Pulse or digital communications – Systems using alternating or pulsating current
Reexamination Certificate
1999-03-29
2003-05-06
Pham, Chi (Department: 2631)
Pulse or digital communications
Systems using alternating or pulsating current
C370S342000
Reexamination Certificate
active
06560291
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a device and method for sending information and a device and method for receiving information.
DESCRIPTION OF THE RELATED ART
Eight-state amplitude modulation (known as “8-AM”) can be described as follows. At the input to the communication channel, an alphabet
A={
−7, −5, −3, −1, 1, 3, 5, 7}
containing eight numbers, referred to as elementary signals, is available. At each instant, r. T, with r=0, 1, 2, . . . , a multiple of an elementary period T, an information source selects a number a of the alphabet A and transmits this number a to a modulator. This modulator produces, between instants r.T and (r+1). T, the electrical signal a.cos(2.&pgr;.f.t) (or more precisely an amplitude signal proportional to a.cos(2.&pgr;.f.t)), where t is the time and f the frequency of the carrier.
To perform this modulation, the modulator uses an energy E(a) substantially proportional to a
2
.T: E(a)=&lgr;a
2
.T., where &lgr; is the proportionality factor. When the alphabet is as described above, this energy will be measured by one of the numbers &lgr;. T, 9.&lgr;. T, 25.&lgr;. T and 49.&lgr;. T. The ratio between the greatest and least of these energies is 49. This number is fairly high and it would generally be preferable to reduce it. These considerations constitute the first aspect of the problem.
A second aspect of the problem will now be considered. A signal received is often corrupted, for example by noise. This means that the received signal s(t) corresponding to a transmitted signal a.cos(2.&pgr;.f.t) (a being in the alphabet A) will be measured and evaluated as corresponding to the transmission of b.cos 2.&pgr;.f.t), a formula in which b can be different from a and is moreover not necessarily an element of A.
Sometimes, the noise level or the corruption, during a period T, are sufficiently high to make b.cos(2.&pgr;.f.t) closer to a*.cos(2.&pgr;.f.t) with a* in A, and a* different from a, than to any other transmittable signal, including a.cos (2.&pgr;.f.t). In this case, the decision rule is to estimate that a* has been transmitted and an estimation error appears. It can be demonstrated that, with white Gaussian additive noise conditions, the probability of such an estimation error depends highly on the quantity (a-a*)
2
.T, and that, the lower the said quantity, the higher will be this probability.
In particular, the probability of estimating a*=−7 when a=7 has been transmitted is very low and the probability of estimating a*=3 when a=1 has been transmitted is higher.
In this situation, there is an interest in making the error probabilities uniform: it is not a problem that very low error probabilities increase if at the same time the highest probabilities of error are considerably reduced.
From a third point of view, it will be noted that with the modulation method described above the value of a transmitted elementary signal a remains identical during a period of T seconds. Consequently, the frequency spectrum where the usable energy is transmitted is fairly narrow, which presents different disadvantages in the case of multiple transmission paths or noise dependent on the frequency. In this situation, in fact, there is interest in spreading the available energy in a frequency spectrum of greater width. in addition, in various situations, spectrum spreading is make obligatory by special regulations.
A fourth reason concerns any fading of the signal. When the quantity of energy used during an elementary period of duration T is a quantity E, not dependent on the transmitted information, it is possible to measure the corresponding received energy. In this case, if during an interval of time [r. T, (r+1).T], the received signal s(t) has an energy &agr;.E, it is possible first of all to replace s(t) by s*(t)=s(t)/{square root over (&agr;)} and estimate the transmitted information by processing s*(t).
As a fifth reason, it is wished to have easy access to the information in receiving the noisy message. This property is referred to as an easy decoding method.
Finally, amongst the spectrum spreading properties, the following are also of interest for practical applications:
on the one hand, the error correction properties offered by the set of sequences: these properties are measured by the minimum distance (the Euclidean distance, for example) between two different sequences and it would be wished for this distance to be as great as possible (sixth reason),
on the other hand, the flow of information produced by the spreading system, a flow which it would be wished to be as high as possible for a fixed correction capacity (seventh reason).
It appears that there is a close link between the minimum distance and orthogonality: if two equal energy sequences E are orthogonal, the Euclidean distance d between them is proportional to {square root over (2.E)}. Conjointly, requiring all the sequences of length n and of energy equal to E to be orthogonal in pairs prevents the transmission of more than (log
2
(n))/T bits of information per second.
A description will now be given of the state of the art concerning these problems and the improvements to be made thereto will also be discussed.
A first way of responding to the third reason mentioned above is to select a sequence h=(h
1
, . . . , h
n
) of length n on an alphabet {−1, +1} and to replace the transmission of each a by A during the period T by the transmission of n letters a.h
i
, each during a period T
. For example, n=8 and h=(+++−+−−−), representing by the sign “+” the numerical value “+1 ” and by the sign “−”, the numerical value “−1 ”, a=−3 is represented by the sequence (−3, −3, −3, +3, −3, +3, +3, +3) in which each component is transmitted for a period T/8. If r =(r
1
, . . . , r
8
), is the sequence received, after the transmission of a certain a.h, an estimation of a is the element â of A whose value is as close as possible to the mean of the r
i
.h
i
values, i ranging from 1 to 8.
Therefore, in addition to the third reason, this method is good for the fifth reason mentioned above. However, it satisfies neither the first nor the fourth, nor the sixth, nor the seventh reasons mentioned above and it has only few qualities with regard to the second reason.
A second solution (see the document EP-A-94.400.936.4, K. Saito et al.) consists of choosing a square Hadamard matrix H of size n×n, that is to say a matrix on the alphabet {−1, +1} which satisfies H.H
T
=n.I
n
, with H
T
being the transposed matrix of H and I
n
being the identity matrix of size n×n. Let also H* be any sub-matrix 7×n of H and let the information be represented by a sequence of 7-tuples on {−1, +1}. Also let
a
be such a 7-tuple and let
v
=(v
1
, . . . v
n
) be the n-tuple on A given by
v
=
a
. H*.
Each component v
i
, of
v
is transmitted for a period T
. For example, with n=12,
a
=[+−+−+++]and
H
*
=
+
-
-
+
+
+
-
-
+
+
-
+
-
-
+
+
+
+
-
+
-
-
+
+
-
+
-
+
+
+
+
-
-
+
+
-
+
+
-
+
+
-
+
+
+
-
+
+
+
-
+
+
-
+
+
+
+
+
+
-
-
+
+
-
+
+
+
+
+
+
-
+
+
-
+
-
+
-
+
-
-
+
+
+
v
is equal to (1, −1, 1, −1, 1, 3, 3, −3, 1, 7, −1, −1). This method is effective vis-a-vis the first five reasons mentioned above. In particular, with regard to the first reason, the above method makes uniform the energy used over all the twelve intervals of time of duration T/12. However, this method does not lead to a good balance between the last two reasons.
BRIEF SUMMARY OF THE INVENTION
The present invention sets out to remedy these drawbacks.
In the remainder of the description:
The expression “matrix with an orthogonal dominant” designates a square matrix H of real numbers such that
Le Dantec Claude
Piret Philippe
Pham Chi
Tran Khai
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