Mean-Square Performance of the Constrained LMS Algorithm

—The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain theoretical insights into the performance of this algorithm, we examine its mean-square convergence and derive an expression for its steady-state mean-square deviation. Our methodology is inspired by the principle of energy conservation in adaptive filters. Simulation results corroborate the accuracy of the derived formula.