Performance Analysis of Frequency Domain Precoding Time-Reversal MISO OFDM Systems

Abstract

Time reversal (TR) recently emerged as an interesting communication technology capable of providing a good spatio-temporal signal focusing effect. New generations of largebandwidth devices with reduced cost leverage the use of TR wideband communication systems. TR can easily be integrated into an orthogonal frequency-division multiplexing (OFDM) system by precoding the signal in the frequency domain. In this paper, we first extend the frequency-domain TR precoding to rate back-off factors (BOFs) different than one. We secondly derive a closed-form mean-square-error (MSE) expression of the received equalized symbols as a function of the BOFs and the number of antennas. The derived MSE formula is validated numerically with Rayleigh fading channels.Index Terms-Time reversal, rate back-off factor, OFDM.

Physical Layer Security in an OFDM Time Reversal SISO Communication With Imperfect Channel State Information

“…The block is then spread in the FD by a back-of-rate U = Q/N thanks to a spreading matrix S of size Q × N . S is the concatenation of U independent N × N diagonal matrices, whose diagonal values are randomly distributed and taken from the set {±1} in order not to increase the peak-to-average power ratio, as suggested in [53], [54].…”

“…The AN signal shares the same spectral content as the data signal and therefore does not disturb any other potential surrounding communications. H * B S is the FD implementation of a TR precoder, [53]. The transmitted sequence becomes:…”

Physical Layer Security in a SISO Communication using Frequency-Domain Time-Reversal OFDM Precoding and Artificial Noise Injection

“…Equations ( 44), (45), and ( 46) are convex expressions that can be minimized as a function of 𝛼. Let's denote 𝛼 𝑆𝐷𝑆 ∞ , 𝛼 𝑀 𝐹 ∞ , and 𝛼 𝑂𝐶 ∞ as the amount of data energy to inject, with respect to AN, in order to guarantee a desired communication SR when 𝛿 𝐸 = ∞, respectively for the first, second and third scenario.…”

“…By replacing the values of 𝛼 in ( 44), (45), and ( 46) respectively by ( 47), (48), and (49), the expressions of Bob's SNR to ensure SR = Δ are found.…”

“…In this paper, an original and novel FD TR precoder in SISO OFDM systems with AN addition is introduced to secure wireless communications. Indeed, TR can be equivalently implemented in FD by replicating and shifting the signal spectrum, [45]. FD implementation has the advantage to be easily performed using OFDM.…”