Method of channel estimation and corresponding receiver

0001The field of the invention is that of the transmission of digital data, in particular in transmission channels having, or which may have, high Doppler fading and low symbol interference (IES). More specifically, the invention relates to the estimation of the transmission channel and the demodulation in receivers of signals transmitted through such channels.

0002A preferred, although not exclusive, field of application of the invention is that of digital communications between satellites and mobiles. It can be considered in particular within the framework of the ICO and Iridium projects. More generally, the invention advantageously applies in all communications systems where the channel has a high Doppler and a low IES.

0003In conventional digital communications systems, synchronization symbols are frequently used. They allow the receiver not only to synchronize, but also to properly estimate the channel to guarantee a good progress of the demodulation phase.

0004In the case of these conventional communication systems, the synchronization symbols are consecutive and form a synchronization sequence, generally placed at the start of the data streams. Synchronization at the receiver is achieved by detecting that the correlation of the samples received with those of the sequence used for synchronization has exceeded the threshold. This synchronization allows on the one hand the detection of the start of a data train and on the other hand the determination with precision of the instants of maximum opening of the diagram of the eye.

0005In the framework of studies carried out for the GSM system, we sought to construct synchronization sequences adapted to the low Doppler and high IES fading channels. These studies have shown the interest, for this kind of channels, of placing these synchronization sequences in the middle of each data stream.

0006The proposed synchronization sequence patterns lead to intuitive and simple to implement synchronization and channel estimation algorithms. They have therefore been adopted in several digital communications systems.

0007They are also envisaged in satellite telephony projects. However, they prove to be much less effective for this type of channel, and lead to significant limitations in terms of performance when tackling high Doppler and low IES channels, such as a satellite channel.

0008The basic principle of time synchronization and channel estimation by the receiver is to transmit a sequence of symbols known to the receiver in the data streams sent by the transmitter. By using a few predefined algorithms, these symbols are used to guarantee not only good synchronization of the receiver, but also a reliable estimate of the channel, thus allowing a good progress of the demodulation phase.

0009In known systems, a synchronization pattern is used which consists of a sequence of grouped symbols having good correlation properties. These properties are mainly used to synchronize well at the receiver. In the framework of radio-mobile communication systems, such as GSM, the channel is almost static during a data train but nevertheless presents very severe IES. These correlation properties then prove to be well suited and even necessary for a simple and direct estimation of the impulse response of the channel.

0010These synchronization sequences can be used in communications systems between satellites and mobiles. It should however be noted that if the channels encountered in this type of application have negligible IES compared to the symbol rate, their variations in the level of received data streams are very large. In other words, the transmission channel cannot then be considered as quasi-static during the duration of a data train (in terms of time-frequency representation, we can say that these channels are the dual of those presented here. -above).

0011Therefore, the use of a conventional synchronization sequence in this type of system is purely arbitrary, and only solves the only synchronization problem at the receiver.

0012More precisely, if the choice of group synchronization in the context of quasi-static channels with high IES (classic case of GSM in particular) is well founded, it is not necessarily the same for channels with high Doppler and low IES. These present considerable variations in the level of data trains received. The sequence of conventional synchronization symbols can guarantee good synchronization of the receiver. On the other hand, the quality of the channel estimation is severely compromised, since it is not representative of the state of the channel during the reception of the useful data from a data stream.

0013Classic synchronization is therefore not suitable for systems communicating through a high Doppler channel, for the channel estimation and demodulation function.

0014The invention particularly aims to overcome these drawbacks of the state of the art, in digital transmission systems organized in data trains, and which may be confronted, at least in certain situations and / or at certain times, with high Doppler channels, which cannot be considered as quasi-static over the duration of a data train.

0015More specifically, one of the objectives of the invention is to provide digital signal structures suitable for transmission in high Doppler channels, and in particular making it possible to perform reliable channel estimation and demodulation in all circumstances.

0016Another objective of the invention is to provide such signals making it possible to optimize simultaneously, in the receivers, the synchronization, the quality of the channel estimation and, if necessary, the efficiency of the interleaving of the coded data. . In other words, it must achieve a compromise between good synchronization, good estimation of the channel at the receiver and good interleaving of the coded data.

0017The invention also aims to provide such signals which are simple to construct, at the level of the transmitters, and simple to decode and analyze in the receivers. Another objective of the invention is also to limit the losses in useful throughput, and therefore to limit the number of reference data required.

0018Another object of the invention is to provide methods of channel estimation, and corresponding receivers, adapted to such signals and, more generally, which can manipulate arbitrary synchronization patterns.

0019A complementary objective of the invention is to provide a channel estimator which can significantly improve its performance by taking into account all or part of the coded structure of the transmitted data.

0020These objectives, as well as others which will appear subsequently, are achieved according to the invention using digital signals organized in data trains, in each of which at least two blocks of distinct reference elements are distributed among the useful data.

0021In other words, the invention relates in particular to a digital signal, organized in consecutive data streams each comprising a predetermined number of successive symbols, and intended to be transmitted to at least one receiver, in a transmission channel which may have variations. notable within a data stream, each of said data streams comprising at least two distinct reference blocks for estimating said channel, distributed among the useful symbols representative of the source signal to be transmitted, each of said reference blocks being formed by at least one reference symbol (also sometimes called subsequently synchronization symbol, when it is also used for synchronization) known to the receiver and / or identifiable by said receiver.

0022The signal of the invention therefore has a structure quite different from that of conventional signals, in which the reference symbols, used to estimate the channel, are systematically grouped into a single synchronization block (generally at the start of the data stream , or possibly in the middle of it).

0023The solution of the invention, which goes against this conventional technique, provides an effective response to the problems associated with high Doppler channels. In addition to the fact that the structure of the signal (distribution of the reference blocks) is completely new, it should be noted that it is by no means obvious to a person skilled in the art, in particular because it is not compatible with conventional methods of channel estimation and decoding using a single reference block. As will be seen below, the invention also relates to new and specific methods and devices for the use of such signals.

0024The reference symbols present in the reference blocks of the invention can be of two types. It could be:<ul id="ul0001" list-style="dash" compact="compact"><li>explicit reference symbols, fixed and known a priori by said receiver; and / or</li><li>implicit reference symbols, produced by links generated between useful symbols by coding. According to a particular embodiment, these implicit reference symbols can correspond to the repetition of a useful symbol, at a predetermined location in said data stream. These implicit reference symbols are therefore obtained in this case using a repetitive code.</li></ul>

0025When the desired performance for the application is compatible with the use of coding, in particular repetition, the two types of reference symbols can be used, the implicit reference symbols being used to optimize the information obtained from the using explicit reference symbols. In the case where there are only implicit reference symbols, it may be necessary to provide a means for removing the phase ambiguity of the carrier which appears on reception.

0026Preferably, said reference blocks are equally distributed within the data stream.

0027As mentioned above, the signal of the invention requires the use of new estimation methods.

0028Thus, a first method for estimating a transmission channel of such a digital signal (organized in consecutive data trains comprising at least two distinct reference blocks for estimating said channel, distributed among the useful symbols representative of the signal source to transmit, each of said reference blocks being formed by at least one reference symbol known to the receiver and / or identifiable by said receiver) implements an Estimation-Maximization (EM) algorithm [2-6] (the references numbered thus are grouped together in a list in the appendix) comprising the following steps, for each of said data streams:<ul id="ul0002" list-style="dash" compact="compact"><li>extracting and / or determining said explicit reference symbols;</li><li>use of said explicit reference symbols, to obtain a first estimate of said transmission channel;</li><li>first estimate of said useful symbols, based on said first estimate of the transmission channel;</li></ul>    and, if necessary (depending for example on the quality of the estimate obtained and the desired precision), at least one iteration of the following steps:<ul id="ul0003" list-style="dash" compact="compact"><li>determination of a second, more precise estimate of said transmission channel, as a function of said first estimate of useful symbols (which may include in particular implicit reference symbols);</li><li>second estimation of said useful symbols, as a function of said second estimation of the transmission channel.</li></ul>

0029According to a particular embodiment, usable in particular when the code implemented is simple (not requiring the calculation of probabilities, for example), said step of second estimation of said useful symbols can be integrated into said step of determining a second transmission channel estimation, the estimation of useful symbols being used directly in the calculation of the transmission channel estimation.

0030In other words, an estimation of the channel is then carried out with implicit estimation of the data.

0031A second method for estimating a transmission channel of such a digital signal comprises a step of writing said estimate in the form of a combination of predetermined basic functions, with a bandwidth greater than or equal to that of the Doppler power spectrum (SPD) of said signal.

0032Preferably, said basic functions are restrictions of discrete flattened spheroidal sequences (SSAD, known in the English literature under the name of "Discrete Prolate Spheroidal Sequences") [8].

0033This type of function makes it possible to obtain a very precise estimate of the channel, from a reduced number of basic functions (for example 3 to 8).

0034According to an advantageous embodiment of the invention, this method comprises a preliminary step of adaptation of the characteristics of said basic functions, in particular as a function of said Doppler power spectrum.

0035A base is thus obtained which is best suited to the channel to be estimated.

0036The invention also relates, of course, to the channel estimation devices and the receivers implementing the methods described above, as well as the signal transmitters and receivers according to the invention.

0037Other characteristics and advantages of the invention will appear on reading the following description of a preferred embodiment of the invention, given by way of simple illustrative and nonlimiting example, and of the appended drawings, among which:<ul id="ul0004" list-style="dash" compact="compact"><li>Figure 1 is a block diagram of a signal transmitter according to the invention;</li><li>FIG. 2 is a block diagram of a receiver according to the invention, capable of receiving the signals of the invention;</li><li>FIG. 3 schematically illustrates the principles of the estimation of the transmission channel according to the invention;</li><li>FIG. 4 shows the operation of a receiver implementing a method according to the invention;</li><li>FIG. 5 illustrates the rapid decrease of the eigenvalues ​​of the correlation matrix of the discrete channel at the level of the transmitted data streams;</li><li>FIGS. 6A to 6G illustrate the eigenvectors corresponding to the most significant eigenvalues ​​of the correlation matrix of the discrete channel at the level of the transmitted data streams;</li><li>FIG. 7 illustrates the weightings of the eigenvectors, of the correlation matrix of the discrete channel at the level of the transmitted data streams, used in the estimation of the channel by the receiver.</li></ul>

1 . General

0038The invention therefore applies in particular to stationary channels with low IES with SPDs of any width and shape. In particular, these channels can be of the Rice or Rayleigh type with horn or flat SPDs. In particular, they can include the case of a static offset in frequency resulting from a partial correction of the frequency error of the local oscillator at the level of the receiver. This correction is generally accomplished by a conventional phase locked loop.

0039The invention provides a new signal structure, in which several reference blocks are distributed in each data stream.

0040Thus, an objective of the invention is to provide the most suitable synchronization pattern for a Doppler channel and a system for communication of given characteristics. This pattern must be sufficiently distributed over a more or less extensive part of the data streams to characterize and estimate at best the significant variations of the channel and distribute the coded data as well as possible. It should therefore not favor the performance of the receiver in terms of synchronization at the cost of sacrificing the quality of the channel estimation and the interleaving of the coded data.

0041The corresponding channel estimation method proposed according to the invention is based in particular on a suitable modeling of the real channel and a new and simplified representation thereof.

0042This representation should take into account as much as possible all the information known on the channel. This information must include at least the maximum width of the Doppler band, which must be known to the receiver.

0043In the case where the shape of the SPD of the channel is not known, the algorithm adopts a flat modeling of this one. This modeling is best suited from the point of view of information theory because it leads to maximum channel entropy [7]. In this case, the discrete channel can be written as a combination of the restrictions on discrete flattened spheroidal sequences (SSAD) on the support of the data stream to be demodulated. These SSADs have a narrow band of width equal to or greater than that of the SPD.

0044There are essentially two criteria that can be used to estimate one of the unknown parameters: the maximum likelihood criterion (MV) and the posterior maximum criterion (MAP) [1]. In the case of the MV criterion, the parameters are assumed to be deterministic but unknown. In the case of the MAP criterion, these parameters are assumed to be random and characterized by an a priori known probability density (PD).

0045The MV criterion is best suited to the problems of estimating the energy per symbol emitted or the variance of noise at the output of a given filter, when these are not known by the receiver. The MAP criterion is best suited to the problem of estimating the discrete channel at the level of transmitted data streams.

0046By means of the simplified representation of the channel developed by the inventors and presented subsequently, and (not necessarily) the reference symbols sent by the transmitter, the receiver implements the EM algorithm to perform an iterative estimation of a part or of all of these parameters according to the corresponding criteria.

0047In other words, this algorithm makes it possible to find the most likely channel realization conditionally on the signal observed at the receiver. It also makes it possible to best estimate the energy per symbol transmitted and / or the noise variance at the output of a given filter when these are not fully known.

0048One of the advantages of the EM algorithm is to be able to optimally use both synchronization symbols (explicit reference) and all or part of the characteristics of the information symbols (implicit reference) composing a train of data to complete channel estimation. More precisely, this algorithm makes it possible to advantageously use the coding undergone by the information data sent to significantly improve the quality of the channel estimation. It also makes it possible to take account of the memory possibly due to the modulation used.

0049This algorithm avoids the systematic use of classical grouped synchronization patterns, which owe their success to their immediate exploitation by intuitive and simple algorithms.

0050The choice of the location of the reference symbols in the data streams is indeed important for the performance of the channel estimator. It is also of capital importance in the correct determination of the initial conditions of the EM algorithm. Indeed, this generally tends to converge towards local maxima of the conditional probability (defined as the posterior probability of a realization of the channel conditionally on the received signal), if the location of the synchronization symbols is poorly chosen.

0051With the aid of the channel estimation, the receiver performs in a standard manner a demodulation and / or a decoding of the information data received according to the criterion of the MV.

2. Principle of a transmitter

0052Figure 1 shows a simplified block diagram of a transmitter of a data train signal according to the invention. The emission process is directly deduced therefrom.

0053We consider an information source 11 of arbitrary rate generating binary data or not corresponding to source signals of any type (sounds, images, data, etc.). These data are possibly subjected to a source coding 12, followed by an error correcting coding 13 adapted to the Rice type channels without IES.

0054The coded data generated from these codes (useful symbols) are then organized into data streams and modulated (14). They are therefore suitably distributed and interleaved on several data streams in order to provide the necessary diversity and to decorrelate the fading affecting the symbols transmitted. Reference elements are also introduced into each data stream, according to the distribution principles specified below. Finally, the data is modulated in phase.

0055The baseband signal generated by the modulator 14 is obtained by filtering the formatting of the symbols making up this train. In the case of MDP2 and MDP4 modulations, the shaping filter is generally a Nyquist root filter to avoid any IES at the output of the adapted filter from the receiver. The baseband signal thus generated is then transposed in frequency, amplified and transmitted (15) through the channel.

3. Example: the ICO system

0056By way of example, the emission characteristics of the Intermediate Circular Orbit (ICO) system for satellite radio communication are presented here, to which the invention advantageously applies.

0057This system is based on a time division multiple access technique (TDMA). It is based on data frames, each composed of 6 time slots (known in English as "time slots"). These frames are transmitted in the uplink (mobile-satellite) and downlink (satellite-mobile) directions for both voice and signaling channels. Each time interval corresponds to a transmitted data train composed of<i>NOT</i> = 120 or 240 symbols, depending on the case.

0058The set of logical channels used by the ICO system is very close to that of GSM. It comprises, in particular, a TCH channel (“Traffic CHannel”) at the level of the uplink and downlink, a BCCH channel (“Broadcast Common Channel”) at the level of the downlink and a RACH channel (“Random Access Channel”) at the uplink.

0059The modulation adopted for the downlink is MDP4 for TCH and MDP2 for BCCH. In these two cases, the number of symbols per data stream is 120 (1 bit per symbol in MDP2; 2 bits per symbol in MDP4). The GMSK modulation with continuous phase, and therefore with memory, is retained at the level of the uplink, for reasons of non-linearity at the level of the mobile transmitters. The number of symbols transmitted is 240 for the TCH, and 120 for the RACH. In both cases, a transmitted symbol corresponds to a transmitted bit.

0060Each logical channel has its own channel coding and interleaving techniques. However, this coding and this interleaving are organized so as to allow, as much as possible, to unify the structure of the decoder. Each logical channel can implement the following sequence of operations (each of these operations being optional):<ul id="ul0005" list-style="dash" compact="compact"><li>the bits of information are coded with an external code in a cyclic and systematic block;</li><li>the binary elements resulting from this coding are then coded by the internal code, either of extended Golay type, or of convolutional type;</li><li>the encoded bits are then encoded using a repeating code;</li><li>the coded bits obtained are finally interleaved with an interleaving function.</li></ul>

0061Among other things, the RACH channel conveys the identity of a mobile terminal that wants to access the services of the ICO system. It requires a larger link margin than traffic channels. For this reason, it implements a Golay code followed by a repeating code (3.13).

0062According to the invention, the reference symbols are distributed in several blocks (of at least one symbol) in each data stream.

0063The number of symbols used for synchronization depends on the characteristics of the actual transmission channel.

0064The transmission channel underlying the logical channel TCH is a Rice type channel (that is to say consisting of a direct path and a multipath part with a relative delay almost zero relative to the latter. ) presenting a report <i>K</i> between the power of the direct path and that of the favorable multi-path, with values of the order of 7 to 12 dB. The TCH channel can use as references only 10% of the symbols of the data stream, that is to say 12 reference symbols per data stream transmitted for the downlink, and 24 reference symbols per data stream transmitted for the uplink.

0065These symbols can be uniformly distributed, one by one, two by two or four by four over an entire data stream (reference blocks comprising 1, 2, or 4 reference symbols).

0066For a better calculation of the initial conditions for the estimation of the discrete channel, it is advised to implement one of the first two forms of synchronization for the downlink.

0067Table 1 illustrates a layout mode in which the reference blocks include 2 reference symbols. This implantation is used for the TCH channel of the downlink.<tables id="tabl0001" num="0001"><table frame="all"><title>Table 1</title><tgroup cols="3" colsep="1" rowsep="1"><colspec colnum="1" colname="col1" colwidth="52.50mm" /><colspec colnum="2" colname="col2" colwidth="52.50mm" /><colspec colnum="3" colname="col3" colwidth="52.50mm" /><thead valign="top"><row><entry namest="col1" nameend="col1" align="center">symbol no.</entry><entry namest="col2" nameend="col2" align="center">field length</entry><entry namest="col3" nameend="col3" align="center">content of the field</entry></row></thead><tbody valign="top"><row><entry namest="col1" nameend="col1" align="center">0-1</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">guard symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">2-8</entry><entry namest="col2" nameend="col2" align="center">7</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">9-10</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">11-28</entry><entry namest="col2" nameend="col2" align="center">18</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">29-30</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">31-48</entry><entry namest="col2" nameend="col2" align="center">18</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">49-50</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">51-68</entry><entry namest="col2" nameend="col2" align="center">18</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">69-70</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">71-88</entry><entry namest="col2" nameend="col2" align="center">18</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">89-90</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">91-108</entry><entry namest="col2" nameend="col2" align="center">18</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">109-110</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">111-117</entry><entry namest="col2" nameend="col2" align="center">7</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row rowsep="1"><entry namest="col1" nameend="col1" align="center">118-119</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">guard symbols</entry></row></tbody></tgroup></table></tables>

0068For the uplink, the third form (table 2) is the most suitable, because it makes it possible to overcome the memory of the GMSK modulation at lower cost when choosing the initial conditions. In this particular case, only part of the waveform corresponding to the blocks of four reference symbols is used for the calculation of these initial conditions.<tables id="tabl0002" num="0002"><table frame="all"><title>Table 2</title><tgroup cols="3" colsep="1" rowsep="1"><colspec colnum="1" colname="col1" colwidth="52.50mm" /><colspec colnum="2" colname="col2" colwidth="52.50mm" /><colspec colnum="3" colname="col3" colwidth="52.50mm" /><thead valign="top"><row><entry namest="col1" nameend="col1" align="center">symbol no.</entry><entry namest="col2" nameend="col2" align="center">field length</entry><entry namest="col3" nameend="col3" align="center">content of the field</entry></row></thead><tbody valign="top"><row><entry namest="col1" nameend="col1" align="center">0-3</entry><entry namest="col2" nameend="col2" align="center">4</entry><entry namest="col3" nameend="col3" align="center">guard symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">4-17</entry><entry namest="col2" nameend="col2" align="center">14</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">18-21</entry><entry namest="col2" nameend="col2" align="center">4</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">22-57</entry><entry namest="col2" nameend="col2" align="center">36</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">58-61</entry><entry namest="col2" nameend="col2" align="center">4</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">62-97</entry><entry namest="col2" nameend="col2" align="center">36</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">98-101</entry><entry namest="col2" nameend="col2" align="center">4</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">102-137</entry><entry namest="col2" nameend="col2" align="center">36</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">138-141</entry><entry namest="col2" nameend="col2" align="center">4</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">142-177</entry><entry namest="col2" nameend="col2" align="center">36</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">178-181</entry><entry namest="col2" nameend="col2" align="center">4</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">182-217</entry><entry namest="col2" nameend="col2" align="center">36</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">218-221</entry><entry namest="col2" nameend="col2" align="center">4</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">222-235</entry><entry namest="col2" nameend="col2" align="center">14</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row rowsep="1"><entry namest="col1" nameend="col1" align="center">236-239</entry><entry namest="col2" nameend="col2" align="center">4</entry><entry namest="col3" nameend="col3" align="center">guard symbols</entry></row></tbody></tgroup></table></tables>

0069The BCCH logical channel is in particular used by mobile terminals to perform synchronization at the level of data trains. The underlying real transmission channel is of the Rice type with a value of<i>K</i> of the order of 0 dB. For these two reasons, 32 explicit reference symbols are provided.

0070Table 3 illustrates the corresponding structure of the data stream. <tables id="tabl0003" num="0003"><table frame="all"><title>Table 3</title><tgroup cols="3" colsep="1" rowsep="1"><colspec colnum="1" colname="col1" colwidth="52.50mm" /><colspec colnum="2" colname="col2" colwidth="52.50mm" /><colspec colnum="3" colname="col3" colwidth="52.50mm" /><thead valign="top"><row><entry namest="col1" nameend="col1" align="center">symbol no.</entry><entry namest="col2" nameend="col2" align="center">field length</entry><entry namest="col3" nameend="col3" align="center">content of the field</entry></row></thead><tbody valign="top"><row><entry namest="col1" nameend="col1" align="center">0-1</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">guard symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">2-8</entry><entry namest="col2" nameend="col2" align="center">7</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">9-10</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">11-28</entry><entry namest="col2" nameend="col2" align="center">18</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">29-30</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">31-46</entry><entry namest="col2" nameend="col2" align="center">16</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">47-72</entry><entry namest="col2" nameend="col2" align="center">26</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols (synchronization word)</entry></row><row><entry namest="col1" nameend="col1" align="center">73-88</entry><entry namest="col2" nameend="col2" align="center">16</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">89-90</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">91-108</entry><entry namest="col2" nameend="col2" align="center">18</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">109-110</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">111-117</entry><entry namest="col2" nameend="col2" align="center">7</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row rowsep="1"><entry namest="col1" nameend="col1" align="center">118-119</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">guard symbols</entry></row></tbody></tgroup></table></tables>

0071Part of these symbols (synchronization word) can then be grouped in the middle of the data stream to maintain acceptable performance in terms of synchronization and determination of the maximum opening of the eye diagram, at the level of the receiver. The other part is then distributed over the rest of the data stream, as is the case for the logical channel TCH.

0072The RACH logical channel is used in the uplink by mobile terminals to request access to the services of the ICO system. The real underlying transmission channel is generally of the same type as that of the BCCH. Unlike the BCCH channel, which is repetitive, the RACH channel is transmitted in isolation, and must therefore be detected in a single pass. Therefore, the number of reference symbols is 44, (instead of 32 for the BCCH), as specified in Table 4.<tables id="tabl0004" num="0004"><table frame="all"><title>Table 4</title><tgroup cols="3" colsep="1" rowsep="1"><colspec colnum="1" colname="col1" colwidth="52.50mm" /><colspec colnum="2" colname="col2" colwidth="52.50mm" /><colspec colnum="3" colname="col3" colwidth="52.50mm" /><thead valign="top"><row><entry namest="col1" nameend="col1" align="center">symbol no.</entry><entry namest="col2" nameend="col2" align="center">field length</entry><entry namest="col3" nameend="col3" align="center">content of the field</entry></row></thead><tbody valign="top"><row><entry namest="col1" nameend="col1" align="center">0-1</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">guard symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">2-7</entry><entry namest="col2" nameend="col2" align="center">6</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">8-31</entry><entry namest="col2" nameend="col2" align="center">24</entry><entry namest="col3" nameend="col3" align="center">useful symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">32-47</entry><entry namest="col2" nameend="col2" align="center">16</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">48-71</entry><entry namest="col2" nameend="col2" align="center">24</entry><entry namest="col3" nameend="col3" align="center">useful symbols (repetition)</entry></row><row><entry namest="col1" nameend="col1" align="center">72-87</entry><entry namest="col2" nameend="col2" align="center">16</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row><entry namest="col1" nameend="col1" align="center">88-111</entry><entry namest="col2" nameend="col2" align="center">24</entry><entry namest="col3" nameend="col3" align="center">useful symbols (repetition)</entry></row><row><entry namest="col1" nameend="col1" align="center">112-117</entry><entry namest="col2" nameend="col2" align="center">6</entry><entry namest="col3" nameend="col3" align="center">explicit reference symbols</entry></row><row rowsep="1"><entry namest="col1" nameend="col1" align="center">118-119</entry><entry namest="col2" nameend="col2" align="center">2</entry><entry namest="col3" nameend="col3" align="center">guard symbols</entry></row></tbody></tgroup></table></tables>

0073As in the case of the BCCH logical channel, a part of these reference symbols can be grouped in order to form synchronization references (2 blocks of 16 symbols). However, since the GMSK modulation used is a memory modulation, the remaining reference symbols must also be grouped before being distributed over the rest of the train. This grouping (two blocks of 6 reference symbols) naturally allows the receiver to temporarily free itself from the modulation memory to calculate the initial conditions of the iterative channel estimation algorithm.

0074In this situation, there are therefore four reference blocks formed by 6 or 16 explicit reference symbols, and three blocks formed by 24 implicit reference symbols, corresponding to the repetition of the same useful symbols.

0075An advantageous compromise is therefore achieved between:<ul id="ul0006" list-style="dash" compact="compact"><li>the presence of relatively long reference blocks (6 or 16 symbols), facilitating synchronization;</li><li>interleaving the code repeatedly (3 blocks distributed over the data stream);</li><li>the number of blocks distributed (4 + 3) for the estimation of the channel.</li></ul>

0076As already indicated, the presence of explicit reference symbols is not compulsory, although it makes it possible to simplify processing. Implicit reference symbols only, obtained by repetition, can also be used. Furthermore, it is recalled that the use of a repetitive code is only an advantageous embodiment, by its simplicity, for obtaining the implicit reference symbols. Indeed, the latter can be obtained whatever the code used, by analyzing the links generated between the useful symbols by this code [6, 9].

0077When the two types of reference symbols are present, the implicit reference symbols are advantageously used to refine the estimation of the channel.

4. Principle of a receiver

0078Figure 2 illustrates an example of a signal receiver according to the invention as well as the corresponding reception method.

0079The signal corresponding to a received data stream is preamplified 31, then converted to intermediate frequency 32 in order to carry out the adapted filtering of channel 33. The signal to intermediate frequency is then converted to baseband 34 on two channels in quadrature, or on a single channel at low intermediate frequency, then sampled (37).

0080The sampled signal is then demodulated (39). Furthermore, it supplies a synchronization module 36 and a transmission channel estimation module 38.

0081The synchronization module 36 uses the synchronization sequence to estimate the symbol rate as well as the instants corresponding to the maximum opening of the eye digram of the baseband signal received. The signal is sampled (37) at these precise times.

0082The samples corresponding to a data stream are also used by the receiver to determine an estimate 38 according to the MAP criterion of the realization of the discrete channel at the level thereof. This estimation 38 is carried out by means of the simplified representation of the discrete channel at the level of the received data stream, the use of the EM algorithm and possibly of an algorithm such as that of Bahl [9].

0083This iterative algorithm, described below, starts from arbitrary initial conditions which can be advantageously obtained thanks to the synchronization symbols known to the receiver.

0084The synchronization distributed over the entire data train according to the invention proves to be of great utility because it makes it possible not only to avoid the convergence of the algorithm towards local maxima of the conditional probability, but also to accelerate this convergence at lower cost.

0085The receiver then uses the estimate 38 at the MAP of the discrete channel at the level of a received data train to demodulate 39 according to a given criterion the symbols carrying information of this train. The demodulator 39 can in particular provide weighted outputs in order to improve the performance of the decoder 310.

0086These outputs, weighted or not, are first of all deinterleaved 311 and grouped in accordance with the interleaving and the distribution carried out at the level of the transmitter, then decoded by the channel decoder 310. The demodulated data are then decoded by the decoder source 312, to provide an estimate of the source signal transmitted.

0087The channel estimation is also used by the receiver to control the progress of the preamplification 31, by means of the use of an automatic gain correction function (AGC) 35.

5. Example: the ICO system

0088By way of example, and in relation to FIG. 3, some of the characteristics of the receiver of the ICO system whose transmitter is presented in the previous section are presented below. At the level of the mobile terminals, the synchronization 41 of the data trains is carried out in a rough manner 411, initially, by virtue of the detection of the power profile on the logical channel BCCH.

0089This synchronization is then refined 412 by means of the symbols for synchronizing the data trains of the BCCH channel.

0090At the level of the space segment (formed, in the case of the ICO system, by all of the satellites and the earth stations, each satellite playing only a repeater role), the coarse 411 and fine 412 synchronizations are accomplished in the same way as by mobile terminals using the RACH logical channel.

0091At the level of the mobile terminals and the space segments, the estimation 421, 422 of the discrete channel at the level of a received data stream is carried out according to the criterion of the MAP. This estimation is carried out using the algorithm described below. The receiver firstly uses the synchronization symbols to establish suitable initial conditions 421 for the proper functioning of the iterative algorithm.

0092At this stage, he has no idea, even partial, of the values ​​probably taken by the coded information symbols. It then attributes to these information symbols uniform conditional probabilities with maximum entropy 431 (according to the method described more precisely below).

0093At the level of the downlinks, the symmetry of the constellations of the MDP2 for the BCCH and of the MDP4 for the TCH then leads to a zero contribution of the information symbols in the calculation of the initial conditions of the iterative algorithm 44 of estimation of channel. These initial conditions are then used by this algorithm to improve the estimation of the channel 422, this time taking into account the additional contribution 432 of the coded information symbols.

0094At the uplink level, the channel estimation at the level of the RACH and TCH logical channels follows roughly the same procedures as in the case of mobile terminals. The only difference here is that the GMSK modulation used in the uplink is a memory modulation.

0095As the synchronization symbols emitted by the mobiles are grouped on the basis of at least four by four symbols (in the case of TCH), the IES due to the modulation memory and to the adjacent unknown symbols does not affect the symbols in the middle of each grouping. These symbols in the middle of each grouping can then be used to calculate the initial conditions of the iterative algorithm. For the following iterations, the iterative algorithm then uses the GMSK modulation trellis to also take into account the remaining synchronization symbols and coded information symbols (for example using the Bahl algorithm).

0096In the particular case of the RACH channel, the reception of data trains by the space segment is done in an almost asynchronous manner. In addition, the implicit references corresponding to the 3 blocks of 24 symbols obtained by the repetition of a Golay code are used. This characteristic of the invention makes it possible to greatly improve the quality of the estimation of the channel, while also retaining a good quality of synchronization, thanks to the grouped explicit references.

0097The position chosen for the implicit reference symbols makes it possible to obtain a good interlacing of the words of the code with repetition (3,1,3). As the taking into account of the repetitive code (3,1,3) can be integrated directly into the estimation algorithm (in the case where the modulation memory can be neglected at the first order), it generates an imperceptible increase in the complexity of it.

6. Modeling and representation of the discrete channel according to the invention

0098One of the aspects of the invention is based on a new simplified modeling and representation of the discrete channel seen at the output of the adapted filter of the receiver at the level of the sent data streams.

6.1 Modeling of the transmission channel

0099The transmission channel is assumed to be of the Rice type. It consists of a direct path and a multi-path part with an almost zero relative delay with respect to the latter. The direct path is specified by a constant complex attenuation factor. The multipath part resulting from terrain reflections is characterized as a stationary Gaussian random process with zero mean [1, 16].

0100This channel is mainly characterized by two parameters. The first is the report,<i>K</i>, between the power of the direct path and that of multi-paths. The second parameter is the channel SPD function<i>S</i>_<i>VS</i>(<i>f</i>).

0101This function is a power spectrum which gives the intensity of the transmission channel as a function of the Doppler frequency. <i>f.</i> It is equal to the Fourier transform of the autocorrelation function φ_<i>VS</i>(τ) of the channel. It has a bounded width support<i>B</i>_D called Doppler extent of the canal. In the context of the invention, this extent is assumed to be small compared to the symbol rate 1 /<i>T</i> .

6.2 Modeling and characteristics of the transmitted and received signals

0102The invention can be applied to many types of modulation. In the context of satellite communications, it particularly concerns the reception of phase modulated data trains. This includes both conventional modulations (MDP2, MDP4, MDP8, MDP16, ...) as well as modulations with memory such as continuous phase modulations (MSK, GMSK, ...).

0103The baseband signal corresponding to a data stream transmitted from <i>NOT</i> symbols are written, in the case of a CDM modulation, in the form (easily adaptable to other types of modulation [1]):<maths id="math0001" num=""><img file="EP0802656A2_D0001.tif" /></maths>    or <i>T</i> is the symbol period, <i>x</i>(<i>t</i>) is a unit standard Nyquist root formatting filter and the <i>at</i>_<i>k</i> are complex symbols belonging to an arbitrary alphabet <i>AT</i>. The module of these symbols is equal to the square root of the energy in baseband per symbol emitted 2<i>E</i>_s.

0104The signal at the receiver input corresponds to the transmitted baseband signal distorted by the channel and corrupted by a complex additive white Gaussian noise of baseband spectral power 2<i>NOT</i>₀.

6.3 Modeling of the sampled signal at the output of the matched filter

0105Doppler spreading <i>B</i>_D is assumed to be weak compared to the symbolic rhythm 1 / <i>T</i>. Consequently, the samples obtained by suitable filtering of the received signal<i>r</i>(<i>t</i>) by the suitable filter <i>x</i>*(-<i>t</i>) and sampling of the resulting signal at symbol rate at the instants of maximum opening of the eye diagram can be approximated, whatever the type of modulation [1], by<maths id="math0002" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">r</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext> = </mtext><msub><mrow><mtext mathvariant="italic">vs</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic">at</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">not</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext>, </mtext><mtext mathvariant="italic">k</mtext><mtext> = 0,1,...,</mtext><mtext mathvariant="italic">NOT</mtext><mtext> - 1</mtext></mrow></math><img file="EP0802656A2_D0002.tif" /></maths>

0106In this expression, <i>vs</i>_<i>k</i>, <i>k</i> = 0,1,...,<i>NOT</i> - 1 represent an embodiment of the discrete channel at the level of the transmitted data stream. In the case of CDM, the<i>not</i>_<i>k</i>, meanwhile, represent an embodiment of a discrete additive Gaussian complex noise. They are independent and have 2<i>NOT</i>₀ as variance. The autocorrelation function, φ_<i>vs</i> (<i>l</i>), the discrete channel is deduced directly from that of the transmission channel, φ_<i>VS</i> (τ), by sampling it at symbol rate.

6.4 Simplified representation of the discrete channel at the level of data streams

0107One of the objectives of the invention is to propose a completely new approach to the simplified representation of the embodiments of the discrete channel at the level of the transmitted data trains. For each data stream, the receiver uses the samples<maths id="math0003" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">r</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext> = </mtext><msub><mrow><mtext mathvariant="italic">vs</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic">at</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">not</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext>, </mtext><mtext mathvariant="italic">k</mtext><mtext> = 0,1,...,</mtext><mtext mathvariant="italic">NOT</mtext><mtext> - 1</mtext></mrow></math><img file="EP0802656A2_D0003.tif" /></maths>    at the output of the filter adapted to detect the corresponding transmitted symbols.

0108Are (·)^<i>t</i> the transpose operator, <maths id="math0004" num=""><math display="inline"><mrow><msubsup><mrow><mtext>vs</mtext></mrow><mrow><mtext>=</mtext></mrow><mrow><mtext>Δ</mtext></mrow></msubsup><msup><mfenced open="(" close=")"><mrow><msub><mrow><mtext mathvariant="italic">vs</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>,</mtext><msub><mrow><mtext mathvariant="italic">vs</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext>,...</mtext><msub><mrow><mtext mathvariant="italic">vs</mtext></mrow><mrow><mtext mathvariant="italic">NOT</mtext><mtext>-1</mtext></mrow></msub></mrow></mfenced><mrow><mtext mathvariant="italic">t</mtext></mrow></msup></mrow></math><img file="EP0802656A2_D0004.tif" /></maths> the vector representing the realization of the discrete channel at the level of the transmitted data stream and <b>L</b> its covariance matrix. The vector<b>vs</b> can then be broken down into the form<maths id="math0005" num=""><img file="EP0802656A2_D0005.tif" /></maths>    where the <b>b</b>_<i>k</i> are the eigenvectors of the covariance matrix <b>L</b> of the vector <b>vs</b> and the <i>e</i>_<i>k</i> are independent complex Gaussian random variables whose variances are equal to the eigenvalues ​​λ_<i>k</i> of the matrix <b>L</b> associated with vectors <b>b</b>_<i>k</i> divided by φ_<i>vs</i>(0).

0109Vectors <b>b</b>_<i>k</i> form an orthonormal basis of the canonical space complex to <i>NOT</i> dimensions. The corresponding eigenvalues ​​are assumed to be arranged in descending order. Vector PD<maths id="math0006" num=""><math display="inline"><mrow><msubsup><mrow><mtext>e</mtext></mrow><mrow><mtext>=</mtext></mrow><mrow><mtext>Δ</mtext></mrow></msubsup><msup><mfenced open="(" close=")"><mrow><msub><mrow><mtext mathvariant="italic">e</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>,</mtext><msub><mrow><mtext mathvariant="italic">e</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext>,...</mtext><msub><mrow><mtext mathvariant="italic">e</mtext></mrow><mrow><mtext>N-1</mtext></mrow></msub></mrow></mfenced><mrow><mtext mathvariant="italic">t</mtext></mrow></msup></mrow></math><img file="EP0802656A2_D0006.tif" /></maths> , noted <i>p</i>(<b>e</b>), is equal to the product of the Gaussian PD of these components.

0110The covariance matrix <b>L</b> is poorly conditioned because Doppler spreading <i>B</i>_D is small in front of the clock rate 1 /<i>T</i>. Consequently, the eigenvalues ​​λ_<i>k</i> show a very steep decay and quickly pass out. One of the contributions of the invention is to take advantage of these qualities of independence of the random variables<i>e</i>_<i>k</i> and rapidly decreasing eigenvalues ​​λ_<i>k</i> to substantially reduce the complexity of the discrete channel estimator.

0111In the general case, the receiver has an incomplete knowledge of the characteristics of its local oscillator and those of the SPD <i>S</i>_<i>VS</i>(<i>f</i>) of the transmission channel. In this case, the most unpredictable SPD from the point of view of information theory [7] is a flat spectrum with bounded support of width equal to the Doppler spread<i>B</i>_<i>D</i><i>.</i>

0112Eigen vectors <b>b</b>_<i>k</i> are equal in this case to the well-defined restrictions on the support of the SSAD data stream [8]. The first eigenvalues ​​λ_<i>k</i> corresponding, normalized by the multiplicative factor <i>B</i>_<i>D</i><i>T</i>/ φ_<i>vs</i>(0), are shown in Figure 5 for <i>NOT</i> = 120 and <i>B</i>_<i>D</i><i>T</i> = 1/45. Eigen vectors<b>b</b>_<i>k</i> corresponding are also shown in Figures 6A to 6G.

7. Estimation of the discrete channel at the level of a data train according to the invention

0113The invention proposes a simple iterative algorithm (FIG. 3) allowing the joint estimation of all the unknown parameters of the receiver that the latter requires to carry out the tasks incumbent upon it.

0114Among these parameters, we can cite, in a non-exhaustive manner, the realization <b>vs</b> of the discrete channel, the variance of the noise 2<i>NOT</i>₀ [6] and the average energy per symbol received<maths id="math0007" num=""><img file="EP0802656A2_D0007.tif" /></maths> If the RFP <i>a priori</i> an unknown parameter of the receiver is known, so it is recommended to estimate it according to the MAP criterion. Otherwise, it is advisable to use the MV criterion for the successful completion of this estimate.

0115The RFP of an achievement <b>vs</b> of the discrete channel at the level of a transmitted data stream is determined indirectly by the DP, <i>p</i>(<b>e</b>), of <b>e</b> which is of course well known to the receiver. The vector<b>vs</b> can then be estimated according to the MAP criterion. PD of 2<i>NOT</i>₀ and 2<maths id="math0008" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext mathvariant="italic">E</mtext></mrow><mrow><mtext>s</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0802656A2_D0008.tif" /></maths> are generally unknown to the receiver. Their estimation is then generally accomplished according to the MV criterion.

0116By way of example, and without any limitation, FIG. 4 presents the case of the estimation according to the criterion of the MAP of the discrete channel. The estimation of additional parameters such as the energy per transmitted symbol can be accomplished in conjunction with that of the channel without much change to the final algorithm [6].

0117Let us note respectively by <b>r</b> = (<i>r</i>_<i>0</i><i>, r</i>_<i>1</i><i>,</i>,..., <i>r</i>_<i>N-1</i>) ^<i>t</i>, <b>at</b> = (<i>at</i>_<i>0</i><i>, at</i>_<i>1</i>,..., <i>at</i>_<i>N-1</i>) ^<i>t</i>, and <b>not</b> = (<i>not</i>_<i>0</i><i>, not</i>_<i>1</i>,..., <i>not</i>_<i>N-1</i>) ^<i>t</i> vectors of samples received, symbols transmitted and noise. For reasons of error correction, synchronization and estimation of the discrete channel at the level of the transmitted data streams, some transmitted symbols are coded or fixed. The vector<b>at</b> of transmitted symbols is then characterized by the discrete PD <i>a priori P</i>(<b>at</b>). The MAP estimate<b>vs</b> of <b>vs</b>, or equivalent, <b>ê</b> of <b>e</b>, is the value<maths id="math0009" num=""><img file="EP0802656A2_D0009.tif" /></maths>    that maximizes conditional PD <i>a posteriori p</i>(<b>e | r</b>).

0118The direct solution of this equation is a problem that is difficult to solve. One of the contributions of the invention is to propose a simple solution to this problem through the use of the iterative algorithm EM. This algorithm inductively re-estimates the vector<b>e</b> so that a monotonous growth in conditional PD <i>a posteriori p</i>(<b>e | r</b>) is guaranteed. This re-estimation is carried out via the maximization of an auxiliary function<i>Q</i>(<b>e, e '</b>) based on the measurement of Kullback-Leibler information and function of the current vector <b>e</b> and the new vector <b>e '</b>.

0119Given the vector received <b>r</b>, the EM algorithm starts with an arbitrary initial value 51 <b>e</b>⁽⁰⁾ of the vector <b>e</b>. Evolution of the estimate<b>e</b>^(<i>i</i>) to re-estimate <b>e</b>^(<i>i</i>+1) is performed via the auxiliary function <i>Q</i>(<b>e, e '</b>) by implicitly performing the following estimation and maximization steps:<ul id="ul0007" list-style="dash" compact="compact"><li>Estimation step 52: Calculate <i>Q</i>(<b>e</b>^(<i>i</i>),<b>e '</b>),</li><li>Maximization step 53: Find the estimate <b>e</b>^(<i>i</i>+1) that maximizes <i>Q</i>(<b>e</b>^(<i>i</i>),<b>e '</b>) in terms of <b>e '</b>.</li></ul>

0120Without any limitation, the iterative estimate (54) of <b>e</b> can be done a finite number <i><b>I</b></i> of times. This number is chosen in such a way that the estimate<b>e</b>^(<i>I</i>) reached is sufficiently close on average to the optimal estimate <b>ê</b> to ensure imperceptible degradation of receiver performance.

0121For an emitted data vector <b>at</b> and a discrete channel realization <b>vs</b> given, taking into account the independence of the components of the noise vector <b>not</b> allows to write the conditional RFP <i>p</i>(<b>r | a, e</b>) of the sample vector received <b>r</b> as the product of the Gaussian conditional PD of the components of this vector.

0122Taking into account explicit expressions of PD <i>p</i>(<b>e</b>) and <i>p</i>(<b>r | a, e</b>) and from the previous formulation of the EM algorithm, gives<maths id="math0010" num=""><img file="EP0802656A2_D0010.tif" /></maths>    as an explicit expression of the <i>m</i>-th component of the estimate <b>e</b>^(<i>i</i>+1).

0123In this expression, <i>b</i><maths id="math0011" num=""><math display="inline"><mrow><mfrac linethickness="0" numalign="left" denomalign="left"><mrow><mtext>(</mtext><mtext mathvariant="italic">m</mtext><mtext>)</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></mfrac></mrow></math><img file="EP0802656A2_D0011.tif" /></maths> represents the <i>k</i>-th component of the basic vector <b>b</b>_<i>m</i> (55) as defined above. In order to further improve the method, provision can be made for the vector base 55 to be adapted so as to better correspond to the channel to be estimated, according to various criteria and in particular the width of the Doppler spread 58. The parameter<i>w</i>_<i>m</i> is a weighting factor 57 which depends on the average signal-to-noise ratio <maths id="math0012" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext mathvariant="italic">E</mtext></mrow><mrow><mtext mathvariant="italic">s</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0802656A2_D0012.tif" /></maths> / <i>NOT</i>₀ 59 at the input of the receiver and of the eigenvalue λ_<i>m</i> divided by the power φ_<i>vs</i>(0) of the discrete channel.

0124Weighting factors <i>w</i>_<i>m</i> are also obtained in the case of the estimation of the discrete channel according to the method of least-squares (MMC) with perfect knowledge of the transmitted data. They measure the quality of the input of a basic vector<b>b</b>_<i>m</i> in the representation of the MAP estimate of the discrete channel.

0125When the power λ_<i>m</i>/ φ_<i>vs</i>(0) of the <i>m</i>-th component <i>e</i>_<i>m</i> of <b>e</b> is larger than the standard noise variance <i>NOT</i>₀ / <maths id="math0013" num=""><math display="inline"><mrow><mover accent="true"><mrow><msub><mrow><mtext mathvariant="italic">E</mtext></mrow><mrow><mtext mathvariant="italic">s</mtext></mrow></msub></mrow><mo>¯</mo></mover></mrow></math><img file="EP0802656A2_D0013.tif" /></maths><i> ,</i> then the contribution of the basic vector <b>b</b>_<i>m</i> in the representation of the channel estimate is very precise. The corresponding weighting<i>w</i>_<i>m</i> is then very close to 1.

0126When this power is smaller than the normalized variance of the noise, the taking into account of the basic vector <b>b</b>_<i>m</i> in the channel estimation provides more noise than useful information. Weighting<i>w</i>_<i>m</i> is then very close to 0. In this sense, the weights <i>w</i>_<i>m</i> play the same role and are based on the same principle as those of adapted filtering.

0127As shown in Figure 7 for <i>NOT</i> = 120 and <i>B</i>_D<i>T</i> = 1/45, the weights <i>w</i>_<i>m</i> quickly fade according to the index <i>m</i> for not too high values ​​of the average signal-to-noise ratio <maths id="math0014" num=""><math display="inline"><mrow><mover accent="true"><mrow><mtext mathvariant="italic">E</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0802656A2_D0014.tif" /></maths>_s / <i>NOT</i>₀. This is of course due to the very rapid decrease in the eigenvalues ​​λ_<i>m</i>. One of the advantages of the invention is then to be able to keep in the channel estimation process, without perceptible degradation of the performance of the estimator, only the first few coefficients of the<b>e</b>^(<i>i</i>).

0128One of the other advantages of the invention is to be able to improve the performance of the estimation of the discrete channel thanks to the taking into account by the receiver of the memory due to the continuous phase modulations (MSK, GMSK, ...) , synchronization symbols and part or all of the coded structure of the other symbols of the received data stream.

0129The inclusion of synchronization symbols in the channel estimation process is immediate. Are<i>S</i> the set of indices of the synchronization symbols in a data stream and α_<i>k</i>, <i>k</i> ∈ <i>S</i>, the values ​​taken by these symbols. As these values ​​are known to the receiver, then the conditional PD<i>p</i>(<i>at</i>_<i>k</i> = <i>at</i><b>| r, e</b>^(<i>i</i>)), <i>k</i> ∈ <i>S</i>, can be systematically replaced by 1 for <i>at</i> = α_<i>k</i> and by 0 if not.

0130It is generally less systematic to take into account the memory of the phase modulation used or the coded structure of the remaining symbols. It can for example be carried out indirectly by determining, via the Bahl algorithm [9] or the SOVA algorithm [10], the conditional PD<i>p</i>(<i>at</i>_<i>k</i> = <i>at</i><b>| r, e</b>^(<i>i</i>)) from the modulation trellis and codes used at the transmitter [13-15].

0131In the particular case where the modulation is without memory and the symbols are not coded or are coded with simple codes such as repeating codes, the coding structure can be integrated directly into the preceding formula.

0132This also applies if, for reasons of complexity, part or all of the coding is not taken into account by the estimator. A typical example is that of serial concatenated codes where the internal code is often the only one to be taken into account in the channel estimation. Another typical example is that of coded memory modulations where only the modulation memory is taken into account in the estimation process.

0133The value of the estimate of the channel towards which the EM algorithm converges is largely conditioned by the initial conditions used by this algorithm. If these initial conditions are badly chosen, the EM algorithm can converge to estimates,<b>ê</b> of <b>e</b>, corresponding to local maxima of conditional PD <i>a posteriori p</i>(<b>e | r</b>).

0134The best way to obtain these initial conditions is of course to use the synchronization symbols which are perfectly known to the receiver. Other techniques for removing ambiguity are also possible.

0135The choice of the location of these synchronization symbols in the transmitted data streams is not only decisive for the quality of the channel estimation but also for the good convergence of the EM algorithm towards the optimal estimation which maximizes <i>p</i>(<b>e | r</b>). The uniform distribution of the synchronization symbols at the level of the transmitted data streams is beneficial not only for a better estimation of the channel but also for a better stabilization and even an acceleration of the convergence of the algorithm EM.

0136For the smooth synchronization of data streams at the receiver, it is sometimes imperative to group the synchronization symbols or to distribute them over a small area of ​​the data streams. In this case, the EM algorithm has instabilities that can severely compromise the quality of the channel estimation.

0137One of the contributions of the invention is to be able to stabilize this algorithm by taking into account part or all of the coded structure of the information symbols of the received data train. Simple codes such as repetitive codes whose code words are well interleaved at the level of the data streams can be advantageously used to accomplish this stabilization task at low cost.

8. Demodulation and decoding of data according to the invention

0138Let us note by <b>ê</b> the <i><b>I</b></i> -th reestimation, <b>e</b>^(<i>l</i>), of <b>e</b>. Based on this estimate and on the vector<b>r</b> of samples at the output of the matched filter, the detector or decoder 510 can be designed to minimize a given criterion. It can in particular minimize the probability of error of the information data or of the coded modulated symbols.

0139As an example, the optimal detector or decoder 510 which minimizes the probability of symbol error must find for an information symbol <i>at</i>_<i>k</i> , <i>k</i> ∉ <i>S</i>, given the symbol<maths id="math0015" num=""><img file="EP0802656A2_D0015.tif" /></maths>    that maximizes conditional PD <i>p</i>(<i>at</i>_<i>k</i> = <i>at</i><b>| r, ê</b>).

0140This detector can take into account the memory of the phase modulation used or the coded structure of the symbols transmitted. This can be taken into account in particular via the Viterbi algorithm [11, 12], the Bahl algorithm [9] or the SOVA algorithm [10]. These last two algorithms can be used advantageously in the case where the receiver requires confidence values ​​of the decoded data. This is particularly the case for communication systems using concatenated coding in series and where the external decoder needs weighted outputs of the internal code to improve its performance.

0141In the particular case where the modulation is without memory and the symbols are not coded or are coded with simple codes such as repeating codes, the coding structure can be integrated directly into the preceding formula.

0142This is also valid in the case where, for reasons of complexity, part or all of the coding is not taken into account by the decoder. A typical example is that of serial concatenated codes where the internal code is often decoded separately from the external code. In this particular case, the structure of the internal code makes it possible to systematically generate weighted outputs for the external decoder at low cost.

APPENDIX: REFERENCES

0143<ul id="ul0008" list-style="none" compact="compact"><li>[1] JG Proakis, "Digital Communications", McGraw-Hill, New York, 1989.</li><li>[2] AP Dempster, NM Laird and DB Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm”, J. Roy. Stat. Soc., Ser. 39, 1977.</li><li>[3] LE Baum, T. Petrie, G. Soules and N. Weiss, "A Maximisation Technique Occuring in the Statistical Analysis of Probabilistic Functions of Markov Chains", Ann. Math. Stat., Vol. 41, 1970.</li><li>[4] LA Liporace, "Maximum Likelihood Estimation for Multivariate Observations of Markov Sources", IEEE Trans. Inform. Theory, IT-28, September 1982.</li><li>[5] BH Juang, “Maximum Likelihood Estimation for Mixture multivariate Stochastic Observations of Markov Chains”, AT&amp;T Technical Journal, vol. 64, no. 6, July-August 1985.</li><li>[6] GK Kaleh, "Joint Carrier Phase Estimation and Symbols Decoding of Trellis Codes", International Symposium on Information Theory, San Diego, Ca, January 1990.</li><li>[7] Louis L. Scharf, "Statistical Signal Processing: detection, estimation, and time series analysis", Addison-Wesley Publishing Company, New York, 1991.</li><li>[8] D. Slepian, "Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty --- V: The Discrete Case", BSTJ, May-June 1978.</li><li>[9] LR Bahl, J. Cocke, F. Jelinek and J. Raviv, "Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate", IEEE Transactions on Information Theory, vol. IT-20, March 1974.</li><li>[10] J. Hagenauer and P. Hoeher, "A Viterbi Algorithm with Soft-Decision Outputs and its Applications", GLOBECOM'89, Dallas, Texas, November 1989.</li><li>[11] GD Forney, Jr., "The Viterbi Algorithm", Proc. IEEE, 61, March 1973.</li><li>[12] GD Forney, Jr., "Maximum Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference", IEEE Trans. Inf. Theory, IT-18, May 1972.</li><li>[13] JK Wolf, "Efficient Maximum Likelihood Decoding of Linear Block Codes Using a Trellis", IEEE Transactions on Information Theory, vol. IT-24, no. 1, January 1978.</li><li>[14] GD Forney, Jr., "The Viterbi Algorithm", Proc. of the IEEE, vol. 61, no. 3, March 1973.</li><li>[15] GD Forney, Jr., "Coset Codes --- Part II: Binary Lattices and Related Codes", IEEE Transactions on Information Theory, vol. 34, no. 5, September 1988.</li><li>[16] RS Kennedy, "Fading Dispersive Communication Channels", John Wiley &amp; Sons, 1969.</li></ul>