Particle Filtering for Blind Equalization with Unknown Noise Variance

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A particle filtering equalization algorithm with unknown noise variance is presented based on the optical particle sampling using the optical importance function. The optical importance function with unknown noise variance is deduced by analytically integrating out the noise variance as a nuisance parameter. And the posterior distribution of noise variance is derived recursively based on its prior distribution. Moreover, the optical particle sampling using the optical importance function is introduced to alleviate the degeneracy phenomenon so that a re-sampling step is avoided in the method. Numerical simulations show that the degeneracy problem of the proposed algorithm is alleviated greatly, and the proposed algorithm attains an approximate performance to the one with known noise variance.