METHOD AND APPARATUS FOR FILTERED MULTITONE MODULATION USING CIRCULAR

CONVOLUTION

% * % H= φ

FIELD OF THE INVENTION The present invention concerns a modulation/demodulation method and apparatus for the multichannel transmission of signals on radio channels, cable and broad band electric lines.

The invention concerns a digital modulation technique that is applied in particular, although not exclusively, to radio communications or broad band cable characterized by effects of frequency distortion and of variance time.

BACKGROUND OF THE INVENTION

Numerical modulation and demodulation techniques are known for communication systems. In particular, broad band communication systems use multi-carrier transmission techniques which consist in sending the information signal in a certain number of narrow band channels. Multi-carrier techniques are used to overcome the phenomenon of distortion introduced by the broad band channels, both radio and cable, which do not have a constant frequency response.

Dividing the broad band signal into a plurality of narrow band signals allows each of said signals to see the relative sub-channel as non-distorting. This translates into a greater simplicity of the reception algorithms and better performance, in particular in terms of better quality of the signal received and reconstructed.

Among the known multi-carrier techniques, in the current state of the art the most widespread is OFDM (orthogonal frequency division multiplexing). This technique has been widely studied, and applied to LAN wireless systems with

IEEE 802.11 standards, to terrestrial digital and to ADSL. This technique has also been proposed for future generation cell radio systems.

Another technique which is having considerable interest is FMT (Filtered Multitone). This technique is described in particular in US-B1-6.665.349, in the name of Cherubini et al.

This technique proposes to obtain better performance than OFDM, since it provides a multi-carrier modulation pattern in which the sub-channels have a more limited frequency response compared with OFDM.

US-Al -2005/0047513, in the name of Vitenberg et al, describes an efficient implementation of FMT modulation by using techniques that reduce computational complexity.

Purpose of the present invention is to achieve a modulation/demodulation method and the relative apparatus for multichannel broad band transmission which allows to increase the OFDM performance, at the same time reducing computational complexity required by FMT.

The Applicant has devised, tested and embodied the present invention to obtain this purpose, and other advantages as identified hereafter. SUMMARY OF THE INVENTION

The present invention is set forth and characterized in the independent claims, while the dependent claims describe other characteristics of the invention or variants to the main inventive idea.

In accordance with the above purpose, a method for multichannel transmission according to the present invention is usable for digital modulation/demodulation of signals transmitted on radio channels, cable, or broad band electric lines.

The transmission of the information signal through the communication channel takes place by modulating sequences of data blocks, representing the signal, by one or more transmitters to one or more demodulators. The communication channel comprises a plurality of sub-channels, each of which is associated both with a predeterminate sub-sequence of data blocks of said sequence of data blocks, and also with a predeterminate modulation sub-carrier of each subsequence. Each subsequence of data blocks is modulated in the associated sub-channel at a predeterminate transmission speed. The transmitter comprises a stand of transmission or synthesis filters, each transmission filter being associated with a predeterminate sub-channel. The receiver comprises a stand of reception or analysis filters, each reception filter being associated with a predeterminate sub-channel.

According to a characteristic feature of the present invention, in each transmission filter a cyclic convolution is effected of each data block of the sequence of data blocks associated with the relative sub-channel, with predeterminate reference transmission wave forms.

According to another characteristic feature of the present invention, in each

reception filter a cyclic convolution is effected of each data block of the sequence of data blocks received and associated with the relative sub-channel, with predeterminate reference reception wave forms.

According to a variant of the present invention both the reference transmission signals and the reference reception signals comprise prototype impulses of the FIR (Finite Impulse Response) type.

Therefore, as will be described in more detail later, one advantage of the modulation/demodulation method for multichannel transmissions according to the present invention allows to improve the performance, compared with known modulations, in time variant and frequency selective communication channels The channels are typical in wireless mobile communications, cable communications and in-line conveyed-wave transmission or powerline.

A further advantage of the method according to the invention is that it is possible to receive signals with very limited time latencies. This renders the modulation/demodulation process particularly suitable for the transmission of data streams comprising multimedia contents or for applications in which a high quality service is required, such as for example for telephone services.

Furthermore, the method according to the invention allows to maintain the orthogonality of the sub-channels even when the means of communication is selective in frequency. This allows to prevent the unwanted introduction of inter- symbol interferences or inter-channel interferences and hence to prevent the introduction of a complex sub-channel equalization.

According to a variant, the method according to the present invention is associated with the transmission of signals for multiple users, in time variant and frequency selective channels in the presence of temporal misalignments, frequency misalignments, such as for example those deriving from maladjustments in the frequency generators and carrier generators, and phase misalignments.

According to another variant of the method according to the present invention, each communication sub-channel is associated with different transmission speeds.

In this way it is possible to adapt a multi-user transmission according to the specific transmission needs or reception capacity of each demodulation device, for example a palmtop and/or mobile device, with fewer processing resources

- A -

than a processing station.

According to another variant, the method according to the present invention is associated with the transmission of signals from multiple antennas for transmission in time variant and frequency selective channels. BRIEF DESCRIPTION OF THE DRAWINGS

These and other characteristics of the present invention will become apparent from the following description of a preferential form of embodiment, given as a non-restrictive example with reference to the attached drawings wherein:

- fig. 1 is a block diagram of a modulation/demodulation in the state of the art; - fig. 2 is a block diagram of a modulation/demodulation according to the present invention;

- fig. 3 is a block diagram of a transmission according to the present invention;

- fig. 4 is a block diagram of a reception according to the present invention;

- fig. 5 is an example of an impulsive and in frequency response of the prototype impulse achieved with the technique of the present invention;

- fig. 6 is a block diagram of a variant reception according to the present invention;

- fig. 7 is a block diagram of a second transmission variant;

- fig. 8 is a block diagram of a third transmission variant. DETAILED DESCRIPTION OF A PREFERENTIAL FORM OF

EMBODIMENT

With reference to the attached drawings, a modulation/demodulation method for multichannel transmission according to the present invention is applicable for radio or cable communications characterized by effects of frequency distortion and variance time.

Fig. 1 shows a conventional communication pattern FMT (Filtered Multitone) according to the state of the art. A transmitter 112, also called synthesis stage, generates a signal given by the expression:

Zt= O Z e Z where Z is the domain of the integers and a (IT ₀ ) is a sequence of data represented by complex symbols (for example belonging to a QAM constellation

- Quadrature Amplitude Modulation) which is transmitted on a sub-channel 113

k - 0,...,M -l at a transmission speed 1/T ₀ . Moreover, T is the sampling period used in the digital synthesis of the system, assuming that T constitutes the unit of time. M is the number of sub-channels 113, T ₀ = NT is the sub-channel symbol period where NjM > l is the over sampling factor, f _k = k/MT is the k- th sub- carrier 115, g(nT) is the prototype impulse. The transmission band width is W = II T and the overall speed of transmission in symbols per second is R = MIT ₀ . The diagram in fig. 1 refers to an FMT modulation sampled in a non-critical manner if the sub-carrier spacing f _k — f _k _ _λ = \IMT is greater than 1/T ₀ , otherwise the diagram in fig. 1 refers to an FMT modulation sampled in a critical manner.

The signal in the expression (1) is converted from digital to analogical (with a digital-analogical convertor (DAC)), transmitted on the channel 14, after having been converted into Radio Frequency (if the transmission is on radio channel). The low pass signal received (after demodulation which takes it to base band) is converted from analogical to digital (with an analogical digital convertor (ADC)) to obtain a y(iT) signal according to the equation y(iT) = x * g _CH (iT) + η(iT) ₍₂₎ in which % 9C _{H \} ^) indicates the linear convolution between %(iT) and 9 _CH {^) , where g _CH (iT) is the equivalent response in discrete time of the channel, that is, of the transmission means and where T](iT) is the noise addition contribution.

The signal received is made to pass through a stand of exponential multipliers 134 which convert it into base band and subsequently through a stand of analysis filters 116 with a prototype filter h(nT) . The output sampled, by a relative sampler 130B, at frequency HT ₀ and corresponding to the sub-channel 113 index k is given by the following expression:

In the FMT modulation the analysis impulse, that is, in reception, is adapted to the synthesis impulse, that is, in transmission, by means of the following equation h(nT) = g ( ^~ nT) where ^* denotes the complex conjugate operation. If g _* h(nT) is an ideal limited band Nyquist impulse with a narrower bandwidth than the spacing between the sub-carriers, and if the channel 14 has a flat

frequency response, the modulation/demodulation system is orthogonal, that is, there is no inter-channel interference (ICI) or inter-symbol interference (ISI) to the output sampled by the stand of analysis filters 116. However, a frequency selective channel 14 introduces temporal dispersions so that normally a sub- channel equalization is required, which can be effected by means of sub-channel equalizers of a known type.

The embodiment of the conventional FMT system as described heretofore is complex inasmuch as it requires the use of exponential modulators, filtering operations on a plurality of sub-channels, and equalization operations. Furthermore, it is not suitable for transmissions that require low latencies, unlike those that provide data block transmission, for example OFDM.

The modulation/demodulation method for multichannel transmission according to the present invention is hereafter also called CB-FMT or Cyclic Block FMT Modulation. The method according to the invention (fig. 2) provides the transmission of a block of L data symbols, one block per sub-channel 13, and K sub-channels 13 (fig. 2). Moreover, a prototype filter with causal impulsive response of finite duration M ₂ T = LNT (FIR) is considered. This condition is not limitative since the impulse can be extended by zeroes (zero padded). According to a characteristic feature of the present invention, the linear convolutions of the expression (1) are replaced by cyclic convolutions, to obtain an output signal from the transmitter 12, or synthesis stage according to the following expression: x(iT) ® _g (iT)]e ^{j2πf ik> ιT} (4) 0,...,M ₂ - l

Ic= O 1= 0 where (iT- /T ₀ )^ = ((J - lN)moάM ₂ )T so that g((iT - IT ₀ ) _M J indicates the response of the impulse rotated in circular manner on a duration support M ₂ samples, from left to right, of the quantity IT ₀ . The circular convolution with period M ₂ is indicated by the operator ® _{(M 2 ) 5} ^an d is substantially a convolution of discrete time information signals and periodic discrete time reference signals, wherein the temporal displacements

(delays/advances) of the signals are achieved in a cyclic or circular manner. The information signals are divided into blocks of L data symbols. The operator (a mod b) indicates the remainder operation in the division between the integers a and b. The data blocks can be transmitted continuously operating block after block, as described by transformation (4).

The stand of analysis filters 16 at exit from the exponential demodulators 32 with carriers 15, exactly like the stand of synthesis filters 19, works with circular convolutions, that is, the output of the &-th filter at instant IT ₀ is obtained as follows: z ^m ( _. ιτ ₀ ) _L _, ₍₅₎ i=0 where h((lT _Q — ϊT) _M ^ ) indicates the analysis impulse turned over and translated in a circular manner.

In this way, by using cyclical convolutions both in transmission, that is, during the synthesis of the signal, and also in reception, that is, during the analysis of the signal, it is possible to reduce the processing latency and render the signal itself more insensitive to the distortions introduced by the channel 14.

If there is no noise, and if the channel 14, that is, the transmission means, is ideal, it is possible to design as shown hereafter a stand of analysis filters 16 with a perfect reconstruction with reference to the circular convolutions so that

Z (IT ₀ ) = V _o a (IT ₀ ) with V ₀ = 1 without losing generality. In particular, a design criterion is supplied for a stand of discrete time filters able to make a perfect reconstruction with real adapted FIR impulses: h(iT) — g (—iT) . To illustrate this an embodiment is first described which is efficient in the frequency domain of said filter stands.

Each of the K subchanels 13 in fig. 2 transports a block of L data symbols in a time interval of LT ₀ seconds. Therefore the speed of transmission R is given by the following equation

R = KfT ₀ (Symbols I s) (6) Furthermore, each complex data symbol transports a number of bits n _b — \og ₂ (C) where C is the size of the constellation, for example n _b — 4 with

a 16 level QAM (Quadrature Amplitude Modulation).

The CB-FMT modulation pattern is efficiently achieved by discrete Fourier transforms (DFT), and even more efficiently by fast Fourier transforms (FFT).

It is assumed that M ₂ = LN > QK for integer numbers L, N, K, Q and that the sub-carriers 15 are defined as in the following expression: f ^w = kQ/M ₂ T k = o,...,κ-i (7).

Subsequently, we calculate the DFT of M ₂ points of the signal (4) and we obtain the following expression:

X(D = YL a^iIT ₀ )GU ₁ - f _kQ )e-^ ^f ' ^'f ^ ₍₈ )

£= 0 /= Q where G(f _t ) is the DFT of M ₂ points of g(iT) at the frequency given by the following expression: fι ^{= i} / ^M 2 ^T , i = 0,...,M ₂ -l (9).

Consequently, by defining

;= o the expression (8) is obtained as follows:

*(/,) = σ A ^« \f, - f _kQ )G(/, - f _kQ ) (11) k= 0

The term A (f _t ) is obtained by calculating a DFT of L points on the data block Cl 0,...,L-l and subsequently by means of a cyclic extension to obtain M ₂ coefficients, that is, A (J ₁ J = A \ J ₁ ^i) for i = L,...,M ₂ -I.

If the DFT of the prototype impulse has only Q coefficients different from zero, that is, if G(f _t ) — 0 for i = Q,...,M ₂ -l, then the expression (11) becomes: X(f _l+kQ ) = A^(Z ₁ )G(Z ₁ ) for i = α...,β-l, * = Q,...,*-1 (12) which means that the block of symbols A (J ₁ ) for z ^' = 0,...,<2-l weighs the coefficients of the impulses in the frequency domain.

One embodiment in the frequency domain of a CB-FMT modulation according to the present invention is shown in fig. 3. A transmitter 12, by means of the series-parallel convertors 34, generates blocks of LK data starting from the input stream of data. Then, by means of a DFT unit 38 associated with each sub- channel 13, it effects a DFT of L points, followed by a cyclic extension by a

cyclic extension unit 42 with Q coefficients which are weighed, that is, multiplied, by the Q coefficients 44 different from zero of the DFT of the prototype synthesis impulse. Finally, by means of an IDFT unit 40 (Inverse Discrete Fourier Transform) an inverse transform IDFT is effected of M ₂ points, followed by a parallel-series conversion by means of a P/S converter 36, which generates the signal x(ϊT) of the expression (4).

One embodiment in the frequency domain of a demodulation according to the present invention is illustrated in fig. 4 with a diagram of a receiver 18.

Hypothesizing that the transmission channel is ideal and that there is no noise, then the DFT of M ₂ points effected by means of a DFT unit 13, of blocks of samples received at output from the series-parallel converter S/P 134 leads to the expression (12).

Thus the symbol /-th of the block transmitted on the &-th sub-channel is obtained by the following transformation: if the stand of CB-FMT filters has a perfect reconstruction, where H(f _t ) is the frequency response of the analysis filter.

The expression (13) can be implemented by adding the last Q-L coefficients to the index coefficients i = o,...,L - i of the block , assuming without loss of generality that L ≤ Q < 2L. This is equivalent to a periodic repetition with period L of the blocks ■ Then to each block an inverse transform IDFT is applied of L points 140 whose outputs are subsequently processed by symbol detectors 24 in order to detect the data transmitted, which are presumed to belong to a predeterminate set, where the weights are defined as H = HyJ ₁ ) m fig. 4.

The perfect reconstruction of the signal received in the CB-FMT demodulation is obtained by means of the following design. A prototype analysis impulse h(iT) = g (—iT) is chosen, adapted to the synthesis impulse Oy ¹ ^- ) which is chosen of the FIR type and satisfies both a first condition, so that the DFT of the prototype impulse has only non null Q coefficients, and also a second condition so that the prototype impulse is orthogonal to its cyclic translations of multiples

T ₀ S(IT ₀ ) _where ι=0

0(IT ₀ ) = 1/ T ₀ for Z = O and <λ '*O) ^~ ^ for l = o, ,L - i, or equivalently, due to Parseval's theorem, g ^(χ ) _(M2) £(IT ₀ ) = ∑ G(/ _; )G ^* (/ _; ) _e ^y * ' = γ _O ^(Zγ _O ) .

In other words, the first condition translates into the absence of inter-channel interference because the sub-channels 13 in fig. 2 are separated by QfM ₂ T . On the contrary, the second condition translates into the absence of inter-symbol interference in every sub-channel 13. Furthermore, the prototype impulse FIR, lasting M ₂ T, is orthogonal to its cyclic translations by multiples of T ₀ only if the periodic repetition of period 1/T ₀ of the DFT of its M ₂ coefficients is constant. This condition is generated by the Nyquist criterion for discrete periodic time signals.

We shall now describe the embodiment according to the present invention of the impulses for CB-FMT modulation. Transmission and reception in the frequency domain suggest a synthesis of the impulse in the same frequency domain with a finite number of frequency components as illustrated hereafter.

Let us consider an impulse that belongs to the Nyquist class with a roll-off parameter p, Nyquist frequency F _N = ) and a frequency response C(f). According to a preferential embodiment, given that in transmission and reception DFT are applied of a size L and LN , both L and N are chosen equal to a power of two so as to allow a quick production through the Fast Fourier Transform. In particular, it is established that

L A ^ - 2

.2J (14) where Q is the number of frequency components of the impulse that differ from zero. The number of channels that can be allocated is given by the following expression:

(15)

Q where [.J indicates the rounding down operator.

Subsequently, the frequency components of the prototype impulse are set equal to G(f _n ) = _λ j C(f _n ) where the samples are taken at frequencies according to the following expression:

9 JP f _{n = nF = n} ^j, n e Z, n \ ≤ Q (16)

L 2 where F _N — 1/2T ₀ .

In this way it is possible to have some degrees of freedom in the choice of a function C(f) and the roll-off factor p. For example it is possible to choose a raised cosine spectrum C(f) with a roll-off factor p > 2/ L or a spectrum that leads to the minimization of the off-band energy ratio on in-band energy of the synthesized impulse.

Since the periodic repetition of C[J _n ) of the impulse with period 1/T ₀ is constant, and since the frequency components of the sub-channels 13 do not overlap, the stand of filters leads to a perfect reconstruction of the signal. Fig. 5 shows an example of prototype impulse and its frequency response generated using the above technique in the hypothesis of using the following parameters M ₂ = LN = 256,512,1024 and Q = 7,11,19. As can be seen, the in-band energy ratio on off-band energy decreases as Q increases, which increases the spectral confinement of the sub-channels 13. The search for optimum impulses can be made by setting this limit. When transmission is made on a channel with a frequency response that is not flat, the signal received is subjected to a distortion and in particular it is extended due to the echoes introduced by the channel (dispersion). The invention is particularly strong against these phenomena. In order to keep the perfect reconstructability of the signal transmitted to the signal in expression (4) a cyclic prefix is added (fig. 4) by the cyclic prefix extension unit 46, with a duration μT greater than the dispersion introduced by the channel. That is, a prefix is prefixed, consisting of μ identical coefficients to the last μ coefficients of the original block. The linear convolution of x(iT) with the channel equals the circular convolution of the coefficients received y(iT) of index i ⁼ M, • • • , M + M ₂ — 1 . The insertion of the cyclic prefix allows to effect an equalization in the frequency domain of a CB-FMT signal with an equalizer of the single coefficient type, or also single tap. The procedure (fig. 4) consists in discarding the cyclic

prefix by means of a unit to remove the cyclic prefix 48 in the signal received and in applying a DFT of M ₂ points in order to obtain the following expression: nf _i+kQ ) = A∞WGWGCH V _W ) + N(f _i+kQ ) for i = 0,..,Q-l (18) where is the DFT of the noise samples in reception with a variance σ , and ^C _H Ut) is the DFT of the channel impulse response.

The single-tap equalization is carried out to produce a decision metric of the data transmitted. The metric for the index symbol /in the block transmitted on the sub-channel k is obtained as follows:

Z ^(k) (lT ₀ ) = ∑ Z^ (i + kQ )e ^{J L} ' , Z^(z + kQ) = Y(f _t+LQ )H _EQ a _+LQ ) (19)

where the coefficients of the equalizer are chosen with the criterion of zero forcing, or minimum mean square error (MMSE). They are expressed respectively in the following two ways:

With zero forcing the stand of analysis filters 16 in fig. 2 is able to produce a perfect reconstruction in the absence of noise even if the channel 14 is selective in frequency.

Finally, the data transmitted are detected by means of a maximum probability detector, that is, a decision is taken on the data transmitted using the criterion of the minimum Euclid distance between (19) and the possible data transmitted: a (IT ₀ ) - ₍₂ i ₎

where A is the set of data symbols, Cl (ιT _Q ) is the estimated datum, and argmin is the function that restores the corresponding argument to the minimum.

Therefore, the demodulation (fig. 4) of the signal received occurs by means of a first conversion of the data received from a serial stream to a parallel stream by means of a series/parallel converter S/P 134, followed by the removal of the cyclic prefix, if any, by the unit to remove the cyclic prefix 48.

Subsequently, a DFT is performed of M ₂ points by means of a DFT M ₂ points unit 138 and the output of the transform are weighed, that is, multiplied by the DFT coefficients of the synthesis impulse 144 of the equalizer indicated by H ^{ή = H _EQ (f _t ) in f _lg . 4. Afterward, since (19) can be written as follows: ι=0 ι= 0 under the hypothesis that L ≤ Q < 2L, it can be implemented by adding the last Q- L coefficients to the index coefficients % = o, , L - 1 of the block

^EQ X ^{1 ~} i ^~ ^VJ , to obtain blocks of L coefficients. Then an inverse transform IDFT is applied by means of an IDFT unit of L points 140 for each sub-channel 13.

Finally, the symbols transmitted are detected by a maximum probability detector 24 as described.

If the sub-channels are narrow enough in frequency, the propagation of the channel can have a flat frequency response so that Gc _H ■

In this case the detector is simplified since the coefficient of the equalizer remains constant for every sub-channel.

The CB-FMT modulation/demodulation method according to the present invention is robust for transmissions on a frequency selective channel 14 (dispersive time).

According to a variant of the present invention, the CB-FMT modulation/demodulation method is also suitable for the transmission of a signal in a time variant channel 14 which is known as detrimental for the performance of modulation systems, such as for example for OFDM modulation. It must be noted that the K sub-channels 13 in fig. 2 are well confined in frequency, therefore the temporal variations of the channel 14, produced for example by the Doppler effect or rapid dissolvence of the wireless channels, do not introduce any inter-channel interference. Any possible inter-block interference, such as for example interference between the L symbols of a data block, can be eliminated as described hereafter. Furthermore, it must be pointed out that in the description of the CB-FMT modulation/demodulation as made heretofore, the sub-channels 13

were spaced by a quantity of Qj 'M ₂ T Hertz. If an impulse withg, < Q components in frequency is used, it is possible to increase the separation between the subchannels 13. Equivalently, it is possible to space the sub-carriers more, so that the sub-channels 13 have a greater frequency separation. This can be done by inserting zeroes between the sub-channels 13 in the embodiment in the frequency domain described before.

We shall therefore now describe a variant of the demodulation method according to the present invention for the reception (fig.6) of a CB-FMT signal transmitted in a frequency selective and time variant channel 14. Let us hypothesize that the response of the channel 14 at instant ιT to an impulse applied at instant nT is §QH yϊJ- il-L) with a shorter duration than the cyclic prefix, that is g _CH (nT;ιT) ≠ 0 only for n so that 0 < nT < N _P T < μT .

Then the output of the DFT of the signal received (hypothesizing absence of noise for notional simplicity) are expressed as follows: UJG _c1 Cf _1n ;/,- f _m ) (22) τn = 0 where the double Fourier transform is used of the impulse response of the time variant channel:

Gc _H (I _n -J ₁ ) = ∑ σ g _CH (nT;lT)e ^~J ^'""e ^' ' ^M ^ (23)

«=0 1= 0

Thus we obtain the following expression: κ-\ Q-i Y Ui) — Z_j 2-y A ^l (fm)G(fw)G _C H(fm + kQ ^' l fi ^~ fm + kq) (24)

I = Q m = 0

If we assume that the channel 14 has a flat frequency response in the band width relative to each sub-channel, the expression (24) can be expressed as follows: γU,) = vj£(/J6W(λ _Q ;/, - L ₊ , _Q ) (25) By designing the system so that the instantaneous Doppler band width equal to

N ₁₃ / M ₂ T is smaller than the guard frequency between two sub-channels, and the prototype impulse is confined in frequency, then the expression (25) can be written as follows:

^γ (l _+ιQ ) = ∑ = 0,...,Q-l (26) m = 0

The expression (26) is the convolution between the block A (f _m )G(f _m ) and i ^' J _m+k Q ) which has a lesser extension than the separation between the sub-channels 13 in accordance with the above hypotheses.

The coefficients in the expression (26) can be processed as described hereafter so as to obtain the following outputs for the sub-channel k at the time instant IT ₀ Z^ (IT ₀ ) = α<*> (Zr ₀ )g(O)g _CH (f _kQ ; IT ₀ ) ₍₂₇ ) that is, as multiplication of the datum transmitted and a weight factor

9(P)S _CH (U JLQJ, T ₀ ..). with 9cH UkQ ^' i ^lT θ ) ^~ ∑^ ^G CIl {fkQ ^' J _ _{Thus the}

final detection of the data symbols transmitted can be achieved using a detector that uses the metric according to the following expression:

The outputs (27) are obtained by making a zero padding of the expression (26) so as to find a block of length M ₂ coefficients, on which an IDFT of M ₂ points is made, followed by the sampling of output on the indexes n - IN, l = o, ,L - i .

Moreover, the fact that in the CB-FMT a prototype impulse orthogonal to its own cyclic translations is used is also exploited.

Therefore, the demodulation of the signal received through a time variant and frequency selective channel 14 (fig. 6) occurs by effecting a conversion of the serial stream of data received into a parallel stream by means of a series/parallel convertor 234 and removal of the cyclic prefix, if any, by means of a second unit to remove the cyclic prefix 248.

Subsequently, a DFT of M ₂ points is performed by means of a second DFT unit of M ₂ points 238. Afterward, the outputs of the DFT relating to each of K sub-channels 13 are grouped together and each output is subjected to zero padding by an extension unit with zeroes 49 to obtain a block of M ₂ coefficients.

Then the inverse transform IDFT is effected, by means of a corresponding IDFT M ₂ points unit 240, on each sub-channel block on which zero padding has

been performed and the output is sampled for indexes n = lN, 1 = 0, ,L - i by means of a sampler 230.

Finally, the L information symbols are detected for each of the K sub-channels by means of the symbol detectors 24. The CB-FMT modulation/demodulation method described provides a stand of filters in reception which allows the perfect reconstruction of the signal. The formation of the impulse is divided in half between the stand of filters of the transmitter, or synthesis stage, and the stand of filters of the receiver, or analysis stage, by means of a root Nyquist impulse. The perfect reconstruction is also obtained by using a Nyquist impulse on the transmitter. In this case the prototype impulse has an impulse response given by the following expression: h(n T) = g ® g_ ^* (nT) (29) and DFT components as in the following expression: Consequently, at exit from the DFT unit 138 of the receiver 18 we obtain the following expression:

Y(f _l ) = A ^w (f _l )H(f _t - f _kQ )G _CH (f _l ) + N(f _l ) (31) fσr i = kQ,...,(k + ϊ)Q - l

The signals are reconstructed perfectly if an inverse transform IDFT of M ₂ points is performed (sampled with a factor N by means of a sampler) in every sub-channel on the coefficients equalized by means of zero forcing as shown in the following transformation:

Z ^(k \lT ₀ ) = ∑Y(f _ι+kQ )H _EQ (f _ι+kQ )e ^M>

where - The last equality is produced by the fact that the prototype impulse is an impulse without inter-symbol interference ISI and with limited band.

The CB-FMT modulation/demodulation method also allows to make a transmission at multiple transmission speed. That is, it is possible to transmit a different quantity of information on each sub-channel 13 in fig. 2.

This can be done by using fewer than L data symbols on some of the sub-

channels 13, or by increasing/decreasing the band width of each sub-channel 13 defining a prototype impulse that has different band widths. With reference to the embodiment in the frequency domain, this leads to sub-channel impulses which have a different number of frequency coefficients. The CB-FMT modulation/demodulation method also allows to be linked to a channel code for the correction and/or detection of errors. One possibility is to use codes of the bit-interleaved type, as shown in fig. 7. At exit from a channel encoder 50 there is a bit interleaver 52, to diffuse the encoded bits both temporally and through the sub-channels 13. In this way it is possible to protect the transmission effectively from errors introduced by the channel 14. In particular this allows to exploit the selectivity of the channel 14 both in time and frequency in the form of gains in code and diversity after the decoding operation to the receiver.

Another possible embodiment is to diffuse the bits/symbols data both in time and in frequency using expansion codes, such as for example Walsh codes (fig.

V).

The CB-FMT modulation/demodulation method also allows to transmit data for multi-users both in up-link and in down-link, such as for example in the connection of a wireless system between a portable device and a base, and vice versa. The multi-user transmission can be made either using a transmission pattern with time division multiple access (TDMA) or by assigning each subchannel 13 to a single user. The second embodiment entails the sharing of the K sub-channels 13 among the users, thus achieving a kind of frequency division multiple access (FDMA), or the transmission of data symbols in a predeterminate block of L symbols that belong to different users.

Since the modulation/demodulation method according to the present invention is suitable for transmission on time variant and frequency selective channels 14, the method is suitable for user multipling in channels 14 with asynchronous multiple accesses which have temporal misalignments, frequency misalignments, phase misalignments and noise.

The CB-FMT modulation/demodulation method can also be applied for radio transmissions with multiple transmission antennas 60 (fig. 8). This can be obtained in two ways. Firstly, a signal modulated according to the CB-FMT

modulation is transmitted by each antenna 60. After reception on the receiver antenna a connected demodulation algorithm is provided to decode the signals of the transmission antennas. Secondly, it is possible to divide the sub-channels 13 and/or the blocks of data symbols by means of a division device 62 and transfer them to different antennas 60. In this way we achieve a form of space-temporal code. It is also possible to obtain orthogonality between signals transmitted by different antennas 60 by exploiting the orthogonality of the CB-FMT channels. The method according to the present invention therefore allows to achieve a frequency division multiplexing also between devices that are not synchronized, guaranteeing in any case the orthogonality of the signals.

It is clear that modifications and/or additions of parts may be made to the method as described heretofore, without departing from the field and scope of the present invention.

It is also clear that, although the present invention has been described with reference to some specific examples, a person of skill in the art shall certainly be able to achieve many other equivalent forms of method and device for multichannel broad band transmission, having the characteristics as set forth in the claims and hence all coming within the field of protection defined thereby.