Computationally Efficient Deep Learning Approach Using IQ-MobNet for Radar DoA Estimation in Limited Snapshot Conditions

Abstract

This paper presents a computationally efficient deep learning framework for accurate direction-of-arrival (DoA) estimation in portable radar applications. Leveraging a MobileNet architecture, the proposed model directly processes raw in-phase and quadrature-phase (IQ) data, enabling more effective learning of both spatial and temporal features. This direct input approach enhances DoA estimation accuracy, particularly under challenging conditions such as low signal-to-noise ratio (SNR) and limited snapshot scenarios. A unified training strategy is adopted for both single-source and multi-source target detection, ensuring consistency and robustness. Comprehensive simulation experiments demonstrate the proposed model’s competitive and robust performance across various conditions, including different SNR levels, closely spaced targets, and random off-grid angles. It also shows that our method achieves performance comparable to or better than recent deep learning approaches in several challenging scenarios, establishing its potential for resource-constrained environments where only low snapshot data are available. The proposed IQ-MobNet DoA estimation model achieves this competitive performance with substantially lower computational complexity, requiring only 0.24 million parameters and 0.42 million Floating Point Operations (FLOPs), representing a reduction of over 96% compared to the recent neural network models. To ensure practical applicability, the proposed IQ-MobNet framework is validated using real-world measured data, confirming its robustness beyond simulated environments.

1. Introduction

Direction-of-arrival (DoA) estimation is a fundamental problem in modern array signal processing, with critical applications in radar, wireless communications, autonomous vehicles, and sonar systems [1,2,3,4]. Automotive radar systems have become a cornerstone of modern vehicle safety and autonomy, enabling reliable detection and localization of surrounding objects. Among the essential signal processing tasks, DoA estimation plays a vital role in determining the angular positions of multiple targets, directly impacting the performance of features such as adaptive cruise control and emergency braking. Over the years, a variety of algorithms have been developed to estimate the directions of signals from targets using sensor arrays. Among the classical techniques, subspace-based methods such as Multiple Signal Classification (MUSIC) [5] and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) [6] stand out as widely adopted super-resolution approaches [7]. MUSIC performs a spectral search over the angular domain and achieves high-resolution estimates, albeit with high computational complexity. ESPRIT, on the other hand, bypasses this search using rotational invariance, offering a more computationally efficient solution. Numerous variants of MUSIC and ESPRIT have been proposed to improve their robustness under non-ideal conditions such as low SNR, snapshot limitations, or model mismatch [8,9,10,11]. Beamforming-based methods, including conventional beamforming (CBF) [12,13], scan the angular space and compute received power, but generally offer lower resolution and are sensitive to interference and noise. Another classical method, the Iterative Adaptive Approach (IAA) [14], provides nonparametric spectral estimation with improved resolution but at the cost of higher computational requirements. Furthermore, sparse reconstruction-based techniques, such as compressed sensing (CS) and sparse Bayesian learning (SBL), have been extensively investigated for DoA estimation by exploiting the inherent sparsity of signal sources in the angular domain [15,16]. These methods have demonstrated high-resolution DoA estimation under limited-snapshot conditions and have been extended to address practical challenges such as off-grid source localization, mutual coupling effects, and multi-snapshot signal recovery [17,18,19,20,21]. Despite their improved estimation accuracy, many sparse reconstruction-based approaches often involve iterative optimization procedures, resulting in increased computational complexity and execution time. More recently, several lightweight solutions have been proposed to reduce the computational burden, such as the ECA-MURE algorithm and manifold-reconstruction-based unitary ESPRIT [22,23]. Furthermore, Nyström approximation has been successfully integrated into Root-MUSIC-based frameworks to accelerate subspace computations and improve scalability for real-time sparse array processing [24,25,26]. Despite their advantages, these methods still struggle in highly noisy environments and deteriorate when only a few snapshots are available.

Besides conventional subspace-based and sparse reconstruction approaches, recent studies have explored low-complexity hardware-oriented AoA estimation techniques. For example, a reconfigurable full-digital AoA estimation architecture was proposed for real-time implementation in [27], while more recently 1-bit conversion-based AoA estimation frameworks have been investigated to further reduce hardware and computational complexity [28]. These approaches highlight the growing interest in complexity-efficient localization systems for resource-constrained sensing platforms.

Recent efforts have turned to deep learning (DL) approaches for DoA estimation. Neural networks can model complex, nonlinear relationships directly from data, making them well-suited for scenarios where traditional methods fail [29,30,31]. Various deep learning architectures have been proposed for DoA estimation, each tailored to address specific challenges. A multitask autoencoder combined with parallel multilayer classifiers introduced in [32] enhances robustness against array imperfections. In [33], a deep convolutional network (DCN) is employed to recover the spatial spectrum by leveraging the inherent sparsity of incoming signals. Convolutional neural network (CNN) architectures such as ResNet [34] and U-Net have also been applied, processing covariance matrices or spectrogram-like inputs to achieve high estimation accuracy [35,36]. SEResNet is a variant of ResNet that integrates Squeeze-and-Excitation (SE) blocks [37]. Multiscale Squeeze-and-Excitation (MSEDOA) approach enhances the SE-ResNet architecture with multiscale feature extraction and channel attention mechanisms [38] for direction-of-arrival estimation in the automotive radar applications. More recently, transformer-based models have gained attention for their ability to capture long-range dependencies in the input signal [39,40,41,42]. Despite their effectiveness, these models are typically resource-intensive, limiting their practicality in real-time or embedded applications. Another key factor influencing DoA estimation performance is the choice of input representation. Many traditional and learning-based methods rely on covariance or correlation matrices, which capture statistical relationships between sensor channels. These matrices are central to subspace methods like MUSIC and ESPRIT, and are often used as inputs to CNN or transformer models. However, these representations are derived from averaging over time snapshots, potentially discarding temporal and phase information. Their accuracy also deteriorates under low SNR or few snapshot conditions due to noisy estimations. In contrast, using raw in-phase and quadrature-phase (IQ) signals as input allows models to directly access the complex input data without intermediate processing. Raw IQ data preserves both amplitude and phase information and eliminates the need to compute and average over covariance matrices, thus reducing computational overhead [35]. This makes raw IQ-based methods more suitable for low-latency and real-time applications.

Recent studies have also investigated hardware-oriented AoA estimation approaches that directly exploit I/Q measurements for efficient angle estimation. For example, phase-interferometric I/Q processing techniques have been employed for full-hardware AoA localization and adaptive beamforming, enabling real-time implementation with reduced processing overhead [43,44]. These studies highlight the potential of directly utilizing I/Q information for computationally efficient localization systems.

To make deep learning-based DoA estimation practical for real-time and embedded systems, recent efforts have proposed lightweight deep-network architectures for DOA estimation [45,46]. For instance, ref. [47] reduces data redundancy and formulates DOA as a regression task to greatly shrink both input/output dimensions and network size. Similarly, ref. [48] applies depthwise-separable convolutions to multi-channel acoustic inputs, achieving a favorable balance between accuracy and computational cost. The IQ-ResNet model proposed in [35], which relies on a deep and computationally demanding residual architecture highlights the advantage of using raw IQ input signal for efficient DoA estimation. The use of depthwise separable convolutions in MobileNet significantly reduces computational complexity, making it ideal for resource-constrained platforms [49]. Despite these advances, lightweight architectures that directly process raw IQ measurements for DoA estimation remain relatively unexplored. Existing lightweight approaches typically achieve complexity reduction through signal preprocessing, engineered feature representations, or dimensionality reduction prior to neural-network processing. In contrast, the proposed IQ-MobNet directly operates on raw IQ measurements and employs depthwise separable convolutions together with inverted residual blocks to learn discriminative spatial-temporal features without covariance matrix computation or other preprocessing. The primary novelty of this work is the development and systematic evaluation of a MobileNetV2-inspired raw-IQ learning framework for limited-snapshot DoA estimation. To the best of our knowledge, the use of a lightweight MobileNet-based architecture for direct raw-IQ DoA estimation estimation in limited snapshot conditions has not been previously investigated. The proposed framework demonstrates that competitive estimation accuracy can be achieved with substantially lower computational complexity than existing raw-IQ deep-learning approaches. Therefore, the primary technical novelty lies in demonstrating that accurate raw-IQ-based DoA estimation can be achieved using a highly compact architecture, resulting in an improved complexity-performance tradeoff suitable for resource-constrained radar platforms.

In this paper, a deep neural network (DNN) framework built upon the MobileNet architecture, designed to process raw in-phase and quadrature (IQ) signals directly is introduced for direction-of-arrival (DoA) estimation. Major contributions of this article are summarized as follows:

• A lightweight deep learning framework, termed IQ-MobNet, is proposed for direction-of-arrival estimation from raw in-phase and quadrature (IQ) radar signals. Unlike covariance-based approaches, the proposed framework directly exploits the spatial-temporal information contained in the received IQ measurements without requiring covariance matrix computation or other preprocessing.
• A MobileNetV2-inspired architecture is adapted for the DoA estimation problem through the integration of inverted residual learning and depthwise separable convolutions. This design enables efficient spatial-temporal feature extraction from raw IQ data while substantially reducing the number of trainable parameters, FLOPs, memory footprint, and inference cost.
• The proposed framework is specifically designed for low-SNR and limited-snapshot scenarios, where reliable covariance estimation becomes challenging. By operating directly on raw IQ measurements, IQ-MobNet effectively utilizes the available signal information and maintains robust estimation performance under these challenging conditions.
• Extensive simulation studies under varying SNR levels, angular separations, source configurations, and off-grid conditions demonstrate that the proposed framework achieves accuracy comparable to state-of-the-art deep learning approaches while significantly reducing computational complexity.
• Validation using measured radar data further demonstrates the practical applicability and generalization capability of the proposed framework in real-world operating environments.

This article is structured as follows: Section 2 presents the proposed classification model for DoA estimation. Simulation results and ablation study are discussed in Section 3. A real-world data validation experiment is discussed in Section 4. Finally, Section 5 concludes the paper.

2. Signal Model, Problem Formulation, and Proposed DoA Estimation Model

In this section, we present IQ-MobNet, a lightweight deep learning architecture designed for DoA estimation directly from raw IQ radar signals. The section starts with array signal modelling and problem formulation, followed by the proposed IQ-MobNet architecture.

2.1. Array Signal Modelling and Problem Formulation

Consider a uniform linear array (ULA) configuration, an arrangement where N equally spaced sensors (antenna elements) are aligned in a straight line as depicted in Figure 1. The inter-element spacing d is a critical design choice, and it is taken as $d=\lambda /2$, where $\lambda$ is the wavelength of the incoming signals. This choice helps to mitigate spatial aliasing [50]. The signals are collected over P snapshots, resulting in a data matrix:

$$R=[r\left(1\right),r\left(2\right),\dots ,r\left(P\right)]\in {\mathbb{C}}^{N\times P}$$

(1)

This matrix R consolidates the received signals across all array elements over multiple time instants. The goal of DoA estimation is to determine the incident angles corresponding to the directions of the K sources (targets)

$$\mathrm{\Theta }=[{\theta }_1,{\theta }_2,\dots ,{\theta }_K]$$

(2)

from the received signal matrix R. When $K=1$ (single-source), DoA estimation is treated as a single-label multi-classification problem. When $K>1$ (multiple-source), it is considered a multi-label multi-classification problem.

Figure 1. Uniform linear array configuration [35].

The received signal vector at time t, $r\left(t\right)\in {\mathbb{C}}^{N\times 1}$ can be represented as

$$r\left(t\right)=A\left(\mathrm{\Theta }\right)s\left(t\right)+n\left(t\right),t=1,2,\dots ,P$$

(3)

where $s\left(t\right)\in {\mathbb{C}}^{K\times 1}$ is the source signal vector, indicating the amplitude and phase of the K signals at time t and $n\left(t\right)\in {\mathbb{C}}^{N\times 1}$ is the noise vector, typically modelled as complex Gaussian noise. $A\left(\mathrm{\Theta }\right)\in {\mathbb{C}}^{N\times K}$ is the array manifold matrix, representing the spatial signature of the array for different directions, i.e, it is the collection of steering vectors associated with each direction ${\theta }_k$, $k=1,2,\dots ,K$, defined as:

$$A\left(\mathrm{\Theta }\right)=[a\left({\theta }_1\right),a\left({\theta }_2\right),\dots ,a\left({\theta }_K\right)]$$

(4)

where the steering vector $a\left({\theta }_k\right)$ represents the response of each array element to a signal arriving from a particular direction ${\theta }_k$ and is given by [35]:

$$a\left({\theta }_k\right)=\left[\begin{array}{c}1\\ e^{-j{\displaystyle \frac{2\pi d}{\lambda }}\sin \left({\theta }_k\right)}\\ ⋮\\ e^{-j{\displaystyle \frac{2\pi d}{\lambda }}(N-1)\sin \left({\theta }_k\right)}\end{array}\right]$$

(5)

In this work, the field of view (FoV) is divided into a grid such that the FoV spans $[-q,q]$ degrees with a resolution of $\delta$ degrees. The discrete set Q is defined as

$$Q=\{-q,-q+\delta ,\dots ,-\delta ,0^{°},\delta ,\dots ,q-\delta ,q\}$$

(6)

The total number of grid points (or classes) is

$$Q={\displaystyle \frac{2\left|q\right|}{\delta }}+1$$

(7)

The most probable angles within this grid are to be identified. A DL based architecture is proposed to meet this objective, with its details provided in the following section.

2.2. Model Architecture

The proposed IQ-MobNet is a neural network architecture explicitly tailored for array signal processing. Unlike prior MobileNet-based or lightweight IQ-input models that adapt image-oriented designs or treat IQ samples as generic feature maps, IQ-MobNet restructures the MobileNet framework to directly process raw complex-valued IQ data and perform multi-label DoA estimation for multiple sources.

The raw complex IQ measurements from an N-element array collected over T temporal snapshots are reshaped into a spatial–temporal representation before being fed to the network, enabling the network to directly learn antenna-domain and temporal correlations intrinsic to DoA estimation rather than image-like textures. The received signal from an N-element antenna array over T temporal snapshots is represented by the complex-valued matrix $(\mathbf{X}\in {\mathbb{C}}^{N\times T})$, where each entry contains the in-phase (I) and quadrature (Q) components of the received signal. To enable processing by the proposed convolutional neural network, the complex-valued measurements are converted into a real-valued tensor by separating the real and imaginary components. Specifically, the I and Q components corresponding to each antenna element are stacked along the channel dimension, resulting in an input tensor of size $(2N\times 1\times T)$. Thus, the first (N) channels represent the in-phase components and the remaining (N) channels represent the quadrature components. This representation preserves both the spatial information across antenna elements and the temporal information across snapshots while avoiding covariance matrix computation or other intermediate preprocessing operations. Depthwise separable inverted residual blocks (IRBs) are beneficial for parameter reduction, as well as to efficiently capture inter-antenna spatial structure with extremely low FLOPs, which is critical for edge radar deployment. Furthermore, global average pooling (GAP) followed by a compact stack of three fully connected layers enables effective aggregation and refinement of spatial–temporal features, improving angular discrimination with minimal computational overhead. Finally, a 121-neuron multi-label output layer mapped to a discretized angular grid allows multi-source DoA estimation in a unified framework, distinguishing IQ-MobNet from existing lightweight architectures which are limited to single-source or coarse angular inference. The model outputs a binary vector representing Q classes, where each class corresponds to a specific angle. Multiple classes can be active at once, representing multiple source directions.

The proposed model architecture is presented in Figure 2. Since, in DoA estimation, spatial correlations between antennas and temporal variations in the snapshots are crucial, a 2D convolution operation is incorporated in the initial convolution layer to capture spatial and temporal features. The operation in the initial convolution layer can be represented as

$$\mathbf{X}=\mathrm{ReLU}6\left(\mathrm{BN}\left(\mathrm{Conv}2\mathrm{D}\left({\mathbf{X}}_{\mathrm{input}}\right)\right)\right)$$

(8)

where Conv2D is the 2D convolution operation that employs a 3 × 3 kernel with stride 1 on the input ${\mathbf{X}}_{\mathrm{input}}$ and BN represents batch normalization. The output of the 2D convolution is normalized and then fed as input to the ReLu(Rectified Linear Unit)6 activation function, which is a rectified linear unit variant that clips outputs at 6, i.e., [49],

$$ReLu6\left(x\right)=\min \left(\max \right(0,x),6)$$

(9)

ReLU6 is a bounded version of the conventional ReLU activation function that restricts the output range to [0, 6] as shown in Equation (9). ReLU6 is used within the IRB modules to remain consistent with MobileNetV2’s design, which is optimized for efficient inference and quantization. It helps to reduce information loss caused by low-precision operations, especially in mobile-friendly models using depthwise separable convolutions. The core component of the MobileNet architecture is the depthwise separable convolution, which significantly reduces computational cost compared to standard convolutions by factorizing them into two simpler operations such as depthwise convolution and pointwise convolution [51]. In particular, MobileNetV2 builds upon this idea by using inverted residual blocks, each consisting of three stages such as pointwise expansion, depthwise convolution, and pointwise projection [49]. Figure 2 also illustrates the core internal flow of inverted residual block and is explained below.

Figure 2. Proposed IQ-MobNet Model Architecture.

The pointwise expansion includes a pointwise convolution operation, batch normalization and ReLu6 activation function. Given an input feature map $\mathbf{X}\in {\mathbb{R}}^{B\times C_{in}\times H\times W}$ with batch size B, channel count $C_{in}$, and spatial dimensions $H\times W$, where H and W refer to height and width respectively, the pointwise convolution is a $1\times 1$ convolution that increases the number of channels from $C_{in}$ to $C^{\prime }=t{C}_{in}$, where t is the expansion factor. The complete pointwise expansion operation is defined as

$${\mathbf{X}}_{\exp }=\mathrm{ReLU}6\left(\mathrm{BN}({\mathbf{W}}_{\exp }\ast \mathbf{X})\right)$$

(10)

where ${\mathbf{W}}_{\exp }\in {\mathbb{R}}^{C^{\prime }\times C_{in}\times 1\times 1}$ is the weight matrix of the expansion layer and ∗ represents the pointwise convolution. This step enriches the feature space before spatial filtering. The depthwise convolution applies a $f\times f$ grouped filter with stride s to each expanded channel, enabling efficient spatial processing without channel mixing, followed by batch normalization and ReLu6 activation function and is represented as

$${\mathbf{X}}_{\mathrm{dw}}=\mathrm{ReLU}6\left(\mathrm{BN}({\mathbf{W}}_{\mathrm{dw}}⊛{\mathbf{X}}_{\exp })\right),$$

(11)

where ${\mathbf{W}}_{\mathrm{dw}}\in {\mathbb{R}}^{C^{\prime }\times 1\times f\times f}$ is the depthwise convolution kernel and ⊛ represents the depthwise convolution operation. Each filter operates on exactly one input channel, and the output maintains the same number of channels C’, preserving spatial structure while enabling channel-wise nonlinear transformations through batch normalization and ReLU6 activation. Since depthwise convolution does not combine information across channels, a final pointwise projection with pointwise $1\times 1$ convolution is applied to reduce the channel dimension back to the desired output size $C_{out}$, followed by batch normalization to get the output as

$${\mathbf{X}}_{\mathrm{proj}}=\mathrm{BN}({\mathbf{W}}_{\mathrm{proj}}\ast {\mathbf{X}}_{\mathrm{dw}}),$$

(12)

where ${\mathbf{W}}_{\mathrm{proj}}\in {\mathbb{R}}^{C_{\mathrm{out}}\times C^{\prime }\times 1\times 1}$. If the input and output dimensions match and the stride is 1, a skip or residual connection is applied to obtain ${\mathbf{X}}_{\mathrm{out}}$:

$${\mathbf{X}}_{\mathrm{out}}=\left\{\begin{array}{cc}\mathbf{X}+{\mathbf{X}}_{\mathrm{proj}},\hfill & \mathrm{if}\mathrm{stride}=1\mathrm{and}{C}_{\mathrm{in}}=C_{\mathrm{out}}\hfill \\ {\mathbf{X}}_{\mathrm{proj}},\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(13)

The addition of $\mathbf{X}$ (the input) and ${\mathbf{X}}_{\mathrm{proj}}$ (the transformed output) is called a residual connection because it allows the block to pass the input directly to the output, enabling the network to learn only the residual information when the input and output dimensions match. Let ${\mathbf{X}}_{\mathrm{out}1}$, ${\mathbf{X}}_{\mathrm{out}2}$, ${\mathbf{X}}_{\mathrm{out}3}$, ${\mathbf{X}}_{\mathrm{out}4}$ be the output feature maps obtained from IRB1, IRB2, IRB3, and IRB4, respectively. After the spatial feature extraction using four inverted residual blocks as shown in Figure 2, the output feature map of IRB4, ${\mathbf{X}}_{\mathrm{out}4}$, is passed to the global average pooling (GAP) layer. GAP operates on each channel of ${\mathbf{X}}_{\mathrm{out}4}$, averaging over all spatial positions to produce a compact feature representation as

$${\mathbf{X}}_{\mathrm{gap}}={\displaystyle \frac{1}{H\times W}}{\displaystyle \sum _{i=1}^H}{\displaystyle \sum _{j=1}^W}{\mathbf{X}}_{\mathbf{out}\mathbf{4}}(i,j)$$

(14)

The pooled output is then passed through three fully connected layers. The first layer transforms the input to a 512-dimensional space as shown in equation below.

$${\mathbf{X}}_{\mathrm{fc}1}=\mathrm{ReLU}({\mathbf{W}}_{\mathrm{fc}1}{\mathbf{X}}_{\mathrm{gap}}+{\mathbf{b}}_{\mathrm{fc}1}),$$

(15)

where ${\mathbf{W}}_{\mathrm{fc}1}\in {\mathbb{R}}^{512\times C_{\mathrm{out}}}$ is the weight matrix and ${\mathbf{b}}_{\mathrm{fc}1}$ is the bias term of the first fully connected (FC) layer. Similarly, the second fully connected layer maps the feature representation to 256 dimensions as

$${\mathbf{X}}_{\mathrm{fc}2}=\mathrm{ReLU}({\mathbf{W}}_{fc2}{\mathbf{X}}_{\mathrm{fc}1}+{\mathbf{b}}_{fc2}),$$

(16)

where ${\mathbf{W}}_{fc2}\in {\mathbb{R}}^{256\times 512}$ is the weight matrix and ${\mathbf{b}}_{fc2}\in {\mathbb{R}}^{256}$ is the bias term of the second FC layer. In our formulation, the network’s final layer contains 121 neurons, each corresponding to a discrete DoA within the FoV range of $[-{60}^{°},{60}^{°}]$. In the single-source scenario, the correct DoA corresponds to a single active target among the 121 possibilities. In the multi-source case (e.g., two-source), the goal is to correctly identify multiple active directions from the same 121-dimensional output, effectively performing multi-label classification. The final fully connected layer produces an output vector whose length corresponds to the number of DoA classes as shown below.

$${\mathbf{X}}_{\mathrm{output}}={\mathbf{W}}_{fc3}{\mathbf{X}}_{\mathrm{fc}2}+{\mathbf{b}}_{fc3},$$

(17)

where the weight matrix, ${\mathbf{W}}_{fc3}\in {\mathbb{R}}^{121\times 256}$ and the bias term, ${\mathbf{b}}_{fc3}\in {\mathbb{R}}^{121}$.

The detailed configuration of the proposed IQ-MobNet architecture is summarized in Table 1. The table reports the input and output tensor dimensions, channel configurations, expansion factors, stride values, and trainable parameters associated with each network component. The proposed IQ-MobNet contains a total of 240,857 trainable parameters. The final output is obtained as a vector of probabilities ($\mathbf{p}$) by applying a sigmoid activation function on ${\mathbf{X}}_{\mathrm{output}}$ as

$$\mathbf{p}=[p_{-q},p_{-q+1},\dots ,p_q]=\mathrm{sigmoid}\left({\mathbf{X}}_{\mathrm{output}}\right)$$

(18)

where each element in $\mathbf{p}$, represented as $p_{\theta }$, $\theta =(-q,-q+1,\dots ,0,\dots ,q-1,q)$ and $p_{\theta }\in [0,1]$ refers to the predicted probability or likelihood of a source being present at angle $\theta$. In this work, the binary cross-entropy (BCE) loss function has been utilized for the DoA estimation. The BCE loss function is defined as [52]

$$L=-{\displaystyle \frac{1}{N_c}}{\displaystyle \sum _{i=1}^{N_c}}{\displaystyle \sum _{j=1}^l}\left[{\theta }_{ij}\log \left({\widehat{\theta }}_{ij}\right)+(1-{\theta }_{ij})\log (1-{\widehat{\theta }}_{ij})\right]$$

(19)

where $N_c$ is the total number of training samples, l is the number of DoA labels. ${\theta }_{ij}$ and ${\widehat{\theta }}_{ij}$ are the ground truth label and the predicted probability respectively for the sample i and class j. The function applies a logarithm to the predicted probabilities, penalizing incorrect predictions more heavily. The DoAs are estimated by selecting the angles with the highest predicted probabilities from the model output. The model can output independent probabilities for each class, allowing it to predict multiple classes. In the multi-label case, this is done by choosing the top-k probabilities, depending on the expected number of sources. The performance and computational efficiency of the proposed model is evaluated under various scenarios in the next section.

Table 1. Detailed architecture configuration of the proposed IQ-MobNet.

Layer	Input Size	Output Size	Operation	Kernel	Stride	Parameters	Activation
Input	($2N\times 1\times T$)	($2N\times 1\times T$)	Complex-to-real IQ mapping	–	–	0	–
Conv1	($24\times 1\times 10$)	($32\times 1\times 10$)	Conv2D + BN	3 × 3	1	6976	ReLU6
Block1	($32\times 1\times 10$)	($16\times 1\times 10$)	IRB (t = 1)	3 × 3	1	1984	ReLU6
Block2	($16\times 1\times 10$)	($24\times 1\times 5$)	IRB (t = 6)	3 × 3	2	5136	ReLU6
Block3	($24\times 1\times 5$)	($32\times 1\times 3$)	IRB (t = 6)	3 × 3	2	10,000	ReLU6
Block4	($32\times 1\times 3$)	($64\times 1\times 2$)	IRB (t = 6)	3 × 3	2	21,056	ReLU6
GAP	($64\times 1\times 2$)	64	Adaptive Avg Pool	–	–	0	–
FC1	64	512	Fully Connected	–	–	33,280	ReLU
Dropout	512	512	Dropout (p = 0)	–	–	0	–
FC2	512	256	Fully Connected	–	–	131,328	ReLU
Dropout	256	256	Dropout (p = 0)	–	–	0	–
Output	256	121	Fully Connected	–	–	31,097	Sigmoid

3. Simulation Results and Discussion

In this section, the simulation setup is outlined, and the DoA estimation results across various scenarios such as varying snapshots, signal-to-noise ratios (SNRs), diverse angular separations, and off-grid random angles are presented. The performance of the proposed IQ-MobNet approach is evaluated against classical methods such as CBF, ESPRIT, MUSIC, IAA, and deep learning-based models such as IQ-ResNet, SEResNet, MSEDOA and Lightweight DNN. Evaluation is conducted in terms of DoA estimation accuracy, with root mean square error (RMSE) employed as the primary performance metric. The computational complexity in terms of the number of FLOPs and parameters is also presented in this section. The implementation is carried out using PyTorch version 2.4.0. and trained on an NVIDIA L4 graphics processing unit (GPU).

3.1. Dataset Generation

To simulate the received radar signals for DoA estimation, a 12-element uniform linear array (ULA) with an FoV spanning from $-{60}^{°}$ to ${60}^{°}$ is considered. This angular range is discretized into 121-angle labels, each with a $1^{°}$ resolution. A binary coding scheme is utilized for labelling, where the 121 grid points, ranging from $-{60}^{°}$ to ${60}^{°}$, are represented by a 121 × 1 binary vector. In this vector, a ‘1’ indicates the presence of a signal source in that direction, while a ‘0’ represents its absence. The target signal $s\left(t\right)$ is modelled as a random phase-modulated complex signal combined with additive zero-mean complex Gaussian (AWGN) noise as shown in Equation (3). The dataset with 180,000 training samples and 20,000 validation samples are generated per SNR varied in the range of [0, 30] dB with a step size of 5dB. As the aim of this work is to achieve accurate DoA estimation in challenging scenarios such as low snapshot availability, the number of snapshots is fixed at 10, which reflects such practical constraints. The maximum number of targets is set to be 3 and the minimum angular separation of targets is set as ${10}^{°}$ in the training data. This constraint ensures that the model is trained only on relatively well-separated sources. During testing, by introducing more challenging conditions such as targets with smaller angular separations and checking how accurately the model resolves closely spaced sources it is not explicitly trained on, the generalization capability of the proposed model is evaluated.

3.2. Training Setup

The proposed IQ-MobNet network is trained using a unified supervised learning framework that jointly incorporates both single-source and multi-source training samples within a single model. This unified framework enables a common architecture to learn generalized spatial feature representations across different source configurations, eliminating the need to train separate models for each scenario. The training dataset consists of 1.26 million samples generated across seven SNR levels, where the number of sources per snapshot is randomly selected between one, two and three with uniform probability. Approximately 420k samples were generated for each source count (419,636 single-source, 419,133 two-source, and 421,231 three-source samples). Training is conducted over 100 epochs using AdamW optimizer, with an initial learning rate of 0.003, adjusted via cosine annealing [53]. Simulation parameters are listed in Table 2.

Table 2. Signal generation and simulation parameters.

Parameter	Value
Number of array elements	12
Field of view	[$-{60}^{°},{60}^{°}$]
Angular resolution	$1^{°}$
Normalized wavelength	$\lambda =0.5$
Train SNR range (dB)	[0, 5, 10, 15, 20, 25, 30]
Test SNR range (dB)	[−25, −23, −21, −19, −17, −15, −13, −11, −9, −7, −5, −3, −1, 1, 3, 5, 7, 9, 11, 13, 15]
Number of maximum targets	3
Number of snapshots	10
Number of training samples per SNR	180k
Number of testing samples per SNR	20k
Modulation	Random phase modulation
Noise type	AWGN
Minimum angular separation	10°
Train batch size	256
Validation batch size	1024
Number of epochs	100
Initial learning rate	0.003

During the inference phase, test samples are processed to generate a pseudo angle spectrum, with the top k local maxima (k highest peaks) identifying the estimated DoAs where k corresponds to the known number of sources for the given test scenario (single-source or two-source). This peak selection strategy allows the unified model to be evaluated consistently across different source configurations without requiring architectural modifications. It should be noted that the current implementation assumes prior knowledge of the number of sources during evaluation. Automatic estimation of source count is identified as a direction for future research. To evaluate the accuracy of DoA estimation, the RMSE is used as the performance metric, which is taken as the minimum error between the true and estimated angles over all possible estimates [38], i.e.,

$$\begin{array}{c}\hfill \mathrm{RMSE}(\theta ,\widehat{\theta })=\underset{\widehat{\theta }\in G}{\min }\sqrt{{\displaystyle \frac{1}{SK}}\sum _{s=1}^S\sum _{k=1}^K{({\theta }_k-{\widehat{\theta }}_k)}^2}\end{array}$$

(20)

where S represents the number of samples, K denotes the number of sources, ${\theta }_k$ is the true angle of arrival, ${\widehat{\theta }}_k$ is the estimated angle of arrival, and G represents the set of all permutations of predicted DoAs (i.e., all possible matchings of predicted to true angles).

3.3. Effect of Training SNR Range

To analyse the effect of the training SNR range, the proposed IQ-MobNet is trained using datasets generated over three SNR intervals: 0–10 dB, 0–20 dB, and 0–30dB. The training loss plots for the proposed model considering these different training SNR ranges are given in Figure 3.

Figure 3. Training curves of proposed model with training SNR range: (a) 0–10 dB (b) 0–20 dB (c) 0–30 dB.

Traing plots show that both training and validation loss are decreasing steadily over the course of 100 epochs. Some fluctuations in validation loss are visible, which is normal as the model adjusts its weights. Training and validation loss are very close in the later epochs, indicating that there is no significant overfitting and the model is learning effectively.

As summarized in Table 3, increasing the diversity of SNR conditions during training consistently improved the validation performance. The model trained using the widest SNR range (0–30 dB) achieved the lowest validation loss (0.0139), highest validation accuracy $(93\%)$, and lowest validation MSE $\left(7.82\right)$. Figure 4 presents the RMSE performance of IQ-MobNet when trained using datasets generated over different SNR ranges (0–10 dB, 0–20 dB, and 0–30 dB).

Table 3. Effect of training SNR range.

Training SNR Range	Best Val Loss	Best Val Accuracy	Best Val MSE
0–10 dB	0.0254	89.69%	8.54
0–20 dB	0.0184	91.70%	8.88
0–30 dB	0.0139	93%	7.82

Note: Bold values indicate the best performance among the evaluated training SNR ranges.

Figure 4. RMSE performance of the proposed IQ-MobNet trained with different training SNR ranges.

The results indicate that the training SNR range has an influence on the estimation performance obtained across the evaluated test SNR conditions. Among the considered configurations, the model trained using the 0–30 dB dataset generally exhibits lower RMSE values over a wider range of operating conditions. This observation suggests that exposing the network to a broader range of noise levels during training may help improve its generalization capability and provide more consistent performance under varying SNR environments. Based on these results, the 0–30 dB training configuration is retained for the proposed framework.

Now, the trained model is evaluated under different unseen test cases such as various untrained SNRs, different angle separations, and untrained random off-grid angles in two-source and single-source scenarios.

3.4. Performance Evaluation in Two-Source Scenario

3.4.1. For Different Number of Snapshots

Figure 5a illustrates the performance of the proposed IQ-MobNet model in terms of RMSE for DoA estimation, evaluated under varying SNRs, angular separations, and number of snapshots. For testing, various SNR levels such as −5 dB, 5 dB and 15 dB are considered, each for angular separations of $6^{°}$ and ${10}^{°}$ across snapshots from 2 to 10. The proposed model, which is trained with 10 snapshots of data, works even for low snapshot data with a minimum RMSE obtained at 10 snapshots for the cases considered here. To evaluate the efficacy of the proposed model in severe low snapshot situations compared to traditional DOA estimation techniques (MUSIC, ESPRIT, and IAA) and other deep learning models, two scenarios are analyzed: (i) an angular separation of $6^{°}$ at 10 dB SNR, and (ii) a low SNR condition of $-5$ dB with the same separation. The resulting log(RMSE) versus snapshots curves are presented in Figure 5b,c. The results demonstrate that the performance of all methods degrades as the number of snapshots becomes extremely small due to insufficient signal information for stable estimation. However, when snapshots are ≥5, the proposed IQ-MobNet performs well in the 10 dB scenario. In contrast, under the more challenging −5 dB low-SNR condition, the proposed model IQ-MobNet consistently outperforms all classical and deep learning baselines, highlighting its strong robustness and generalization capability in noisy environments where classical subspace methods struggle to separate sources reliably.

Figure 5. Evaluation of DoA estimation accuracy with respect to the number of snapshots (a) Proposed model in various scenarios (b) Comparison with other methods in scenario-$\Delta \theta =6^{°}$ and SNR = 10 dB (c) $\Delta \theta =6^{°}$ and SNR = −5 dB.

To investigate the effect of longer observation intervals, we conducted additional experiments using datasets generated with $T=100$ snapshots. Three cases were considered: (i) evaluating the model trained with $T=10$ snapshots on $T=10$ snapshot data, (ii) evaluating the model trained with $T=10$ snapshots on $T=100$ snapshot data and (iii) retraining the proposed IQ-MobNet using $T=100$ snapshots and evaluating it on $T=100$ snapshot data.

Figure 6 compares the RMSE performance of the model across different SNR levels. The results show that directly applying a model trained with T = 10 snapshots to T = 100 snapshot data does not yield performance improvement, indicating that the network learns representations that are adapted to the snapshot conditions encountered during training. In contrast, when the proposed IQ-MobNet is trained and evaluated using T = 100 snapshots, a substantial reduction in RMSE is observed across a wide SNR range. This demonstrates that the architecture is capable of effectively utilizing the additional temporal information available in longer observation intervals when such information is incorporated during training.

Figure 6. RMSE performance of the proposed IQ-MobNet for different numbers of snapshots (T = 10 and T = 100) as a function of SNR.

3.4.2. At Fixed SNR and Angular Separation

In this experiment, the angular separation between two incoming sources is maintained at 4.7°, while the angle of arrival from the first source is ranged from −60° to 55° in 1° increments. Consequently, the angle of arrival from second source is varied from −55.3° to 59.7° in 1° steps, yielding a total of 116 test cases. The objective of this setting is to evaluate how effectively the proposed model resolves sources with small angular separation, while facilitating a comparison with related works. The DoA estimation results for these scenarios at a fixed SNR of 12dB using CBF, ESPRIT, MUSIC, IAA, ResNet, SEResNet, MSEDOA and the proposed IQ-MobNet are presented in Figure 7a–f, with the respective DoA estimation error depicted in Figure 8a–f.

Figure 7. Results for DoA estimation performance at fixed SNR and angular separation for the following methods: (a) CBF, (b) ESPRIT, (c) MUSIC, (d) IAA, (e) ResNet, (f) SEResNet, (g) MSEDOA, and (h) Proposed.

Figure 8. Results for DoA estimation errors for the following methods: (a) CBF, (b) ESPRIT, (c) MUSIC, (d) IAA, (e) ResNet, (f) SEResNet, (g) MSEDOA and (h) Proposed.

To ensure a fair evaluation of typical estimation performance, extreme boundary-condition samples were excluded from the error metrics for all methods. The findings reveal that the proposed model consistently surpasses the traditional methods across all test cases, achieving an error range between [−1.3°, 1°]. Whereas, CBF, MUSIC, ESPRIT, IAA, ResNet, SEResNet exhibit larger error ranges of [−18°, 23°], [−31°, 45°], [−3.5°, 4.8°], [−98°, 98°], [−1.35°, 2°] and [−2°, 1.7°] respectively. It can be seen that CBF, MUSIC, and IAA face difficulties in distinguishing the targets, whereas ESPRIT, IQ-ResNet, SEResNet, MSEDOA and the proposed models showcase better performance compared to the classical methods. A closer examination of the error distributions in Figure 8 provides further insight into the behavior of the different methods. The classical beamforming and subspace-based approaches exhibit significantly larger error variations and several large outliers across the evaluated angular range. In particular, CBF suffers from limited angular resolution, while MUSIC and IAA occasionally fail to correctly separate the two closely spaced sources, resulting in substantial estimation deviations. Although ESPRIT demonstrates considerably lower errors than the other classical methods, its performance still exhibits greater variability than the deep learning-based approaches. In contrast, the deep learning models produce more concentrated error distributions with significantly fewer outliers, indicating improved robustness to variations in source location. Among these methods, the proposed IQ-MobNet maintains a consistently narrow error spread across the entire angular range, demonstrating satisfactory estimation performance while achieving substantially lower computational complexity than the deeper network architectures. Among the evaluated methods, the proposed model demonstrates consistently competitive performance with lower computational complexity.

3.4.3. For Various SNR Levels

This study assesses the performance of proposed model across an SNR range of −25 dB to 15 dB varied at intervals of 2 dB. For this experiment, two sources at an angular separation of 6.1° are considered. Here, a target spacing of 6.1° is used, consistent with prior works such as [38], to facilitate a fair comparison with existing deep learning-based benchmarks. This setup reflects a moderately separated source condition, complementing the tighter spacing used in Section 3.4.2. The signal from the first source is sampled uniformly from [−60°, 53°], while the second source covers angles in the range of [−53.9°, 59.1°]. Across all scenarios, the RMSE is computed for 10,000 Monte Carlo simulations. Figure 9a shows the DoA estimation accuracy of different models for various SNR conditions.

Figure 9. Performance comparison of different methods: (a) Various SNR condition, (b) Diverse angular separations, (c) Random angles.

As SNR increases, the RMSE consistently decreases in all methods under consideration. At an extremely low SNR of −25 dB, noise prevails, and the RMSE values for all the methods are similar. In circumstances where the SNR is high, deep learning-based approaches tend to show almost the same behaviour in RMSE. The proposed method exhibits similar performance to the NN models under consideration and outperforms the classical techniques throughout the entire range of SNR values. Thus, it can be seen that the proposed method generalizes effectively to unseen SNR conditions.

3.4.4. At Diverse Angular Separations

In this experiment, the performance of various DoA estimation methods across different angular separations in the angle range of [$-{60}^{°}$, ${60}^{°}$] is assessed. The antenna array receives signals from two sources separated by an angle $\Delta \theta$. The first source is fixed at $0^{°}$, while the second is positioned at $0^{°}$ + $\Delta \theta$. The SNR is set to 5 dB and seven distinct $\Delta \theta$ values: 1°, 2°, 5°, 8°, 10°, 15°, and 20° are considered, with each scenario tested with 1000 Monte Carlo simulations. DoA estimation results are depicted in Figure 9b. It can be seen that even at low angular separations, the proposed method demonstrates superior performance when compared to other approaches except ESPRIT. From a 5° separation onwards, the proposed model achieves near-zero RMSE and is comparable with other DL models.

3.4.5. At Off-Grid Random Angles

In this test scenario, the DoA of signals from two sources are evenly spread between $-{60}^{°}$ and ${60}^{°}$. The signals are produced with SNRs varying from −25 dB to 15 dB, with increments of 2 dB. To guarantee statistical significance and robustness of the findings, 10,000 samples are produced at each SNR level. The DoA estimation accuracy of various techniques are presented in Figure 9c. This simulation is an off-grid DoA estimation because the true DoA angles are randomly generated within a continuous range [$-{60}^{°}$, ${60}^{°}$], rather than being restricted to a predefined grid of discrete angles such as $1^{°}$ resolution. The RMSE of the deep learning-based methods tends to show constant RMSE behaviour at high SNR levels, showing little improvement as SNR levels rise further. It should be noted that the proposed framework is formulated as a grid-based multi-label classification problem using a predefined 1° angular resolution. During training, the target DoAs are generated exclusively from discrete grid locations, and the corresponding binary label vector activates only the neurons associated with the true angular positions. Consequently, no off-grid targets or soft-label interpolation schemes are employed during training. In the off-grid evaluation, however, the true DoAs are randomly generated from a continuous angular range and may lie between adjacent grid points. Since the estimated DoAs are selected from the predefined output grid, an inherent quantization error is introduced for off-grid targets. As the SNR increases, noise-induced estimation errors become negligible and the remaining error is increasingly dominated by this discretization effect, resulting in the nearly constant RMSE behaviour observed for deep learning-based methods in Figure 9c. Despite this limitation, the proposed IQ-MobNet demonstrates good generalization capability and maintains estimation accuracy comparable to the competing methods under off-grid conditions. Future work will investigate soft-label encoding and gridless regression-based formulations to further reduce discretization-induced errors.

3.4.6. Analysis Using Pseudo-Angle Spectrum

The pseudo-angle spectrum is a visualization of the neural network’s output over the angular grid. Although the model is trained as a multi-label classifier, its output vector can be interpreted as the likelihood of a source being present at each angle. The model’s resolution capabilities can be understood from the plot. In the proposed approach, the deep neural network is trained to perform multi-label classification across a predefined angular grid from $-{60}^{°}$ to ${60}^{°}$ in $1^{°}$ steps. A sigmoid function is applied at the output of the final FC layer of the proposed model to produce a vector of probabilities as mentioned in Equation (18). The resulting vector $\mathbf{p}$ is plotted against the angle grid to form the pseudo-angle spectrum. Peaks in this curve indicate potential DoAs. Conventional spectral methods, such as MUSIC, are based on analytical models rooted in array signal processing theory. In contrast, the neural network learns a data-driven approximation of these spectral patterns, capturing angular information through training, thus forming a pseudo-angle spectrum. Figure 10 presents a visual comparison of the pseudo-angle spectra produced by the IQ-ResNet model considered in [35] and the proposed model in a two-source scenario.

Figure 10. Pseudo-angle spectrum comparison for two targets at angles ([7°, 11.7°]) scenario demonstrates the models’ resolution capabilities for closely spaced sources for (a) IQ-ResNet model and (b) Proposed IQ-MobNet model.

Red dots denote the estimated DoAs (obtained from local maxima), while blue dashed lines indicate ground truth DoAs. Compared to IQ-ResNet in Figure 10a, the proposed model in Figure 10b demonstrates sharper peaks and higher localization accuracy, closely aligning with true directions. This supports its robustness and precision in resolving closely spaced sources. Table 4 presents the estimated DoA values along with their associated likelihoods for both the ResNet model and the proposed model, evaluated across various source position scenarios with an angular separation of 4.7°.

Table 4. Comparison of likelihood values obtained from pseudo-angle spectra for various cases.

True DoA Case	IQ-ResNet [35]		Proposed IQ-MobNet
	Estimated DoA	Likelihood	Estimated DoA	Likelihood
[−1°, 3.7°]	[−1°, 4°]	0.53, 0.84	[−1°, 4°]	0.94, 0.98
[−12°, −7.3°]	[−12°, −7°]	0.4, 0.6	[−12°, −7°]	0.98, 0.88
[27°, 31.7°]	[27°, 32°]	0.66, 0.53	[27°, 32°]	0.73, 0.8
[−24°, −19.3°]	[−24°, −20°]	0.6, 0.7	[−24°, −19°]	0.96, 0.99
[−58°, −53.3°]	[−58°, −54°]	0.52, 0.53	[−58°, −53°]	0.86, 0.64

The proposed IQ-MobNet model consistently demonstrates higher likelihood values for estimated DoAs compared to the recent IQ-ResNet model [35]. The improved likelihood suggests better discrimination and robustness in resolving multiple sources.

3.4.7. For Different Number of Sources

In this test scenario, multi-source (number of sources ranging from 1 to 7) simulations are conducted under two conditions: (i) an SNR of 5 dB with an angular separation of 4°, and (ii) a low-SNR case of −5 dB with the same angular separation of 4°. The performance of all deep learning–based models is evaluated alongside classical DOA estimation methods, with results obtained from 2000 Monte Carlo simulations. The performance results are shown in Figure 11a,b. All methods exhibit an increase in estimation error as the number of sources increases. The proposed model demonstrates robust performance, achieving low RMSE values for up to three sources and showing performance comparable to other DL-based approaches while consistently outperforming classical methods for up to seven sources. In the negative-SNR scenario, when the number of sources exceeds two, the proposed model achieves performance comparable to SE-ResNet and outperforms all remaining methods considered.

Figure 11. Performance comparison of different methods in multi-source scenario: (a) at 5 dB SNR and an angular separation of 4; (b) at low-SNR scenario of −5 dB.

It should be noted that the training dataset contains samples with a maximum of three simultaneous sources. Therefore, the experiments involving four to seven sources represent out-of-distribution evaluation scenarios that were not observed during training. These experiments provide additional insight into the behavior of the proposed framework under increasingly challenging source configurations beyond those encountered during training. The results indicate that IQ-MobNet continues to produce reasonable estimates under such conditions; however, performance in these scenarios may be further improved by incorporating higher-order source configurations into the training dataset.

3.4.8. Robustness Under Mutual Coupling Effects

To evaluate the robustness of the proposed IQ-MobNet against practical array imperfections, additional simulations were conducted in the presence of mutual coupling between antenna elements. The mutual coupling effect is modeled through a coupling matrix

$$\mathbf{C}=\left[\begin{array}{ccccc}1& c& c^2& \cdots & c^{N-1}\\ c& 1& c& \cdots & c^{N-2}\\ c^2& c& 1& \cdots & c^{N-3}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ c^{N-1}& c^{N-2}& c^{N-3}& \cdots & 1\end{array}\right],$$

(21)

where c denotes the mutual coupling coefficient [50]. The steering vector in the presence of mutual coupling is given by

$${\mathbf{a}}_c\left(\theta \right)=\mathbf{C}\mathbf{a}\left(\theta \right),$$

(22)

resulting in the coupled array observation

$$\mathbf{X}=\mathbf{C}\mathbf{A}\mathbf{S}+\mathbf{N},$$

(23)

where A is the ideal steering matrix, S is the source signal matrix, and N denotes additive noise. For this experiment, two-source scenarios with a fixed angular separation of $6^{°}$ were considered. The source locations were systematically varied from $(-{30}^{°},-{24}^{°})$ to $({24}^{°},{30}^{°})$ in $1^{°}$ increments, resulting in 55 distinct source configurations. The proposed IQ-MobNet was trained using the original ideal-array dataset and subsequently evaluated under coupled-array conditions without retraining. The mutual coupling coefficient was varied from 0 to 0.3, while the performance was assessed at SNR values of −5 dB, 0 dB, and 5 dB. For each configuration, 100 Monte Carlo trials were performed and the logarithmic root-mean-square error (log-RMSE) was computed.

Figure 12 illustrates the variation in ${\log }_{10}\left(\mathrm{RMSE}\right)$ with increasing mutual coupling coefficient. It can be observed that the proposed IQ-MobNet maintains stable performance under weak coupling conditions and exhibits only a gradual degradation as the coupling strength increases. At low SNR ($-5$ dB), the performance is primarily limited by noise, resulting in only minor variations with increasing coupling. As the SNR increases, the effect of mutual coupling becomes more apparent due to the mismatch between the ideal array model used during training and the coupled array responses encountered during testing. Nevertheless, the proposed framework continues to provide reliable DoA estimates under the considered coupling conditions, indicating a degree of robustness to practical array imperfections despite being trained using ideal-array data.

Figure 12. Performance of IQ-MobNet in the presence of mutual coupling between antennas.

3.4.9. Performance Under Coherent Sources

To evaluate the robustness of the proposed IQ-MobNet under coherent signal conditions, an additional experiment is conducted using two-source scenarios with fixed angular separation of $6^{°}$. Five representative angle pairs spanning the field of view were selected and, for each pair, 1000 Monte Carlo realizations were generated at SNRs ranging from $-25$ dB to 15 dB. For the coherent-source case, both sources are assigned identical complex baseband waveforms, resulting in fully coherent arrivals. The independent-source case employed statistically independent source signals and serves as a reference. The root mean square error (RMSE) obtained by averaging over all angle pairs and Monte Carlo realizations is shown in Figure 13.

Figure 13. RMSE performance comparison between coherent and non-coherent sources for the proposed IQ-MobNet.

As illustrated in Figure 13, the proposed IQ-MobNet is capable of operating under coherent-source conditions, although a performance degradation is observed compared with the non-coherent-source case. At low SNRs, the performance of both scenarios is similar since noise dominates the estimation error. As the SNR increases, the RMSE decreases for both coherent and non-coherent source scenarios. However, the coherent-source case consistently exhibits higher estimation errors than the non-coherent case. This trend can be attributed to the increased challenge of distinguishing sources that share highly correlated signal waveforms, which effectively reduces the diversity of the received observations and makes source separation more difficult. These results indicate that IQ-MobNet retains a reasonable degree of robustness in the presence of source coherence, despite not being explicitly designed or trained for coherent-source scenarios.

3.5. Performance Evaluation in Single-Source Scenario

This section presents the evaluation results of all methods under a test scenario involving a single target. Although the models are trained on multi-target data, they are evaluated here on single-target inputs to assess their generalization capability in untrained scenarios.

3.5.1. At Fixed SNR

This test checks how well different algorithms such as the proposed model, classical techniques, (CBF, MUSIC, ESPRIT, and IAA) and other deep learning-based approaches (Lightweight DNN, IQ-ResNet, SEResNet, MSEDOA) can estimate the direction-of-arrival in a single-source situation under a fixed SNR condition. Figure 14a shows the DoA estimation error values of all the methods across the full angle range index considered. The proposed model demonstrates minimal error, mostly zero across all indices. With the exception of ResNet, all DNN-based models achieve zero error throughout the entire range, except at the extreme boundary cases.

Figure 14. Single-source test evaluation results: (a) Performance comparison of different methods (b) Various SNR conditions (c) Random angles.

3.5.2. For Various SNR Levels

The goal of this test is to assess the model’s accuracy in estimating the direction of an untrained single-source by analyzing the RMSE across different SNR levels. In this test case experiment, single-source signals are generated at random angles in the range $\left[-{60}^{°},{60}^{°}\right]$. The SNR is varied from −25 dB to 15 dB with increments of 2dB to analyze robustness under different noise conditions. The RMSE is computed between the true and estimated angles for the proposed model, as well as for other models under consideration, over multiple Monte Carlo trials. Figure 14b shows the outcomes in the single-source scenario considering various SNR values. In the low SNR range, the proposed model gives better performance when compared to other methods and in high SNR region, the proposed model gives almost the same accuracy as the other NN models under consideration.

3.5.3. At Off-Grid Random Angles

This experiment evaluates the model’s accuracy in estimating the DoAs for a single signal source at off-grid angles. Unlike on-grid based settings, here the DoAs are randomly sampled from a continuous uniform distribution over [−60°, 60°], making this an off-grid evaluation scenario. Signals are generated across various SNR levels from −25 dB to 15 dB in 2 dB steps, and the RMSE is computed over multiple Monte Carlo trials to assess performance. The corresponding results are plotted in Figure 14c. It can be seen that the proposed model demonstrates better performance in low SNR conditions, and its performance in medium and high SNR ranges remains comparable to other state-of-the-art methods.

Table 5 and Table 6 summarize the worst-case $lo{g}_{10}\left(RMSE\right)$ performance for two-source and single-source DOA estimation, respectively, across different SNR and angular separation conditions. For DoA estimation performance across angle indices, worst-case values in terms of DoA error (in degrees) are reported. In both single-source and two-source scenarios, classical methods exhibit consistently higher errors, particularly under low-SNR and closely spaced source conditions. While heavier DL-based models such as IQ-ResNet, SE-ResNet, and MSEDOA achieve improved accuracy, the proposed method attains comparable or lower worst-case RMSE across most operating conditions. Notably, the proposed model achieves this performance advantage with a more balanced trade-off between accuracy and model complexity, outperforming the lightweight DNN and remaining competitive with deeper architectures in both single- and multi-source settings.

Table 5. Two-source DOA estimation performance (worst case).

Method	Angle Index	Low SNR	Mid SNR	High SNR	2° Sep	5° Sep	10° Sep
IAA [14]	92°	1.88	1.84	1.64	1.68	1.59	1.46
CBF [1]	23°	1.80	1.69	1.52	1.19	1.36	0.90
ESPRIT [6]	4.8°	1.86	1.76	1.16	1.67	0.86	0.11
MUSIC [5]	45°	1.79	1.55	0.98	1.55	1.34	−0.26
IQ-ResNet [35]	2°	1.80	0.68	0.63	1.54	0.20	0.06
SE-ResNet [37]	1.7°	1.77	0.87	0.76	1.39	0.12	−0.01
MSEDOA [38]	1°	1.73	0.64	0.61	1.40	0.38	−0.03
Lightweight DNN [47]	45°	1.89	1.87	1.22	1.4	1.42	1.42
Proposed	1°	1.76	0.89	0.29	1.31	0.13	0.19

Table 6. Single-source DOA estimation performance (worst case).

Method	Angle Index	Low SNR	Mid SNR	High SNR	Random Angle
IAA [14]	4°	1.73	1.73	1.68	1.69
CBF [1]	0°	1.67	0.55	0.15	1.66
ESPRIT [6]	0.55°	1.71	1.68	1.66	1.71
MUSIC [5]	0°	1.66	0.23	0.13	1.65
IQ-ResNet [35]	1°	1.65	0.57	0.55	1.67
SE-ResNet [37]	1°	1.62	0.60	0.46	1.68
MSEDOA [38]	0°	1.59	0.58	0.71	1.61
Lightweight DNN [47]	50°	1.74	1.7	1.13	1.73
Proposed	0°	1.59	0.53	0.32	1.62

3.6. Complexity Analysis

Table 7 compares the total parameters and FLOPs of IQ-ResNet, SEResNet, MSEDOA, and the proposed IQ-MobNet, along with inference time, memory footprint, power consumption, and throughput. While the lightweight DNN model exhibits the lowest model complexity (2217 trainable parameters and 2315 FLOPs) among the evaluated deep learning approaches, its DoA estimation accuracy is comparatively lower under the considered evaluation scenarios.

Table 7. Performance comparison of different models in terms of complexity and inference metrics.

Model	Total Params	FLOPs	Inference Time (ms)	Memory Footprint (MB)	Avg. Power Consumption (W)	Throughput (Samples/s)
IQ-ResNet [35]	$6.79\times {10}^6$	$6.87\times {10}^6$	$1.93(\pm 0.04)$	27.26	$27.53(\pm 0.19)$	519
MSEDoA [38]	$6.70\times {10}^7$	$9.82\times {10}^7$	$11.13(\pm 0.14)$	268.85	$30.39(\pm 4.18)$	90
SE-ResNet [37]	$5.75\times {10}^7$	$5.84\times {10}^7$	$5.64(\pm 0.06)$	230.89	$34.22(\pm 4.95)$	177
IQ-MobNet (Proposed)	$\mathbf{2.41}\times {\mathbf{10}}^{\mathbf{5}}$	$\mathbf{4.15}\times {\mathbf{10}}^{\mathbf{5}}$	$\mathbf{1.79}(\pm \mathbf{0.05})$	$\mathbf{1.05}$	$\mathbf{27.09}(\pm \mathbf{0.09})$	$\mathbf{559}$

Note: Bold values indicate the best performance for each evaluation metric.

Among the models considered in this complexity analysis, the proposed IQ-MobNet reduces the total number of parameters by 96.45%, 99.64%, and 99.58% compared to the models such as IQ-ResNet, MSEDoA, and SEResNet respectively. Similarly, it reduces FLOPs by 93.96%, 99.58%, and 99.29%, respectively. These substantial reductions are achieved without compromising performance, even under low snapshot conditions (10 snapshots), where all models are trained and evaluated under identical settings. To further evaluate the computational efficiency and real-time potential of the proposed IQ-MobNet, Table 7 also presents a comparative analysis of inference performance against existing deep learning baselines (IQ-ResNet, SE-ResNet, and MSEDoA). Inference time is the time taken by the model to process a single sample (in ms), memory footprint refers to the GPU memory consumption (in MB) required for inference. Average power consumption (in Watts) indicates the energy usage during inference. Throughput refers to the number of samples processed per second, indicating overall processing efficiency. With a batch size of one, the proposed lightweight model attains the minimum inference time of 1.79 ms and highest throughput of 559 samples/s. Moreover, IQ-MobNet uses only 1.05 MB of memory and exhibits the lowest power consumption among all the models evaluated. From Table 5 and Table 6, it is evident that the proposed model outperforms classical methods in most cases and achieves performance comparable to recent deep learning-based approaches. Table 7 clearly shows that the proposed method exhibits the lowest complexity among all neural network models considered. These results collectively confirm that the proposed model achieves a favorable balance between accuracy and computational cost, making it substantially more practical for deployment in resource-constrained radar edge platforms and real-time DoA estimation systems.

It should be noted that the inference time and throughput measurements reported in Table 6 were obtained using an NVIDIA L4 GPU. While these results provide a useful comparative assessment of the computational efficiency of the evaluated deep learning models under a common hardware environment, they may not directly reflect performance on resource-constrained edge platforms used in practical portable radar systems. Therefore, evaluation of the proposed IQ-MobNet framework on embedded processors, FPGA-based implementations, and other low-power hardware platforms remains an important direction for future work.

3.7. Ablation Analysis

In this section, an ablation study is performed, which is essential for understanding the contribution of individual components in a neural network model. By systematically modifying or removing specific elements, their impact on overall performance can be assessed, thereby guiding model optimization and improving efficiency. In this study, ablation analysis is conducted on the proposed model by exploring two key modifications: (1) removing and adding some inverted residual blocks (IRBs) and (2) replacing global average pooling with flattening. The performance metrics are evaluated for all cases considered and given in Table 8, where the model configuration refers to the key elements contained in the ablation study. The proposed model is treated as the reference model for the ablation analysis. Firstly, this ablation study investigates the impact of removing the IRB4 block from the proposed model architecture. By eliminating this block, its contribution to the model’s performance in terms of accuracy, training speed, and generalization is analyzed. In the proposed model, each IRB block processes feature maps and progressively changes their dimensions. When we remove IRB4, the final feature map reaching the fully connected (FC) layer has fewer channels than in the original model. That means, without block 4, the last feature map remains at 32 channels instead of 64, and the network may exhibit reduced capacity to learn complex data patterns, leading to limited generalization. Furthermore, when the last two blocks, IRB3 and IRB4, are removed, the final feature map reaching the FC layer is further reduced to 24 channels, and even though it reduces the training time and complexity, it results in further reduces accuracy. When the block size increased to 5, it also results in a drop in accuracy, along with an increase in complexity as well as overall training time. The first test shows that cutting down on the number of inverted residual blocks made validation more accurate but made generalization worse on test data, which could mean that important feature representations are lost. Hence, it is essential to keep 4 IRBs, as in the proposed model. Further, the role of the pooling mechanism in feature aggregation and their influence on model performance is examined. To achieve this, the global average pooling layer is replaced with flattening. Unlike GAP, which reduces each feature map to a single scalar by averaging across spatial dimensions, flattening retains all spatial information, transforming the full feature map tensor into a 1D vector. It resulted in an increase in space complexity (number of total parameters) as well as time complexity. The accuracy also has deteriorated because of the possible risk of overfitting, underscoring the importance of global average pooling as in the proposed classification based model.

Table 8. Ablation study showing how different configurations of the proposed model (number of IRBs and feature aggregation strategy) affect complexity, training cost, and generalization performance.

Ablation Study 1: Altering Number of Blocks
Model Configuration	Time Complexity (FLOPs)	Space Complexity (Parameters)	Epoch × Training Time	Accuracy	Observation
4 IRBs (Proposed)	$4.15088\times {10}^5$	$2.40857\times {10}^5$	$100\times 76$ s	93	Good Generalization
3 IRBs	$3.47824\times {10}^5$	$2.03417\times {10}^5$	$100\times 71$ s	92.99	Poor Generalization
2 IRBs	$3.03760\times {10}^5$	$1.89321\times {10}^5$	$100\times 66$ s	92.85	Poorer Generalization
5 IRBs	$5.26960\times {10}^5$	$2.95129\times {10}^5$	$100\times 81$ s	92.74	Accuracy dropped
Ablation Study 2: Altering Global Average Layer
Flatten Layer Type	Time Complexity	Space Complexity (Parameters)	Epoch × Training time	Accuracy	Observation
Global Average Pooling	$4.15088\times {10}^5$	$2.40857\times {10}^5$	$100\times 76$ s	93	Good Generalization
Flatten	$4.47664\times {10}^5$	$2.73625\times {10}^5$	$100\times 77$ s	92.62	Accuracy dropped

Thus, ablation studies highlight the significance of retaining all four IRB blocks for strong generalization, while employing global average pooling helps reduce complexity and avoid overfitting by preserving robustness and accuracy in the proposed architecture.

4. Validation with Real-World Data

To assess the practical generalization capability of the proposed model beyond simulated environments, real-world validation is conducted using measured array data. In this work, real measurements were obtained from the publicly released Deep-RSA-DOA dataset (https://github.com/ruxinzh/Deep_RSA_DOA), accessed on 10 December 2025 [54], which contains complex baseband signals collected using a ten-element uniform linear array. The dataset was generated in a parking-lot scenario using a stationary vehicle equipped with a TI cascade imaging radar, where signals were collected from a corner reflector placed approximately 15 m away while covering a wide range of incident angles. This process yielded 195 high-SNR single-target measurements corresponding to different directions, and multi-target scenarios were synthesized by superimposing these measured signals [55]. All deep learning models, including the proposed MobNet-based architecture as well as ResNet, SE-ResNet, and MSEDOA, are trained solely on simulated data and evaluated on real measurements. Prior to inference, the measured radar data from the Deep-RSA-DOA dataset were loaded as complex-valued array measurements. To ensure compatibility with the trained IQ-MobNet architecture, the measurements were arranged into the same input dimensionality and representation used during training. The corresponding real and imaginary components were retained as the in-phase (I) and quadrature (Q) inputs to the network. No covariance matrix estimation, spatial spectrum generation, beamforming preprocessing, or other preprocessing was performed. Consequently, the measured data were processed using the same raw-IQ representation adopted for the simulated training data, enabling a consistent evaluation of the model’s simulation-to-real generalization capability. Figure 15 shows the DoA estimation validation results of all models considered. Performance was compared against both learning-based baselines, MLP [56] and SADOANet [54] and classical signal processing methods DBF and IAA [14], following the same evaluation methods adopted in the reference study, thereby ensuring a fair and reproducible comparison under realistic operating conditions. Performance is assessed using peak confidence level and the shape factor of the spatial pseudo-spectrum, which quantifies spatial selectivity, together with computational complexity metrics such as inference time and total trainable parameters. The shape factor is taken as the ratio between the angular width of the normalized spatial spectrum measured at 10% of the peak magnitude and the angular width measured at the 3-dB point, where the 3-dB point corresponds to 0.707 times the peak magnitude. A lower shape factor indicates improved spatial selectivity. The corresponding numerical results are summarized in Table 9, where S1 and S2 denote the two sources. In the two-target scenario with ground-truth DoAs of [0, 7°], the proposed method reliably resolves both sources, achieving near-ideal confidence levels (1 and 0.995) while requiring significantly fewer parameters than competing deep learning models, thereby demonstrating a favorable accuracy–complexity trade-off.

Figure 15. DoA estimation performance validation results with real-world data: (a) ULA configuration, (b) DBF vs. IAA, (c) MLP, (d) SADOANet, (e) IQ-ResNet, (f) SE-ResNet, (g) MSEDOA, (h) Proposed. Dashed vertical lines represent the ground-truth DoAs.

Table 9. Performance and complexity comparison of DOA estimation methods validated on real-world data.

Method	Confidence Level		Shape Factor		Inference Time (ms)	Total Params
	S1	S2	S1	S2
DBF	1	0.165	3.46	6.67	0.177	–
IAA [14]	0.550	1	3.25	4	6.439	–
MLP [56]	1	0.912	2	2	0.526	2,848,829
SADOANet [54]	1	0.9	1.5	1.5	1.167	4,106,301
IQ-ResNet [35]	1	-	1	-	1.905	6,758,717
SE-ResNet [37]	1	0.522	1	1	6.021	57,290,685
MSEDOA [38]	1	0.983	1	1	11.232	67,002,131
Proposed	1	0.995	2	1.33	2.339	613,341

Although both the simulated and measured datasets are derived from the Deep-RSA-DOA framework, their generation processes differ substantially. The simulated dataset is generated using analytical array signal models with randomly generated target reflections and controlled SNR conditions, whereas the measured dataset is collected using a TI cascade imaging radar in a real parking-lot environment. The measured dataset consists of 195 experimentally acquired single-target responses from different directions, and multi-target scenarios are constructed by superimposing these measured responses. Consequently, the measured data capture practical characteristics of the sensing environment and radar hardware that are not fully represented by the simulation model. Despite these differences, the proposed IQ-MobNet demonstrates reliable performance on the measured dataset, indicating good simulation-to-real generalization capability.

Potential estimation errors may arise in challenging scenarios involving closely spaced sources, off-grid target locations, coherent source signals, mutual coupling effects, or source configurations that differ significantly from those represented in the training data. In such cases, overlapping spatial signatures, source correlation, and array-model mismatches may reduce angular separability and increase localization errors. Furthermore, the measured multi-target scenarios are generated through superposition of experimentally acquired single-target responses and may not fully capture all characteristics of practical multi-target environments. Although additional simulation studies have been conducted to assess the robustness of the proposed framework under several challenging conditions, comprehensive validation across a wider range of real-world measured radar datasets remains limited by the availability of publicly accessible experimental DoA datasets. These factors represent limitations and motivate future work on evaluating the proposed framework using larger and more diverse real-world datasets.

It should be noted that the current implementation assumes prior knowledge of the number of signal sources during inference, and the final DoA estimates are obtained by selecting the top-k output probabilities. While this assumption is commonly adopted in benchmark evaluations, practical radar systems often operate under unknown source-number conditions. In such scenarios, the proposed framework could be combined with source-number estimation techniques, including threshold-based peak detection, or dedicated source-count estimation networks. Extending the framework to jointly estimate the number of sources and their corresponding DoAs will be considered in future work. Future work may also focus on extending the proposed framework toward regression-based DoA estimation and supporting different array geometries.

5. Conclusions

Direction-of-arrival (DoA) estimation is key to accurately localizing sources and improving the performance of many radar and wireless systems. This work presented a lightweight, effective deep learning approach which can directly process raw IQ data for DoA estimation in portable radar applications. By directly utilizing raw IQ signals, the proposed model avoids the need for preprocessing steps. Through extensive evaluations under various challenging conditions such as low SNR, closely spaced sources, and off-grid scenarios, it is demonstrated that the proposed IQ-MobNet model consistently outperforms conventional techniques such as MUSIC, ESPRIT, CBF, IAA as well as Lightweight DNN and achieves performance comparable to deep learning models such as ResNet, SEResNet, and MSEDOA. Notably, IQ-MobNet achieves this competitive performance with significantly reduced computational complexity, requiring only 0.24 million parameters and 0.42 million FLOPs—a reduction of over 96% compared to the recent ResNet-based models. Furthermore, an ablation study demonstrated the significance of our architectural choices, reinforcing the importance of the proposed model. Validation with real-world data confirms the robustness and practical applicability of the proposed model beyond idealized environments and highlighting its strong generalization capability. These results underline the effectiveness, efficiency, and suitability of IQ-MobNet for portable radar applications requiring computationally efficient models for real-time deployment. Future work includes implementing the proposed model on an FPGA to demonstrate its real-time performance and hardware efficiency in embedded applications.