The stability of the broadband channel estimation capabilities is provided by the normalized least mean square (NLMS) approaches. When compared to compression sensing‐based algorithms, the NLMS is very effective to perform in the channel estimation model, and also, the computational complexity of these algorithms is very low. But the important drawback of these algorithms is the intrinsic sparsity of broadband communication channels is not effectively utilized in these systems. The channel sparsity is exploited using invariable step‐size zero‐attracting NLMS algorithms in the adaptive sparse channel estimation techniques. The best trade‐off between the computational complexity and the cost function cannot be obtained, and the convergence rate is low in the ISS‐ZA‐NLMS, and a new algorithm is developed with the help of existing ISS‐ZA‐NLMS. The objective of this research work is to develop a novel channel estimation mechanism for broadband wireless communication systems using the enhanced NLMS method with the usage of a hybrid heuristic strategy. This work designs and develops an efficient channel estimation technique named as hybrid heuristic‐based invariable step‐size zero‐attracting modified NLMS for enhancing efficiency. The heuristic algorithms like rat swarm optimizer and red deer algorithm are fused together to get hybrid rat red deer swarm optimization for estimating the channels with higher efficiency. The main scope of the implemented scheme is to offer better performance regarding the mean square error (MSE) measures. The simulation analysis is made finally to estimate the performance of the investigated HH‐ISS‐ZA‐MNLMS with the comparison of conventional approaches.