# Sparse Channel Estimation with Gradient-Based Algorithms: A comparative Study

## TL;DR

This paper compares gradient-based algorithms for sparse channel estimation in wireless systems, demonstrating that the Least Mean Mixed Norm (LMMN) algorithm outperforms others in convergence speed and accuracy.

## Contribution

It provides a comparative analysis of LMMN with other LMS-based algorithms for sparse channel estimation, highlighting its superior performance.

## Key findings

- LMMN outperforms LMS, ZA-LMS, and NLMS in convergence speed.
- LMMN achieves lower steady state error.
- Simulation results confirm LMMN's effectiveness for sparse system identification.

## Abstract

Channel state information (CSI) is very crucial for any wireless communication systems. Typically, CSI can be characterized at the receiver side using channel impulse response (CIR). Many observations have shown that the CIR of broadband multipath wireless channels are often sparse. To this point, the family of least mean square (LMS)-based algorithms have been widely used to estimate the CIR, unfortunately, the performance of LMS family is not much accurate in terms of sparse channel estimation. The Least Mean Mixed Norm (LMMN) algorithm combines the advantages of both the Least Mean square (LMS) and the Least Mean Fourth (LMF)algorithm, which makes this algorithm stands in a very special position among the family members in terms of convergence and steady state error. In this paper, we held a fair comparative study between the LMMN and a number of the LMS-based algorithms, such as the LMS algorithm, the zero-attracting (ZA-LMS) algorithm, and the normalized (NLMS) algorithm. Simulation results are carried out to compare the performance of all these algorithms with the LMMN algorithm. The results show that the LMMN algorithm outperforms the rest of these algorithms in the identification of sparse systems in terms of both fast convergence and the steady state error.