  Constrained adaptive filtering algorithms inculding constrained least mean
square (CLMS), constrained affine projection (CAP) and constrained recursive
least squares (CRLS) have been extensively studied in many applications. Most
existing constrained adaptive filtering algorithms are developed under mean
square error (MSE) criterion, which is an ideal optimality criterion under
Gaussian noises. This assumption however fails to model the behavior of
non-Gaussian noises found in practice. Motivated by the robustness and
simplicity of maximum correntropy criterion (MCC) in non-Gaussian impulsive
noises, this paper proposes a new adaptive filtering algorithm called
constrained maximum correntropy criterion (CMCC). Specifically, CMCC
incorporates a linear constraint into a MCC filter to solve a constrained
optimization problem explicitly. The proposed adaptive filtering algorithm is
easy to implement and has low computational complexity, and in terms of
convergence accuracy (say lower mean square deviation) and stability, can
significantly outperform those MSE based constrained adaptive algorithms in
presence of heavy-tailed impulsive noises. Additionally, the mean square
convergence behaviors are studied under energy conservation relation, and a
sufficient condition to ensure the mean square convergence and the steady-state
mean square deviation (MSD) of the proposed algorithm are obtained. Simulation
results confirm the theoretical predictions under both Gaussian and non-
Gaussian noises, and demonstrate the excellent performance of the novel
algorithm by comparing it with other conventional methods.
