Geometry-Constrained Detection in MIMO Systems: A Feature-Space Perspective

Abstract

Detection performance in MIMO communication systems is commonly analyzed in terms of Signal to Noise Ratio (SNR), channel conditions, and detector design. However, the role of post-equalization feature-space geometry in shaping detection behavior remains insufficiently understood. In this paper, a geometry ratio, defined as the ratio between inter-class separation and intra-class dispersion, is introduced to characterize the separability of received symbol representations in feature space. Extensive simulations are conducted across SISO and MIMO configurations using 16-QAM and 64-QAM modulation over AWGN and Rayleigh fading channels with ZF and MMSE equalization. The results show a strong statistical relationship between the proposed geometry ratio and Bit Error Rate (BER) across classical, MMSE-SIC, and learning-based detectors, including SVM and neural-network classifiers. Additional analyses demonstrate that the geometry ratio exhibits substantially stronger association with BER than inter-class separation or intra-class dispersion considered individually. Furthermore, increasing modulation order and MIMO dimensionality are shown to degrade post-equalization feature-space separability, leading to increased class overlap and reduced detection reliability. These findings suggest that feature-space geometry provides a useful and interpretable framework for understanding performance trends across different communication scenarios and detector families, while highlighting the influence of symbol separability on achievable detection performance.