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DeepMUSIC: Multiple Signal Classification via Deep Learning
Ahmet M. Elbir
TL;DR
DeepMUSIC addresses the limited multi-target capability of prior deep-learning DOA methods. It partitions the angular spectrum across CNNs that map array covariance matrices to regional MUSIC spectra, and simulations report competitive estimation performance with lower computation time than the compared methods.
Problem
Prior deep-learning DOA studies mostly consider single or two-target scenarios, while multiple-target estimation is needed beyond that limited setting.
Method
DeepMUSIC uses multiple CNNs dedicated to non-overlapping angular subregions, taking the array covariance matrix as input and producing the corresponding MUSIC spectra.
Results
0.0020 s computation time for DeepMUSIC versus 0.0110 s for MLP, 0.0300 s for spectral MUSIC, and 0.0040 s for Root-MUSIC.
Takeaways & Limitations
DeepMUSIC handles multiple targets and provides lower computational complexity than the compared conventional techniques.
Abstract
from arXiv · showhide
This letter introduces a deep learning (DL) framework for direction-of-arrival (DOA) estimation. Previous works in DL context mostly consider a single or two target scenario which is a strong limitation in practice. Hence, in this work, we propose a DL framework for multiple signal classification (DeepMUSIC). We design multiple deep convolutional neural networks (CNNs), each of which is dedicated to a subregion of the angular spectrum. In particular, each CNN is fed with the array covariance matrix and it learns the MUSIC spectra of the corresponding angular subregion. We have shown, through simulations, that the proposed DeepMUSIC framework has superior estimation accuracy and exhibits less computational complexity in comparison with both DL and non-DL based techniques.
I. INTRODUCTION
DOA estimation is important across several fields, but existing learning-based approaches largely address only single or two-target cases. DeepMUSIC addresses this limitation by using multiple CNNs for partitioned angular subregions.
- DOA estimation supports direction finding in radar, sonar, acoustics, and communications, with MUSIC described as the most popular method.
- Existing model-based DOA algorithms strongly depend on the quality of their input data, motivating learning-based approaches that learn nonlinear input-output relationships.
- Prior deep-learning DOA studies mainly resolve one or two targets, including MLP and CNN architectures for two signals and an MLP for a single wideband sound target.
- DeepMUSIC partitions the angular spectrum into non-overlapping subregions and assigns a dedicated CNN to each subregion for multiple-target estimation.
II. ARRAY SIGNAL MODEL
The signal model represents K far-field targets impinging on an M-element uniform linear array and formulates DOA estimation from received-array statistics. The framework uses covariance data to produce MUSIC spectra whose largest peaks indicate target directions.
- The model considers K far-field signals received by an M-element uniform linear array, with each target characterized by a DOA angle and emitted signal.
- The steering vector a(θk) describes the array response to target k, with its m-th element determined by the target angle and array geometry.
- The received signal includes zero-mean spatially and temporally white additive Gaussian noise with variance σ2_n.
- The covariance matrix is eigendecomposed into signal and noise subspaces, whose orthogonality underlies the MUSIC spectrum construction.
- The MUSIC spectrum's largest K peaks correspond to the target DOA angles, while the deep network uses the sample covariance matrix as input.
- The DL framework maps the array covariance matrix to MUSIC spectra at its output for estimating the target DOAs.
III. DOA ESTIMATION VIA DEEP LEARNING
DeepMUSIC partitions the angular spectrum across multiple CNNs that map array covariance-matrix inputs to MUSIC spectra for separate subregions. The framework defines subregion labels and covariance-matrix channels, then trains identical networks for these mappings.
- Framework design: DeepMUSIC accepts the array covariance matrix as input and outputs MUSIC spectra for angular subregions.Each network learns the spectrum associated with its dedicated subregion.
- Framework design: Q ≥ K CNNs are dedicated to non-overlapping angular subregions, reducing the need for one network to represent all candidate multiple-target locations.The single-network training-data complexity increases on the order of N^K for N angular grid points.
- Spectrum partitioning: The full MUSIC spectrum p ∈ R^N is partitioned into Q subregions, each represented by an L × 1 vector with L = N/Q.The subregions are non-overlapping and together cover the angular set Θ.
- Network input: Each CNN receives an M × M × 3 real-valued matrix containing the covariance matrix’s real parts, imaginary parts, and angle values.These three quantities form the input channels of X.
- Network architecture: Each subregion network is a 17-layer nonlinear mapping from X ∈ R^(M×M×3) to its spectrum vector p_q.The architecture includes convolutional, normalization, ReLU, dropout, softmax, fully connected, and regression layers.
IV. NUMERICAL SIMULATIONS
Simulations evaluate DeepMUSIC across target counts, SNR, correlation, and computational complexity. It supports multiple-target estimation, tracks MUSIC closely in several settings, and has the lowest reported computation time.
- Simulation settings: The simulations use K = 5 targets randomly located in Q = 8 angular subregions over [−60°, 60°].Training uses N = 212 grid points; the reported dataset contains 40,000 samples, with 80% for training and 20% for validation.
- DOA estimation performance: For K = 2, DeepMUSIC outperforms MLP and provides performance close to spectral and Root-MUSIC.
- DOA estimation performance: For K = 6, DeepMUSIC performs better than MUSIC at low SNR and closely follows MUSIC as SNR increases.
- Performance limits: For SNR ≥ 20 dB, DL-based methods and spectral MUSIC max out without further improvement.The paper attributes this to the angular resolution limit and precision loss in biased deep-network estimators.
- Correlated targets: DeepMUSIC closely follows MUSIC for correlated targets and provides less RMSE when the correlation coefficient is ρ = 1.
- Computational complexity: 0.0020 s is DeepMUSIC’s computation time for K = 2, compared with 0.0110 s for MLP, 0.0300 s for spectral MUSIC, and 0.0040 s for Root-MUSIC.The authors attribute the speed to convolutional layers and parallel processing across multiple networks.
V. SUMMARY
The paper introduces DeepMUSIC, a deep-learning framework for DOA estimation that supports multiple targets while reducing computational complexity relative to conventional techniques.
- DeepMUSIC is a DL framework for DOA estimation that can work with multiple targets and has lower computational complexity than conventional techniques.