Method for generating a pulse-position-modulated signal, demodulation method and corresponding computer program product and devices

A method comprising the following steps executed by a demodulating device:

• receiving a modulated signal from a transmission channel with a radiofrequency (RF) receiver, the modulated signal resulting from a pulse-position modulation of a signal and from a transmission of the modulated signal in the transmission channel,
• said modulated signal comprising a temporal succession of waveforms among Ns waveforms,
• a k-th waveform among said Ns waveforms being associated with a k rank symbol of a constellation of Ns symbols, k being an integer from 0 to Ns−1,
• said k-th waveform resulting from a circular permutation of the pattern of variation of a basic waveform over a duration Ts, obtained by a time shift of k times an elementary time duration Tc, such that Ns*Tc=Ts;
• and
• for M samples representing a waveform included in said modulated signal:
• applying forward or inverse Fourier transformation to said M samples of said received signal and delivering N transformed samples Y, l being an integer varying in a set Sη sized N;
• obtaining of a set of N modulation coefficients cl(k), l being an integer varying in the set Sη,
• a modulation coefficient of index n among said N modulation coefficients, denoted as cn(k), being expressed as the product of a reference modulation coefficient of index n, denoted as cn(r), multiplied by a phase-shift term the argument of which is proportional to n,
• said reference modulation coefficient cn(r) coming from the Fourier series decomposition of a reference waveform among the Ns waveforms associated with a symbol of rank r,
• said set of N modulation coefficients or said reference modulation coefficients being stored in a storage device, thereby reducing at least one of a number of calculations performed by the demodulating device or consumption of storage space of the storage device;
• determining Ns decision components from said N transformed samples and N modulation coefficients obtained,
• a decision component of index l, denoted as a component Dl, being expressed as a function of a forward or inverse Fourier transform of N terms with l being an integer from 0 to Ns−1,
• a term of index n among said N terms, n an integer varying in the set Sη being a function of a product of a transformed sample Yn multiplied by said obtained reference modulation coefficient cn(r) or by the conjugate complex of said obtained reference modulation coefficient;
• deciding on the rank {circumflex over (k)} of the symbol carried by the waveform associated with said M samples, on the basis of the decision component having an extremum value among said Ns decision components, of index k, denoted as Dk;
• and
• outputting the symbol with the decided rank {circumflex over (k)}.

A non-transitory computer-readable medium comprising a computer program product stored thereon comprising program code instructions for implementing a method of generating a pulse-position-modulated signal, when said program is executed on a processor of a modulating device,

• said modulated signal comprising a temporal succession of waveforms among Ns waveforms,
• an s-th waveform among said Ns waveforms being associated with a k rank symbol of a constellation of Ns symbols, k being an integer from 0 to Ns−1,
• said s-th waveform resulting from a circular permutation of the pattern of variation of a basic waveform over a duration Ts, obtained by a time shift of k times an elementary time duration Tc such that Ns*Tc=Ts,
• wherein the method comprises the following steps, executed by the modulation device:
• for a k rank symbol of the constellation of Ns symbols:
• obtaining a set of N modulation coefficients cl(k), l being an integer varying in a set Sη sized N,
• a modulation coefficient of index n among said N modulation coefficients, denoted as cn(k), being expressed as the product of a reference modulation coefficient of index n, denoted as cn(r), multiplied by a phase-shift term of which the argument is proportional to n,
• said modulation coefficient referenced cn(r) coming from the Fourier series decomposition of a reference waveform among said Ns waveforms, associated with a symbol of rank r,
• generating M temporal samples of a k-th waveform by forward or inverse Fourier transform of said set of N modulation coefficients cl(k);
• and
• using said generated M temporal samples to modulate a radiofrequency carrier, and
• sending a resulting radiofrequency modulated signal to a radiofrequency transmitter (RF) for transmission in a transmission channel.

A device for generating a pulse-position modulated signal,

• said modulated signal comprising a temporal succession of waveforms among Ns waveforms,
• a k-th waveform among said Ns waveforms being associated with a k rank symbol of a constellation of Ns symbols, k being an integer from 0 to Ns−1,
• said k-th waveform resulting from a circular permutation of the pattern of variation of a basic waveform over a duration Ts, obtained by a time shift of k times an elementary time duration Tc such that Ns*Tc=Ts,
• wherein the device comprises a reprogrammable computing machine or a dedicated computing machine configured to:
• obtain a set of N modulation coefficients cl(k), l being an integer varying in a set Sη,
• a modulation coefficient of index n among the N modulation coefficients, denoted as cn(k) being expressed as the product of a reference modulation coefficient of index n, denoted as cn(r), multiplied by a phase-shift term, the argument of which is proportional to n,
• said reference modulation coefficient cn(r) coming from the Fourier series decomposition of a reference waveform among the Ns waveforms associated with a symbol of rank r;
• generate M time samples of a k-th waveform by forward or inverse Fourier transformation of said set of N modulation coefficients cl(k);
• use said generated M time samples to modulate a radiofrequency carrier;
• and
• send the resulting radiofrequency modulated signal to a radiofrequency (RF) transmitter for transmission in a transmission channel.

An apparatus comprising:

• a radiofrequency (RF) receiver;
• and
• a reprogrammable computing machine or a dedicated computing machine, configured to:
• receive a modulated signal from a transmission channel with the radiofrequency (RF) receiver, the received modulated signal resulting from a pulse-position modulation of a signal, transmission of the modulated signal in the transmission channel, and reception of the transmitted modulated signal by the RF receiver,
• said modulated signal comprising a temporal succession of waveforms among Ns waveforms,
• a k-th waveform among said Ns waveforms being associated with a k rank symbol of a constellation of Ns symbols, k being an integer from 0 to Ns−1,
• said k-th waveform resulting from a circular permutation of the pattern of variation of a basic waveform over a duration Ts, obtained by a time shift of s times an elementary time duration Tc such that Ns*Tc=Ts,
• demodulate the modulated signal by:
• applying a forward or inverse Fourier transformation to the M samples of the received signal and delivering N transformed samples Yl, l being an integer varying in a set Sη sized N;
• obtaining a set of N modulation coefficients cl(k), l being an integer varying in the set Sη,
• a modulation coefficient of index n among the N modulation coefficients denoted as cn(k), being expressed as the product of a reference modulation coefficient of index n, denoted as cn(r), multiplied by a phase-shift term the argument of which is proportional to n,
• said reference modulation coefficient cn(r) coming from the Fourier series decomposition of a reference waveform, among the Ns waveforms, associated with a symbol of rank r,
• said set of N modulation coefficients or said reference modulation coefficients being stored in a storage device, thereby reducing at least one of a number of calculations performed by the apparatus or consumption of storage space of the storage device;
• determining Ns decision components from the N transformed samples,
• a decision component of index l, denoted as the component Dl, being expressed as a function of a forward or inverse Fourier transform of N terms, with l being an integer from 0 to Ns−1,
• a term of index n among said N terms, n being an integer varying in the set Sη, being a function of a product of a transformed sample Yn multiplied by an obtained reference modulation coefficient cn(r) or multiplied by the complex conjugate of said obtained reference modulation coefficient;
• deciding the rank {tilde over (k)} of the symbol carried by the waveform associated with said M samples, from the decision component presenting an extremum value among the Ns decision components, of index k, denoted as the component Dk;
• and
• outputting the symbol with the decided rank {tilde over (k)}.

A non-transitory computer-readable medium comprising a computer program product stored thereon comprising program code instructions for implementing a method of demodulating a received modulated signal, when said program is executed on a processor of a demodulating device, wherein the instructions configure the demodulating device to:

• receive a modulated signal from a transmission channel with a radiofrequency (RF) receiver, said received modulated signal resulting from a pulse-position modulation of a signal, transmission of the modulated signal in the transmission channel and reception of the transmitted modulated signal by the RF receiver,
• said modulated signal comprising a temporal succession of waveforms among Ns waveforms,
• a k-th waveform among said Ns waveforms being associated with a k rank symbol of a constellation of Ns symbols, k being an integer from 0 to Ns−1,
• said k-th waveform resulting from a circular permutation of the pattern of variation of a basic waveform over a duration Ts, obtained by a time shift of k times an elementary time duration Tc, such that Ns*Tc=Ts,
• perform the following steps for M samples representing a waveform included in said modulated signal:
• applying forward or inverse Fourier transformation to said M samples of said received signal and delivering N transformed samples Yl, l being an integer varying in a set Sη sized N;
• obtaining of a set of N modulation coefficients cl(k), l being an integer varying in the set Sη,
• a modulation coefficient of index n among said N modulation coefficients, denoted as cn(k), being expressed as the product of a reference modulation coefficient of index n, denoted as cn(k), multiplied by a phase-shift term the argument of which is proportional to n,
• said reference modulation coefficient cn(r) coming from the Fourier series decomposition of a reference waveform among the Ns waveforms associated with a symbol of rank r,
• said set of N modulation coefficients or said reference modulation coefficients being stored in a storage device, thereby reducing at least one of a number of calculations performed by the demodulating device or consumption of storage space of the storage device;
• determining Ns decision components from said N transformed samples and N modulation coefficients obtained,
• a decision component of index l, denoted as a component Dl, being expressed as a function of a forward or inverse Fourier transform of N terms with l being an integer from 0 to Ns−1,
• a term of index n among said N terms, n an integer varying in the set Sη being a function of a product of a transformed sample Yn multiplied by said obtained reference modulation coefficient cn(r) or by the conjugate complex of said obtained reference modulation coefficient;
• deciding on the rank {circumflex over (k)} of the symbol carried by the waveform associated with said M samples, on the basis of the decision component having an extremum value among said Ns decision components, of index k, denoted as Dk;
• and
• outputting the symbol with the decided rank {circumflex over (k)}.