PROCÉDÉ ET DISPOSITIF DE MODULATION DE PHASE D'UNE ONDE PORTEUSE ET APPLICATION À LA DÉTECTION DE SIGNAUX NUMÉRIQUES MULTI-NIVEAUX CODÉS EN PHASE

Method and phase modulation means of a carrier wave and application to the detection of multi-level digital signals coded domain phase of the invention

The present invention relates to a phase modulation method of a carrier wave, which carrier wave can be of electromagnetic type, since the low frequency domain to the optical domain, or audio-type.

The invention also relates to an application to a method of conveying binary information by phase encoding single-sideband (SSB).

The invention further relates to a method of generating orthogonal signals to single sideband for application to coding and detection of digital multi-level SSB signals.

The invention further relates to a method of transmitting in phase and out of phase binary signals encoded single sideband phase.

The invention also concerns an application to a mixed modulation method amplitude-phase single sideband.

The invention further relates to devices for implementing the above methods.

BACKGROUND

From the early development of telephony and a radio, the signals broadcast were transported through modulation amplitude or phase of a sinusoidal carrier wave of frequency higher than the frequency domain of these signals. In all known processes it is found that the modulation produces a bilateral frequency spectrum, that is to say, with frequency components above and below the carrier frequency. In general, the information contained in the upper band is the same as that contained in the lower band.

Also the engineers sought to find ways to keep only sideband to optimize the occupation of the allocated frequency band (see eg US 1,449,382). While each user occupies a smaller frequency space, the number of users will be increased and costs per user will be reduced.

The current method for obtaining a single sideband (SSB) (in English or "single side band" or "SSB"), is to remove, after generation of the modulated signal, the undesired sideband. The simplest is the type of filtering bandpass.

A better method is filtering Hilbert transform. Proposed by Hartley 1928 (see US 1,666,206), it consists, using a broadband 90 ° phase shifter, to build the sum (respectively the difference) of the in-phase part and the quadrature modulated signal to obtain the upper sideband (respectively bottom).

A variant was then proposed by Weaver, in the article by DK Weaver Jr., entitled "A third method of generation and detection of single- sideband would sign" appeared in "Proceeding of the IRE", pages 1703-1705, June 1956 .

The Hilbert transform method is particularly suited today with the onboard digital computers (in English "Digital Signal Processor" or "DSP").

Moreover, for many applications, it seeks to generate orthogonal signals SSB. The use of the form of orthogonal waves are many applications ranging from signal analysis to the signal transmission. In the latter case, the intended application is the data multiplexing. Early approaches have consisted of performing amplitude modulation of a carrier wave by a signal formed of the sum of orthogonal signals multiplied by the information bit to be carried.

Orthogonal means that the integral of the product of two distinct waveforms is zero over a finite length (here the duration T _s of a waveform of emission (or 'symbol') encoding a bit of information). An example of mutually orthogonal wave functions is given by the set: sin2-t / T _s, sin4-t / T _s, sin6-t / T _s, etc ....

Variants using the generation of orthogonal polynomials have been described in US 3,204,034.

It was also suggested using variations generation Hermite functions, such as in US 3,384,715.

It may be noted that the modulation by sine functions mentioned above also returns to frequency modulation (and therefore the phase) where the carrier frequency takes the values £ f _c f _c +/- _Sl lf +/- 2ft _Sr c +/- 3 / T _s, etc .... The latter solution was the most developed in the field of digital data transmission. The process is called in English "Orthogonal Frequency Division Multiplexing" or "OFDM" and is described in particular in US 3488445. It is used for example for ADSL, radio or digital terrestrial television and more recently in mobile networks 4G. From a carrier frequency using a plurality of frequency sub-carriers each of which carries a binary information. Each subcarrier is the vector of a binary channel, the simultaneous use of the N subcarriers to multiplexing of N bits. In this method, the signals carried by each subcarrier should have the orthogonality property in order to avoid co-channel interference and be able to find, after demodulation, the information for each channel.

The orthogonality is assured if the distance between frequency subcarriers is a multiple of the inverse of the symbol duration T _s. During the transmission duration T _s, the N-bit modulation signal transmitted in parallel is generated by the Fourier transform of the N bits and is then multiplied to the carrier frequency. At the reception, after demodulation of the carrier to recover the modulation signal, an inverse Fourier transform is applied to it in order to find the value carried by each of the N bits.

The methods described in the preceding paragraph all generate a double sideband signal. The generation of orthogonal functions also require for their synthesis a complex analog or digital operation (multiple leads and summations for orthogonal polynomials or Hermite functions, Fourier transformation for OFDM).

It also presents below a brief history of phase encoding. The transmission of digital data by binary coding phase

(Or its equivalent phase shift) is commonly used in modern digital communications. Different forms were used.

The simplest, called in English "Binary Phase Shift Keying" or "B-PSK" is to modulate the phase of a carrier in the amount of 0 or π. To transmit the k ^th bit duration T _b in the time interval {k - \) T _b <T≤ kT _bl phase takes the constant value b _k where ¾% = l for the bit b and _k = o for bit ^0%. To allow a higher rate of transmission of information, the principle was extended to quadrature modulation (in English "Quadrature Phase Shift Keying" or "Q-PSK") which for k even phase is b _k n in interval (k - \) T _b <T≤ kT _b and k odd, the phase is n / 2 + b _k in the shifted interval (k -1/4) 7 <T≤ (£ + 1/4 ) 2; .

Temporal discontinuities Phase introducing spectral density of slowly decaying tails on either side of the carrier frequency, softer modulations of phase have been introduced in order to have a more compact spectrum, thereby reducing interference between independent digital signals carried by adjacent carrier frequency, as described for example in US 2,977,417.

For example, frequency variation by coding methods, known in English as "frequency shift keying" or "FSK" are a linear interpolation of the phase variation over time (which amounts to perform a frequency offset where the term FSK). The stage then is continuous but its derivative is not.

The most advanced modulation in this direction is obtained by the gaussian minimum phase shift modulation method called English "Gaussian minimum-shift keying" or "GMSK" and is used for example in GSM telephony (see for example the article by HE VK Rowe and Prabhu, entitled "Power of a digital spectrum, frequency-modulated signal," in The Bell System Technical Journal, 54, No. 6, pages 1095-1125 (1975).

In this method, when transmitting a data bit, the derivative of the phase is a positive square signal (bit 1) or negative (bit 0) of duration T _b convolved with a Gaussian function to mitigate discontinuities. Modulating the carrier phase is then obtained by integration of its derivative and phase increment of the amplitude is adjusted to be + π / 2 for the bit 1 or -π / 2 for the bit 0. The GMSK method provides a very contained spectral range, typically with a reduced spectral power -20dB beyond the frequency / _c ± 1/27; . This is illustrated in Figure 4 where only the upper band of the bilateral spectrum is shown. All these processes give a spectrum double sideband.

Purpose and brief description of the invention

As seen above, there is no known modulation system has the property of directly generating a single sideband. By "directly" means a generation without post treatment as described above.

The present invention seeks to address this shortcoming and to enable the direct generation of a modulated single sideband signal. The invention therefore addresses the problems of the prior art with a phase modulation method of a carrier wave, characterized in that one creates a set of signals s _h (t) consist of a wave of frequency carrier f _c which φ phase (= Α φ ₀ (Υ) is modulated in time t such that s _ll (t) = cos (2NF _c t + h (p ₀ (t)), where h is a number integer and where φ ₀ 0) = 2 arctan ((t - t ₀₎ / w _0), the modulation corresponding to a single phase pulse centered in the time period characteristic _w0 positive and incrementing the phase of the s signal _h (t ) of the hin amount, such that it directly generates a frequency spectrum of single sideband.

The carrier may be of electromagnetic type, since the low frequencies to the optical frequencies, or audio-type.

The invention further relates to a method of conveying binary information by phase encoding single sideband modulation applying the method according to the invention, characterized in that for the binary coding of the phase, it is determined that the k ' ^th bit duration T _b contributes to the total phase cp (t) of the carrier by the amount 2 b _k ARCT ((t - kT _b) / w) where b _k = l or 0 and the width w is comparable or greater smaller than the symbol duration T _b or one considers that the derivative of the phase is a sum of Lorentzian 2WL {{t - kT _b) ² + ²⁾ centered in k and weighted by bit¾ then integrates the phase which is then Assistant to the next carrier a phase modulation method, the quantities cos <p (t) and sin <p (t) are the in-phase and quadrature modulation signal is calculated and combined with amplitudes in ∞s phase 2 f _c t and quadrature sin ln f _c t of the carrier to obtain the signal to be transmitted in the form: = Cos (27r _c t) cos9 (t) -sin (27i / _^"c t) sin9 (t).

The invention further relates to a method of generating orthogonal signals to single sideband modulation of applying the method according to the invention, characterized in that to generate a set of orthogonal functions u _h {t), h - 1,2,3 ... N over a finite duration T _b. for their use in data transmission with a rate 1 / T _b per information channel, first consider the case where T _b is infinite, which defines a single pulse and provides a basis of orthogonal functions of the

form in which the phase is

(T + iwf

<p ₀ (= 2 arctan (t / w) or considering the signals s _l (t) = e "" ^{fo (t)} = - then

(t -iw) is ensured by the separation of two signals orthogonality _h s (t) and _h s (t) by performing the following integration δ = ,, ,,, where

^ - = 2w / (t ² + w ²⁾ appears as a weight for integrating the signals _h s (t) is constant amplitude and spectrum of the signals _h s (t) is single sideband.

According to a particular aspect of this method, we generalize to orthogonal functions on an interval not infinite but finite Tb considering a periodic series of spaced phase pulses of length T _b to obtain the periodic signals of the form ih <f ₀ (l, T _b) sin (n (t + iw) IT _b)

_h s (t) = e where the derivative of the phase p is ₀ s {n {t - iw) IT _{b) /}

periodic sum of Lorentzian functions, this amount can be rewritten in the form of a periodic function of the form:

- ^ - = - .-- sh (2NW / T _{b) o} ^ ^ _{sj ευχ} g _nal by different integers dt T _b ² sin (nt / T _b) + sh ² (Tiw / T _b)

h and h 'satisfy an orthogonality relation on the time slot 7b acting as vehicles for the integration, so that in calculating then by carrying out an integration for dt

obtain the phase (p ₀ (t, T _b) before synthesizing the s signal _h {t) = e ^{il "f <i (GRT),} we obtain, with a simple multiplication of the phase by an integer, a set constant amplitude signals having the orthogonality character and obtaining a spectrum, discreet, which retains the single-sideband property.

The process according to the invention is thus a new phase modulation method which is distinguished in that it generates orthogonal signals with a spectrum having a single side band and the orthogonal functions used of order N> 1 are generated simply multiplying by an integer phase for generating the orthogonal function of order 1. While the OFDM has a bilateral spectrum of width N / T _s flanked spectrum slowly decaying tails (power law), the invention proposes multiplexing whose spectrum is without lower sideband and the upper strip has a primary width N / T _s with a tail spectrum exponentially decreasing rapidly.

It is of course also possible, by a reversal of the sign of the phase, to realize multiplexing whose spectrum is without upper sideband and the lower strip has a primary width N / T _s with a tail spectrum exponentially decreasing rapidly. The invention also concerns a transmission method in phase and out of phase binary signals encoded single sideband phase applying the modulation method according to the invention, characterized in what is independently modulates the in-phase component and quadrature component of the carrier in order to double the information rate, the signal being considered of the form being made up of the sum of two amplitudes and not being constant amplitude:

s (t) = cos (t + 9 2NC _{c j} (t)) + sin (2NF _c t + φ ₂ (t)) with the phase (t) = Σb _{k 0} (t - kT _b) ek ₂ ( t) = Σb _{k 2} q _Q (t - kT _b) o \ i is used kk

two independent bits of games to double the speed, the spectrum of each of the amplitudes out of phase and in phase being single sideband, the total signal itself having the single-sideband property.

The invention also relates to a mixed modulation method of a carrier signal in both amplitude and phase modulation by applying the method according to the invention, characterized in that for pulses where the phase is expressed as the form φ (ί) = ₀ Λφ (ί) (= 1,2,3,

...) producing a signal of the form

s (t) = cos (27i / _c t) - (-1) * cos (2 f _c t + h q> _in (t)) where the resulting spectrum is single sideband.

The invention also relates to a device for generating phase pulses single sideband, for the implementation of the method according to the invention, characterized in that it comprises a fast processor dedicated DSP or a fast processor reconfigurable FPGA, a digital / analog converter, the first and second determining modules respectively sin quantities <p (and _∞ 8φ _{(/ the first and} second mixers for multiplying said SINQ quantities> (and cos q> (/) the in-phase part and respectively the quadrature phase portion of the wave carrier frequency fc and an adder circuit for combining the signals delivered by said first and second mixers.

More specifically, the invention also relates to a phase pulse generating device single sideband, for the implementation of the method according to the invention, characterized in that it comprises generating analog device 2N periodic pulse sequences of _Qs (t) ldt period 2NT _b, each sequence being offset in time from the preceding Tb., the analog device using a basic stage <p _{0> i} (such as the overlap between pulses separate phases of 2NTb is negligible, in order to obtain a synthesis of d <(t) l dt and a multiple frequency harmonic generating device l / 2NT _b for synthesizing a periodic sequence of signals <ç _Qs ^q (t) ldt = Σdy _0s (t- (k + q) T _b) ldt, -N≤q <N, a demultiplexer k = -∞

configured to, in the time interval (kN + \ / 2) / 2T _b ≤t <(k + N - \ / 2) / T _bf demultiplexing the bits to index as b _{k + q} and using gate function width of 2NTb construct the derivative of the total phase:

Ap (i) / dt = £ b _{k + q} Π (ί - k + q) T _b) Λρ _0> (t- (k + q) T _b) / dt The invention also relates to a demodulation device a signal phase-encoded single sideband, characterized in that it comprises a local oscillator frequency f _cl of the first and second mixers and a phase shifter 0 ° - 90 ° allowing to obtain respectively the components in phase and in quadrature cos ((p () and sin ((p () of the modulation signal, a bypass module of each component in-phase and quadrature cos ((p (t)) and sin (cp () of the modulation signal and multiplying each of the derivatives obtained by the other in-phase components and quadrature cos ((p (t)) and sin (cp () of the modulation signal, to obtain the derivative of the phase άφ / ώ 9 = cos (u? (sin 9 () ^ -sin 9 (i) i (cos 9 () ^, and a recovery module of a series of Lorentzian pulses initially generated comprising a threshold detector with a value half the amplitude of a single Lorentzian pulse to ensure discrimination of the value of a bit b _k = 1 or 0 at a time t _k = kT _b.

The invention also relates to a signal demodulating device by a base orthogonal periodic signals comprising four amplitude levels including zero amplitude, characterized in that it comprises a local oscillator frequency f _below the first and second mixers and a phase shifter 0 ° - 90 ° allowing to obtain respectively in-phase components and quadrature cos (<p (t)) and sin (cp () of the modulation signal, a separate device for detecting four levels / 7 = 0, 1, 2 and 3 quaternary bits by forming for each of the four amplitude levels by a demodulation module associated with a Lorentzian generator period T _b, the two quantities _h R (t) = (cos ( q> (t) - h (p ₀ (t, T _b))) ^ dt and _h (t) = (sm ((p (t) - hp ₀ (t, T _b))) ^ -, a apparatus for determining the

dt

convolution with a function of gate width in time T _b giving t + T _m / 2 t + T _b / 2

R _h (t) = R _h (t -) d and I _h (t) = W _H (t - x) dt from Rh quantity (t) and _b tT / 2 t ~ T _b / 2

I _h (t), a device for calculating the quantity R _h {tf + I _h (t) ² and a threshold detection device configured to determine a peak observed in this amount R _h (t) ² + I _h (t) ² at a time t = kT _b for the level Q = 1, 2 or 3 indicates that the bit is _¾.

The invention also relates to a generation of single sideband phase pulses device in the optical domain, characterized in that it comprises a data providing module b _k = \ o 0, a Lorentzian generator, a module phase generation, a phase integration module, a laser generator carrier frequency and an electro-optical phase modulator configured to directly modulate the phase of the wave, so that, under the effect of a voltage proportional to the variation of the desired phase, a BLU phase modulated optical signal is generated in the modulator for transmission in an optical communication network.

Brief Description of Drawings

Other features and advantages of the invention will become apparent from the following description of particular embodiments, given as examples, with reference to the accompanying drawings, wherein:

1A to 1C show curves giving the spectral density of the single-sideband spectra signals corresponding to a single phase pulse whose carrier is phase-modulated for different values ​​of integer h defining the modulation index in accordance with one aspect of the invention; Figures 2A and 2B represent graphs showing the spectral density of the signal spectra whose carrier is phase-modulated for different values ​​of a non-integer defining the modulation;

The Figure 3A and 3B show curves showing the spectral density of the single-sideband spectra signals whose carrier is phase-modulated for different Gaussian values ​​by defining a modulation scheme having a BLU character close to 100%, according to one aspect of the invention;

Figure 4 shows curves giving the relative amplitude of the signal based on the frequency offset from a carrier defining a double sideband spectrum in accordance with the prior art;

Figures 5A and 5B show, as part of a digital encoding method using the single-sideband modulation phase in accordance with the invention, curves showing the one hand the phase derivative signal generated and the other from the integrated phase signal;

Figure 6 shows the diagram of an exemplary digital coding device using the phase modulated single sideband according to the invention;

Figure 7 shows a plot of the spectral density of a function of the signal frequency for signals encoded single sideband according to the invention, with a phase increment exactly equal to 2n;

Figures 8A and 8B show curves showing the spectral density of a function of the signal frequency for signals encoded single sideband according to the invention, with a phase increment respectively equal to 0.965 x 2n and 0.9123 x 2n;

Figure 9 shows a plot of the spectral density of a function of the frequency signal to coded signals which are no longer single-sideband, that with respect to the formula leading to the curve in Figure 7, the Lorentzian were replaced by Gaussian;

10 shows the diagram of an exemplary device for demodulating a phase-encoded signal to one sideband according to the invention;

Figure 11 shows a plot of the spectral density of a coded multilevel Phase signal is averaged according to an exemplary embodiment of the invention;

Figure 12 shows a plot of the spectral density of a signal encoded in multilevel phase which is obtained with a phase shift modulation according to the prior art, the spectrum is double band-like;

Figure 13 shows the diagram of an example of signal demodulation device with a base of orthogonal periodic signals according to the invention;

Figures 14A to 14E show curves representing a start signal and then four graphs representing the bit selective detection of signal levels 3, 2, 1 and 0 respectively, as part of a signal demodulating method by a base orthogonal periodic signals according to the invention;

Figures 15A to 15C show curves representing firstly a phase derivative signal used to generate a signal to be detected and on the other hand a value of bits of the detection signal value of 0 and 1 as part of a method for demodulating a binary coded signal in phase according to the invention;

Figures 16A and 16B show, for a transmission method in phase and out of phase binary signals phase encoded single sideband according to the invention, respectively the real and imaginary parts of the detected signal (or demodulated) for a series of bits according to a first exemplary embodiment, the modulation phase derived from the encoded signal being included in each graph;

Figure 17 shows a plot of the spectral density of the binary signals coded according to a single sideband phase according to the invention, as illustrated in the example of Figures 16A and 16B;

Figures 18A and 18B show, for a transmission method in phase and out of phase binary signals encoded single sideband phase according to the invention, respectively the real and imaginary parts of the detected signal (or demodulated) for a series of bits according to a second exemplary embodiment, the modulation phase derived from the encoded signal being included in each graph;

Figure 19 shows a plot of the spectral density of the binary signals coded according to a single sideband phase according to the invention, as illustrated in the example of Figures 18A and 18B;

Figures 20A-20C show curves giving a modulated amplitude-phase mixed modulation signal single sideband according to an exemplary embodiment of the invention, for values ​​of the modulation index h respectively equal to 1, 2 and 3 ; and

Figure 21 shows the diagram of an exemplary digital coding device using the phase modulated single sideband according to the invention in the context of an application to the optical domain;

Detailed description of specific embodiments

Disclosed is a wave modulation method. First, the process allows an original time incrementing the phase of a carrier wave of directly generating a signal whose frequency spectrum is single-sideband (SSB), ie a signal whose frequency content is within a range either higher or lower than the frequency of the carrier wave, but not both at once.

Second, maintaining the same temporal form of the phase increment but by multiplying it by an integer, the method according to the invention to generate an original basic orthogonal time signals between them and that retain the property of BLU .

On the other hand the resulting frequency spectrum is picked up with an exponential decay of the spectral power in the single sideband. The method may be applied to any type of waves, for example electromagnetic waves (lower frequencies to the optical domain) or many acoustic waves.

An immediate application concerns the physical coding of information by phase modulation for digital data transmission (eg, GSM, Bluetooth, WiFi, digital TV, satellite communications, RFID, etc ... for the microwave field or example the high speed transmission to the optical domain).

The invention proposes a special form of phase modulation of a carrier wave which alone is capable of generating a frequency spectrum of single sideband.

Consider the set of s _lt signal (t) consisting of a carrier wave of frequency f _c which φ phase ( is modulated in time ts _h (t) + H <p ₀ (t)) and where h is a positive or zero integer and where φ ₀ (t) = 2 arctan ((t - t ₀₎ / W _0). The modulation is a single phase pulse centered at time ¾ WQ characteristic term (> 0) and incrementing the phase of the signal s _h (t) of the amount hl%. To refer to the terminology used in the context of digital communications based on phase modulation, h is identified with the modulation index (or English "modulation index").

The spectral density P ,, (/) = | ¾ () |² signal, wherein s _h (f) is the Fourier transform of s _h (t) is shown in Figures 1A-1C for values equal to 1 respectively, 2 and 3.

It is seen that the spectrum is single side band: the spectrum does not have any component in the frequency band lower than £.

It should be noted that if we had chosen h <0 would have a spectrum mirror with respect to the carrier frequency and any components in the upper band.

The choice of ¾ and w ₀ can be arbitrary but will not change the single sideband property.

Explicitly, the spectral density is given by an exponential decay multiplied by Z. Laguerre polynomials _h (x) of degree -1.

If P _h) = [L _h W ^~ fc MF e * - ^* if _c f≥f

W) = 0 if f <f _c

Remarkably, the single sideband spectrum is maintained if the phase variation is generalized to the sum of φ increments (= Σ h, φ, (/) where h are positive integers and φ · (= 2 arctan ((t - _t;) / w ,..) with w> 0 and arbitrary £.

The condition of having the whole h _{all of the same sign can not be derogated to keep SSB property. The form φ (φ = Σ Α ,. ,. (ί) will be used and operated further in the examples of applications for the transport of binary information by phase encoding single sideband.

Below will give some important properties of the SSB phase modulation.

- For a single phase pulse, only the generic form

φ ₀ (ί) = arctan 2 ((t - t ₀₎ / w ₀₎ is capable of generating a single sideband, and & WQ being arbitrary. Any other form of temporal variation will lead to a double sideband spectrum. SSB property is maintained if the phase is a sum of the form of phase pulses similar to φ ₀ with an arbitrary width, generated at arbitrary times and multiplied by an arbitrary positive integer.

- A single sideband spectrum mirror, with respect to the carrier frequency, is obtained if the sign of the phase is reversed.

- The multiplicative factor h (more generally all h _t,

absolutely the same sign) must be full.

- Figures 2A and 2B show that the spectra obtained for

signals s _k (t) = ∞s (2 f _c t + (p ₀ (t)) where -X (replacing h) is non-stationary are not single sideband.

- The proliferation of φ ₀ by a positive integer to generate a base of orthogonal functions as will be explained later.

We will clarify below BLU criteria for modulations which while not constituting a perfect modulation, approaching the perfect modulation and thereby also within the scope of this invention. A modulation phase increment which is not a multiple of 2π, shows the second side strip even if the form of modulation is unchanged, i.e. a Lorentzian for phase derivative. This is what is clearly apparent in Figures 2A and 2B. To quantify the BLU character, the ratio of the sum of the spectral power can be defined for frequencies higher than the carrier divided by the sum of the total spectral power: _BLU c = ■

In Figures 2A and 2B, respectively for modulation with λ = 0.5 to 1.5 is found C LU _B = 56.9% and 61.7% respectively, that is to say very distant spectra those expected for a single sideband (C LU _B = 100%).

In some examples of application, the variation of the phase φ ₀ (/) = 2 arctan ((t - t ₀₎ / w ₀₎ may be considered too slow to reach the value 2n. Indeed: ₀ φ (ί) ^{χ π-nw} / t, t → ∞. It may be useful to define an approximate form of (p ₀ (t) wherein the slow part is truncated. This is what will be done in the example considered for application to a mixed amplitude-phase modulation single sideband .

Multiply the Lorentzian d (p ₀ (t) / dt by a Gaussian of width s. The derivative of the approximate phase denoted (p _{0 j} (t) is then d <s> _{Q s} (t) l dt = μεχρ (-ί ² / 2s ²⁾ 2w / (t ² + w ²⁾ where μ is a parameter multiplier which keeps a total phase increment equal to 2n. the spectral power (t) = ∞s (2n f _c t + _{s 0} (t)) is shown in figures 3A and 3B for a Lorentzian width of w = 0.37 and two Gaussian widths s = 2.7 and 1.85 (μ · = 1.112 and 1.165 respectively). As the derivative of the phase now differs from a Lorentzian, a lower sideband appears. However the s >> w values allow to maintain a BLU character close to 100% (v _B w = 95.9% and 95% respectively). will now be described an application example of the present invention for transferring a binary information by single sideband phase encoding.

It was mentioned above, in reference to Figure 4, known methods for phase encoding, which all give a spectrum double sideband. Below will be described in accordance with the present invention, the principle of digital coding using the phase modulated single side band:

As an application of the present invention, consider the following coding phase: the k ^th bit time 7 _^"b contributes to the total phase (p (t) of the carrier by the amount 2 b _k arctan ((f - A7) / w) where ¾ = l or 0 and comparable wes width or smaller than the symbol duration _7b.

In practice it is easier to consider the derivative of the phase. It is then a sum of Lorentzian 2WL {{t - kT _b) ² + w ²⁾ centered in k T _b and weighted by bit¾. Figure 5A shows the generated phase derivative signal. The phase is then integrated, as shown in Figure 5B, then Assistant to the carrier by a conventional method of phase modulation.

The quantities cos 9 (and 9 sin (are calculated and combined with amplitudes in ∞s2n stage f _c t and quadrature s 2NC _c t of the carrier to obtain the signal to be transmitted: s (t) (p ()) = cos (27i / _^"c t) cos9 (t) -sin (27r _c t) sinc (t). A block diagram of a device for performing such a digital coding is provided on the Figure 6.

In Figure 6, there is shown a data providing modulelOl b _k = \ or 0, a 102 Lorentzian generator, a module 103 for phase generation, a module 104 for phase integration, modules 105 and 106 generating respectively cos p quantity (t) and sin φ (a generator 107 of carrier frequency, a module 108 phase shift, the mixer circuits 109, 110 and an adder circuit 111 so as to combine the quantities cos φ (and sin φ ( the amplitudes in phase ∞s 2n f _c t and quadrature sin 2NC _c t of the carrier to obtain the signal to be transmitted: s (t) <P (t)) = cos (2NF _c t) ∞s (p (t) -s (2 f _c t) sm q> (t). An output amplifier 112 is connected to a transmit antenna 113 .

Consider now the spectrum coded signals in phase single sideband. The spectral power of the signal is shown in Figure 7 for a pulse width such that w / T _b = 0.37. The frequencies are in increments of

1 / T _b. The carrier has a frequency equal to 10/7; . The choice of another carrier frequency will give a spectrum similar BLU around thereof.

The spectrum clearly shows the single sideband property. To the left of the carrier frequency, the spectrum decreases extremely rapidly, its finite being only due to the finite size effects. To the right of the carrier frequency, the spectral power decreases abruptly 20dB at the frequency /, - + 1/7, then 20dB still at the frequency f _c + 2 / T _b and so on. Compaction of the decay at higher frequencies is put on the account of the calculation comprises a number of finished samples (average of 32 spectra corresponding to independent draws a random series of 259 bit length 7 ^_"b).

If we opted for a smaller width _b WLT components

Fourier will extend higher frequency. Indeed the power decreases exponentially _e - ^IT ™ ^"for a frequency increase del / T _b, ie 1/100 (-20dB) for w / T _b = Q 37.

Is also observed on the spectrum of purposes peaks, called spectral lines centered at frequencies f _c + f _ct IT _bl f _c + 2 / T _bf etc. They are due to the choice of a phase increment exactly equal to 2 π. This effect has been noted for the conventional methods of phase modulations which est27t increments as indicated in Section HE Rowe and VK Prabhu, entitled "Power spectrum ofa digital, frequency-modulated signal," in The Bell System Technical Journal, 54, No. 6, pages 1095-1125 (1975).

In this process, it is important not to deviate from this value as this would lead to the reappearance of a lower sideband of the spectrum.

However, in practice, the lower sideband spectrum is negligible if the increment is a few% or less than 2 π while the peak ends of the spectrum are reduced or even eliminated. This is shown in Figure 8A for a spectrum whose phase increment is 0,965x2

. Lower peaks purposes is accompanied by a noisy portion of the curve for frequencies between 9.5 and 10 evidencing the occurrence of a low but non-zero contribution in the lower sideband. To a phase increment 0,9123x2 π phenomenon is somewhat larger (see Figure 8B). To a phase increment less than 0.9 (2π) or greater than 1.1 (2π), it is assumed that the SSB is lost. Finally Figure 9 shows the spectrum obtained if we replace in dy / dt \ es Lorentzian by Gaussian (keeping the same phase increment and a pulse width comparable). The spectrum difference is striking. The presence of a lower sideband is very marked.

will now be described with reference to Figure 10, an exemplary method and apparatus of demodulation signal phase-encoded single-sideband in accordance with the invention.

At the reception by an antenna 201 and an amplifier 202, the first demodulating step for extracting the carrier signal is conventional. A local oscillator 203 of frequency f _c associated to mixers

204, 205, 206 to a phase shifter of 0 ° - 90 ° provides the in-phase and quadrature∞s (<p () and sin (q> () of the modulation signal Differentiating thereof and. multiplying them by their partner in a calculation module 207 we find the derivative of the phase

<Fp / dt = cos φ (ί) d (sin φ (ί)) / dt- sin (t) d (cos φ () / dt.

This allows to reconstruct the Lorentzian pulse series initially generated as those in Figure 5A. By placing a threshold detector 208 to an amplitude of half the value of a single Lorentzian the value of a bit or ¾ i = 0 at time t _k = kT _b is easily discriminated. A clock 209 provides the threshold detector 208 pulses at a rate of 1 / T _b.

In practice, the detected signal is added the detection noise. Deriving a signal, here sincp- and cos φ, has the effect of increasing the effect of noise. Another means of demodulation that does not appeal to a branch can be used, as will be described below, in reference to the orthogonality property of phase pulses SSB. Will now be described a method of generating orthogonal signals to single sideband.

This is to generate a set of orthogonal functions _h u (t), h = 1,2,3, ..., N on the finite duration T _b. for their operation, for example in data transmission with the flow rate 1 / T _b by information channel.

To construct these orthogonal functions, it is useful to first consider the case where _Tb is infinite (single pulse).

orthogonal is: where we used phase

φ ₀ (= 2 arctan (t / w) defined above.

By choice of simplicity, the functions are centered at f = 0. One can check that ut) u At) dt = δ, ,,,.

In practice it may be more interesting to consider the signals _h s (t) = e "" ^{9o (t)} = - then ensure the separation of two orthogonal

{T-iw) '

s signals _h (t) and _h s (t) by performing the integration:

-f ^∞ s (t) s 2w / (t ² + w ²⁾ appears as a

weight (or measure) for integration.

With this definition, the s signals _h (t) are constant amplitude (unit module) which may be of practical benefit for their generation (power constant emission). The spectrum of s _h (t) is single sideband.

The generalization of orthogonal functions on a not infinite but finite interval T _b is obtained by considering the periodic series of spaced phase pulses of length T _b. This gives the periodic signals, sin α f (n (t + iw) / T _h X],., ■>,.

_h s (t) = e ^{Ψο (Ά)} = - -. The derivative of the phase φ ₀ ·. is a

^ Sin (n (t - iw) IT _b) j

periodic sum of Lorentzian.

This amount can be rewritten in the form of a periodic function: dcp ₀ π sh {l wl% T _b)

dt T _b ² sin (nt / T _b) + sh ² (nw / T _b)

Two different signals by integers and 'satisfy an orthogonality relation of the time interval 7 _£>: - ^{[HV / 2} s _i ^* (t) s _ll (t) ^ - dt = 8 _hi where

2TC ^D - ^{7 "/} 2 dt again plays the role of weight for integration.

dt

In practice is calculated (or generated) and then integrated to give y> ₀ (t, T _b) dt

then 5 _/, (= e ^{'7, l |> o (': rf ')} is synthesized is seen that a simple multiplication of the phase by an integer makes it possible to obtain a set of signals having a constant amplitude. the orthogonal character. on the other hand the spectrum, now discreet, retains the single sideband property.

We now give an example of application to the detection of multi-level digital signals phase encoded. We first consider the choice of multi-level phase encoding.

It is to encode 2 bits of four levels such as 2B1Q amplitude modulation method ( "2Binary-lQuaternary") but here transposed into phase modulation.

Of course we can generalize to N levels (N-ary bit) with h = o, l, ..., N s and N = 2 ^P The rate in bits per second is no longer LFT _b as above but becomes p / Tb. We could choose a coding <p phase (t) = _k Σb <p ₀ (t-kT _b, T _b) where the

k

bit bk vaut¾ = 0,1,2,3 (respectively 00, 01, 10 and 11) and is defined in the interval (k-H2) T _b ≤t <(k + \ l2) T _b.

So could fully exploit the orthogonal ity of s _bt signals (t-kT _b) = e ^ ^ibk '- ^{KTL "Tb)} on each interval [k / 2, k + l / 2] t _b to find the value quaternary bit b _k demodulation. This is one possible implementation of the present invention.

However, for two consecutive bit bk and bk + i of different values, there is a discontinuity of the derivative of the phase equal to (b _{+ l k} -b _k) d (p ₀ (T _b / 2, T _b) / dt. the discontinuities tails will generate spectra descending slowly. in the application example chosen here, we made the choice to privilege the compactness of the spectrum at the expense of poorer operation of the orthogonality property. for this the phase is coded as described above with q> (t) = Σb _k <p ₀ (t-kT _b) where

k

φ ₀ (ί) = φ ₀ (ί, Γ ₆ = ∞) = 2arctan (t / w) and b _k = 0,1,2,3.

The derivative of the phase is thus a sum of Lorentzian whose amplitude random value takes four levels. This encoding ensures the absence of discontinuity of the phase. However, the signals β * ^{Φ "(,)} ηβ not check on orthogonality relations with the functions e '^' ^ to be used to recover by demodulation bk, but they only check the approximate orthogonality relations. Demodulation remains effective in practice.

The block diagram for the transmission of data is similar to Figure 5A and 5B, but where the binary bits 0, 1 are replaced by quaternary bits b _k = 0,1,2,3. We will now describe the spectrum of the encoded multi-level-phase signal.

Proposed as an example of application, we consider the spectrum of a signal composed of a series of quaternary 33 bits ( "Quaternary") of duration T _b. The signal generated is: or

16

φ (= Σb _{k Q} (t - kT _b) quaternary bits b _k = 0, 1, 2, or 3 (corresponding to i = -16.

binary bits 00, 01, 10, 11) are selected using a pseudorandom number generator for representing a data sequence. The flow rate is 2 / T _b bits per second. The carrier frequency is selected as 10 / T _b and width w = 0.3T _b.

11 shows the frequency spectrum averaged corresponding to 32 sequences of different quaternary bits.

The character single sideband spectrum is checked. The spectrum does not contain a significant component for frequencies lower than the average carrier frequency (/) = f _c + {b _k) lT _b = \ \ .5IT _b.

For higher frequencies (f) + 2 / T _br spectrum rapidly decreases exponentially, lOdB approximately every 1 / T _b (20db for increased frequency equal to the bit rate 2 / T _b). W A larger width would provide an exponential decay even faster. For comparison the following graph, illustrated in Figure 12, is the result of a type of frequency-shift keying (or English type Frequency Shift Keying (FSK)), where the frequency is modulated on four levels (c. A.D. d <p (t) / dt = _k 2nΣb (l / T _b)).

It is seen that, for this embodiment not forming part of the present invention, around the average carrier frequency ^{1-5 / 7} _t / ^spectrum is double band-like. Its main width 2 / T _b but the spectrum is flanked spectrum slowly decaying tails and not exponentially.

We will now describe a method and a device for demodulating signals by a base orthogonal periodic signals.

On reception, the first demodulating step for extracting the carrier signal is conventional and similar to the example given above with reference to Figure 10. The signal received by an antenna 301 is amplified in an amplifier 302. An oscillator local 303 of frequency f _c associated with mixers 304, 305 and a phase shifter 306 0 ° - 90 ° provides the in-phase and quadrature cos (cp () and sin (cp (t)) of the signal modulation. in a first embodiment, one could follow the same pattern as in Figure 10 and obtain the derivative of the phase of the modulated signal. However, a detection of the four amplitude levels (including zero amplitude) appears difficult because of the overlap between the Lorentzian different amplitude issued neighboring moments.

Also, a preferred solution is to use the basis of signals

sin (7i (t + iw) / T _b)

periodic orthogonal s _h (t) = e

sin ((t - iw) IT _b)

In practice, it sends the separate detection of the four levels h = 0, 1, 2 and 3 quaternary bits. This is achieved by forming by a suitable demodulating means referenced 307 in Figure 13, the four quantities

R _h (t) = {∞s ((t) - h ₀ (t, T _b))) ^ and / _Λ (φ = (- Αφ Μ ₀₎₎₎ ^ then at at performing a module 308 in the convolution with a function door

_b t + T / 2 t + T _b / 2

width time T _b giving R _h (t) = j ,, (t - x)? dx and _h (t) = jl _h (t - x) dt.

tT _h / 2 I-T 2 Next, in a module 309, one computes the amount R _h (tf + I _h {t) ^2.

A peak observed in this amount (which is a bit-level detection signal h or English a "bit level h detection signal") at a time t = kT _b to level = 0, 1, 2 or 3 points that the bit h is h. This provides four threshold detectors 310-313 for levels h = 0, 1, 2 and 3 respectively.

A clock 314 makes it possible to deliver pulses at a rate of

1 / T _b.

Figure 13 shows yet generator Tb period periodic Lorentzian function and a module 316 for providing the module 307 the values sin (hcpo (t, T _b)) and cos (h (po (t, T _b) ).

Figures 14A-14E show, from bottom to top, the start signal

16

d / dt = _k d Σb <p ₀ (t - kT _b) / dt (Figure 14A) and four graphs representing

£ = -16

the bits of the selective detection of signal level h = 3, 2, 1 and 0 (Figures 14B-14E).

The information to be considered for a multi-level bit i is given by the value of the detection signals taken at exactly t = kT _b. For example, for k = -8, the level of the detected signal for h = 3 (Figure 14B) takes a large value and shows a peak, while for the graphs corresponding to h = 0, 1 and 2 (Figures 14E, 14D and 14C), the signal level is low, the bit bk = -s is therefore 3 (or 11). For h = l and 2 levels (14D Figures and 14C), also sometimes found significant values for t / T integer _b which do not correspond to peaks but hollow and are not intended to identify the value of _¾ ■ for example, for k = -2, t = 0 is identified by a peak in the detection signal with h = 0 (Figure 14E), while the value of the detection signal with h = l (Figure 14D) provides a but non-zero value associated with a trough. Despite the large recovery Lorentzian, it is seen that the method of projecting the signal on the basis of periodic signals allows sorting of bits according to their level and is very effective.

again Consider demodulating the binary coded signal in phase as given above by way of example.

As mentioned above, the recovery of the derivative phase may not be effective for the case of noisy signals detected. The method of demodulation using the orthogonality property, as explained above for quaternary bits, is preferable and applies equally and efficiently even for a binary signal.

As before, detection is to calculate cos (PC (Y) - λφ ₀ (t, T _b)) dq> ₀ 1 dt J + (J ^ _{/ 2} sin (<p (i) - Λφ ₀ (t, T _b)) άφ ₀ 1 dt) OR

16

Now h = l or 0 and <p (t) = _k Σb <p ₀ (t - kT _b).

k = - \ 6

Again, q> ₀ (t) does not check an orthogonality relation with φ ₀ 0.7) but the recovery is sufficient for effective demodulation.

15A to 15C show, for the last 38 bits of the 259 bits of sequence shown in Figure 4, the detection signal of the bit value 0 (Figure 15A) and value 1 (Figure 15B). Figure 15C recalls the signal derived by phase having served to generate the signal to be detected. The present invention lends itself to various applications and in particular to the emission phase and out-phase binary signals encoded single sideband phase:

In this application, it is proposed to exploit the possibility of independently modulating the in-phase component and the quadrature component of the carrier in order to double the information rate (i.e., having a bit rate or " bit rate "equal to twice the symbol rate or" symbol rate ").

In the previous examples, the signals were to power (or amplitude) with constant y ₀ (t-kT _b).

In this case, the signal being the sum of two amplitudes will not be constant amplitude:

+ _Φ ι (t)) + sin (2NF _c t + φ ₂ (t))

Here (? _S (t) = ₀ Σb _kl (t-kT _b) ek (p ₂ (t) = _k2 Σb <? ₀ (t-kT _b) where we used two kk

independent bits games -¾, i ₍₂₎ for the double speed.

The spectrum of each of the amplitudes out of phase and in phase being SSB, the total signal still has the BLU property (see Figures 17 and 19).

Is discussed in the following procedure to retrieve information about the transmitted bits during demodulation.

We restrict ourselves to simplify the case of binary bits. For proper demodulation, it is shown that the phase relative changes in φ (ί) and φ ₂ (must remain small. These variations originate from the interference (overlap) between the adjacent phase pulses (also referred to as "Inter-Symbol interference "or" ISI "), a constraint that was non relevant in the example of figures 3A and 3B.

A demodulation of the carrier, there is obtained the part in phase and out of phase, respectively:

Re (= cos ((p (i)) -sin (cp ₂ ())

Im (/) = sin (9 _{1 (Listing} i)) + cos ((p ₂ (i)) In the case where w << T _b (no ISI), for t = kT _b was Re (kT _b ) = cos (b _tl n) -sin (b _k2 n) n \ t 1 or -1 for b _kl = 0 or 1 respectively and independently of the value of b _k2.

Similarly, we have: im (kT _b) = s (b _kl n) + cos (b _k2) is 1 or -1 b _{k 2} = 0 or 1, respectively, regardless of the value of b _k,.

R _e gives the information on the first set of bits and I _m that the second set of bits. In the case where W / T _b is larger an additional step 9 _j = Σ _k h ₀ ((kk) T _b) is added to the expected phase k '≠ k

. T _{b (p]} (kT _b) = b _k + Q n ₁ Similarly, a stage Θ2 affects -q> 2 was then:

Re (kT _b) = cos _(kl b n + G _j) - sin (9 ₂₎

lm (kT _b) = sin (Q _l) + cos _{(è. 2} π + θ ₂₎

It is imperative to have | θ ₁ | "π / 4εί | e ₂ |" / 4to find no errors each bit emitted at time kT _b. (Ie so that Re and Im are always significantly positive value (bit 0) or negative (bit 1) but not close to zero).

If a temporal filtering of d (p / dt is limited to the ISI bits transmitted between the time (k ± N) T _b or will fi ^^ * (y + hi (N)) w / T _b "π / 4, where

7 = 0.577 ... is Euler's constant. This gives virtually N << 4.7 w / T _b = 0.37, N << 6.5 w / T _b = 0.32 and N << 39 w / T _b = 0.185. In all cases a temporal filtering limiting the interference between adjacent phase pulses is required.

Examples are given below.

One way to reduce ISI is to use for the derivative of the phase a Lorentzian-Gaussian as discussed above with reference to Figures 3A and 3B, with the elementary phase pulse obtained by integrating d _{0 s} (t) / dt = μ εχρ (-ί ² / 2s ²⁾ 2w I (t ² + ¾> ²⁾ where the parameter μ is a coefficient to maintain a total phase increment equal to 2n.

Figures 16A and 16B show in arbitrary units the signals Re (Figure 16A) and Im (Figure 16B) for a series of bits with w / _b = 0.32 and T s / T _b = 3.2 (- μ = 1 , 0811) as well as _l (t) l dt = b _u d _1ij k l dt çk

The frequency spectrum corresponding to a carrier frequency f _c = 13 (units 1 / Tb) is shown in Figure 17.

The BLU character is well preserved except for a small spectrum component in the lower band as the derivative of elementary phase is no longer strictly a Lorentzian. It is seen that more than 90% of the spectrum is concentrated in a frequency band 1 / Tb is half the bit rate ( "bit rate").

The following example shows that one can reach 98% of the spectrum in a frequency band equal to half the bit rate (bit rate) with the parameters: w / T _b = 0.37 and s / T _b = 2, 7 (· μ = 1.112). Figures 18A and 18B show the signals Re (Figure 18A) and Im (Figure 18B) and Figure 19 shows the spectrum.

These two examples show that spectral efficiency (bit rate relative to the spectral width) very high ~ 2 bit / s / Hz can be achieved with a spectrum BLU very compact.

We will now describe an application in a mixed-phase amplitude-modulated single side band:

Direct application of the present invention to modulate the carrier signal in both amplitude and phase.

In the above, we have only seen a modulation of the PC phase (t). The principle is to manage a pulse signal, ie a starting signal then returning to zero. For a single pulse centered and width w ₀ and the elementary pulse of φ phase (Υ) = φ ₀ (= 2 arctan ((t - t ₀₎ / w _0):

The signal may also be written in the form of a modulation of amplitude cos (q> ₀ (/ 2) and phase <p ₀ (f) / 2: s (t) = 2cos (ip ₀ (t) / 2) cos (2 f _c t + ^) _Q (t) / 2).

therefore can be generalized for pulses where φ (ί) = λφ "(ί)

(Λ = 1,2,3, ...) with:

s (t) = cos (2 f _c t) - (-l) ^h cos (2NF _c t + _h (t))

Figures 20A to 20C show the signal s (t) respectively for h = l, 2 and 3 and a W / T _b = width modulation with a carrier fc 0.37 = 13. The timing signals are mutually orthogonal.

The resulting spectrum is given by the sum of the spectrum SSB (∞s term (27c _c i + q> (f))) and localized to the frequency spectrum f _c (term cos (2n / _c t)), c ' is therefore a spectrum Single Side Band. It is identical to that given in Figures 1A-1C, for h = l, 2 and 3 respectively, except a frequency reinforcing £ ■

below we will give some practical examples of phase pulse generating single sideband:

It can perform any digital summary of the carrier and its modulation: for phase pulses generated until the rate of several million pulses per second, and carrier GHz up to the state of the art , numerical methods using fast processors dedicated (in "digital Signal processor" or "DSP"), or reconfigurable processors faster (in English "Field Programmable Gate array" or "FPGA") are available. For lower rates, currently below the one million pulses per second, but may increase with changes in technology, economic solutions based on software Yadio card (in English "software radio") may be used. After digital / analog conversion quantities sin φ (ί) and cos φ (are generated and sent separately to the mixer as in the embodiment of Figure 6 for multiplying the in-phase part and the quadrature portion of the carrier.

Alternatively, again by digital synthesis, the φ phase (Υ) is calculated followed by a digital / analog conversion and then sent to an oscillator or a phase shifter controlled by voltage.

One can also carry out an analog synthesis. In this case, using an elementary Phase φ _{0 ί} (such as the overlap between the separated phases of pulses 2NT _b is negligible, the synthesis of dy (t) / dt is obtained from the generating 2N periodic sequences pulse of _{Q s} {t) ldt period 2NT _b, each sequence being offset in time from the preceding T _b. The periodic sequence dy _{0 s} ^g (t) / dt = Σdq> _{0 s} (t - (k + q) T _b) / dt - N≤q <N, is easy to synthesize by generating multiple frequency harmonics l / 2NT _b with the amplitude and the correct phase.

In the time interval (k - N + \ / 2) / 2T _b <t <k + {N - \ lt) IT _b or \ demultiplexes the bits to index as b _{k + q} and by using the gate - / \ ή 2NT width _b can be constructed the derivative of the total phase:

</ <P (/ dt = Σ b _{k g +} U (t - (k + q) T _b) άψ ^ (t - (k + q) T _b) / dt This procedure to generate periodic pulses by synthesis multiple frequency harmonics of l / 2NT _b can be easily achieved in the frequency range up to tens of GHz by cascading frequency multipliers or using frequency comb generators for generating the basic harmonic

In the optical domain, it is possible to directly modulate the phase of the wave with electro-optical modulators, the voltage applied to the modulator is proportional to the phase variation as shown in the embodiment of Figure 21. in Figure 21, there is shown a supply 401 of module data b _k = 1 or 0, a generator 402 Lorentzian, a module 403 for phase generation, a module 404 phase integration, a laser generator 406 frequency carrier and an electro-optical phase modulator 405 that directly modulate the phase of the wave, so that, under the effect of a voltage representing the desired change in phase signal to an optical phase modulation BLU is generated in the modulator 405 to be transmitted in the optical communication network.

Various modifications and additions can be made to the embodiments described without departing from the realization framework defined by the appended claims.

In particular, various embodiments can combine them if otherwise not in the description.