Browse Prior Art Database

Greedy Waterpouring Recipe for Fourier Transform

IP.com Disclosure Number: IPCOM000122666D
Original Publication Date: 1991-Dec-01
Included in the Prior Art Database: 2005-Apr-04
Document File: 4 page(s) / 140K

Publishing Venue

IBM

Related People

Feig, E: AUTHOR [+2]

Abstract

Most coding and modulation schemes designed around the specific signal- to-noise power ratio function (of frequency) are based on the classical waterpouring recipe (1,2), and leave a wide gap between theory and actual obtained rates. This disclosure presents a frequency-designed modulation scheme which increases rates considerably whenever the signal-to-noise ratio function is far from flat.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 49% of the total text.

Greedy Waterpouring Recipe for Fourier Transform

      Most coding and modulation schemes designed around the
specific signal- to-noise power ratio function (of frequency) are
based on the classical waterpouring recipe (1,2), and leave a wide
gap between theory and actual obtained rates.  This disclosure
presents a frequency-designed modulation scheme which increases rates
considerably whenever the signal-to-noise ratio function is far from
flat.

      The basic tool employed is the FTDM (Fourier Transform Division
Multiplexing) method to design signals for transmission.  These have
been studied in (3 - 5). Basically, data is encoded in the frequency
domain, Fourier transformed to yield a real sequence, and a signal is
transmitted whose sampled values are precisely the computed sequence.
Spectral characteristics for the code are easily obtained because it
is designed in the frequency domain. The transmitter is summarized at
the top of the figure.

      A message is first encoded into finite sequences of complex
numbers.  One can think of the message as a sequence of binary data.
This data is segmented into blocks, and an appropriate error control
redundancy scheme is employed. Here, one does not deal with
traditional error correcting methods; one simply assumes that they
are built into the original binary sequence.  This disclosure is
concerned with how to encode the binary sequence into a sequence of
complex numbers.  In standard time-domain methods, such encodings are
quite popular, as with PSK and QAM methods, and the more recent and
very powerful trellis- coded modulation schemes (6).

      Each finite sequence (or vector) of complex numbers is
symmetrized; that is, one adjoins to the sequence the complex
conjugate of its reverse sequence.  This is done to guarantee that
the Discrete Fourier Transform (DFT) of the resulting sequence is
real valued.  To this real valued sequence one adds some redundancy
which will help with the equalization at the receiver.  The ideal
transmitted signal is the unique analog signal whose sampled values
(at the Nyquist rate) are the real sequence.  However this signal may
exhibit spurious peaks that may overload the channel. Therefore, the
sequence is first clipped at some appropriate level.  The resulting
sequence is passed through a D/A converter, low pass filtered, and
transmitted to the channel.

      The receiver is pictured at the bottom of the figure. The
signal out of the channel is low-pass filtered and passed through an
A/D converter, yielding a real sequence. This sequence is equalized
and the output subjected to an Inverse Discrete Fourier Transform
(IDFT) which yields a complex sequence.  This last sequence is passed
both to a final decoder, which estimates the initial binary sequence
from it, and also to logic for updating the equalizer coefficients.
The latter is used also for timing recovery and automatic gain
control.

      One assumes that as long as...