Research On Single-Carrier Fractional Fourier Domain Equalization System And Its Key Technologies

Single-carrier frequency domain equalization(SC-FDE) can effectivily cope with the multipath fading caused by frequency selective fading channels, it is an important technique in broadband wireless communication systems. It has similar computation modules as the orthogonal frequency division multiplexing(OFDM) system. However, its Peak-to-Average power ratio is much lower; and it is less sensitive to the frequency offset, thus SC-FDE has become the main technology of the fourth generation mobile communication system. While the wireless channel is fast time-varying, SC-FDE system which is based on Fourier transform would suffer severe sub-channel interference; this would significantly decrease the performance of the system. To solve the problem of sunchannel interference under fast time-varying channels, our paper proposes the SC-Fr FDE system which is based on fractional Fourier transform. Through inserting the proper cyclic prefix(CP) and choosing the optimal transform order, the SC-Fr FDE system can effectively reduce the sub-channel interference caused by the time varying channels and improving the system performance. More specifically, the main work and contribution of this dissertation are summarized as follows:(1) The application status and definition of fractional Fourier transform is introduced in this paper. As the signal used in the system is discrete signal, the definition of discrete fractional Fourier transform and one of its important property—— the implicit chirp periodicity is detailedly described. After the signal is transformed to the farctional Fourirer domain through DFr FT, to decrease the sub-channel interference and realize the simple equalization in fractional Fourier domain, the fractional circular convolution is studied.(2) This paper gives the SC-Fr FDE system model based on chirp CP; afterwards the SC-Fr FDE system model based on zro prefix is proposed. The method of inserting chirp CP is copying the last few data to the guard interval according the implied chirp periodcity. The method of inserting zero prefix is making both the guard interval and the last few data of the transmitting signal be the zero sequence. Despite of the guard interval we use, the SC-Fr FDE system all outperform the SC-FDE system under the optimal frational Fourier transform order.(3) The criterion of choosing the optimal fractional Fourier transform order is given. And the search algorithm based on coarse searching and precise searching is proposed to calculate the criterion. Fractional Fourier transform is more flexible than Fourier transform in that it has a free parameter——transform order. To calculate the optimal fractional Fourier transfom order, the criterion of choosing the optimal fractional Fourier transform order is given in this paper. However, if we search the optimal order one by one according to the criterion, the computation is a hug project. To simplify the searching process, our paper proposes the searching algorithm based on coarse searching and precise searching.(4) A piece-wise linear time-varying channel estimation scheme based on pilots is introduced in SC-Fr FDE system. To calculate the optimal transform order, it is essential to know the information about the time-varying channel. This paper gives the transform order used for channel estimation and studies the inserting method about the comb pilots in SC-Fr FDE system. When the relative Doppler frequency is smaller than 0.1, the channel can be assumed as the piece-wise linear channel model and it can be estimated through the channel estimation method paoposed in this paper.(5) The application of SC-Fr FDE system is extended from the Single-input Single-output antenna to the Multiple-input Multiple-output antenna; just similar to the Single-input Single-output SC-Fr FDE system, the criterion of choosing the optimal fractional Fourier transform order under multiple antennas is deduced. Finally, to show the practicablity of the MIMO SC-Fr FDE, the complexity of the system is analyzed in this paper. If the relative movement between transmitter and receiver is faster in wireless communication systems, the wireless channel would be time-varying in one data block. In this circumstance, the frequency domain channel matrix would no longer be a block diagonal matrix and there exists severe sub-channel interference in MIMO SC-FDE system. To reduce the interference, this paper proposes the MIMO SC-Fr FDE system which adopts fractional Fourier domain equalization to replace the conventional frequency domain equalization in this system.