Frequency Domain Equalization And Antenna Calibration Under Time-varying Channels

The equalization is the key technology effective against multipath interference, i.e.the inter-symbol interference (ISI), in a wireless communication system. At thereceiving end, Single carrier frequency domain equalization SC-FDE technique caneffectively eliminate ISI and has low complexity; At the transmitting end, thepre-equalization technique can be used to pre-compensate for the channel fading andeliminate ISI, especially for time division duplex (TDD) system, without feedback,simply using the antenna calibration technology to ensure the channel reciprocity, Thetransmitting terminal can use channel reciprocity to obtain the channel information, andoperate the pre-equalization effectively and simply.But the wireless communication channel also is time-varying. When the channelchanges fast, the inter-carrier interference ICI caused by the time-varying channel andISI will lead to the rapid performance deterioration of the SC-FDE and increase itscomplexity. At the same time, the time-varying channel brings calibration error to thechannel antenna calibration technology, resulting in the loss of channel reciprocity, sothat the pre-equalization performance degradation. Therefore, the study of frequencydomain equalization and antenna calibration technique under the time-varying channelhas important significance.In this paper, against the problems on frequency domain equalization on thereceiving side and pre-equalization on the transmitting side caused by the time-varyingchannel, we launch the following research:We study the frequency domain equalization under the time-varying channel at thereceiving end. Firstly, the bit error rate (BER) of the system with static channel usingthe linear frequency domain equalization is derived and analyzed; analysis proved thatthe frequency domain channel matrix under time-varying channels is a banded matrix.Through the selection of the matrix band width by window function, we cancompromise between the system performance and its complexity. Digital simulationresults proved the correctness of the theoretical formula, and the linear frequencyequalization can’t effective against ISI and ICI. Secondly, we study decision feedback equalization under the time-varying channeland the time-invariant channel. By the equalized signal modeling, according to theaverage minimum mean square error principle, mathematical expression of decisionfeedback equalization filter is derived. Simulation results and theoretical analysis showthat frequency domain decision feedback equalization performs better than linearequalizer. Through the studies of equalization gain, interference and noise power andprobability density distribution of the equalized signal, we can calculate the bit softinformation. And by iterative update of the soft information, frequency domain Turboiterative equalization is designed. Simulation results and theoretical analysis show thatTurbo iterative equalization is effective to eliminate ISI and ICI.We study the antenna calibration technique on the transmitting side under thetime-varying channel. Firstly, the models of single-antenna TDD pre-equalizationsystem and antenna calibration are studied. Under the time-varying channel, throughtheoretical derivation, we get the bit error rate formula of the system using thetraditional calibration technique. Based on this, in this paper, we proposed an antennacalibration method based on channel prediction. By channel prediction, antennacalibration error caused by the time-variability is reduced. Through theoreticalderivation, we get the BER formula when using the proposed method. Digitalsimulation results and theoretical analysis proved that the theoretical BER performancecoincide with actual simulation, and the proposed antenna calibration method caneffective against time-variability of the channel, and improve the performance ofantenna calibration and pre-equalization.Secondly, we promote the conclusion about antenna calibration in single-antennaTDD pre-equalization system to the multi-antenna TDD pre-coding system. Throughtheoretical derivation, we get the capacity formula of the system using traditionalantenna calibration and antenna calibration based on channel prediction. Through digitalsimulation we get the conclusion consistent with that in single-antenna case.In summary, frequency domain equalization and antenna calibration technology arekey technologies to ensure the system performance. In this paper, we studied in depthfrequency domain equalization, and the proposed antenna calibration technology based on channel prediction is applicable to time-varying channels which has theoretical studyand practical application value.