| Communications through frequency-selective fading channels suffer inter-symbol interference (ISI), which limits the data rate. Complex equalizers are usually needed to compensate for the channel distortion. Orthogonal Frequency Division Multiplexing (OFDM) divides the channel spectrum into many sub-bands, each of which carries low-rate data. Since each sub-channel is narrow band, communications through it experience only flat-fading. The sub-channels are separated with the minimum space required by channel orthogonality. Therefore, a large number of low-rate data streams can be transmitted in parallel and aggregate to a high-rate one.; For coherent detection of the information symbols, the channel gain of each sub-carrier is needed. This problem is further complicated by the time-varying nature of the channel fading and the correlation between the sub-channels due to Doppler frequencies.; The contribution of this dissertation is a Kalman filter based framework of channel equalizer for OFDM systems in a time-frequency-fading environment. The gains of the sub-channels are defined as the state variables, and an AR process is used to model the dynamics of the channel. Then the Kalman filter can be applied to estimate the channel from the received OFDM signals when pilot symbols are available. This Kalman filter is of a dimension equal to the product of the number of sub-carriers and the order of the AR model, which can be very large. To reduce its complexity, per-subcarrier Kalman filter scheme is proposed, that is, the Kalman filter channel estimator is applied to obtain the gain of each sub-carrier independently, and then a minimum mean-square-error (MMSE) combiner is used to refine the estimates. The per-subcarrier Kalman estimator explores the time-domain correlation of the channel, while the MMSE combiner explores the frequency-domain correlation. This two-step solution offers a performance comparable to the much more complicated Kalman joint estimator.; The Kalman filter method is also extended to give a blind channel estimation algorithm based on the mixture Kalman filter (MKF). The MKF uses Monte Carlo simulations to do filtering. By simulating the transmitted symbol sequences according to their a posteriori probabilities, so called importance sampling, and feeding them to the Kalman filter channel estimator, a Bayesian estimate of the channel can be obtained through averaging the Kalman filter output of each simulation. The MKF method applies to the joint estimation of all sub-carriers and also works in the per-subcarrier fashion with a much reduced complexity. In addition to the channel estimate, the MKF can directly give symbol detection. |
