  Time reversal (TR) recently emerged as an interesting communication
technology capable of providing a good spatio-temporal signal focusing effect.
New generations of large-bandwidth devices with reduced cost leverage the use
of TR wideband communication systems. While TR is usually implemented in the
time domain, the same benefit can be obtained in an orthogonal frequency
division multiplexing (OFDM) system by precoding the information in the
frequency domain. Besides using multiple antennas, the focusing effect of TR
also comes from the use of a high rate back-off factor (BOF), which is the
signal up-sampling (or down-sampling) rate in the original time-domain TR
precoding. However, a frequency-domain TR precoding in the literature has only
considered BOF of one, which does not fully exploit the focusing property of
TR. In this paper, we discuss how to properly implement different BOFs using
frequency-domain TR precoding in the OFDM system. Moreover, we demonstrate that
increasing the BOF and/or the number of transmit antennas significantly
improves the focusing gain at the intended position. In contrast, the
unintended positions receive less useful power. Furthermore, closed-form
approximations of the mean-square-errors (MSEs) of equalized received signals
at either intended or unintended positions are derived, expressing the focusing
gain as a function of the BOF and the number of antennas. Numerical simulations
with multi-path channels are carried out to validate the MSE expressions.
