Estimation of channel and data statistics in some digital wireless communication systems

Blind estimation of noise variance and data statistics in some classes of M-symbol wireless digital communication systems is studied. Automatic gain control in pulse amplitude modulation systems und the reference carrier in coherent demodulation systems provide the noise-free signal values for the set of symbols at the receiver. This reduces the problem of channel and data statistics estimation to the estimation of the common component variance and mixing probabilities in a finite Gaussian mixture, with known values for component means. Using these known component means, μ₁.....μ_M, a set of non-linear transformations, sinh(μ_ix) and cosh(μ_ix) of the data (mixture random variable X) are used to develop convergent and computationally efficient estimators for both the noise variance and the vector of symbol probabilities. The estimation equations can be implemented recursively or with a batch processing algorithm. Asymptotic variances of the estimates are derived and the developed estimator is simulated for a specific problem.