Construction of a multicarrier signal

Method for the transmission, of a digital signal especially in a non-stationary transmission channel, characterized in that it comprises the following steps:

• channel encoding a digital signal to be transmitted, delivering real digital coefficients am,n chosen out of a predetermined alphabet;
• constructing a signal a(t) complying with the following equation:
• s(t)=Σam,nxm,n(t)
• where:
• m is an integer representing frequency dimension;
• n is an integer representing temporal dimension;
• t represents time;
• xm,n(t) is a basic flnction translated into the time-frequency space of one and the same even-order prototype function x(t) taking real or complex values, namely:
• xm,n(t)=±im+nei(2πτsv0+φ)x(t−nτ0) with ν0τ0=½
• where φ is an arbitrary phase parameter,
• the Fourier transform X(f) of the function x(t) having a support extending beyond the interval (−v0,v0),
• said basic functions {xm,n} being mutually orthogonal, the real part of the scalar product of two different basic functions being zero;
• and
• transmitting a signal, having said signal s(t) as its complex envelope, to at least one receiver.

Method for the reception of a signal corresponding to the frequency multiplexing of several elementary carriers extending in temporal and frequency domains, each carrier corresponding to a series of symbols, two consecutive symbols being separated by a symbol time τ0, the spacing ν0 between two neighboring carriers being equal to half of the reverse of the smbol time τ0,

• and each carrier having a spectrum with a filtered shape having a bandwidth strictly greater than twice the spacing between carriers ν0 and each symbol element being concentrated in temporal and frequency domains, characterized in that the method comprises the following steps:
• receiving the signal having, as its complex envelope, a signal r(t);
• estimating the response of the transmission channel comprising an estimation of the phase response θm,n and of the amplitude response ρm,n;
• demodulating said signal r(t) comprising the following steps:
• multiplying said signal r(t) by the prototype function x(t);
• aliasing the filtered waveform modulo 2τ0;
• applying a Fourier transform (FFT);
• correcting the phase θm,n induced by the transmission channel;
• correcting the phase corresponding to the term im+n;
• selecting the real part of the coefficient obtained ãm,n corresponding to the coefficient am,n transmitted weighted by the amplitude response ρm,n of the transmission channel.

Method for the construction of a prototype function x(t) for a signal, corresponding to the frequency multiplexing of several elementary carriers extending in temporal and frequency domains, each carrier corresponding to a series of symbols, two consecutive symbols being separated by a symbol time τ0, the spacing ν0 between two neighboring carriers is equal to half of the reverse of the smbol time τ0,

• and each carrier having a spectrum with a filtered shape having a bandwidth strictly greater than twice the spacing between carriers vo and each symbol element being concentrated in temporal and frequency domains, the signal having a complex envelope responds to the following equation:
• s ⁢ ( t ) = ∑ m , n ⁢ α m , n ⁢ x m , n ⁡ ( t ) ;
• where:
• a−m,n is a real coefficient chosen out of a predetermined alphabet of modulation;
• m is an integer representing the frequency dimension;
• n is an integer representing the temporal dimension;
• t represents time;
• x−m,n(t) is a basic fimction translated into the time-frequency space of one and the same even-order prototype finction x(t) taking real or complex values, namely:
• x−m,n(t)=±im+nei(2IIriν0rtφ)x(t−nτo) with ν0τ0=½
• where φ is an arbitrary phase parameter
• the Fourier transform X(f) ofthe function x(t) having a support extending beyond the interval [−ν0,ν0], and where said basic functions {xm,n} are mutually orthogonal, the real part ofthe scalar product of two different basic functions being zero;
• and further characterized in that the method comprises the following steps:
• selecting a normalized Gaussian function G(f) of the type:
• G(ƒ)=(2a)1/4eπg2;
• determining said prototype function x(t) such that:
• x ⁢ ( t ) = y ⁢ ( t ) t 0 ⁢ ∑ k ⁢ [LeftBracketingBar] ( y ⁢ ( t - k ⁢ ⁢ τ 0 ) ) 2 [RightBracketingBar]
• the function y(t) being defined by its Fourier transform Y(f):
• Y ⁢ ( f ) = G ⁢ ( f ) υ 0 ⁢ ∑ k ⁢ [LeftBracketingBar] G ⁢ ( f - k ⁢ ⁢ υ 0 ) [RightBracketingBar] 2