Receiver structure for OFDM

Field of the Invention

The present invention relates to telecommunication systems of the type known as OFDM (Orthogonal Frequency Division Multiplexing) or digital data transmission systems with orthogonal frequency division multiplexing, where data arriving from a source is subdivided in a certain number of data sequences which are multiplexed according to a frequency division format. One preferred, but not restrictive application lies in the field of digital television signal transmission by radio as well as by cable.

In systems of the type generically known as muiticarrier or multitone systems, one of the primary objects is to define an optimum compromise between a maximization of the exploitation of the transmission channel bandwidth in order to be able, for example, to transmit as much per time unit as possible (in the range of 30 Mbit/s through a 8 MHz band (channel)), and the requirement to exclude the possibility of data errors caused by channel fading phenomenons, impulsive noise and other typical signal quality degrading phenomenons attributed to variable or predetermined characteristics of the specific transmission channel.

Different solutions for these problems can be compared in terms of computational complexity or operations (complex multiplications) to be carried out per time unit by the different functional units which set up the architecture of the OFDM transmitters, and which influence the complexity and the realization costs of such systems. The computational complexity is therefore a merit figure which refers to the efficiency and/or reliability of assuring a non degraded reception of the digital signals and/or their correct reception also under impairments of the transmission channel.

The principle of OFDM systems is based on the subdivision of the available bandwidth in a plurality of sub-bands (for example in the range of hundreds or thousands), where each sub-band carries a part of the data flow to be transmitted. Each sub-band is modulated by applying a signal which is orthogonal to the modulation signals of the other sub-bands. The channel channel distortion creates interference problems among the bits in a digital transmission. In order to control such interference two alternative approaches are commonly used. The first is to separate the symbols one from the other on a time base considering the fact that the interference due to echo phenomenons has a limited time duration, while a second approach is to operate a signal manipulation by using a filter bank suitable to reconstruct through a pulse shaping operation information degraded by the channel. The first filterless approach implies the use of less complex hardware for the absence of the relative filters, but it obviously limits the exploitation of the available transmission channel bandwidth thus limiting the transmission efficiency (bit/s/hertz).

In both types of systems OFDM-PS and OFDM-NPS (where the suffix indicates in the first case a system with Pulse Shaping and in the second case a system with no Pulse Shaping) it is anyhow necessary in practice to implement in the receivers also an equalization stage to correct the degradation of the signal due to linear distortions. The equalization may be introduced alternatively either before the OFDM demodulator, i.e. working on the baseband signal, or after the OFDM demodulator at a much lower symbol rate. Although the second solution entails the realization of a number of equalization units which is at least the same number as that of the sub-bands, this solution is generally preferred compared to the difficulty to realize an equalization unit operating at a high symbol rate as required by the first solution.

While in a system with pulse shaping (OFDM-PS) the equalization can be limited to the time domain (distortion due to interference phenomenons between following bits) being the distortion effects in the frequency domain (distortion due to cross-talk phenomenons among adjacent or neighbour subchannels) cancelled by the spectral definition of the pulses and by the peculiar orthogonality of the modulation signals, in the case of systems without pulse shaping (OFDM-NPS) the equalization may be limited to the multiplication for a constant. This happens in consideration of the fact that the effects of the distortion in time domain is cancelled by effect of the guard interval, introduced on purpose on the time domain, at least until the used guard interval remains longer than the more persistent echo introduced by the channel [2].

However also in the OFDM-NPS systems, even if it is theoretically possible to use the technique of introducing a guard interval between symbols in time base to make the equalization trivial, in the specific case of single frequency network (SFN) the use of the data symbol separation technique with guard interval would imply the use of an extremely big and complex discrete Fourier transform block, practically difficult to be implemented at the present state of the art due to synchronization problems still to be solved, or in any case requiring a very complex and expensive hardware. Therefore the equalization is often necessary also in OFDM-NPS systems [3].

It is known and proved [2] that carrying out an equalization procedure at a rate which is multiple compared to the symbol frequency, in other words with a fractional sampling period compared to the sampling period of the transmission system, can give better results than conventional symbol rate equalization.

On the other hand the architecture of a multicarrier OFDM modemodulator device is conventionally considered to be implementable by a relatively simple hardware, only if this responds to certain precise requirements of a so-called Complex Standard Scheme (SCS), and precisely: <ul id="ul0001" list-style="none" compact="compact"><li>C1) the output bit rate F₀ has to be exactly N times the input bit rate, where N is the number of branches or sub-bands of the modemodulator device, and therefore the spacing in input time base T turns out to be N times the spacing in output time base T₀, being<maths id="math0001" num=""><math display="block"><mrow><msub><mrow><mtext>F</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext> = NF   T = NT</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>;</mtext></mrow></math><img file="EP0719005A2_D0001.tif" /></maths></li><li>C2) the filters of all sub-bands have to be identical: G_n(t₀) = h(t₀), where: n=0,1,...,N-1;</li><li>C3) the carrier frequencies have to be spaced out by a same interval F with respect to the baseband with high bit rate (0,F₀), i.e. f_n = nF, where n=0, 1, ..., N-1.</li></ul>

If the system satisfies the conditions C1), C2) and C3), an SCS with N subchannels is completely specified by the input bit rate F and by the filter h(t₀), commonly called "reference filter".

The common thesis in the practical realization of these systems is in fact that an SCS can be realized in an efficient way using: <ul id="ul0002" list-style="dash" compact="compact"><li>a processor with N points (or with the dimension N) which computes the inverse discrete Fourier transform (N-size IDFT) in the case of a transmitter, and the discrete Fourier transform (N-size DFT) in case of a receiver;</li><li>a polyphase network with N branches (N-branch PPN);</li><li>a parallel/serial (P/S) converter in case of a transmitter or serial/parallel (S/P) in case of a receiver. The polyphase network may be visualized as a bank or array of filters sampled at the symbol rate.</li></ul>

Background Art

A system of this type is for example described in the patent US-A-4,300,229 in the name of B. Hirosaki.

An improved elaboration of this type of systems suitable to achieve substantially a halving of the computational complexity of the system or, alternatively, to allow the transmission of a double number of channels with the same complexity of the circuit units is disclosed in EP 668678 in the name of the same applicant. The relevant description and the relative illustrations of this previous application are adduced hereafter for explicit reference.

In some OFDM-PS systems (with pulse shaping) of the known type the structure SCS_R of the receiver produces directly signals with a double bit rate [1]. The post-processing circuit unit of these receivers which commonly follows in cascade the unit SCS_R could in fact be modified in such a way to produce fractioned output flows (with double sampling frequency) to be transmitted to the inputs of the equalizer. However, in more general terms, either the post-processing unit of output flows produced by the SCS_R of the receiver cannot be modified for other reasons, or in many cases this unit does not exist. This is for example the case of the conventional systems of the filterless type (i.e. without pulse shaping), in which the unit SCS_R of the receiver produces output signals at the symbol rate. In all these cases the problem of synthesizing a receiver unit SCS_R with fractionally spaced outputs remains unsolved.

In other words, at the present state of art there are the problems to conciliate the need of using an equalizer advantageously operating with a multiple sampling rate compared to the system symbol rate thus to increase the recovery capacity of the signal quality even if there are strong linear channel distortions, with the need to maintain in acceptable terms the consequent increase in the complexity and therefore guarantee the practical realizability of the OFDM receiver demodulator suitable to produce output flows with said multiple sampling rate, and therefore suitable to ber followed by multiple sampling rate equalizers.

Object of the Invention

It is therefore a primary object of the present invention to supply an OFDM demodulation method and system suitable to produce a plurality of frequency multiplexed signals with a multiple symbol rate compared to the system symbol rate, or a fractionized sampling period satisfying moreover the criterions of a Standard Complex Scheme (SCS) and which is therefore realizable by units which can be implemented efficiently.

This object is completely achieved by the present invention.

Disclosure of the Invention

Fundamentally the method of the invention consists in splitting up a conventional SCS structure with N subchannels (or sub-bands), virtually in a number 2k of SCS structures, each one with N/2^k output flows with a rate which is 2 ^k times the symbol rate. This first step of the synthesis procedure of the invention consists in the hypothesis of the use of a plurality of first identical sections (K(f)) of an identical generic subchannel decimation filter (H(f)) sampled at said rate 2^k higher than the symbol rate. The output flows from said first filter (K(f)) sections may therefore be arranged in a number 2^k of groups, each one with N/2^k flows, a first group being composed by the output flows of all said first filter (K(f)) sections with a zero frequency offset, and therefore intrinsically in conformity with a SCS scheme, while each one of the other groups are set up by the N/2^k output flows of all said first filter (K(f)) sections having a same frequency offset compared to a said first group of output flows in conformity with the definition conditions of an SCS. Modulating the output flows of said other groups with a frequency corresponding to the respective frequency offset of the group, it is possible to reset a <u>per group conformity</u> to a SCS scheme substantially of all N output flows with a rate 2^k higher than the symbol rate. In practice, 2^k separate SCS structures are thus defined, each one with N/2^k subchannels, and all with a rate 2^k higher than the symbol rate of the system.

At the receiver the reciprocal scheme is used, and after the 2^k SCS_s the N flows are rearranged in such a way to reset their coherence, in practice eliminating the arrangement in groups previously operated, and the N output flows of the N/2^k distinct SCS are filtered with a number N of second identical sections (F(f)) of said generic subchannel decimation filter (H(f)), essentially <u>not sampled</u>, and such to produce jointly at the respective first filter section (K(f)) the decimation filter function (H(f))=K(f)F(f) with an output flow at the same bit rate of the input flow, satisfying also in this post-filtering step the needs of a SCS scheme.

Having in this way defined said plurality of SCS units, each one of N/2^k branches or subchannels, it is possible to realize each one of these SCSs according to a so-called "efficient implementation" using for each SCS unit with N/2^k branches a polyphase network with N/2^k branches (N/2^k-branch PPN), a processor (DFT) with N/2^k points suitable to compute the discrete Fourier transform, and compensating the offset in frequency of the N/2^k output flows of the processors DFT relative to said other groups, modulating the output signals with a frequency corresponding to the group offset. The N flows with a sampling rate 2^k higher than the symbol rate of the system are therefore simply rearranged, in case of filterless systems (without pulse shaping), and possibly filtered by filters essentially <u>not sampled</u>, in case of systems with pulse shaping.

In this way, N data flows are obtained with a fractioned symbol spacing in time base, and therefore manageable by an equalization or equalizer filter array advantageously operating with a sampling rate equal to 2^k times the symbol rate of the system. This important result is obtained by a moderate increase of the complexity of the units composing the OFDM demodulator, as illustrated hereafter in the description. The architecture of the OFDM demodulator is moreover suitable for a simplified realization of the polyphase network through merging in single identical complex units of a number N/2^k of the original N units of said poliphase network, in turn derived from the transfer function of said first filter sections of the conventional scheme (inefficient) of the relative SCS, according to a whatsoever form of splitting up of the "reference" filter, thus obtaining a further simplification of the hardware, as will be illustrated hereafter.

The system of the invention can be applied to different known schemes, as to the so-called full complex scheme, where the structure is doubled for the real part and for the imaginary part of a certain transmission signal, and, as aforesaid, in case of a system which applies the pulse shaping technique as well as in case of a so-called filterless system which does not apply the pulse shaping technique.

The number 2^k of splitting of the output flow sampling period of the demodulator to be equalized, and therefore of the number in which the conventional original structure SCS of the demodulator will be virtually subdivided, will depend on the cost/benefit considerations based on an optimum relation between complexity and total number of the necessary devices.

In general terms, a demodulation and equalization system according to the present invention may be defined as a structure which includes: <ul id="ul0003" list-style="none" compact="compact"><li>2^k serial/parellel conversion devices suitable to receive as input a baseband reception signal and to produce 2^k groups of N/2^k output flows with a bit rate equal to 2^k times the symbol rate F of the system, where k is a whole number;</li><li>units of a polyphase network with N/2^k branches sampled to said multiple rate, each one of those is suitable to receive as input one of said output flows of said serial/parallel conversion devices, and to produce through N/2^k outputs the same number of output flows;</li><li>2^k processors working at said multiple sampling rate, each one of the dimension N/2^k, the N/2^k inputs of which are respectively connected to the outputs of said first units, each one suitable to compute a discrete Fourier transform and to produce N/2^k output flows;</li><li>modulation devices connected to the outputs of said processors suitable to remove the respective frequency offset to reset in conformity with a SCS scheme of all output flows of said 2^k processors;</li><li>equalization means with N branches working at said multiple 2^kF sampling rate with N inputs connected respectively to said N output flows to said multiple rate of said modulators.</li></ul>

Brief Description of the Drawings

The features of the present invention which are believed to be novel are set forth with particularity in the appended claims. The invention, together with further objects and advantages thereof, may be understood with reference to the following description, taken in conjunction with the accompanying drawings and in which: <ul id="ul0004" list-style="none" compact="compact"><li>Figure 1 is a general scheme of a multicarrier OFDM transmission-reception system;</li><li>Figure 2 is a multicarrier transmission-reception scheme according to a standard complex scheme;</li><li>Figures 3 and 4 illustrate the synthesis of a SCS for the transmitter and for the receiver, respectively;</li><li>Figure 5 shows a splitting-up process, according to the invention, of the reference filters of a SCS into two parts;</li><li>Figure 6 illustrates a rearrangement of different paths after the filters splitting into two separate parts;</li><li>Figure 7 schematizes the definition of two virtual schemes SCS after the splitting-up of the filters, the rearrangement and the modulation of the various signals;</li><li>Figures 8, 9, 10 and 11 illustrate the efficient implementation procedure of the distinct SCSs in order to reduce the circuit complexity;</li><li>Figure 12 shows a receiver with efficient realization for a system with N subchannels with fractionally spaced outputs according to the present invention;</li><li>Figure 13 is a scheme of the complex units which set up the polyphase network of the receiver of Fig. 12;</li><li>Figure 14 is a general scheme of a transmission-reception system, using an equalizer in the receiver;</li><li>Figure 15 shows three different decomposition alternatives of the reference filter of the original SCS;</li><li>Figures 16, 17, 18, 19 and 20 illustrate the synthesis processing of a receiver with fractionally spaced outputs, according to the present invention and according to a Full Complex Scheme;</li><li>Figures 21, 22 and 23 illustrate the synthesis procedure of a receiver with fractionally spaced outputs for a filterless system, i.e. without pulse shaping;</li><li>Figure 24 is a scheme of an OFDM receiver with efficient realization, with sixteen outputs with a fractioned sampling rate which is four times higher than the symbol bit rate of the system.</li></ul>

Detailed Description of a Preferred Embodiment

The scheme of a multicarrier system (MCS) with N branches or subchannels is illustrated in Fig. 1. The transmitter has an input sampling frequency F=1/T and an output sampling frequency F_<b>o</b>=1/T_o. The N blocks G_n(f) represent as many interpolator filters, and the N flows are modulated at the corresponding N carrier frequencies: f₀, f₁, ..., f_N-1.

The receiver (MCS_R) has a scheme which is dual with respect to the scheme of the transmitter. From the receiver the respective carrier frequencies are subtracted during the respective modulation stages, and the blocks G_n(f)R represent the same number of decimation filters. In practice, the receiver is essentially specified by the parameters of the relative transmitter. The transmitter MCS and the receiver MCS_R represent the fundamental scheme of an OFDM system neglecting minor accessory operations which involve anyhow an additional negligible computation complexity.

It is proved that an MCS unit cannot be implemented in an efficient way, that is in an economically feasible way, if it does not satisfy certain conditions specified by the definition of a so-called Standard Complex Scheme (SCS), as already indicated before.

As shown by the diagram associated to the example schemes of the respective SCS units (of a transmitter) and SCS_R (of a receiver) of Fig. 2, the SCS scheme provides, for a number N=8 of subchannels, for an output sampling frequency F₀ which is exactly eight times the input sampling frequency F. Therefore the input timebase spacing T is N times the output spacing in timebase T₀ (referring to the case of the SCS of the transmitter).

Once satisfied the conditions defining an SCS, it is shown that the scheme of an SCS (transmitter) may be synthesized in the way illustrated in Fig. 3, and analogously an SCS_R (receiver) may be synthesized in the way illustrated in Fig. 4.

An SCS of the dimension N, with an input bit rate F and a reference filter h(t₀), may be synthesized as follows: <ul id="ul0005" list-style="none" compact="compact"><li>1) use a processor with N points to carry out the inverted discrete Fourier transform (IDFT), to process the input vector [S₀(t), ..., S_N-1(t)] in the vector [s₀(t), ..., s_N-1(t)] for each instant t=kT, where k is a whole number, according to the expression:<maths id="math0002" num=""><img file="EP0719005A2_D0002.tif" /></maths></li><li>2) use a polyphase network with N branches (PPN) to filter the signals [s₀(t), ..., s_N-1(t)] according to v_n (t)=h_n*s_n (t);</li><li>3) carry out a parallel/serial conversion of the N signals v_n(t) in a high frequency signal v(t₀) according to the rule v(t+nT₀)=v_n(t).</li></ul>

The filters of the polyphase network are correlated to the reference filter of the SCS as follows:    h_n(t) are a serial/parallel conversion of the response to the pulse of reference filter h(t₀), in other terms:<maths id="math0003" num=""><math display="block"><mrow><msub><mrow><mtext>h</mtext></mrow><mrow><mtext>n</mtext></mrow></msub><msub><mrow><mtext> (t)=h(t+nT</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>).</mtext></mrow></math><img file="EP0719005A2_D0003.tif" /></maths>

As already said the synthesis of an SCS_R for the receiver turns out to be already defined by the parameters elaborated for the SCS transmitter, inverting the relative position of the converter which will be of the serial/parallel type, and of the processor with N points which will carry out the discrete Fourier transform (DFT).

The method of the invention to synthesize a demodulator with fractionally spaced outputs, that is with output flows having a subdivided symbol period (with respect to the base symbol period of the transmission system), is based on a splitting-up of the SCS structure of the demodulator in a number of SCS structures. For illustration conveniences the method of the invention is illustrated with reference to an SCS transmitter unit, taking into consideration the fact that the result of a splitting-up and synthesis operated for the transmitter is realizable in a specular way in the receiver.

Taking into consideration an SCS base structure as that of the transmitter part of the OFDM system of Fig. 2, where the reference filter is H(f), the input and output sampling frequencies F=1/T and F₀=1/T₀, respectively, let us for the moment split up the unit SCS in two parts A and B as illustrated in Fig. 5, where the intermediary sampling frequency will be 2F=2/T. To this aim, each interpolator filter H(f) may be subdivided in two parts F(f) and K(f), where F(f) is an interpolator filter with an input frequency F and an output frequency 2F (interpolation of a factor 2), and the filter K(f) is an interpolator filter with an input frequency 2F and an output frequency F₀ (interpolation of a factor N/2). This splitting-up is not a unique one, but it can be carried out in different ways as will be described hereafter. For the moment, let us suppose that both filters F(f) and K(f) are defined. Clearly, both subunits A and B, into which the original SCS structure has been split, do no more satisfy the needs of an SCS scheme, and therefore they cannot be implemented in an efficient way.

Fig. 6 shows the decomposition scheme into two parts A and B for an original SCS having a number N=8 branches or subchannels according to a splitting scheme similar to that shown in Fig. 5. If we arrange the N output flows of the filters F(f) (unit A) in two groups of subchannels to be identified as even and odd as illustrated in the scheme of Fig. 6, the upper half of unit B, which contains the filters K(f) and the modulators, turns out to satisfy the needs of an SCS scheme with parameters K(f), 2F, N/2, whereas the lower half of unit B does not satisfy the needs of an SCS unit due to the presence of a spurious frequency offset of the modulators equal to F.

Focusing the attention on unit B and neglecting for a moment unit A, it is possible to compensate this offset by premodulating the respective flows before the filters with a frequency equal to the offset F, substituting the filters K(f) with filters given by<maths id="math0004" num="(2)"><math display="block"><mrow><mtext>K'(f) = K(f-F)</mtext></mrow></math><img file="EP0719005A2_D0004.tif" /></maths>

This results in a scheme like the one shown in Fig. 7, where unit B turns out to be virtually split in two SCSs: the upper one with parameters K(f), 2F, N/2 and the lower one with parameters K'(f), 2F, N/2.

In fact the new modulation carried out before the filters takes place at a frequency 2F and corresponds therefore in the time domain to a multiplication by (-1)ⁿ where n is the running time. An array of multipliers of this type by (-1)ⁿ has clearly no computational complexity.

Now the two distinct SCSs are suitable for an efficient implementation as shown in a schematic way by Fig. 8.

At this point a practical synthesis of the OFDM modulator turns out to be particularly efficient, despite the fact that it is relatively heavier than that of a modulator according to the original SCS scheme (unfractioned). In fact the computational complexity of two SCSs with N/2 branches, realized using the respective processors (I)DFT and polyphase networks PPN, turns out to be higher than -the complexity of a single SCS with N branches. However, the complexity may be significantly reduced in virtue of the fact that the reference filters of the two distinct SCSs, in which the original unitary structure SCS is subdivided, are <u>tightly correlated</u> according to the relation (2). It is therefore possible to merge some filtering operations which are similar in two distinct SCSs.

Analyzing the efficient realization of both SCSs of Fig. 8, the summing of the signals may be transferred before the parallel/serial conversion, so that each input of the converter P/S assumes a scheme like the one shown in Fig. 9, where k_i(t) and k'_i(t) represent the poliphase components of the filters k(t₀) and k'(t₀).

The relations being:<maths id="math0005" num="(3)"><math display="block"><mrow><mtext>K'(f) = K(f-F)</mtext></mrow></math><img file="EP0719005A2_D0005.tif" /></maths><maths id="math0006" num=""><math display="block"><mrow><mtext mathvariant="italic">k</mtext><mtext>'</mtext><mfenced open="(" close=")"><mrow><msub><mrow><mtext mathvariant="italic">nT</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></mfenced><mtext>=</mtext><mtext mathvariant="italic">k</mtext><mfenced open="(" close=")"><mrow><msub><mrow><mtext mathvariant="italic">nT</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></mfenced><mtext mathvariant="italic">e</mtext><msup><mrow><mtext>​</mtext></mrow><mrow><mtext mathvariant="italic">j</mtext><mtext>2π</mtext><msub><mrow><mtext mathvariant="italic">FnT</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></msup><mtext>=</mtext><mtext mathvariant="italic">k</mtext><mfenced open="(" close=")"><mrow><msub><mrow><mtext mathvariant="italic">nT</mtext></mrow><mrow><mtext>0</mtext></mrow></msub></mrow></mfenced><mtext mathvariant="italic">e</mtext><msup><mrow><mtext>​</mtext></mrow><mrow><mtext mathvariant="italic">j</mtext><mtext>2π</mtext><mfrac><mrow><mtext>n</mtext></mrow><mrow><mtext mathvariant="italic">N</mtext></mrow></mfrac></mrow></msup></mrow></math><img file="EP0719005A2_D0006.tif" /></maths>

Then, the PPN decomposition yields:<maths id="math0007" num=""><math display="block"><mrow><msub><mrow><mtext>k</mtext></mrow><mrow><mtext>i</mtext></mrow></msub><mtext></mtext><mfenced open="(" close=")"><mrow><mtext>n½T</mtext></mrow></mfenced><mtext>= k</mtext><mfenced open="(" close=")"><mrow><msub><mrow><mtext>T</mtext></mrow><mrow><mtext>o</mtext></mrow></msub><mfenced open="(" close=")"><mrow><mtext>i + n½N</mtext></mrow></mfenced></mrow></mfenced></mrow></math><img file="EP0719005A2_D0007.tif" /></maths><maths id="math0008" num="(4)"><math display="block"><mrow><msubsup><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow><mrow><mtext>'</mtext></mrow></msubsup><mtext>(</mtext><mtext mathvariant="italic">n</mtext><mfrac><mrow><mtext>1</mtext></mrow><mrow><mtext>2</mtext></mrow></mfrac><mtext mathvariant="italic">T</mtext><mtext>)=</mtext><mtext mathvariant="italic">k'</mtext><mtext>(</mtext><msub><mrow><mtext mathvariant="italic">T</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>(</mtext><mtext mathvariant="italic">i</mtext><mtext>+</mtext><mtext mathvariant="italic">n</mtext><mfrac><mrow><mtext>1</mtext></mrow><mrow><mtext>2</mtext></mrow></mfrac><mtext mathvariant="italic">N</mtext><mtext>))</mtext><msub><mrow><mtext mathvariant="italic">=k</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow></msub><mtext>(</mtext><mtext mathvariant="italic">n</mtext><mfrac><mrow><mtext>1</mtext></mrow><mrow><mtext>2</mtext></mrow></mfrac><mtext mathvariant="italic">T</mtext><msup><mrow><mtext>)(-1)</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msup><msubsup><mrow><mtext mathvariant="italic">W</mtext></mrow><mrow><mtext mathvariant="italic">N</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow></msubsup></mrow></math><img file="EP0719005A2_D0008.tif" /></maths><maths id="math0009" num=""><math display="block"><mrow><mtext mathvariant="italic">i</mtext><mtext>=0,...,</mtext><mfrac><mrow><mtext>1</mtext></mrow><mrow><mtext>2</mtext></mrow></mfrac><mtext mathvariant="italic">N</mtext><mtext>-1</mtext></mrow></math><img file="EP0719005A2_D0009.tif" /></maths>

With the notations indicated in Fig. 9 and employing the formula (4), it is possible to write the following z-transform relation:<maths id="math0010" num="(5)"><math display="block"><mrow><mtext mathvariant="italic">S</mtext><mtext>(</mtext><mtext mathvariant="italic">z</mtext><mtext>) = </mtext><mtext mathvariant="italic">A</mtext><mtext>(</mtext><mtext mathvariant="italic">z</mtext><mtext>)</mtext><msub><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow></msub><mtext>(</mtext><mtext mathvariant="italic">z</mtext><mtext>)+</mtext><mtext mathvariant="italic">B</mtext><mtext>(</mtext><mtext mathvariant="italic">z</mtext><mtext>) </mtext><msubsup><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow><mrow><mtext>'</mtext></mrow></msubsup><mtext> (</mtext><mtext mathvariant="italic">z</mtext><mtext>)</mtext></mrow></math><img file="EP0719005A2_D0010.tif" /></maths>

Let us decompose the terms K_i(z) in terms with even index and odd index coefficient of the filter, it is possible to write:<maths id="math0011" num="(6)"><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow></msub><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced><mtext>=</mtext><msubsup><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow><mrow><mtext mathvariant="italic">a</mtext></mrow></msubsup><mfenced open="(" close=")"><mrow><msup><mrow><mtext mathvariant="italic">z</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></mrow></mfenced><mtext>+</mtext><msup><mrow><mtext mathvariant="italic">z</mtext></mrow><mrow><mtext>-1</mtext></mrow></msup><msubsup><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow><mrow><mtext mathvariant="italic">b</mtext></mrow></msubsup><mfenced open="(" close=")"><mrow><msup><mrow><mtext mathvariant="italic">z</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></mrow></mfenced></mrow></math><img file="EP0719005A2_D0011.tif" /></maths>    and to define <i>b</i>'(<i>n</i>)=<i>W</i><maths id="math0012" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">i</mtext></mrow><mrow><mtext mathvariant="italic">N</mtext></mrow></mfrac></mrow></math><img file="EP0719005A2_D0012.tif" /></maths>·<i>b</i>(n)

In virtue of the relations (4) we get:<maths id="math0013" num="(7)"><math display="block"><mrow><msubsup><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow><mrow><mtext>'</mtext></mrow></msubsup><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced><mtext>=</mtext><msubsup><mrow><mtext mathvariant="italic">W</mtext></mrow><mrow><mtext mathvariant="italic">N</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow></msubsup><msub><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow></msub><mfenced open="(" close=")"><mrow><mtext>-</mtext><mtext mathvariant="italic">z</mtext></mrow></mfenced></mrow></math><img file="EP0719005A2_D0013.tif" /></maths>    and replacing (6) and (7) in (5) we obtain:<maths id="math0014" num="(8)"><math display="block"><mrow><mtext mathvariant="italic">S</mtext><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced><mtext mathvariant="italic">=</mtext><mfenced open="[" close="]"><mrow><mtext mathvariant="italic">A</mtext><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced><mtext>+</mtext><mtext mathvariant="italic">B'</mtext><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced></mrow></mfenced><msubsup><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow><mrow><mtext mathvariant="italic">a</mtext></mrow></msubsup><mfenced open="(" close=")"><mrow><msup><mrow><mtext mathvariant="italic">z</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></mrow></mfenced><mtext>+</mtext><msup><mrow><mtext mathvariant="italic">z</mtext></mrow><mrow><mtext>-1</mtext></mrow></msup><mfenced open="[" close="]"><mrow><mtext mathvariant="italic">A</mtext><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced><mtext mathvariant="italic">-B'</mtext><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced></mrow></mfenced><msubsup><mrow><mtext mathvariant="italic">K</mtext></mrow><mrow><mtext mathvariant="italic">i</mtext></mrow><mrow><mtext mathvariant="italic">b</mtext></mrow></msubsup><mfenced open="(" close=")"><mrow><msup><mrow><mtext mathvariant="italic">z</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></mrow></mfenced></mrow></math><img file="EP0719005A2_D0014.tif" /></maths>

The interpretation of the equation (8) results in the definition of the scheme of a unit FP(k_i) with a structure shown in Fig. 10, in which the unit <i>W</i><maths id="math0015" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext mathvariant="italic">N</mtext></mrow></mfrac></mrow></math><img file="EP0719005A2_D0015.tif" /></maths> represents a multiplier by a constant, and the unit z^-1 represents a sample delay unit.

In this way the complexity of two distinct polyphase networks can be practically halved.

This simplification results in the complete block scheme shown in Fig. 11 which, as said before, has been synthesized as a SCS transmitter for convenience.

Naturally these manipulations have no importance for the transmitter of an OFDM system, but for a receiver. In virtue of the specular relation between transmitter and receiver, a final demodulator block scheme for OFDM receivers with eight subchannels with fractionally spaced outputs according to the present invention is shown in Fig. 12.

Naturally, as shown in Fig. 13, the units FP_R(k_i) are essentially identical with the units FP(k_i) defined for the hypothetical case of a transmitter with the only difference that the unit z introduces the anticipation of a sample and <i>W</i><maths id="math0016" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">-n</mtext></mrow><mrow><mtext mathvariant="italic">N</mtext></mrow></mfrac></mrow></math><img file="EP0719005A2_D0016.tif" /></maths> represents the multiplication by a constant. The multiplication by constant carried out by the unit <i>W</i><maths id="math0017" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">-n</mtext></mrow><mrow><mtext mathvariant="italic">N</mtext></mrow></mfrac></mrow></math><img file="EP0719005A2_D0017.tif" /></maths> represents, in the frequency domain, a modulation with a certain frequency, and carrying out the arrangement of the flows in groups at the inputs of the respective DFT processors, the relative units <i>W</i><maths id="math0018" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">-n</mtext></mrow><mrow><mtext mathvariant="italic">N</mtext></mrow></mfrac></mrow></math><img file="EP0719005A2_D0018.tif" /></maths> may be transferred after the respective DFT processor.

The rearrangement of the N output flows and the possible filtering carried out in the unit Rearr&amp;postfilter restores the coherence to the original arrangement of the eight output flows from the units FP_R(k_i), and realizes a possible filtering by means of a bank of ordinary filters, <u>not sampled</u>, in substitution of the sampled filters F(f) of unit A defined by the splitting-up of the original SCS unit according to the schemes of Fig. 5 and 6.

As final result we get an OFDM demodulator structures <u>with efficient implementation</u> which produces N output signals with a halved sampling period.

With reference to a generic OFDM system scheme shown in Fig. 14 the structure of the receiver provides for the presence of a post-process unit for the N flows before the equalization unit. Modifying the structure SCS_R of the demodulator according to the invention, it is necessary to modify the post-process unit in order to work at the multiple rate of the output flows of the demodulator. The functions normally carried out in the modified post-process unit will depend on the particular scheme of the demodulator, but these may essentially consist in one or more of the following functions: rearrangement of the flows, modulation, conjugation, extraction of the real part, multiplication by one complex constant and delay of T/2^k according to the common processing techniques used in these systems. The major part of the components do not require modifications if designated to work also at the multiple rate of the flows, with the exception of the modulators which, in function of the frequency increase, will have to be replaced by suitable modulators.

Returning for the moment to the decomposition scheme H(f)=F(f)K(f) of the Fig. 5 and 6, it is evident that the decomposition is not unique. The diagrams of Fig. 15 show in an exemplifying way the needs in domain of frequency of the filters K(f) and F(f) for three distinct decomposition cases of the reference filter H(f) of the original SCS.

In the case of an OFDM-PS system, analysing the problem in z-domain (time), the filters F(z) perform a preliminary (or completion in the case of a receiver) shaping of the pulse which is therefore completed (or preliminarily carried out in the case of a receiver) by the filter K(z). The first decomposition case illustrated in Fig. 15 concerns a sampling system in which f(t) is the sampled version of the filter h(t); it is possible to demonstrate that the filter K(z) may be defined by the polynominal ratio (according to the notation of z-transform):<maths id="math0019" num=""><math display="block"><mrow><mtext mathvariant="italic">K</mtext><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced><mtext>=</mtext><mfrac><mrow><mtext mathvariant="italic">H</mtext><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced></mrow><mrow><mtext mathvariant="italic">F</mtext><mfenced open="(" close=")"><mrow><msub><mrow><mtext mathvariant="italic">z</mtext></mrow><mrow><mtext>1</mtext></mrow></msub></mrow></mfenced></mrow></mfrac></mrow></math><img file="EP0719005A2_D0019.tif" /></maths>    where z₁ = z^N/2

In this particular case the problem is that H(z) is in general not exactly divisible by F(z₁), so that the filter K(z) has an IIR format, and therefore an approximation is necessary to obtain again a FIR format of the filter. This first type of decomposition may be considered as a combination of a shaping carried out exclusively by the filter F(z₁) and of a cancellation of the undesired periodical repetitions made by the filter K(z).

The second splitting case by pure interpolation may be realized by a filter F(z₁)=F₀, i.e. by a pure interpolator, and all computational complexity is shifted to the filter H(z).

In a third possible case of the intermediate type, the shaping function is distributed on both filters F(z₁) and K(z). In this case the problem of the decomposition of the filter H(z) can be considered as a problem of approximating the function H(z) by the product K(z)F(z₁). A possible solution of this problem is to consider a multirate decomposition of H(z):<maths id="math0020" num=""><img file="EP0719005A2_D0020.tif" /></maths>    where Q = log₂ N-1.

The decomposition can only be realized with a certain degree of precision (based on the frequency domain requirements), but there is a processing method which is suitable to define immediately the filters K(z) and F(z₁) as:<maths id="math0021" num=""><math display="block"><mrow><mtext mathvariant="italic">K</mtext><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced><mtext>=</mtext><msub><mrow><mtext mathvariant="italic">L</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mfenced open="(" close=")"><mrow><mtext mathvariant="italic">z</mtext></mrow></mfenced><msub><mrow><mtext mathvariant="italic">L</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msup><mrow><mtext>(z</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><mtext>)...</mtext><msub><mrow><mtext mathvariant="italic">L</mtext></mrow><mrow><mtext mathvariant="italic">Q</mtext><mtext>-1</mtext></mrow></msub><mtext>(z</mtext><msup><mrow><mtext>​</mtext></mrow><mrow><msup><mrow><mtext>2</mtext></mrow><mrow><mtext mathvariant="italic">Q</mtext><mtext>-1</mtext></mrow></msup></mrow></msup><mtext>),     </mtext><mtext mathvariant="italic">F</mtext><mfenced open="(" close=")"><mrow><msub><mrow><mtext mathvariant="italic">z</mtext></mrow><mrow><mtext>1</mtext></mrow></msub></mrow></mfenced><mtext>=</mtext><msub><mrow><mtext mathvariant="italic">L</mtext></mrow><mrow><mtext mathvariant="italic">Q</mtext></mrow></msub><mtext>(</mtext><mtext mathvariant="italic">z</mtext><msup><mrow><mtext>​</mtext></mrow><mrow><msup><mrow><mtext>2</mtext></mrow><mrow><mtext mathvariant="italic">Q</mtext></mrow></msup></mrow></msup><mtext>)</mtext></mrow></math><img file="EP0719005A2_D0021.tif" /></maths>

For instance, given a filter for N=512 with coefficient number of the filter H(f), M_H=4096 (P = 8 taps per subchannel), it is possible to obtain a decomposition with the same frequency characteristics of the filter H(f) employing a filter K(z) with 1473 taps and a filter F(z₁) with 13 taps.

Application of the invention to a full complex scheme

Referring again to a transmitter for convenience reasons, an OFDM transmitter can be implemented according to a scheme which carries out a final extraction of the real part of a signal <b>[1]</b>. This operation implies that the computations carried out on the transmitter are redundant as the imaginary part of the generated signal is discarded. The synthesis of an OFDM architecture suitable to manage a complex signal so that a double number of subchannels can be modulated with the same computional complexity of the modulator described in the publication <b>[1]</b>, obtaining in this way full efficiency, is the subject of the mentioned previous patent EP 668678 and published in the report <b>[4]</b> recently presented at the convention GLOBECOM 94. Fig. 16 shows a basic block scheme of the transmitter part of an OFDM system with Full Complex Scheme according <b>[1]</b> and <b>[4]</b>, which content has been incorporated here for explicit reference.

Applying the theorem of an efficient implementation and applying the structure division process according to the method of the present invention with the aim of achieving the definition of a demodulator with fractionally spaced outputs for the receiver part, the following condition has to be satisfied:<maths id="math0022" num=""><math display="block"><mrow><mtext mathvariant="italic">H'(f)</mtext><mtext> = </mtext><mtext mathvariant="italic">H"(f -F)</mtext></mrow></math><img file="EP0719005A2_D0022.tif" /></maths>

Through the necessary processing the structure of Fig. 16 can be converted in a structure similar to the one shown in Fig. 17 in which the <u>two</u> polyphase networks are pointed out, a first one determined by the efficient implementation of the Fully Complex Scheme according to what described in <b>[1]</b> and <b>[4]</b>, while the other polyphase network results from an efficient implementation process of the fractioning of the two original SCSs, according to the method of the present invention.

Moreover in virtue of the near similarity of the units FP(k'_i) and of the units FP(k"_I) of both polyphase networks and of the orthogonal characteristics of the signals OFDM, it is possible, through the same block simplification procedure already applied for the definition of the two distinct block arrangements FP of the two polyphase networks, to sum up the two FP units as schematized in Fig. 18, achieving in this way the definition of a new complex unit FPP(k_i') with the structure illustrated in Fig. 19. Even in this case we obtain a halving of the computational complexity.

The multiplication by the constant <i>W</i><maths id="math0023" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext>2</mtext><mtext mathvariant="italic">i</mtext></mrow><mrow><mtext mathvariant="italic">N</mtext></mrow></mfrac></mrow></math><img file="EP0719005A2_D0023.tif" /></maths> of each complex unit FPP(k_i) can be transferred before the processor (IDFT) by a reordering of the input flows. For the specular conditions the final block scheme of the demodulator with fractioned outputs of a receiver is schematically shown by Fig. 20. Naturally in this case the function of multiplication by constant is transferred after the corresponding processor DFT.

Application to an OFDM-NPS system (without Pulse Shaping)

An OFDM-NPS system is composed by an SCS whose reference filter is a rectangular pulse:<maths id="math0024" num=""><img file="EP0719005A2_D0024.tif" /></maths>

In this case the polyphase filters may be replaced by a simple multiplication by a constant. In particular the units FP(k_i) become simpler, as way indicated in Fig. 21 and 22, for the case of the transmitter and for the case of the receiver respectively. The scheme of a filterless demodulator with fractioned outputs realized according to the present invention is shown in Fig. 23.

Extension to a subdivision by T/4

The fractioning and resynthesis method of the invention makes it possible to define a demodulator with fractioned outputs even with fractioning periods of the output flows inferior to T/2 of the examples illustrated until now.

The scheme of Fig. 24 shows the synthesis of a demodulator with T/4 fractionally spaced outputs. In this case the original unit SCS with N branches turns out to be virtually subdivided in four SCSs with N/4 branches which, according to an efficient implementation comprises the use of four distinct processors with N/4 branches. Even in this case the arrangement in groups of the output flows from the complex units FG(k_i) (which in this case are in a number of four per block) makes it possible to transfer the multiplication function per constant after of the respective processor DFT.

<u>Bibliography</u>:

<ul id="ul0006" list-style="none" compact="compact"><li><b>[1]</b> B. Hirosaki, "An Orthogonally Multiplexed QAM System using Discrete Fourier Transform", IEEE Trans. on Communications, COM-29, No. 7, July 1981.</li><li><b>[2]</b> B. Hirosaki, "An Analysis of Automatic Equalizers for Orthogonally Multiplexed QAM Systems", IEEE Trans. on Communications, COM-28, no. 1, pp 73-83, January 1980.</li><li><b>[3]</b> G. Cariolaro, G. Michieletto, L. Vangelista, "A Comparison between two OFDM Modulation Systems for Digital Terrestrial Television Broadcasting", HDTV '93 Proceedings, session 4B.</li><li><b>[4]</b> G. Cariolaro, "An OFDM Scheme with Half Complexity", GLOBECOM '94 Conference Proceedings.</li></ul>