A Complexity-Aware Theoretical Framework for the Performance Analysis of Linear MIMO Equalizers in Coherent Spatial-Division Multiplexing Transmission Systems

Analyzing the performance of coherent spatial-division multiplexing (SDM) transmission systems is challenging as it requires expensive experimental testbeds and/or lengthy numerical simulations. In this paper, we propose a theoretical framework for accurately and efficiently calculating the signal-to-noise ratio (SNR) at the output of linear multi-input multi-output (MIMO) equalizers, which consists of a bank of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2N\times 2N\times M$</tex-math></inline-formula> adaptive filters corresponding to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> spatial modes and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> taps per filter in coherent SDM receivers. We demonstrate a speed-up of more than three orders of magnitude in computation time compared to Monte-Carlo simulations, while maintaining the same level of accuracy in predictions. This model is useful in complexity-aware design and characterization of future SDM transmission systems.