This thesis describes the use of scattering functions to characterize time-varying multipath radio channels. Channel Impulse responses were measured at Edwards Air Force Base (EAFB) and scattering functions generated from the impulse response data. From the scattering functions we compute the corresponding Doppler power spectrum and multipath intensity profile. These functions completely characterize the signal delay and the time varying nature of the channel in question and are used by systems engineers to design reliable communications links. We observe from our results that flight paths with ample reflectors exhibit significant multipath events. We also examine the bit error rate (BER) performance of a reduced-complexity equalizer for a truncated version of the pulse amplitude modulation (PAM) representation of SOQPSK-TG in a multipath channel. Since this reduced-complexity equalizer is based on the maximum likelihood (ML) principle, we expect it to perform optimally than any of the filter-based equalizers used in estimating received SOQPSK-TG symbols. As such we present a comparison between this ML detector and a minimum mean square error (MMSE) equalizer for the same example channel. The example channel used was motivated by the statistical channel characterizations described in thisthesis. Our analysis shows that the ML equalizer outperforms the MMSE equalizer in estimating received SOQPSK-TG symbols.

Orthogonal Frequency Division Multiplexing (OFDM) techniques have been used in many wireless communication systems to improve the system capacity and achieve high data-rate. It possesses good spectral efficiency and robustness against interferences. The OFDM system has been adopted in many communication standards, such as the 802.11a/g standards for the high-speed WLAN, HIPERLAN2, and IEEE 802.16 standard, and meanwhile, it is also employed in the European DAB and DVB systems. To avoid the inter-block interference (IBI), usually, in the transmitter of OFDM systems the redundancy with sufficient length is introduced, it allows us to overcome the IBI problem, due to highly dispersive channel. Many redundancy insertion methods have been proposed in the literatures, there are cyclic prefix (CP), zero padding (ZP) and the pseudorandom postfix (PRP). Under such system we have still to know the correct channel state information for equalizing the noisy block signal. Especially, in time-varying channel, the incorrect channel state information may introduce serious inter-symbol interference (ISI), if the channel estimation could not perform correctly. In this thesis, the PRP-OFDM system is considered. According to the PRP-OFDM scheme, the redundancy with pseudorandom postfix (PRP) approach is employed to make semi-blind channel estimation with order-one statistics of the received signal. But these statistic characteristics may not be available under time-varying channel. Hence, in this thesis, we propose a modified PRP-OFDM system with assistant training sequences, which is equipped with minimum mean-square-error equalizer and utilize Kalman filter algorithm to implement time-varying channel estimation. To do so, we first model time-varying channel estimation problem with a dynamic system, and adopt the Kalman filter algorithm to estimate the true channel coefficients. Unfortunately, since most parameters in dynamic system are random and could not to be known in advance. We need to apply effective estimation schemes to estimate the statistics of true parameters for implementing the Kalman filter algorithm. When the channel state information is known, MMSE equalizer follows to suppress the inter-symbol interference (ISI). Moreover, after making decision the binary data can be used to re-modulate PRP-OFDM symbol and to be re-used in Kalman filter to obtain more accurate CSI to improve the effectiveness of the equalizer. Via computer simulations, we verify that desired performance in terms of bit error rate (BER), can be achieved compared with the CP-OFDM systems.