Method and device for phase modulation of a carrier wave and application to the detection of multi-level phase-encoded digital signals
View Patent ↗The method of phase modulating a carrier wave involves creating a set of signals s h (t) constituted by a carrier wave of frequency f C and of phase φ(t)=hφ 0 (t) that is modulated in time t in such a manner that s h (t)=cos(2πf C t+hφ 0 (t)), where h is an integer and where φ 0 (t)=2 arctan((t−t 0 )/w 0 ). The modulation corresponds to a single phase pulse centered on a time t 0 of characteristic duration w 0 that is positive, and incrementing the phase of the signal s h (t) by the quantity h2π, in such a manner as to generate a single sideband frequency spectrum directly. The carrier wave may be of electromagnetic type or of acoustic type. The method applies in particular to transporting binary information by single sideband phase coding, to generating single sideband orthogonal signals, to detecting single sideband phase coded multiple-level digital signals, to transmitting single sideband phase coded binary signals in-phase and out-of-phase, and to single sideband combined amplitude-and-phase modulation.
1. A method of phase, modulation comprising:
creating a set of signals s h (t) constituted by a carrier wave of carrier frequency f C and of phase φ(t)=hφ 0 (t) that is modulated in time t in such a manner that s h (t)=cos(2πf C t+hφ 0 (t)), where h is an integer and where φ 0 (t)=2 arctan((t−t 0 )/w 0 ), wherein the modulation of the carrier wave corresponds to a single phase pulse centered on a time t 0 and having a positive characteristic duration w 0 ;
incrementing the phase of the set of signals s h (t) by the quantity h2π; and
generating a single sideband frequency spectrum directly from the phase-incremented set of signals.
2. The method according to claim 1 , wherein the carrier wave is of electromagnetic type.
3. The method according to claim 1 , wherein the carrier wave is of acoustic type.
4. The method according to claim 1 , comprising:
determining that a k th information bit of duration T b contributes the quantity 2 b k arctan((t−kT b )/w) to the total phase ϕ(t) of the carrier wave, where b k =1 or 0, and where the width w is comparable to or smaller than the symbol duration T b , or else considering that the derivative of the phase ϕ(t) is a sum of Lorentzian functions 2w/((t−kT b ) 2 +w 2 ) centered on kT b and weighted by the information bit b k ;
integrating the phase ϕ(t);
phase modulating the carrier wave using the integrated phase ϕ(t);
calculating in phase and quadrature components of the phase ϕ(t) as cos φ(t) and sin φ(t);
calculating in-phase amplitude cos 2π f C t and quadrature amplitude sin 2π f C t of the carrier wave; and
generating the set of signals s h (t) according to:
s h ( t )=cos(2π f C t +φ( t ))=cos(2π f C t )cos φ( t )−sin(2π f C t )sin φ( t ).
5. The method according to claim 1 , comprising:
independently modulating an in-phase component and a quadrature component of the carrier wave;
generating the set of signals s h (t) according to:
s h ( t )=cos(2π f C t+φ 1 ( t ))+sin(2π f C t+φ 2 ( t ))
with the phases
φ
1
(
t
)
=
∑
k
b
k
,
1
φ
0
(
t
-
kT
b
)
and
φ
2
(
t
)
=
∑
k
b
k
,
2
φ
0
(
t
-
kT
b
)
,
where bits b k,1(2) represent two independent sets of bits used to double the bit rate, the spectrum of each of the out-of-phase and in-phase components being a single sideband spectrum.
6. The method according to claim 1 , comprising:
generating the set of signals s h (t) according to:
s h ( t )=cos(2π f C t )−(−1) h cos(2π f C t+hφ α′ ( t )).
7. A device for demodulating a single sideband phase coded signal, the device comprising:
a local oscillator of frequency f C ;
first and second mixers; and
a 0°-90° phase shifter configured to obtain respectively the in-phase and quadrature components cos(φ(t)) and sin(φ(t)) of a modulation signal;
a circuit configured to differentiate each of the in-phase and quadrature components cos(φ(t)) and sin(φ(t)) of the modulation signal and to generate a phase derivative as:
dφ/dt =cos φ( t ) d (sin φ( t ))/ dt −sin φ( t ) d (cos φ( t ))/ dt ; and
a circuit for reconstituting an initially generated series of Lorentzian function pulses, the circuit comprising a threshold detector with a value of half the amplitude of a single Lorentzian function pulse so as to discriminate the value of a bit b k =1 or 0 at a time t k =kT b .
8. A device for demodulating signals by a base of orthogonal periodic signals comprising four amplitude levels including zero amplitude, the device comprising:
a local oscillator of frequency;
first and second mixers;
a 0°-90° phase shifter configured to obtain respectively the in-phase and quadrature components cos(φ(t)) and sin(φ(t)) of a modulation signal;
a detector configured to separately detect the four levels h=0, 1, 2, and 3 of quaternary bits by using a demodulator associated with a Lorentzian function generator of period T b , to form the following two quantities for each of the four amplitude levels:
R
h
(
t
)
=
(
cos
(
φ
(
t
)
-
h
φ
0
(
t
,
T
b
)
)
)
d
φ
0
dt
and
I
h
(
t
)
=
(
sin
(
φ
(
t
)
-
h
φ
0
(
t
,
T
b
)
)
)
d
φ
0
dt
a circuit configured to convolve the two formed quantities R h (t) and I h (t) with a gate function of time width T b giving:
R
h
_
(
t
)
=
∫
t
-
T
b
/
2
t
+
T
b
/
2
R
h
(
t
-
τ
)
d
τ
and
I
h
_
(
t
)
=
∫
t
-
T
b
/
2
t
+
T
b
/
2
I
h
(
t
-
τ
)
d
t
a circuit configured to calculate the quantity R h (t) 2 + I h (t) 2 ; and
a threshold detector configured to determine that a peak observed in the quantity R h (t) 2 + I h (t) 2 at an instant t=kT b for the level h=0, 1, 2, or else 3 indicates that the bit b k is equal to h.
9. A device for generating single sideband (SSB) phase pulses in the optical domain, the device comprising:
a circuit configured to supply data b k =1 or 0;
a Lorentzian function generator;
a phase generator circuit;
a phase integrator circuit;
a laser generator configured to generate a carrier frequency; and
an electro-optical phase modulator configured to modulate the phase of a carrier wave directly, under the effect of a voltage proportional to a desired phase variation, to generate an SSB phase modulation optical signal for transmission over an optical communications network.