Channel and Data Estimation for Ad Hoc Networks and Cognitive Radio

Estimation of channel and data characteristics by the receiver is important in adaptive wireless transmission protocols and in cognitive radio. This paper formulates the estimation problem with the help of an illustrative example from the IEEE 802.11a OFDM standard. The problem reduces to the estimation of the common component variance and mixing probabilities in a finite Gaussian mixture, with known values for component means. Using the known component means, μ₁, ... , μ _M , a set of non-linear transformations, ${\sinh \mu_i x}$ and ${\cosh \mu_i x}$ 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 and the Cramer–Rao minimum variance bounds are derived. The estimates converge to true unknowns even when the sequences of noise and data symbols are dependent sequences. The OFDM example is simulated with parameters corresponding to the highest acceptable error rate. For a time-varying channel model chosen from the literature, it is shown that our estimator receives considerably more than adequate amount of data during an average time interval of unchanging channel characteristics. Analytical results, numerical results and related issues are discussed.