System and method for sending and receiving a digital signal over a radio pathway
A constant-amplitude and continuous-phase modulation method for modulating digital data and for demodulating said modulated signal, said data taking the form of symbols a(n) that can take a number M of states at least equal to 2, the method including, in transmission, use of a voltage-controlled oscillator (VCO) for which the control is the sum of pulses he(a(n), t−n T), the form and the amplitude of which depends on the value of a(n); and, in reception, use of a single impulse response filter C0(t) regardless of the value of M in transmission, said functions he and C0 having a number of parameters that are optimized in the design of the system in order to obtain at the output of the filter C0 a constellation that is as close as possible to the theoretical constellation.
1. A constant-amplitude and continuous-phase modulation method for modulating digital data and for demodulating said modulated digital data, said digital data being in the form of symbols having M number of states, where M is an integer greater than 2, the method comprising:
recovering the symbols a(n) of the digital data to be transmitted, the symbols a(n) of the digital data being recovered periodically at a constant time interval T;
associating, with each symbol a(n), a frequency pulse denoted h e (a(n)) having a frequency pulse of length L T, where L is an integer greater than or equal to 1, and having a form dependent on the value of a(n);
weighting the frequency pulse h e (a(n), t) by a total phase variation associated with a(n), the total phase variation being in the form π(2a(n) −(M−1))/M, where a(n) is an integer less than or equal to M−1, and for a symbol of value m, where m is less than M, said function h e having a form corresponding to a combination of 2 K +1 individual pulses:
h
e
(
m
,
t
)
=
∑
i
=
1
K
w
e
(
m
,
i
)
(
g
(
+
a
e
,
m
,
i
,
σ
e
,
m
,
i
,
t
)
+
g
(
m
,
-
a
e
,
m
,
i
,
σ
e
,
m
,
i
,
t
)
)
+
(
1
-
2
∑
i
=
1
K
w
e
(
m
,
i
)
)
g
(
0
,
σ
e
,
m
,
0
,
t
)
where the function g is a continuous function of standard deviation σ and optimized weighting coefficients, where w e,m,i , and σ e,m,i , a e,m,i are the symbol and a number of successive derivatives of the function g to limit the spectral width of the digital data sent, a is an integral equal to 1, K is the degree of freedom associated with the weight w(i), and t is a given instant;
applying a sum of successive weighted pulses to an input of a voltage-controlled oscillator to generate the modulated digital data to be sent; and
filtering, on reception, the received modulated digital data by a single impulse response filter C 0 (t) regardless of the number of states of the modulation,
wherein the parameters of the frequency pulses h e (a(n), t) and impulse response filter C 0 (t) are optimized to minimize inter-symbol interference of the digital data.
2. The method as claimed in claim 1 , wherein the function g(a, σ, t) is a standardized Gaussian of average a, a being a point about which the function g is centered, and of standard deviation σ, where t is a given instant.
3. The method as claimed in claim 1 , wherein the function g(a, σ, t) is a function of adjustable width and position having a given number of degrees of continuity.
4. The method as claimed in claim 1 , wherein filtering of the received modulated digital data comprises constructing a filter receiving the impulse response C 0 (t) by:
choosing a reception pulse h r (t) constructed according to the same method as the pulses h e (m, t) according to:
h
r
(
t
)
=
∑
i
=
1
K
w
r
(
i
)
(
g
(
+
a
r
,
i
,
σ
r
,
i
,
t
)
+
g
(
-
a
r
,
i
,
σ
r
,
i
,
t
)
)
+
(
1
-
2
∑
i
=
1
K
w
r
(
i
)
)
g
(
0
,
σ
r
,
0
,
t
)
where the function g is a continuous function of standard deviation σ and optimized weighting coefficients, w r,i and a r,i are the symbol and a number of its successive derivatives to limit the spectral width of the modulated digital data sent, a is an integral equal to 1, K is the degree of freedom associated with the weighting coefficients w(i), and t is a given instant;
calculating an integral of h r (t), denoted f r (t), according to:
f
r
(
t
)
=
∫
-
∞
t
h
r
(
x
)
ⅆ
x
;
determining the function S 0 (t), according to:
S
0
(
t
)
=
sin
(
π
2
f
r
(
t
)
)
0
≤
t
≤
LT
S
0
(
t
)
=
sin
(
π
2
(
1
-
f
r
(
t
-
LT
)
)
)
LT
≤
t
≤
2
LT
; and
determining the filter C 0 (t) according to:
C
0
(
t
)
=
∏
i
=
0
L
-
1
S
0
(
t
+
iT
)
.
5. The method as claimed in claim 4 , wherein the function g(a, σ, t) is a standardized Gaussian of average a and of standard deviation σ.
6. The method as claimed in claim 4 , wherein the function g(a, σ, t) is a function of adjustable width and position of given degrees of continuity.
7. A constant-amplitude and continuous-phase modulation system for modulating digital data and for demodulating said modulated digital data, the system being configured to execute the method according to claim 1 , said digital data being in the form of symbols having M number of states, where M is an integer greater than 2, the system comprising:
a transmission module comprising a bank of filters having a transfer function determined by implementation of the method as claimed in claim 1 ;
a summer combining said modulated digital data;
a voltage-controlled oscillator; and
a single impulse response filter C 0 (t) regardless of the number of states of the modulation, the single impulse response filter C 0 (t) being obtained by implementation of the method as claimed in claim 1 .
8. The system as claimed in claim 7 , further comprising at least one bandpass filter inserted in the transmission module or in the single impulse response filter C 0 (t), the at least one bandpass filter being matched to limit the bandwidth of the transmitted digital data or to avoid receiving frequency-offset interference from the modulated digital data.