13-02-2013, 04:53 PM
Time Reversal Compared To Inverse Filtering
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Abstract
Inverse filtering is the compensation of the magnitude
and phase distortion caused by a linear time invariant system.
Recently, time reversal is proposed as a new technique suitable
for UWB systems. In this paper, the theory of electromagnetic
time reversal is compared to the process of inverse filter design.
From a signal processing point of view, time reversal is
equivalent to a phase equalizer. Time reversal can compensate
for the phase distortion in UWB, but at the same time it doubles
the magnitude distortion. This fact is illustrated experimentally.
INTRODUCTION
The first aim in this paper is to expose the real history of
time reversal (TR) in electrical engineering. In the year 1957,
TR was proposed by B. P. Bogert, from Bell Labs, as an
automatic technique for the correction of delay-distortion of
transmission networks [1]. A block diagram of the technique
presented in that paper is shown in Fig. 1. Experiments were
performed on data transmissions on a 5 KHz loop from Murray
Hill, NJ, to Los Angeles, CA and back. The data was received
in LA, recorded, reversed in time and retransmitted back to
Murray Hill. Picture quality enhancement was achieved using
this technique. A paper which is very similar to Bogert’s paper
appeared in the IBM journal in 1965 [2]. That paper deals with
the problem of automatic distortion correction for efficient
pulse transmission over telephone networks. In the abstract of
[2], it is mentioned explicitly that time reversal systems
compensate for the distortion in the phase characteristic only.
The same idea appeared in a paper in the IEEE transactions on
acoustics, speech and signal processing in 1974 [3]. In
EXPERIMENTAL RESULTS
The conclusion presented in the last section is verified
experimentally. A vector network analyzer with two ports is
connected to two century bandwidth Cone-Blade antennas
resulting in a 175% BW channel. The antennas are located in a
lab room as an indoor channel. A frequency sweep is done
from 800 MHz to 12 GHz. The causal time domain impulse
response is calculated from the complex S21 and S12 data (which
are equal due to the system reciprocity) using inverse Fourier
transform. Causality of the calculated impulse responses is
enforced by relating the real and imaginary parts of the
measured data by the Hilbert transform. The results are shown
in Fig. 2. The time domain response h(t) is calculated from the
S21, then flipped in time, and convolved with the reponse
calculated from S12. This represents the TR output Rhh(t) in Fig.
2. The function Rhh(t) in the frequency domain has a perfectly
linear phase response, but at the same time has a magnitude
which is equal to the square of S21.