The existing time reversal receiver for time-varying channels. In a data block, the channel is assumed to be time-invariant, i.e., . Frequent updates of the channel estimation are needed to track channel variations.
The proposed time reversal receiver over time-varying doubly spread channels. It uses the channel spreading function estimates rather than the channel impulse response estimates. The proposed time reversal receiver has a two-layer structure for coherent summation combining. The inner layer contains rake-like structures. Each rake is composed of fingers to compensate for possible Doppler shifts . The outer layer is multichannel combining.
The complexity-reduced time reversal receiver over time-varying doubly spread channels. It uses the estimates of delay, Doppler and amplitude parameters . The low complexity time reversal receiver has a two-layer structure for coherent summation combining. The inner layer contains rake-like structures. The rake is composed of fingers to compensates for Doppler shifts . The outer layer is multichannel combining.
(Color online) Simulation configuration and acoustic ray paths of an underwater multipath channel. A vertical receiving array (VRA) composed of 16 sensors is deployed 1 km far away from the source. The transmitter is moving towards the VRA with a horizontal velocity m/s. The propagation rays from the source to the first and last sensors are plotted using dashed and solid lines, respectively.
(Color online) The spreading function of the channel between the source and the second sensor (channel 2) obtained by the geometric structure of the transmitter and receiver. (a) Contour plot of the 2-D spreading function; (b) the delay profile ; (c) the Doppler profile . The paths are labeled as D (direct arrival), B (bottom scattered arrival), S (surface scattered arrival), BS (bottom then surface), SB (surface then bottom), BSB (bottom-surface-bottom), SBS, BSBS, SBSB, and BSBSB.
(Color online) Estimate of the spreading function of channel 2 using OMP. An upper bound is taken as the number of effective multipath arrivals. (a) Contour plot of the 2-D spreading function estimate ; (b) the delay profile estimate ; (c) the Doppler profile estimate .
Impulse response estimates of channel 2 obtained by (a) the LS method and (b) the OMP.
Scatter plots of the received signal and the outputs of the three time reversal receivers at SNR dB. (a) The received signal of channel 2; (b) the output of the proposed SFTR; (c) the output of the IRTR-LS; (d) the output of the IRTR-OMP.
The -functions of the proposed time reversal receiver over doubly spread channels with different number of sensors . (a) (single sensor); (b) ; (c) ; (d) ; (e) ; and (f) .
SER versus number of sensors.
MSE versus number of sensors.
The output SNR versus number of sensors.
Residual ISI versus number of sensors.
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