Markus Glugla, Ralf Kiran Schulz

• The quality of the reference signal is essential for the adaptation process of an LMS or one of its derivatives. The reference signal affects the stability, the convergence rate and the maximum achievable attenuation. Since the error signal and the control signal are available as numerical values in the algorithm for the LMS, the reference signal can be calculated from both signals. The error signal is the interference between the control signal and the reference signal. This interference of the control signal and the reference signal can be noted mathematically as a simple addition. It is therefore possible to deduce the reference signal from a known error signal and control signal. This approach is the basis of the generated-x LMS (GxLMS) developed by us. It calculates the reference signal itself without having to rely on an externally supplied reference signal. The advantages of the GxLMS are primarily in fields where the reference signal is difficult or impossible to detect. For example, the detection of the reference signal canThe quality of the reference signal is essential for the adaptation process of an LMS or one of its derivatives. The reference signal affects the stability, the convergence rate and the maximum achievable attenuation. Since the error signal and the control signal are available as numerical values in the algorithm for the LMS, the reference signal can be calculated from both signals. The error signal is the interference between the control signal and the reference signal. This interference of the control signal and the reference signal can be noted mathematically as a simple addition. It is therefore possible to deduce the reference signal from a known error signal and control signal. This approach is the basis of the generated-x LMS (GxLMS) developed by us. It calculates the reference signal itself without having to rely on an externally supplied reference signal. The advantages of the GxLMS are primarily in fields where the reference signal is difficult or impossible to detect. For example, the detection of the reference signal can be problematic due to design reasons or measurement technology. For example, flow noise could have a negative effect on an acoustic detection of the reference signal. However, the calculation of the reference signal in the GxLMS represents a further feedback signal path, which affects the stability of the algorithm as a whole. Based on the theoretical principles mathematically sufficient convergence conditions can be formulated taking into account the delays existing in the signal paths. The experimental testing took place on an acoustic duct with monofrequency disturb signals. Since the use of an efficient design of experiments (DoE) could be excluded, the measurement was designed as parameter variation (one factor at time) and therefore very time-consuming. The theoretical background of the GxLMS as well as the results from the experiments are presented.…