Pulse or digital communications – Receivers – Particular pulse demodulator or detector
Reexamination Certificate
2000-12-21
2004-01-06
Ghebretinsae, Temesghen (Department: 2631)
Pulse or digital communications
Receivers
Particular pulse demodulator or detector
C375S340000
Reexamination Certificate
active
06674819
ABSTRACT:
DISCUSSION OF THE BACKGROUND
1. Field of the Invention
The present invention relates to a method of estimating a transmission or telecommunications channel which uses complementary sequences. The method results either in obtaining an optimal estimation of the phase and of the attenuation in the case of a single-path channel if the arrival time of the signal is known, or in obtaining a very effective estimation of the delays, phases and attenuations of the different paths in the case of a multipath channel. The method also makes it possible to obtain an estimation in the case of a channel of which it is not possible to distinguish the different paths or in the case of a multipath channel, of which one of the paths is very powerful in comparison with all the others, as long as the arrival time of the signal is known.
2. Background of the Invention
In a telecommunications system, information circulates between transmitters and receivers through-channels. In this connection,
FIG. 1
illustrates a model, which is discrete in time, of the transmission chain between a transmitter
1
and a receiver
2
through a transmission channel
3
. As a general rule, the transmission channels can correspond to different physical, radio, wire, optical media etc., and to different environments, fixed or mobile communications, satellites, submarine cables, etc.
As a result of the multiple reflections of which the waves emitted by transmitter
1
can be the object, channel
3
is a multipath channel which is generally modelled as
FIG. 1
indicates. It is then considered to be a shift register
30
comprising L serial cells (referred to by a subscript k able to take values of between 1 and L) and the contents of which are shifted towards the right of
FIG. 1
each time a symbol arrives at its input. The output of each cell with the subscript k is applied to a filter
31
representing the interference undergone by this output and introducing an attenuation of the amplitude a
k
, a phase shift &agr;
k
and a delay r
k
. The outputs of the filters are summed in a summer
32
. The total impulse response thus obtained is marked h(n).
The output of summer
32
is applied to the input of an adder
33
which receives, moreover, a random signal, modelled by a Gaussian white noise, w(n) which corresponds to the thermal noise which is present in the telecommunications system.
In
FIG. 1
, the reference h(n) has been used, in channel 3, for the register
30
, the filters
31
and the summer
32
, followed by an adder which adds the noise w(n).
It will be understood that, if the transmitter
1
transmits the signal e(n), the signal received r(n), in the receiver
2
, is thus:
r
(
n
)
=
e
(
n
)
*
h
(
n
)
+
w
(
n
)
=
e
(
n
)
*
∑
k
=
1
L
a
k
δ
(
n
-
r
k
)
ⅇ
j
α
k
+
w
(
n
)
=
∑
k
=
1
L
a
k
e
(
n
-
r
k
)
ⅇ
j
α
k
+
w
(
n
)
In these expressions
h
(
n
)
=
∑
k
=
1
L
a
k
δ
(
n
-
r
k
)
ⅇ
jα
k
denotes the impulse response of the channel, &dgr;(n) being the Dirac impulse. The operator * denotes the convolution product, defined by the following relation:
c
(
n
)
=
a
(
n
)
*
b
(
n
)
=
∑
m
=
-
∞
+
∞
a
(
m
)
·
b
(
n
-
m
)
Thus it is generally necessary to determine the characteristics of channel
3
, at a given moment, in order to thwart the induced distortion of the transmitted signal e(n). In order to obtain an estimation of h(n), i.e. of the coefficients a
k
, r
k
and &agr;
k
of the model of channel
3
, it is necessary to repeat this operation at a greater or lesser frequency depending on the rate at which the characteristics of the channel evolve.
A widespread method of estimating the channel consists in transmitting, via transmitter
1
, signals e(n) which are predetermined and known to receiver
2
, and in comparing the signals received r(n) in receiver
2
, by means of a periodic or a periodic correlation, with those which are expected there in order to deduce from them the characteristics of the channel. The a periodic correlation of two signals of length N has a total length 2N−1 and is expressed, from the convolution product, by the relation:
ϕ
a
,
b
(
n
)
=
a
*
(
-
n
)
*
b
(
n
)
=
∑
m
=
0
N
-
1
a
(
m
)
·
b
(
m
+
n
)
(
1
)
,
[
m
]
=
0
,
1
,
…
,
N
-
1
for two signals a(n) and h(n) of finite length N, where the operator * denotes the complex conjugate operation.
The correlation of the received signal r(n) with the known transmitted signal e(n) translates as:
r
(
n
)*
e
*
(−
n
)=[
e
(
n
)*
h
(
n
)+
w
(
n
)]*
e
*
(−
n
)
&PHgr;
e,r
(
n
)=&PHgr;
e,e*h
(
n
)+&PHgr;
e,w
(
n
)
=&PHgr;
e,e
(
n
)*
h
(
n
)+&PHgr;
e,w
(
n
)
The result of the correlation operation constitutes the estimation of the impulse response of the channel: the quality or the precision of the estimation is all the better if e(n) tends towards h(n). The latter is directly dependant on the choice of transmitted sequence e(n); to optimise the estimation process, the signal e(n) should be chosen in such a way that &PHgr;
e,e
(n) tends towards k·&dgr;(n), k being a real number, and that &PHgr;
e,w
(n)/&PHgr;
e,e
(n) tends towards zero. In fact, in this case, the estimation of the channel becomes:
&PHgr;
e,r
(
n
)=
k
·&dgr;(
n
)*
h
(
n
)+&PHgr;
e,w
(
n
)
=
k·h
(
n
)+&PHgr;
e,w
(
n
)
&PHgr;
e,r
(
n
)≈
k·h
(
n
)
It has been demonstrated that no single sequence exists for which the function of a periodic auto-correlation &PHgr;
e,e
(n) tends toward k·&dgr;(n).
SUMMARY OF THE INVENTION
One object of the present invention consists in using pairs of complementary sequences which have the property that the sum of their auto-correlations is a perfect Dirac function. Let s(n) and g(n), n=0,1, . . . , N−1 be a pair of complementary sequences:
&PHgr;
s,s
(
n
)+&PHgr;
g,g
(
n
)=
k.
&dgr;(
n
) (1)
Several methods of constructing such complementary sequences are known in the literature: Golay complementary sequences, polyphase complementary sequences, Welti sequences, etc. By way of information, one will be able to refer, in this connection, to the following technical documents which deal with the introduction to complementary sequences and, in particular, to Golay complementary sequences as well as to a Golay correlator:
1) “On a periodic and periodic complementary sequences” by Feng K., Shiue P. J. -S., and Xiang Q., published in the technical journal IEEE Transactions on Information Theory, Vol. 45, no. 1, January 1999,
2) “Korrelationssignale” by Lüke H. -D, published in the technical journal ISBN 3-540-54579-4, Springer-Verlag Heidelberg New York, 1992,
3) “Polypbase Complementary Codes” by R. L. Frank, published in the technical journal IEEE Transactions on Information Theory, November 1980, Vol. IT26, no. 6,
4) “Multiphase Complementary Codes” by R. Sivaswamy, published in the technical journal IEEE Transactions on Information Theory, September 1978, Vol. IT-24, no. 5,
5) “Efficient pulse compressor for Golay complementary sequences” by S. Z. Budissin, published in the technical journal Electronics Letters, Vol. 27, no. 3, January 1991,
6) “Complementary Series” by M. J. Golay, published in the technical journal IRE Trans; on Information Theory”Vol. IT-7, April 1961,
7) “Efficient Golay Correlator” by B. M. Popovic, published in the technical journal IEEE Electronics Letters, Vol. 35, no. 17, August 1999.
Reference can also be made to the descriptions of the documents U.S. Pat. Nos. 3,800,248, 4,743,753, 4,968,880, 5,729,612, 5,841,813, 5,862,182 and 5,961,463.
The property of complementary sequences in having a perfect sum of autocorrelations is illustrated in
FIG. 2
, taking, by way of example, a pair of Golay complementary sequences of length N=16 bits.
In
FIG. 2
are plotted on the x-co-ordinates the time
Jechoux Bruno
Rudolf Marian
Ghebretinsae Temesghen
Mitsubishi Denki & Kabushiki Kaisha
Oblon & Spivak, McClelland, Maier & Neustadt P.C.
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