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Steady state performance analysis of an approximately optimal variable step size LMS (VSSLMS) algorithm namely Shinpsilas algorithm is given in this paper. Based on the analysis, mathematical formulations of the steady state step size and excess mean square error (EMSE) are also obtained which helps the parameter choice of Shinpsilas algorithm. Simulations are performed under different noise conditions to support the theoretical analysis. As can be seen from the simulation results, Shinpsilas algorithm has a good convergence rate under both high and low noise conditions, and the simulation results fit the theoretical analysis quite well.