  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.
