A Primer on Evolutionary Optimization Frameworks for Near-Field Multi-Source Localization
Authors: Seyed Jalaleddin Mousavirad, Parisa Ramezani, Mattias O'Nils, Emil Björnson
Organizations: Department of Computer and Electrical Engineering, Mid Sweden University, Sundsvall, Sweden · the school of electrical and data engineering, University of Technology Sydney, Sydney, Australia · the Department of Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden
This paper introduces evolutionary optimization as a grid-free training-free continuous-domain search mechanism for near-field multi-source localization, addressing the major limitations of grid-based subspace methods such as MUSIC and data-driven deep learning approaches. To this end, we develop two complementary evolutionary localization frameworks that operate directly on the continuous spherical-wave signal model and support arbitrary array geometries without requiring labeled data, discretized angle-range grids, or architectural constraints. The first framework, termed NEar-field MultimOdal DE (NEMO-DE) associates each individual in the evolutionary population to a single source and optimizes a residual least-squares objective in a sequential manner, updating the data residual and enforcing spatial separation to estimate multiple source locations. To overcome the limitation of NEMO-DE under large power imbalances among the sources, we propose the second framework, named NEar-field Eigen-subspace Fitting DE (NEEF-DE), which jointly encodes all source locations and minimizes a subspace-fitting criterion that aligns a model-based array response subspace with the received signal subspace. The proposed formulations are not intrinsically tied to a specific optimizer; however, this work adopts differential evolution (DE) as a representative evolutionary search strategy because of its simple implementation, small number of control parameters, and strong empirical performance in continuous nonconvex optimization problems. Numerical results show that the proposed frameworks provide competitive accuracy compared with MUSIC-type baselines while avoiding pre-defined grid construction and labeled training data. This work establishes evolutionary computation as a powerful and flexible paradigm for model-based near-field localization, paving the way for future innovations in this domain.
Figures & tables
Fig. 1 : System model for near-field multi-source localization.
Aspect
NEMO-DE (Sequential Multimodal DE)
NEEF-DE (Joint Subspace Fitting DE)
Representation
Single-source representation \bm{\theta}=[\phi,r]^{\mbox{\tiny\mathrm{T}}} ; each DE run estimates one source location.
Expanded joint representation \mathbf{x}=[\bm{\theta}_{1}^{\mbox{\tiny\mathrm{T}}},\dots,\bm{\theta}_{K}^{\mbox{\tiny\mathrm{T}}}]^{\mbox{\tiny\mathrm{T}}} ; all source locations are estimated simultaneously.
Search Strategy
Sequential multimodal evolutionary search; K DE runs.
Single joint evolutionary search in a 2K -dimensional space; one DE run.
Objective Function
Residual reconstruction error in the data domain; depends on residual signal after each detection.
Subspace mismatch; uses the signal subspace and is evaluated once per candidate solution.
Multimodality Handling
Explicit multimodality via repeated searches, penalization, and residual updates.
Implicit multimodality arising from joint parameterization and the objective function landscape.
Residual Update
Yes; contribution of each detected source is subtracted after each run.
No residual update required; all sources modeled jointly.
Penalization
Explicit distance-based penalization to avoid redundant detections.
Not required; joint search inherently avoids repeated solutions.
TABLE I : Comparison Between NEMO-DE and NEEF-DE Localization Frameworks
Parameter
Value
Np
50
Gmax
300
F
0.5
Cr
0.8
δmin
0.08
α
1000
TABLE II : DE parameter values.
Fig. 2 : RMSE vs. SNR for NEMO-DE, 2D MUSIC, and modified MUSIC. The BS antennas are spaced by λ/4 .
Fig. 3 : RMSE vs. number of sources for NEMO-DE, 2D MUSIC, and modified MUSIC. The BS antennas are spaced by λ/4 .
Fig. 4 : RMSE vs. SNR for NEMO-DE and 2D MUSIC. The BS antennas are spaced by λ/2 .
Fig. 5 : RMSE vs. number of sources for NEMO-DE and 2D MUSIC. The BS antennas are spaced by λ/2 .
Fig. 6 : Exact locations and estimated ones by NEMO-DE and MUSIC for three sources over 10 random realizations.
Fig. 7 : RMSE of NEEF-DE, NEMO-DE, 2D MUSIC, and modified MUSIC under unequal received SNRs across sources.
Fig. 8 : Exact locations and estimated ones by NEEF-DE and MUSIC for three sources over 10 random realizations.
Method
Runtime [s]
RMSE [m]
NEMO-DE
4.101
0.0293
NEEF-DE
70.64
0.0788
3D MUSIC
355.3
0.0687
TABLE III : Runtime and RMSE for DE-based schemes and MUSIC.
The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · Southern University of Science and Technology, Shenzhen, China · The University of Hong Kong, HK SAR, China +1
School of Electrical and Electronic Engineering, Nanyang Technological University. Address: 50 Nanyang Avenue, Singapore 639798 · NTU–VinUni Joint Research Laboratory for Embodied AI and Robotics, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 and VinUniversity, Hanoi, Vietnam
School of Electrical and Computer Engineering, University of Georgia, Athens, GA, USA · Scripps Institution of Oceanography, University of California, San Diego, CA, USA