Soft decision rule for demodulation of bi-orthogonal signals

Details Soft decision rule for demodulation of bi-orthogonal signals Soft decision rule for demodulation of bi-orthogonal signals

1999-03-09

2002-08-13

Olms, Douglas (Department: 2661)

Multiplex communications

Generalized orthogonal or special mathematical techniques

C375S340000

Reexamination Certificate

active

06434111

ABSTRACT:

BACKGROUND OF THE INVENTION
The invention relates to a process for the demodulation of signals indicative of sequences emitted in a communications system, such as, for example, a system of spread band communications making use of orthogonal or bi-orthogonal modulation. Such a communications system is, for example, a multiple access communications system, such as a wireless telephone system or a communications system of the satellite repeater type. For example, the present invention may apply to a communications system which uses the CDMA system (Code Division Multiple Access).
A spread band communications system to which the process according to the invention may apply is known, and is, for example, of the type which is described in U.S. Pat. No. 5,602,833. As shown in
FIG. 1
, such a system is essentially constituted, on the transmission side, by an encoder
10
, a modulator
20
, and a transmitter unit
30
transmitting on a channel
40
. On the reception side, it is constituted by a receiver unit
50
, a demodulator
60
, corresponding to the modulator
20
, and a decoder
70
which corresponds to the encoder
10
. In general, such systems likewise comprise an interleaver
15
, which is located between the encoder
10
and the modulator
20
, as well as a de-interleaver
65
, corresponding to the interleaver
15
, and located between the demodulator
60
and the decoder
70
.
The encoder
10
and the interleaver
15
are known in the art, and are provided in order to encode, with repetition and interleaving, an incoming bit stream representing speech signals, data signals, or other signals, for example, first amplified, filtered, and digitized. This encoding is of the type which allows the implementation of error detection and correction functions. In association with an interleaving processing system, this encoding also allows the system to operate with low noise-to-signal ratio and low interference signal ratio. The signals resulting from the encoding and interleaving processes are a sequence of k-area words or symbols consisting of k elements generally referred to as 1 and −1 (or 0 and 1).
This sequence of symbols is subjected, in the modulator
20
, to a modulation process referred to as orthogonal modulation or bi-orthogonal modulation.
In the case of orthogonal modulation, the modulator
20
comprises a generator
21
of orthogonal words. Such words are also referred to sequences or functions. In the remainder of the description, they are referred to by the term “functions”.
These functions may be Walsh functions, which are derived on the basis of Walsh matrices, known by the name of Hadamard matrices. It is reminded that Hadamard matrices are matrices which are derived in a recursive manner, such that a matrix of functions of the order n can be written:
W
⁡
(
n
)
=
&LeftBracketingBar;
W
⁡
(
n
)
/
2
W
⁡
(
n
/
2
)
W
⁡
(
n
/
2
)
W
⁡
(
n
/
2
)
_
&RightBracketingBar;
where W represents the logical complement of the matrix W. In addition, the matrix W(1) of dimension 1, is equal to 1.
Each column or line of a matrix W(n) of the order n is called a Walsh function, and is annotated S
p
(n), where p is the number of the column or line of the function under consideration, and n is the dimension of the function. It will be more simply also annotated as S
p
.
For example, the Walsh matrix of the dimension 8 is written as follows:
W
⁡
(
8
)
=
[
1
1
1
1
1
1
1
1
1
-
1
1
-
1
1
-
1
1
-
1
1
1
-
1
-
1
1
1
-
1
-
1
1
-
1
-
1
1
1
-
1
-
1
1
1
1
1
1
-
1
-
1
-
1
-
1
1
-
1
1
-
1
-
1
1
-
1
1
1
1
-
1
-
1
-
1
-
1
1
1
1
-
1
-
1
1
-
1
1
1
-
1
]
Also by way of example, the sequence S
4
is written {1,−1,−1,1,1,−1,−1,1}.
It will be noted that the elements 1 and −1 have been used, but the elements 0 and 1 respectively could also be used.
Digital modulation consists of assigning to each possible symbol p deriving from the interleaving device
15
a sequence to be transmitted SE
p
. In the case of orthogonal modulation, the assigned sequences SE
p
correspond to the Walsh functions S
p
(n). Accordingly, the symbols of three bits can be modulated by way of the Walsh functions of dimension 8, and, in general terms, symbols of k bits will be modulated by way of N (=2
k
) sequences SE
p
of dimension n (=
2
k
).
For example, for two-bit incoming symbols, a list is given in Table 1 below of the corresponding SE
p
sequences transmitted and attributed by the modulator
20
.
TABLE I
Incoming symbol
Sequence attributed
  1   1
SE
1
= S
1
(4) = {1,1,1,1}
−1   1
SE
2
= S
2
(4) = {1,−1,1,−1}
  1 −1
SE
3
= S
3
(4) = {1,1,−1,−1}
−1 −1
SE
4
= S
4
(4) = {1,−1,−1,1}
Bi-orthogonal modulation consists of attributing to an incoming symbols p a corresponding sequence, SE
p
, either an orthogonal function, such as, for example, a Walsh function S
q
of dimension n=2
k−1
, when the last element (k
th
element) is in an first state, or a logic complement of this function S
q
, of the same dimension n, when the last element (k
th
element) is in a second state. In general terms, the k bits symbols are modulated by means of N (=2
k
) sequences SE
p
, of length n (=2
k−1
). Bi-orthogonal modulation is described, for example, in the European Patent document EP-A-809 364.
For example, for the two-bit incoming symbols, the list of the corresponding sequences attributed by the modulator
20
is shown in Table II below
TABLE II
Incoming symbol
Sequence attributed
  1   1
SE
1
= S
1
(2) = {1,1}
−1   1
SE
2
= S
2
(2) = {1,−1}
  1 −1
SE
3
= −S
1
(2) = {−1,−1}
−1 −1
SE
4
= −S
2
(2) = {−1,1}
The sequences SE
p
attributed during orthogonal or bi-orthogonal modulation are then processed and transmitted by the transmitter unit
30
. They are transmitted, via the channel
40
, to the receiver unit
50
and to the demodulator
60
, which are respectively the corresponding of the transmitter unit
30
and the modulator
20
.
The demodulation process which is implemented in the demodulator
60
consists accordingly in recovering, in the signal transmitted by the receiver unit
50
, the sequence SE
p
, used during the modulation, and then in recovering, on the basis of this sequence, the modulated symbol p.
Several processes could be carried out.
The first consists of selecting the sequence the correlation value between the signal transmitted by the receiver unit
50
and the corresponding function of which is the strongest. It accordingly consists of selecting the sequence SE
p
the probability of which that it has been transmitted is the greatest. The sequence SE
p
having been selected, the symbol p associated with this sequence is then recovered and supplied to the de-interleaver
65
and then to the decoder
70
.
The decoder
70
is, for example, a decoder of the maximum probability type, for example such the one described by A. J. Viterbi in an article appearing in the IEEE Transactions on Communications Technology of October 1971, entitled “Convolutional codes and their performance in communication systems”.
This method is referred to in the technical domain as the Hard Decision Method.
Another method, referred to as the Soft Decision Method, consists of determining, on the basis of the correlation values obtained by a correlation process between the signal transmitted by the receiver unit
50
and each of the functions that could be used during the modulation process, a confidence value for each sequence SE
1
to SE
N
associated with each of the said functions. It also consists in deducing from this group of confidence values a soft decision value to be attributed to each element of the demodulated

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