Accelerating the MUSIC Algorithm via Tensor Computing in Multi-Antenna Direction-Finding Systems

Abstract

The rapid evolution of 5G Advanced and 6G networks necessitates real-time direction-of-arrival (DOA) estimation within Massive MIMO systems. Traditionally, the computational complexity of subspace-based algorithms like MUSIC has required low-level C++ implementations or specialized FPGA hardware to overcome the performance limitations of high-level languages. This paper proposes a unified tensor-based approach utilizing Einstein summation notation, implemented through NumPy and PyTorch frameworks. By shifting from iterative loops to tensor contractions, we effectively offload the computational burden from the Python interpreter to multi-threaded and vector processing units. Experimental results demonstrate that for a 128-element antenna array, the PyTorch-optimized tensor kernel achieves a 150x speedup for $\mathrm{M} = 128$ antenna arrays, while NumPy tensors yield up to 190x for small-scale configurations $(M=4)$, compared to classic iterative methods. We observe anerror saturation effect where the maximum divergence decreases with array scaling, reaching the machine epsilon limit of $1.32 \times 10^{-16}$, proving enhanced stability for high-dimensional systems. This architecture offers a scalable migration path from edge-SDR processing to GPU-accelerated clusters, demonstrating that Python can serve as a high-performance engine for real-time Massive MIMO signal processing.