Experimental analysis of tensor LMS for determining the long-range outdoor acoustic transfer function

In this experimental study, we investigated the effectiveness of the Tensor Least Mean Squares (TLMS) algorithm compared to the traditional Least Mean Squares (LMS) method for determining long-range outdoor acoustic attenuation transfer functions under variable weather conditions. We conducted an outdoor long-range field experiment over a 326-meter range to capture the effect of time-varying environmental conditions on sound propagation. The input signal was a 3-second linear sweep ranging from 125 Hz to 4 kHz, transmitted every 10 minutes for an hour. We continuously monitored weather conditions, including wind speed and direction. We first conducted a convergence analysis and impulse response evaluation using both TLMS and LMS algorithms. Our results show that TLMS significantly outperforms the traditional Least Mean Squares (LMS) method in channel estimation accuracy, achieving a Mean Square Error (MSE) of approximately ${10}^{-38}$ compared to ${10}^{-8}$ for LMS. This demonstrates TLMS's superior adaptability to time-varying characteristics of outdoor acoustic channels. Subsequently, the study evaluated the transfer function through spectral analysis, revealing the impact of atmospheric conditions on acoustic signal propagation and providing insights into the time-variance of the acoustic channel. The findings confirm the potential of TLMS for advanced acoustic modeling in outdoor environments, thus validating its implementation for real-time acoustic transfer function estimation.