathrm{TRP}={\displaystyle \frac{1}{4\pi }}{{\displaystyle \int }}_0^{2\pi }{{\displaystyle \int }}_0^{\pi }\mathrm{EIRP}\left(\theta ,\varphi \right)sin\theta d\theta d\varphi .$$

(1)

3. Experiment Configurations

3.1. Dataset Generation

The study investigated six prevalent antenna types, covering the widely used bands from 2G to 5G wireless technology [14] (Figure 3). They are the most commonly used antenna types, including inverted-F antennas (IFAs) and printed IFAs (PIFAs) [18,19], monopole antennas [20] and monopole slot antennas [21], and loop antennas [22]. Among them, the PIFA and monopole are the most commonly used antenna types in mobile phones [23]. Comprehensive information about these antenna types is available in [18,19,20,21,22,23]. The operating principles of these antennas are well documented in [24,25].

For Ant. 1, Ant. 4, and Ant. 6, there are some overlaps in the frequency bands encompassed by antennas of various sizes, which are included to enrich the dataset. The parameters for Ant. 1–6 can be adjusted according to the methods described in [22,26,27,28].

A simplified 6.1-inch mobile phone model measuring 71.5 mm in width, 147.5 mm in length, and 7.85 mm in thickness, and consisting of eight components, is utilized (Figure 4a). Each antenna is positioned at various locations within the phone to simulate diverse antenna arrangements typical of real phones [14]. The top and bottom antennas are adjusted along the x and y axes in 1 mm increments, covering an area of 70 × 25 mm², respectively. The side antenna is relocated along the x and y axes in 1 mm increments over an area of 146 × 20 mm², respectively (Figure 4b). The distance between the antenna patch and the back cover remains fixed at 0.5 mm. Using Antenna Type Ant. 1 as an illustrative example, we selected ten antennas of varying dimensions within the Ant1 type. For each antenna, positions were sampled following the previously described position adjustment method. Ultimately, we sampled 240 distinct positions for each of the ten antennas (the number of sampling positions varied based on antenna structure and size). This process resulted in the creation of 2400 mobile phone models under the Ant1 type (

Table 1. Operating frequencies supported by the antennas used in the study.

fre (MHz)	Bands	Ant.
		1	2	3	4	5	6
850	GSM850,WCDMA	√	√	√	√	√	√
900	GSM900,UMTS900	√	√	√	√	√	√
1800	GSM1800, WCDMA,FDD-LTE	√	√	√	√	√	√
1900	GSM1900,TD-SCDMA,TDD-LTE	√	√	√	√	√	√
2000	TD-SCDMA	√	√		√	√	√
2100	WCDMA,CDMA2000	√	√	√	√	√	√
2600	TDD-LTE	√			√		√
Number of antennas		10	1	1	7	1	14
Number of samples		2400	200	220	1600	180	2400

The symbol “√” indicates that the corresponding antenna supports the specified operating frequency band.

). Ultimately, 7000 mobile phone models featuring various antenna configurations were produced.

The simulation is conducted using SEMCAD V19.2 (SPEAG AG, Zurich, Switzerland), employing the FDTD algorithm. Adaptive non-uniform grids are utilized to preserve antenna details in the discretization process. The maximum grid step size is set at 2 mm, with a non-uniform edge ratio maintained at no more than 1.2. The calculations were performed over 30 periods. Dielectric parameters, from references [1,4], are applied to the SAM and hand phantoms. When the phone is in FS, a Huygens’ box measuring 72 × 148 × 7.9 mm³ surrounding the phone is established to record the NEMF. The results were generated and exported for the NEMF in FS (complex (which include magnitude and phase) vector field $E_x,E_y,E_z$ and $H_x,H_y,H_z$ with a spatial interval of 0.5 × 0.5 × 0.1 mm³), as well as the SARs (WBSAR, SAR-1g, SAR-10g), TRP, and EIRP (angular resolution of 5°) in various configurations. All simulation results have been normalized to a 1 W input power.

The numerical simulations for EMF were conducted using a workstation with two Intel Xeon Gold 6230 CPUs (Intel, Santa Clara, USA) @ 2.1 GHz, 64 GB RAM, and two Quadro P5000 GPUs (NVIDIA, Santa Clara, USA; 32 GB memory on board).

3.2. Data Preprocessing for RTEEMF-PhoneAnts

The normalization and standardization methods are employed to enhance the convergence of the model [29]. In this study, the frequency normalization process is executed as follows:

$$fr{e}^{\prime }={\displaystyle \frac{fr{e}_{MHz}-600}{6000-600}},$$

(2)

where $fr{e}_{MHz}$ represents the operational frequency in MHz.

SAR and OTA performance standardization process is performed as follows:

$$x^{\prime }={\displaystyle \frac{x-\mu }{\sigma }},$$

(3)

where $x$ represents SARs, TRP, and EIRP for various configurations, $\mu$ denotes the population mean, and $\sigma$ indicates the standard deviation.

The NEMF is uniformly resampled into an array with a spatial resolution of 0.5 × 0.5 × 0.1 mm³, 1 × 1 × 0.2 mm³, and 2 × 2 × 0.5 mm³. Correspondingly, the model inputs for these resolutions are 143 × 295 × 79, 72 × 148 × 40, and 36 × 74 × 16, respectively.

3.3. Training Configurations for RTEEMF-PhoneAnts

The workstation is equipped with two Intel^® Xeon^® Gold 5218 CPUs and four NVIDIA V100 GPUs, which are utilized for model training and testing. The optimized hyperparameters are as follows: a batch size of 4, a base learning rate of 0.02, the use of the Adam optimizer, and a maximum of 200 iterations.

3.4. Evaluation Criteria and Numerical Validation

The Root Mean Squared Error (RMSE) is utilized as the loss function to optimize network parameters.

$$los{s}_x=\sqrt{{\displaystyle \frac{1}{N}}{{\displaystyle \sum }}_{i=1}^N{\left(y_i-{\widehat{y}}_i\right)}^2},$$

(4)

where $y_i$ signifies standardized simulation results for SARs, TRP, and EIRP, while ${\widehat{y}}_i$ represents the model’s predicted results for these metrics. The comprehensive loss function is articulated as follows:

$$Loss=Los{s}_{SAR}+Los{s}_{EIRP}.$$

(5)

The SAR component of the loss is calculated using

$$Los{s}_{SAR}={\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^4{\left(los{s}_{WBSAR}+los{s}_{SAR-1g}+los{s}_{SAR-10g}\right)}_i}{12}},$$

(6)

where $i$ represents the four configurations of the SAR test.

The EIRP component of the loss is calculated using

$$Los{s}_{EIRP}={\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^7{\left(los{s}_{EIRP}\right)}_i}{7}},$$

(7)

where $i$ represents the seven configurations of the OTA test.

To evaluate the model’s accuracy, model inference outcomes were compared with simulation results. The WSR test [16] was used to determine the model’s precision in SAR and TRP metrics. FSV [17] was applied to gauge the EIRP’s accuracy. The analyses were performed using SPSS 19.0 (SPSS Inc., Chicago, IL, USA) and Matlab 2019 (MathWorks, Apple Hill Drive, Natick, MA, USA).

Stratified Sampling (SS) and the Leave-One-Antenna-Out (LOAO) approach were used to verify the model’s generalizability. SS required a random partition of each antenna category into training and testing sets in a 9:1 ratio. In contrast, the LOAO approach involved training on five antennas, while setting aside one antenna exclusively for testing. The SS method can demonstrate the model’s generalization performance across diverse frequencies and antenna positions. Conversely, the LOAO method is capable of evaluating the model’s generalization across various antenna types.

4. Experiment Results

4.1. Performance of the Proposed Model

To determine the most effective configuration for our approach, the dataset was partitioned into training and test sets using Stratified Sampling (SS). The model’s accuracy was influenced by various factors, including the ResNet3D model depth, NEMF spatial resolution, and data formats (complex (magnitude and phase) vector field and Root Mean Square (RMS) vector field). Figure 5 illustrates the average RMSE on the test dataset, reflecting the impact of these factors.

Initially, complex NEMF, with a resolution of 0.5 × 0.5 × 0.1 mm³ was input into three models of varying depths (illustrated by black squares, red circles, and blue triangles in Figure 5). The RMSEs for WBSAR and TRP predictions showed minor variations across different model depths, with ResNet3D-18 yielding the most accurate results for SAR-1g and SAR-10g.

Subsequently, ResNet3D-18 served as the backbone network, and the impacts of three distinct NEMF spatial resolutions (indicated by red circles, green inverted triangles, and pink left triangles in Figure 5) were compared. The analysis revealed that NEMF resolutions of 1 × 1 × 0.2 mm³ and 2 × 2 × 0.5 mm³ resulted in higher RMSEs for SARs and TRP.

Finally, when applying a resolution of 0.5 × 0.5 × 0.1 mm³ for both complex and RMS NEMF (represented by red circles and brass right triangles in Figure 5) with ResNet3D-18 as the framework, a significant discrepancy in SAR-1g from the reference value was observed using RMS NEMF as the input.

The WSR test reveals no significant differences (p > 0.05) between the predicted SAR and TRP and the SEMCAD results (

Table 2. Comparison of the results by the model proposed in this study and SEMCAD.

Configurations			25th Percentile		75th percentile		Z-Value	p-Value
			SEMCAD	RTEEMF-PhoneAnts	SEMCAD	RTEEMF-PhoneAnts
“cheek” position (W/kg)	left	WBSAR	0.05	0.05	0.13	0.12	−0.20	0.84
		SAR-1g	6.35	6.74	20.43	20.84	−0.06	0.95
		SAR-10g	1.81	1.79	13.66	13.78	−1.77	0.08
	right	WBSAR	0.05	0.05	0.13	0.13	−0.71	0.48
		SAR-1g	14.50	13.31	38.40	40.35	−0.20	0.84
		SAR-10g	7.70	7.40	16.99	16.65	−0.22	0.83
“tilt” position (W/kg)	left	WBSAR	0.06	0.06	0.13	0.13	−0.20	0.84
		SAR-1g	2.18	2.26	13.89	15.11	−0.59	0.56
		SAR-10g	1.27	1.27	5.80	5.92	−1.07	0.29
	right	WBSAR	0.06	0.06	0.13	0.12	−0.82	0.41
		SAR-1g	7.92	7.41	23.37	20.89	0.00	1.00
		SAR-10g	2.15	2.03	8.30	8.05	−0.47	0.64
free space (dB)		TRP	2.53	1.69	3.56	3.91	0.00	1.00
“cheek” position (dB)	left	TRP	−6.02	−5.04	−0.08	−0.04	0.00	1.00
	right	TRP	−5.59	−5.42	0.10	0.11	−1.37	0.17
“data” mode (dB)	left	TRP	0.32	0.18	1.65	1.55	−1.77	0.08
	right	TRP	−0.36	−0.33	1.80	1.96	0.00	1.00
“talk” mode (dB)	left	TRP	−0.34	−0.34	2.00	1.95	−0.63	0.53
	right	TRP	−8.70	−8.43	−4.37	−2.93	−1.37	0.17

), highlighting the proposed methodology’s consistency with the established methods.

Figure 6 shows the predicted EIRPs from diverse model configurations. EIRP distributions estimated by the model utilizing RMS NEMF or a coarser spatial resolution exhibit notable variance from the SEMCAD results. In contrast, greater consistency in distribution is observed with the SEMCAD results when employing the finest spatial resolution and complex NEMF with ResNet3D-34.

Figure 6 shows that the regions with higher EIRP values, depicted in deep red, represent the main lobe of the EIRP. The results from Figure 6b–d demonstrate good agreement with the simulation results obtained using the commercial software SEMCAD V19.2, accurately reflecting the main lobe. Notably, the highest consistency in distribution with the SEMCAD results is achieved when employing the finest spatial resolution and the complex NEMF with ResNet3D-34, as shown in Figure 6d.

The precision of the predicted EIRP was evaluated via FSV (Figure 7), demonstrating “excellent” amplitude concordance [30] between the proposed model and SEMCAD results as per ADM (amplitude difference measure). In contrast, the FDM (Feature Difference Measure) and GDM (Global Difference Measure) reveal broader probability density functions, indicating variability in findings between the proposed model and SEMCAD results, thereby underscoring challenges in predicting detailed local EIRP [31]. This inconsistency arises from the absence of constraints on adjacent elements in the terminal fully connected layer of the EIRP prediction module. Implementing smoothing constraints after the EIRP module could ameliorate this issue.

4.2. Efficiency of the Proposed Model

In terms of computational efficiency, SEMCAD assessed antenna configurations at a specific frequency, without accounting for the time that the simulation engineers invest in configuring scenarios. FDTD analysis requires approximately 5 h per scenario (4 SAR configurations plus 7 EIRP configurations) using the accelerating hardware and the commercialized software, whereas the proposed model processes all scenarios in less than 3 s using the proposed method. Thus, simulation resources are significantly saved. As shown in

Table 3. Comparison of time cost by the proposed model and full-wave simulation method.

Configurations		Time Cost (min)
		Full-Wave Simulation for One Band		RTEEMF-PhoneAnts
		Position of Phone	Simulation	Training (Number of Training Data = 7000, Batch Size = 4, Epoch = 200)	Inference (Batch Size = 1)
SAR evaluation	Left cheek	0.5	20	29,167	2.025
	Left tilt	2	24
	Right cheek	0.5	20
	Right tilt	2	24
OTA evaluation	Phone in free space	0	2
	Left cheek	0	0
	Right cheek	0	0
	Left hand in “data” mode	3	30
	Right hand in “data” mode	3	30
	Left hand and head in “talk” mode	4	65
	Right hand and head in “talk” mode	4	65

, the proposed model significantly reduces the time cost compared to the full-wave simulation method.

Typically, a mobile phone antenna can accommodate multiple frequency bands. According to the 3GPP TS 36.101 standard [32,33], User Equipment (UE) can have up to 90 Uplink (UL) operating frequency bands. Commercially available mobile phones typically feature multi-antenna configurations, often with ten or more antennas [34].

The full-wave simulation technique is used for simulations, each of which corresponds to an individual frequency band of a mobile phone. As illustrated in Figure 8, when this technique is used to simulate more than approximately 100 frequency bands, the time consumption gradually surpasses the time required to train a DL model. Concurrently, the prediction time of the DL model is approximately 2000 times faster than that of the full-wave simulation method. Therefore, as the number of frequency bands simulated increases, the time efficiency advantage of the DL model also increases correspondingly.

4.3. Model Generalization across Diverse Antenna Types

Table 4. Comparison between the model proposed in this study and the SEMCAD calculation results.

Configurations			Mean ± Std of Deviation (%), $\mathrm{Deviation}\mathbf{=}\frac{\mathbf{\left(}\mathrm{Simulation}-\mathrm{DL}\mathbf{\right)}}{\mathrm{Simulation}}\mathbf{\times }\mathbf{100}\mathbf{\%}$
			Stratified Sampling	Leave-One-Antenna-Out
				Ant.1	Ant.2	Ant.3	Ant.4	Ant.5	Ant.6
“cheek” position	left	WBSAR	5.84 ± 2.52	6.35 ± 4.25	7.82 ± 4.61	4.97 ± 4.07	9.5 ± 3.66	8.51 ± 3.58	9.06 ± 3.94
		SAR-1g	5.71 ± 2.84	5.99 ± 5.59	5.98 ± 3.87	5.75 ± 3.36	8.25 ± 3.14	5.76 ± 4.52	8.85 ± 3.61
		SAR-10g	3.71 ± 0.28	5.3 ± 0.43	3.73 ± 0.46	3.71 ± 0.5	4.33 ± 0.56	4.58 ± 0.39	5.76 ± 0.55
	right	WBSAR	4.93 ± 2.29	6.63 ± 4.04	5.09 ± 3.05	5.54 ± 2.74	8.74 ± 2.95	5.26 ± 3.41	7.64 ± 4.25
		SAR-1g	2.15 ± 0.75	2.5 ± 1.09	3.61 ± 1.18	2.68 ± 1.12	3.92 ± 1.19	3.61 ± 1.02	3.34 ± 0.77
		SAR-10g	3.22 ± 1.88	3.82 ± 2.81	3.24 ± 2.25	3.7 ± 2.09	5.7 ± 3.76	4.36 ± 2.53	4.99 ± 2.99
“tilt” position	left	WBSAR	5.26 ± 2.63	6.07 ± 2.84	7.36 ± 4.21	7.76 ± 4.72	9.69 ± 4.82	7.51 ± 3.59	8.16 ± 3.61
		SAR-1g	7.17 ± 3.97	10.5 ± 4.67	7.35 ± 5.48	7.28 ± 4.23	9.98 ± 5.25	7.71 ± 7.8	11.11 ± 4.69
		SAR-10g	6.04 ± 2.96	7.97 ± 4.7	7.35 ± 3.52	6.97 ± 4.15	10.86 ± 4.6	7.39 ± 4.29	9.36 ± 3.32
	right	WBSAR	3.46 ± 1.83	4.61 ± 2.93	5.57 ± 2.51	4.03 ± 2.23	4.35 ± 1.97	4.21 ± 3.27	5.36 ± 2.93
		SAR-1g	6.09 ± 2.88	8.43 ± 4.97	8.21 ± 3.9	8.31 ± 4.13	9.79 ± 4.1	7.21 ± 5.03	9.44 ± 3.22
		SAR-10g	5.07 ± 2.8	6.32 ± 4.25	6.22 ± 5.24	6.78 ± 3.37	7.86 ± 5.49	6.67 ± 2.91	7.86 ± 4.48
free space		TRP	0.24±0.12	1.91 ± 0.93	2.49 ± 1.16	2.97 ± 1.04	2.15 ± 1.31	2.1 ± 1.03	3.32 ± 1.56
“cheek” position	left	TRP	3.92 ± 1.16	5.26 ± 1.82	5.24 ± 1.95	4.09 ± 2.05	6.92 ± 2.32	4.08 ± 2.05	6.08 ± 2.24
	right	TRP	3.48 ± 1.55	4.78 ± 3.08	3.75 ± 2.66	4.76 ± 2.24	4.8 ± 2.22	4.47 ± 1.67	5.4 ± 2.2
“data” mode	left	TRP	1.9 ± 1.18	2.22 ± 2.17	3.05 ± 2.11	2.8 ± 1.22	3.39 ± 2.05	2.97 ± 1.58	2.95 ± 1.78
	right	TRP	1.81 ± 0.82	2.35 ± 1.53	2.83 ± 1.45	2.13 ± 1.41	2.06 ± 1.4	2.09 ± 1.29	2.8 ± 1.09
“talk” mode	left	TRP	2.87 ± 1.37	3.71 ± 1.73	2.98 ± 2.35	3.05 ± 1.46	3.43 ± 2.17	3.89 ± 2.09	4.44 ± 2.55
	right	TRP	7.88 ± 4.49	9.41 ± 8.72	8.79 ± 6.11	8.54 ± 6.72	9.83 ± 7.93	7.93 ± 8.16	12.21 ± 8.4

details the average deviation values and their corresponding standard deviations. The elevated average deviation associated with the Leave-One-Antenna-Out (LOAO) method compared to the Stratified Sampling (SS) method implies a significant influence of the antenna type on the model ability to generalize. Both the SS and LOAO methods exhibit an average deviation (%) within the range of 8% and 13%, and a maximum deviation within 13% and 25%, respectively. When the LOAO method is applied with Antenna 2 and Antenna 3 designated as test sets, the deviation decreases, with an average deviation within 9% and a maximum deviation within 18%.

IEC/IEEE 62209-1528 [4] stipulates that the uncertainty in SAR testing should be less than 30%. Concurrently, the OTA measurement standard [1] asserts that the uncertainty in Free Space (FS) measurements should be less than 2 dB (approximately 58.5%), while the uncertainty requirements for the aforementioned six other configurations are more lenient (2.2–2.4 dB). This suggests that our model demonstrates generalization capabilities for different antenna types, varying frequencies, and antenna positions.

Additionally, the deviations are reduced for Ant.2 and Ant.3 when designated as test sets, potentially due to the narrower sampling intervals in the training dataset, which facilitate the assembly of more extensive training sets (Table 1). Conversely, selecting Ant.1 and Ant.6 as test sets yields elevated average deviation compared to other validation frameworks. This increase is tentatively linked to a paucity of data, which tends to entrap the model in a state of overfitting. Hence, it is critical to augment the volume of training data.

As discerned from Table 4, Antenna 6 exhibits the greatest deviation when compared to the simulation results. Consequently, it was used as a test set in the study, and the consistency of the model predictions with the SEMCAD simulation results was assessed using the WRS test and FSV, as shown in

Table 5. Comparison between the model proposed in this study and the SEMCAD calculation results.

Configurations			25th Percentile		75th Percentile		Z-Value	p-Value
			SEMCAD	RTEEMF-PhoneAnts	SEMCAD	RTEEMF-PhoneAnts
“cheek” position (W/kg)	left	WBSAR	0.04	0.05	0.13	0.13	−1.34	0.18
		SAR-1g	13.05	13.34	41.37	42.90	−0.42	0.68
		SAR-10g	5.92	5.97	18.50	18.06	−0.39	0.69
	right	WBSAR	0.02	0.02	0.08	0.08	−0.77	0.44
		SAR-1g	1.75	1.71	13.88	13.57	−0.67	0.50
		SAR-10g	1.13	1.20	7.97	7.67	−0.22	0.83
“tilt” position (W/kg)	left	WBSAR	0.05	0.06	0.13	0.13	−0.72	0.47
		SAR-1g	13.56	13.55	35.55	34.76	−0.98	0.33
		SAR-10g	7.36	7.54	17.04	18.10	−2.37	0.02
	right	WBSAR	0.02	0.02	0.08	0.08	−1.13	0.26
		SAR-1g	2.27	2.16	14.37	14.24	−0.38	0.70
		SAR-10g	1.27	1.34	8.18	7.61	−0.44	0.66
free space (dB)		TRP	2.99	2.92	3.60	3.73	−0.04	0.97
“cheek” position (dB)	left	TRP	−6.43	−6.89	−0.09	−0.09	−0.05	0.96
	right	TRP	−5.95	−5.37	0.11	0.11	−1.66	0.10
“data” mode (dB)	left	TRP	0.37	0.32	1.72	1.79	−1.17	0.24
	right	TRP	−0.35	−0.34	2.40	2.36	−1.09	0.28
“talk” mode (dB)	left	TRP	−0.33	−0.34	2.36	2.25	−0.17	0.86
	right	TRP	4.64	4.43	9.11	8.02	−0.16	0.87

and Figure 9, respectively.

Firstly, Table 5 shows that there is no significant difference (p > 0.05) in the SAR and OTA performance for Ant.6 when compared to the SEMCAD and model predictions. Secondly, the FSV presented in Figure 9 shows that the magnitude of the EIRP predicted by the model is in good agreement with the SEMCAD results (ADM exhibits “Excellent” and “Very good”). However, more than 30% of the predictions of the FDM and GDM exhibit “Poor” or “Very poor” results. This suggests that improvements are needed for the predictions of the EIRP details.

Admittedly, the proposed framework aims to provide an alternative method for estimating antenna performance while saving the simulation time in R&D. Hence, the generated DL model does not aim to provide a versatile solution for estimating the performance of each antenna. The dimensions and material of the mobile phones were not considered as the variables in the study. This is feasible because the dimensions and materials are convergent for the current mobile phones. For example, a survey performed by UBI Research revealed that a total of 122 OLED (Organic Light-Emitting Diode)-screen handsets were launched between January and June of 2021, and of those, 97.5% (or 119, to be exact) were in the 6-inch size range. In addition, a recent study [35] revealed no significant statistical differences between groups of smartphones based on their construction materials. As mentioned previously, the types of antennas used in current mobile phones are limited [14]. Therefore, the results are representative, and the framework we proposed is applicable to R&D.

We have established that a spatial resolution of less than 1/30 of the wavelength is instrumental in maintaining a relative error below 1% [13]. This finding has significant implications for the standardization of inputs to our DL model. By transforming the antenna geometry into NEMF distributions on a Huygens’ box, we can streamline the input process for the DL model.

This study presents several limitations. Firstly, the transferability of the model could be compromised by the constrained scope of antenna types and configurations evaluated, encompassing only six prevalent antenna patterns. Secondly, the use of a streamlined mobile model disregarded the intricacies and heterogeneity of materials found in genuine phone components, which may result in divergences when assessing authentic antenna functionality.

5. Conclusions

We have developed a DL framework for evaluating mobile phone antenna performance, utilizing operating frequency and NEMF to estimate SAR and OTA performance with notable precision across various configurations. This framework enables preliminary assessment of SAR and EIRP while significantly reducing the need for repetitive simulations using specialized computational software. By leveraging DL, we streamline the evaluation process, making it more efficient and accessible. We convert antenna features and internal mobile phone components into near-field EMF distributions within a Huygens’ box. This simplifies input for the DL model. Our DL model adopts a divide-and-conquer approach, splitting SAR and EIRP estimation into eight modules. This reduces training complexity and improves convergence rates. Compared to full-wave simulations, our proposed model achieves remarkable computational efficiency. It processes all scenarios in seconds, making it a valuable tool for practical R&D.

We use the WSR test for SAR and TRP accuracy evaluation. Additionally, FSV assesses EIRP accuracy. While our model demonstrates excellent agreement with SEMCAD results, challenges remain in predicting detailed local EIRP due to the lack of constraints on adjacent elements in the terminal fully connected layer. Despite these limitations, our framework provides a valuable alternative to time-intensive simulations. To enhance its applicability, future work should expand the dataset to include additional antenna types and configurations, as well as more realistic mobile models.

In summary, our DL framework provides an efficient means of assessing mobile phone antenna performance. Future work should address model transferability and consider material heterogeneity for more accurate evaluations. Overall, our study is accessible on GitHub for free use (https://github.com/licongsheng/rteemf-phoneants, accessed on 10 August 2024). Engineers can customize the model using their own datasets, presenting a viable substitute for traditional electromagnetic field simulations.