In a general setup of a wireless communication system, the transmit signal passes through the wireless medium and reaches the receiver. The wireless medium is generally called the wireless channel. Wire- less channels are mathematically modeled as pseudo-differential operators. In this framework, wireless channel estimation amounts to approximately identifying the operator, and equalization amounts to ap- proximately computing the operand, i.e. the transmit signal, using the estimated kernel and the output of the operation, i.e. the receive signal. With the current technology, reception of the mobile WiMAX (IEEE 802.16e) in the proximity of a highway is unreliable because of the Doppler effect due to user mobility, which dramatically hinder the quality of service (QoS). The QoS depends mainly on wire- less channel estimation, equalization and signal encoding. In this dissertation, we address problems of channel estimation and equalization for the Orthogonal Frequency Division Multiplexing (OFDM) based communication systems over rapidly varying wireless channels, like mobile WiMAX. We use established mathematical models describing the wireless channels and communication systems. As a contribution to the wireless communication technology, we propose novel algorithms for channel estimation and equal- ization for systems using the OFDM setup with severe channel distortions.
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