DP-DRSN: Lightweight Dual-Path AMC Model

• The paper introduces DP-DRSN as a compact model for automatic modulation classification that fuses dual I/Q and A/P representations with a hybrid CNN-LSTM extractor.
• It employs a dual-path deep residual shrinkage denoiser with learnable Garrote thresholding to effectively suppress noise, particularly at low SNRs.
• Ablation studies confirm that the dual-path strategy and Garrote shrinkage boost accuracy with minimal parameter increase, ensuring suitability for edge deployment.

Dual-Path Deep Residual Shrinkage Network (DP-DRSN) is a low-complexity, lightweight deep learning architecture for automatic modulation classification (AMC) in resource-constrained edge devices, introduced in "A Lightweight Deep Learning Model for Automatic Modulation Classification using Dual Path Deep Residual Shrinkage Network" (Suman et al., 7 Jul 2025). The model is motivated by the need to balance spectrum-efficiency-oriented AMC performance with the memory, compute, and energy limits of IoT sensors and related on-edge platforms. Its defining features are a dual-input representation of received signals in both in-phase/quadrature (I/Q) and amplitude/phase (A/P) form, a compact hybrid CNN-LSTM feature extractor, and a dual-path deep residual shrinkage denoiser that uses learnable Garrote thresholding to suppress noise while preserving informative coefficients.

1. Problem setting and design rationale

Efficient spectrum utilization is described as critical to meeting the growing data demands of modern wireless communication networks, and AMC is presented as a key capability for dynamic spectrum allocation and interference mitigation, particularly in cognitive radio systems (Suman et al., 7 Jul 2025). In that setting, secondary users must opportunistically access spectrum without harming primary users, while radios also benefit from modulation and coding strategies adapted to prevailing channel conditions.

The central design problem is the tension between model size and robustness. Many high-accuracy deep AMC models are stated to have hundreds of thousands to millions of parameters, which is prohibitive for devices constrained by memory, compute, and energy. At the same time, aggressive simplification can reduce robustness, especially at low signal-to-noise ratio (SNR), where practical radios must still make decisions. DP-DRSN is presented as directly targeting this gap by combining lightweight feature extraction with residual shrinkage denoising.

Two architectural principles are emphasized. First, dual-path hybrid feature extraction is tailored to radio signals: a compact CNN learns local spatial features such as symbol shape and constellation structure, while a small LSTM captures temporal dependencies such as burst structure and pulse shaping across both I/Q and A/P views. Second, a deep residual shrinkage network is upgraded to a dual-path variant that estimates per-channel, data-adaptive thresholds from both global average and global max statistics. The use of non-negative Garrote thresholding is intended to reduce the bias associated with soft thresholding, especially for large coefficients, which is significant under noisy low-SNR conditions. This suggests that DP-DRSN is designed less as a generic compact classifier than as a denoising-aware AMC model whose efficiency claims depend on preserving discriminative radio structure under channel impairment.

2. Signal representations and hybrid feature extraction

The architecture consumes two synchronized signal representations in parallel (Suman et al., 7 Jul 2025). The first is the raw complex baseband input,

$$X_{IQ} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} X_I[1] & \cdots & X_I[N] \ X_Q[1] & \cdots & X_Q[N] \end{bmatrix},$$

which retains the native Cartesian structure used by most receivers. The second is the derived amplitude/phase representation,

$$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$

$$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$

The rationale is explicitly complementary. The I/Q branch is described as suitable for decoding constellation geometry, phase rotations, and IQ imbalance effects, whereas the A/P branch emphasizes amplitude envelope and phase trajectory continuity, which often improves separability of certain analog and CPFSK/GFSK modulations. The model therefore treats modulation recognition as a multi-view representation problem rather than relying on a single coordinate system.

Within each path, the feature extractor combines a small recurrent branch and a compact convolutional branch. The LSTM branch uses 4 units with return_sequences=True, after which its output is reshaped to align with CNN features for concatenation. The CNN branch uses two asymmetric dilated Conv2D layers:

• Conv2D(filters=4, kernel=(3,1), dilation_rate=(2,2))
• Conv2D(filters=4, kernel=(1,3), dilation_rate=(2,2))

The asymmetric decomposition is described as reducing parameters while capturing horizontal and vertical structure, and dilation widens the receptive field without adding parameters. The kernel initializer is He normal, and L2 kernel regularization is set to $10^{-4}$. Within each path, CNN and LSTM features are concatenated along the channel dimension, producing a compact multiscale representation that mixes temporal and spatial cues. A layer-by-layer outline further specifies the reshape from $(N,2)$ to $(L=N,2,1)$, concatenation of the asymmetric CNN outputs along axis $2$, and subsequent concatenation of CNN and LSTM outputs along axis $3$.

3. Residual shrinkage denoiser and Garrote thresholding

The denoising stage is the defining component of DP-DRSN. Each input path contains a denoiser stack of four residual-shrinkage blocks with $(\text{filters}, \text{kernel}, \text{stride})$ equal to $(9,3,(2,2))$, $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$0, $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$1, and $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$2 (Suman et al., 7 Jul 2025). Each block uses identity shortcuts, with average-pooling downsampling and padding in the skip connection when spatial dimensions or channel counts change, so that residual addition remains feasible even when stride differs from $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$3.

Let the input to a residual shrinkage block be $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$4. The residual path applies two successive BN-ReLU-Conv operations:

$$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$5

$$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$6

With $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$7, the block computes per-channel global descriptors using both global average pooling and global max pooling:

$$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$8

Each descriptor is passed through an FC-BN-ReLU-FC-sigmoid tower to produce coefficients $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$9 and $$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$0:

$$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$1

These are combined using a learnable convex weight $$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$2 and a learnable positive scale $$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$3:

$$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$4

Thresholds are therefore per-channel and data-adaptive, then broadcast across the spatial dimension. This is the “dual-path” mechanism internal to the shrinkage block: GAP and GMP contribute separate statistics to threshold estimation.

The non-negative Garrote shrinker is then applied elementwise to signed entries of $$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$5, with $$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$6 to avoid division by zero:

$$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$7

The equivalent form without $$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$8, for $$X_{AP} \in \mathbb{R}^{2 \times N} = \begin{bmatrix} A[1] & \cdots & A[N] \ P[1] & \cdots & P[N] \end{bmatrix}.$$9, is

$10^{-4}$0

The block output is

$10^{-4}$1

where $10^{-4}$2 denotes the identity mapping, possibly with downsampling and padding to match shape.

The model explicitly contrasts Garrote and soft thresholding. Soft thresholding,

$10^{-4}$3

is stated to have approximately constant bias $10^{-4}$4 for large true coefficients. By contrast, for Garrote shrinkage, if $10^{-4}$5 and $10^{-4}$6, the bias behaves as $10^{-4}$7, which decays with signal magnitude. The stated implication is lower mean-squared error than soft thresholding for large components and smoother behavior near threshold, with less artifacting. In the AMC setting, the shrinkage stack is placed between feature extraction and classification so that denoising acts on learned feature maps rather than on raw samples, a placement described as improving noise suppression with minimal information loss.

4. End-to-end architecture, fusion, and optimization

After the denoiser stack in each path, the architecture applies BatchNorm, ReLU, and Global Average Pooling to form a compact embedding $10^{-4}$8 (Suman et al., 7 Jul 2025). The embeddings from the I/Q and A/P branches are then concatenated and mapped linearly to logits,

$10^{-4}$9

followed by

$(N,2)$0

The AMC objective is written as

$(N,2)$1

and the loss is categorical cross-entropy:

$(N,2)$2

Training uses Adam with initial learning rate $(N,2)$3, ReduceLROnPlateau with factor $(N,2)$4 if validation loss stalls for 5 epochs, and EarlyStopping with patience of 30 epochs. Batch size is 64 and training proceeds for up to 200 epochs. L2 regularization of $(N,2)$5 is applied on convolutional and fully connected layers, He normal initialization is used, and no explicit dropout is used. Frameworks are Keras and TensorFlow.

The reported model complexity is $(N,2)$6 parameters for RML2016.10a and RML2016.10b with $(N,2)$7, and $(N,2)$8 parameters for RML2018.01a with $(N,2)$9. FLOPs are approximately $(L=N,2,1)$0 million for $(L=N,2,1)$1 inputs and $(L=N,2,1)$2 million for $(L=N,2,1)$3 inputs. Model size is $(L=N,2,1)$4 kB. Inference latency per sample, measured on Windows 11 with an Intel Core i9 at 2.6 GHz, 64 GB RAM, and an NVIDIA GeForce RTX 4080, is reported as $(L=N,2,1)$5 to $(L=N,2,1)$6 ms depending on input length, and energy per sample as $(L=N,2,1)$7 to $(L=N,2,1)$8 mJ. A notable implementation caveat is that TensorFlow reserves approximately $(L=N,2,1)$9 GB on GPU by default; the source explicitly identifies this as allocator behavior rather than model memory.

5. Datasets, reported results, and ablations

The empirical evaluation uses standard train/validation/test splits without special data augmentation beyond dataset-built-in channel impairments and SNR variations (Suman et al., 7 Jul 2025). RML2016.10a consists of $2$0 complex samples per example with SNR from $2$1 to $2$2 dB and a $2$3 split. RML2016.10b also uses $2$4 inputs, SNR from $2$5 to $2$6 dB, and a $2$7 split. RML2018.01a uses $2$8 inputs and is described as having SNR from $2$9 to $3$0 dB in 2 dB steps over 26 levels, 24 modulations, 4096 examples per modulation/SNR, and a total of $3$1 examples; the listed modulations include BPSK, QPSK, 8PSK, 16QAM, 64QAM, CPFSK, GFSK, GMSK, 4ASK, PAM4, AM-DSB, AM-SSB, FM, WBFM, and OOK. Channel impairments include sample-rate and symbol-rate offset, carrier frequency offset, selective fading, and AWGN.

The reported overall average and maximum accuracies are summarized below.

Dataset	Configuration	Reported accuracy
RML2016.10a	$3$2; $3$3	61.20% average; 91.23% max
RML2016.10b	$3$4; $3$5	63.78% average; 93.64% max
RML2018.01a	$3$6; total $3$7	62.13% average; 97.94% max

Accuracy is reported to rise smoothly with SNR. For RML2018.01a, DP-DRSN with Garrote thresholding shows notably better low-SNR performance than soft thresholding, with an average gain of about $3$8 over $3$9 dB to $(\text{filters}, \text{kernel}, \text{stride})$0 dB. Confusion matrices are described as showing common confusions at $(\text{filters}, \text{kernel}, \text{stride})$1 dB among closely related digital modulations such as 16QAM versus 64QAM and between analog AM variants and WBFM, while at high SNR the matrices become near-diagonal.

The ablation studies separate the effects of dual-path threshold estimation and Garrote thresholding. Replacing DP-DRSN with single-path shrinkage using only GAP reduces average accuracy on RML2018.01a from $(\text{filters}, \text{kernel}, \text{stride})$2 to $(\text{filters}, \text{kernel}, \text{stride})$3, reduces maximum accuracy to $(\text{filters}, \text{kernel}, \text{stride})$4, lowers parameters to $(\text{filters}, \text{kernel}, \text{stride})$5, and leaves FLOPs unchanged. Replacing Garrote with soft thresholding reduces average accuracy to $(\text{filters}, \text{kernel}, \text{stride})$6 and maximum accuracy to $(\text{filters}, \text{kernel}, \text{stride})$7. The stated interpretation is that the slightly higher complexity of dual-path shrinkage is justified by the accuracy gain, while Garrote especially benefits low-SNR operation.

The comparison on RML2018.01a situates DP-DRSN among compact and heavier baselines. With approximately $(\text{filters}, \text{kernel}, \text{stride})$8 parameters and $(\text{filters}, \text{kernel}, \text{stride})$9 million FLOPs, it achieves $(9,3,(2,2))$0 average and $(9,3,(2,2))$1 maximum accuracy, compared with ResNet at $(9,3,(2,2))$2 parameters, $(9,3,(2,2))$3 million FLOPs, and $(9,3,(2,2))$4 average accuracy; LSTM at $(9,3,(2,2))$5, $(9,3,(2,2))$6 million FLOPs, and $(9,3,(2,2))$7 average accuracy; CDSCNN at $(9,3,(2,2))$8, $(9,3,(2,2))$9 million FLOPs, and $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$00 average accuracy; and CV-TRN at $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$01, $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$02 million FLOPs, and $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$03 average accuracy. DP-DRSN is reported to provide a favorable accuracy/efficiency trade-off and the fastest per-sample inference among the compared methods at $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$04 ms.

6. Interpretation, limitations, and prospective extensions

DP-DRSN is framed as a model for on-edge AMC rather than as a pure accuracy-maximizing architecture (Suman et al., 7 Jul 2025). Its key reported balance is approximately $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$05 parameters, $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$06 to $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$07 million FLOPs, $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$08 to $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$09 ms latency, and average accuracy in the $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$10 to $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$11 range across RML2016.10a, RML2016.10b, and RML2018.01a. This suggests that the architecture should be understood through the lens of accuracy-efficiency co-optimization: compactness and denoising robustness are co-equal design criteria.

Several limitations are stated directly. Although exceptionally compact and fast, the average accuracy of roughly $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$12 trails heavier models that reach roughly $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$13 to $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$14 average accuracy on RML2018.01a in some comparisons. Performance still drops at very low SNRs, and class confusions remain among similar digital modulations and between analog types at mid SNR. Results are reported as single-run metrics, and variance across random seeds is not provided. Generalization is evaluated on widely used synthetic/OTA benchmarks; broader testing on real-world captures and unseen channel models is identified as necessary to strengthen claims.

The implementation notes also address a common misconception about memory footprint. The approximately $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$15 GB GPU memory usage under TensorFlow is explicitly characterized as allocator behavior rather than model memory; the model itself is reported as $$A[i] = \sqrt{X_I[i]^2 + X_Q[i]^2}, \qquad P[i] = \arctan(X_I[i]/X_Q[i]),$$16 kB. No pruning or quantization is applied, and the listed future directions include pruning and quantization for smaller on-device models, attention or learned moments pooling on top of DP-DRSN, curriculum over SNRs, domain adaptation to channel mismatch, further FLOP reductions through depthwise or separable convolutions, and energy profiling on embedded SoCs and MCUs.

In summary, DP-DRSN combines two complementary signal views, a tiny LSTM plus asymmetric dilated CNN feature extractor, and per-channel shrinkage thresholds learned from both global average and global max statistics. The reported outcome is a lightweight AMC architecture whose denoising mechanism aims to preserve salient coefficients while suppressing noise, particularly at low SNR, and whose empirical profile is oriented toward practical cognitive-radio and IoT receivers operating under tight resource budgets.