Pulse or digital communications – Systems using alternating or pulsating current – Plural channels for transmission of a single pulse train
Reexamination Certificate
2000-06-14
2003-10-07
Phu, Phuong (Department: 2631)
Pulse or digital communications
Systems using alternating or pulsating current
Plural channels for transmission of a single pulse train
C708S408000, C708S406000
Reexamination Certificate
active
06631167
ABSTRACT:
FIELD OF THE INVENTION
The invention relates to transforming a stream of respective groups of 2N real input data into a stream of complex output symbols respectively formed of N complex output samples, by interleaved type processing. The invention applies advantageously, but not limitingly, to systems transmitting information coded according to Orthogonal Frequency Division Multiplex (OFDM) coding.
BACKGROUND OF THE INVENTION
Systems transmitting information using OFDM coding form, for example, the receiving part of a very high speed digital modulation/demodulation device (VDSL modem). In OFDM coding, the signal to be transmitted is coded on N carriers which are phase-modulated and amplitude-modulated as a function of the content of the information to be transmitted. Each carrier has a predetermined frequency and all the frequencies of the carriers are a submultiple of a predetermined sampling frequency. Also, each symbol is formed of N digital carriers, which are N complex samples sampled at the sampling frequency, and must be transformed into a group of 2N real data sampled at twice the sampling frequency. This allows the symbols to be transmitted over a transmission channel, such as a telephone line.
The transformation of a complex symbol respectively formed of N complex samples into a group of 2N real data can be performed in several ways. A first approach performs an inverse Fourier transform of twice the size, i.e., size 2N. However, this approach requires the addition of an extra processing stage as well as the addition of extra memory. A second approach performs an inverse Fourier transform of single size, i.e., size N, followed by a complex filtering. Such an implementation leads to a relatively complicated hardware embodiment.
A third approach also performs an inverse Fourier transform of size N, but is followed by a real filtering. However, this approach, which is simpler to implement than the previous approach, is approximate with regards to the accuracy obtained by reason of a signal
oise ratio which may turn out to be relatively large. A large signal
oise ratio leads to signal degradations. Also, the increase in the performance of this approach, i.e., the reduction in the signal
oise ratio, requires the use of an extremely large real filter. An extremely large real filter involves an expensive hardware implementation.
Another approach includes performing the transformation of the stream of complex symbols respectively formed of N complex samples into a stream of respective groups of 2N real data, by processing of the interleaved type. The theoretical formulation of interleaved type processing is well known to one skilled in the art.
The main characteristics of a processing of the interleaved type are recalled here for all useful purposes. The real signal x(t) corresponding to an OFDM symbol, for example, is defined by formula (I):
x
(
t
)
=
∑
k
=
1
N
-
1
M
k
·
cos
(
2
π
f
k
t
+
ϕ
k
)
(
I
)
M
m
denotes the amplitude of the carrier of rank k, &phgr;
k
denotes its phase, f
k
denotes its frequency, and N−1 is the number of carriers. When the frequencies of the carriers are all multiples of a frequency f
1
, then formula (I) becomes formula (II) in complex notation:
x
(
t
)
=
Re
[
∑
k
=
1
N
-
1
C
k
·
ⅇ
2
j
π
kf
1
t
]
(
II
)
in which C
k
denotes the complex sample representative of the carrier of rank k. C
k
is defined by formula (III):
C
k
=M
k
·e
j
&phgr;
k
(III)
With a sampling of the signal at the frequency Nf
1
and by extending the length of the symbol to N carriers (by adding the carrier C
0
taken equal to 0), it can then be shown that the N real data of even ranks, corresponding to the N complex samples of the input symbol, are given by formula (IV):
{
x
2
p
}
=
Re
(
IFFT
N
{
(
C
k
+
C
_
N
-
k
)
+
j
(
C
k
-
C
_
N
-
k
)
ⅇ
j
π
N
k
}
)
(
IV
)
The real data of odd ranks x
2p+1
are given by formula (V):
{
x
2
p
+
1
}
=
Im
(
IFFT
N
{
(
C
k
+
C
_
N
-
k
)
+
j
(
C
k
-
C
_
N
-
k
)
ⅇ
j
π
N
k
}
)
(
V
)
In formulas (IV) and (V), {overscore (C)}
N−k
represents the complex conjugate of the complex number C
N−k
, IFFT
N
represents the “inverse Fourier transform of size N” operator, Im denotes the imaginary part of a complex number, and Re denotes the real part of a complex number. It is therefore seen that the processing of the interleaved type comprises a preprocessing phase in which, for each symbol received formed of N complex samples C
k
, a symbol formed of N complex samples AA
k
is formulated. Each complex sample AA
k
is defined by formula (VI):
AA
k
=(
{overscore (C)}
k
+C
N−k
)+
j
(
C
k
−{overscore (C)}
N−k
)
e
j&pgr;&kgr;/N
(VI)
After this preprocessing, a processing phase is performed, which comprises for each symbol formed of the samples AA
k
an inverse Fourier transform calculation of size N. The result of this inverse Fourier transform is a set of N complex coefficients A
k
which, after rearrangement to retrieve the input order, makes it possible to obtain the 2N real data corresponding to the input symbol. This is because the real data of even and odd ranks correspond respectively to the real parts and imaginary parts of the complex samples A
k
successively obtained after rearrangement.
Once the 2N real data have been transmitted over the telephone line, they need to be recovered to perform a transformation thereof into a stream of complex symbols so as, in this instance, to obtain the complex carriers C
k
. Here again, several approaches are conceivable. A first approach includes performing a direct Fourier transform of twice the size, i.e., size 2N. A second approach includes performing a Fourier transform of single size, i.e., size N, followed by a complex filtering. A third approach also includes performing an inverse Fourier transform of size N, but this time followed by a real filtering.
However, all these approaches have the same drawbacks as those which have been discussed above with regards to the sending part. This is the reason why one preferably performs the transformation of the stream of respective groups of 2N real input data into a stream of complex output symbols formed of N complex output samples by a processing of the interleaved type.
The main characteristics of interleaved type processing performed on reception of the real input data are recalled here for all useful purposes. As made explicit in formula (VII) below:
{
U
k
}
0≦k<N−1
=FFT
N
{(
X
2p
+jx
2p−1
)
0≦p<N−1
} (VII)
The notation FFT
n
denotes the direct Fourier transform operator of size N, and U
0
is equal to 0. The initial symbols A
k
with p varying from 0 to n−1, is defined by a formula (VIII):
A
p
=x
2p
+jx
2p+1
(VIII)
These symbols are formulated in a phase of initial processing.
Each initial complex sample A
p
has a real part formed by an input data item of even rank and an imaginary part formed by the succeeding input data item of odd rank. These N initial complex samples are ordered according to a natural order corresponding to the natural order of reception of the input data x
p
.
The direct Fourier transform calculation of size N then makes it possible to obtain N auxiliary complex samples U
k
which are delivered conventionally in a so-called reverse order (bit reverse) with respect to the natural order. These auxiliary samples U
k
must thereafter undergo a phase of subsequent processing in accordance with formula (IX) below. This processing includes a rearrangement and a specific processing employing each auxiliary sample U
k
and the paired auxiliary sample U
N−k
, so as to deliver again in the natural order, the N complex output samples C
k
Barthel Dominique
Cambonie Joël
Lienard Joël
Mejean Philippe
Allen Dyer Doppelt Milbrath & Gilchrist, P.A.
Jorgenson Lisa K.
Phu Phuong
STMicroelectronics S.A.
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