On the 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 analytical insights into the performance of this algorithm, we examine its mean-square performance and derive theoretical expressions for its transient and 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.