Comparison between LC-LMS and LC-RLS Algorithms for Improving Adaptive Beamforming

Abstract

Adaptive filtering is a crucial technology that enables interference suppression and enhances signal quality. This research presents a sophisticated adaptive beamforming method that minimises the Mean Squared Error (MSE) and significantly increases convergence rates by employing the Recursive Least Squares (RLS) algorithm. Utilising the RLS algorithm, which is renowned for its quick convergence and resilience to changing signal conditions, the antenna array\'s weights are dynamically modified. The suggested approach outperforms more established algorithms like Least Mean Squares (LMS) in terms of quicker convergence and lower MSE, as demonstrated by comprehensive simulations and real-world applications. The findings demonstrate the significant efficacy of the RLS-based adaptive beamforming technology in real-time applications, providing improved signal clarity and reliability in challenging and noisy environments. The potential of RLS to develop adaptive beamforming technologies and open the door to more dependable and effective systems for communication is highlighted in this work.

Introduction

Adaptive filters are digital systems that automatically adjust their coefficients in real time to minimise an error function, typically the mean square error (MSE). Unlike fixed filters, they can adapt to changing signal and noise conditions, making them well suited for environments where signal statistics are unknown or time-varying. The adaptive filtering process involves generating an output, comparing it with a desired signal to obtain an error, and using this error to update filter coefficients iteratively.

Adaptive beamforming extends this concept to array signal processing, where sensor or antenna weights are dynamically adjusted to enhance desired signals while suppressing interference and noise. Its performance is usually measured by improvements in metrics such as the Signal-to-Interference-plus-Noise Ratio (SINR).

The Least Mean Squares (LMS) algorithm is one of the most widely used adaptive techniques due to its simplicity and low computational cost. It updates filter weights using a stochastic gradient descent approach to minimise MSE, but its performance depends heavily on the choice of step size. The Normalised LMS (NLMS) improves LMS by adapting the step size based on input signal power, resulting in better stability and convergence. In contrast, the Recursive Least Squares (RLS) algorithm minimises a weighted least squares error and offers much faster convergence, though at the expense of higher computational complexity and memory requirements.

The Linearly Constrained Minimum Variance (LCMV) beamformer generalises the MVDR beamformer by introducing multiple linear constraints that preserve desired signal components while suppressing interference. It determines optimal weights by minimising output power subject to these constraints, providing flexibility and robustness in beam pattern design.

To handle time-varying environments, LCMV is implemented adaptively using LMS or RLS frameworks. The LCMV-LMS method combines constraint projection with LMS updates for simplicity and adaptability, while the LCMV-RLS method integrates constraint handling with RLS to achieve faster convergence and improved interference suppression. Together, these adaptive LCMV techniques provide effective, real-time beamforming solutions in dynamic signal environments.

Conclusion

The main agenda of this project goal is to enhance adaptive filtering, which yields the accurate approximation of the intended signal from the interference signals and exhibits high-performance outcomes. Implementation, analysis, and comparison of the Least Mean-Square (LMS), Normalised Least Mean-Square (NLMS), and Recursive Least Square (RLS) algorithms are conducted. These algorithms are studied using three performance criteria: the Beam pattern, the error performance, and the rate of convergence. After comparing the algorithms, it can be concluded that the RLS algorithm achieves the fastest convergence rate and a lower mean square error. While the RLS algorithm provides better results than the LMS algorithm, it is preferred in situations requiring high precision and rapid convergence, while the LMS algorithm is better suited for applications. However, it must be kept in mind that the input data, including the reference signal and the noise sequence, have an effective response on the performance of the system. As an output, the optimal adaptive filtering method depends on the application. Finding the adaptive filtering algorithm that suits better for the particular design and application demands better may be accomplished by testing many input datasets using the provided test environment, regardless of whether they are simulation or actual measurement data from the industry. The RLS adaptive filtering technique will be implemented in an integrated data processing unit in future development.

References

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Copyright

Copyright © 2026 Gaddam Aishwarya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.