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    • 专利摘要:
    The invention proposes an apparatus and method for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, in which the symbols transmitted to the rest of the equipment have a symmetrical extension. In reception, these extensions are detected, and from them blocks 10 to 18 generate sequences that allow estimating the beginning of the symbol and the displacement in the carrier frequency by means of block 25. For the implementation of this last block they propose four different methods. (Machine-translation by Google Translate, not legally binding)
    公开号:ES2639054A1
    申请号:ES201600324
    申请日:2016-04-25
    公开日:2017-10-25
    发明作者:José PIÑEIRO AVE；Fernando CRUZ ROLDÁN；Manuel Blanco Velasco
    申请人:Universidad de Alcala de Henares UAH；
    IPC主号:
    专利说明:

    APA ~ ATO and SYNCHRONIZATION PROCEDURE IN A SYSTEM WITHMUULTIPORTER OR SINGLE CARRIER MODULATION WITH EXTENSIONSYMBOL IN THE SYMBOLS
    TECHNICAL SECTOR
    The invention is framed in the telecommunications sector. Examples Illustrative non-limiting utility of the invention may be: communications through of the conventional power grid (Power Une Communications), band communications Wide (xDSL (Digital Subscriber Une), Wi-Fi (Wireless Fidelity), WiMax (Wireless Interoperability for Microwave Access)) and ultra-Wide (Ultra-Wide Band), mesh networks, digital audio broadcasting (DAB) and Video (DVB) broadcasting - digital terrestrial television broadcasting, mobile communications, Software-Defined Radio systems, Cognitive Radio systems, etc. In short, all those techniques that use multi-carrier and single-carrier modulation with trigonometric discrete transforms.
    STATE OF THE TECHNIQUE
    Fixed broadband telephony systems, as well as wireless technologies, have experienced a boom in the last two decades. Future generations of wireless communications systems demand large bandwidths and high transmission rates to provide the user with improved data services. For this, robust access techniques to the environment are needed against the different effects of the channel, such as multipath propagation and dispersive effect [1].
    Media access techniques based on multi-carrier modulation (MCM), among which are OFDM (Orthogonal Frequency Division Multiplexing - multiplex by orthogonal frequency division) for wireless systems, and DMT (Discrete Multitone Modulation - discrete multitone modulation) for xDSL technologies (Digital Subscriber Une - digital subscriber line), will increase their implementation in future generations of broadband communication systems. MCM has been recommended in numerous standards for data transmission in broadband communication systems. As an example, it is the modulation that is recommended in the IEEE1901 standard for data transmission over the conventional power grid.

    Discrete multitone modulation (DMT) or orthogonal frequency division multiplexing (OFDM) are examples of channel partitioning techniques, which use the data entry strategy in each transmitted symbol [2], [3]. Replicas of a part of the data or the inclusion of zeros, both called samples
    5 redundant, allow a partition of the channel in a set of independent subchannels in which the matching can be easily performed. Additionally, these replicas of the samples can be used to detect the moment of onset of the symbols as well as to correct the offset (offset) in the carrier frequency.
    DMT and OFDM systems are efficiently implemented using discrete Fourier transform (DFT). However, these technologies have a number of drawbacks, such as sensitivity to temporary offsets and carrier frequency. The estimation of the start time of the symbols and the frequency of the
    15 bearers are of crucial importance to recover the transmitted signal. For this reason, numerous methods have been proposed for DFT-based systems over these years, among which the maximum likelihood estimation algorithm [4] and the Schmidl & Cox method [5], in addition to a long list of recent synchronization techniques [6].
    As an alternative to DFT-based systems, several authors have proposed the use of different transforms, such as the discrete transform of the cosine (DCT) type-II pair (DCT2e) [7], [8], type-IV pair (DCT 4e ) [9], [10], or the transformed Hartley [11], [12]. However, even though synchronization is crucial and critical for the right
    25 system operation, the problem of finding a robust technique for DCT-based transceivers is not yet solved.
    Thus, in this invention simple and novel algorithms are described to efficiently estimate the temporal and frequency offset for systems based on OCT. The insertion of redundant samples introduces similarities or correlation in the transmitted symbol, which is used to estimate temporal and frequency offsets. The underlying idea of these techniques is to multiply a set of samples with the conjugate of separate ones N (in the case of the cyclic prefix) or N / 2 samples (in the case of using training symbols) [4], [5] . In the case of absence of noise and ideal channel, the maximum value occurs when the two sets of samples are correlated. The temporal instant of this maximum correlation is used
    to detect the start of the symbol, while the correlation phase provides an estimate of the frequency.
    The methods proposed in this invention are intended to be used in DCT-based transceivers, considering that the redundancy introduced has a symmetry and specular antisymmetry in the redundant samples. In this way, new algorithms for temporal and frequency synchronization are presented in multi-carrier systems based on DCT2e and DCT 4e.
    Figure 1 shows the general block diagram for implementing a multi-carrier modulation, although the procedures are also applicable to single carrier systems. In the transmitter, the data is processed with a fast algorithm of
    implementation by an inverse transform of N points T -I, where N is the
    to
    number of subchannels or subcarriers. In the receiver a discrete transform 1; quot; also implemented with a fast algorithm.
    In OFDM / DMT systems, each block of Figure 1 is defined as follows. In the transmitter, T-I is a 10FT, parallel data is converted to serial data by means of a
    to
    parallel-series converter, and finally some redundancy of length NR, for example, a cyclic prefix (CP) (see figure 2), is introduced at the beginning of each symbol x that is transmitted. The CP is necessary to convert the linear convolution associated with the channel (x * h) into a circular convolution for the samples of interest (O ~ n ~ (N -1). In the receiver, the equalizer in the time domain w shortens effective channel response
    heh to an appropriate length [13], a serial-parallel converter converts the data into Nx1 vectors after the elimination of the prefix. Next, a DFT is performed on the Te block and finally an equalizer in the frequency domain (FEO) corrects the dispersive effect of the channel.
    The design of multi-carrier transceivers that employ DCT2e on the transmitter (T-I) Y
    to
    in the receiver (1 ;,) with symmetric extensions (SE) is described in [7]. The result is expanded in [9] for any type of DCTs, and subsequently, multi-carrier or single-carrier systems based on DCT4e using SE or zero-padding (lP) are described in [10].
    The methods proposed in this invention are focused on systems based on symmetrical extension (SE), in which, unlike DFT-based systems that use only a redundant prefix (CP) (Figure 2), two extensions are used Symmetric NR samples: a left prefix or extension (LE)
    5 Yun suffix or right extension (RE) [9], [10]. Be an extended block
    x. = [:: l
    of length N + 2NR; The prefix and suffix are defined as follows:
    X ~ E = [xN.-Igt; ..., xo] '
    x ~ = [axN_p ..., axN _N.],
    10 where a = 1 for DCT2e, while a = -1 for DCT systems 4e [7], [9]. Examples of symmetric extensions for DCT-based systems are shown in Figures 3 (a) and 3 (b). A more detailed description of the operation of DCT-based transceivers can be found in [7], [8], [9], [10].
    15 DESCRIPTION OF THE FIGURES
    Figure 1. Block diagram of a multi-carrier system based on transforms on a channel with additive noise.
    20 Figure 2. Illustration of a signal with cyclic prefix for DFT-based systems.
    Figure 3. Illustration of two signals with symmetric extensions (SE) for systems based on (a) DCT2e and (b) DCT4e, where HS and HA indicate half-sample symmetry and half-sample antisymmetry, respectively.
    Figure 4. Sliding windows for the detection of the symbol's temporary offset (STO) in DFT-based systems.
    Figure 5. Sliding windows for STO detection in DCT based systems.
    Figure 6. Block diagram describing the device and the proposed synchronization procedures.
    Figure 7. General block diagram of the temporal offset estimators 5 proposed in block 25. (a) Echo implementation (1). (b) Echo implementation (2). (c) Echo implementation (3). (d) Echo implementation (4).
    DESCRIPTION OF THE INVENTION
    This invention relates to different procedures and the corresponding apparatus for performing the STO estimation for multi-carrier and single-carrier systems.
    The analysis of the correlation between two signals provides a quantitative measure of the similarity between them. For the estimation of the STO, the objective of the correlation function 15 is to find the similarities between a part of the received symbols and the redundancy introduced to diagonalize the channel.
    Thus, depending on the type of redundancy introduced in each symbol (see figure 3), to find the temporary offset in DCT-based systems, the use of four
    20 sliding windows of length NG, which are W 1p and W 2p to identify the symmetrical extension LE, and W 1s and W 2s to detect RE, as shown in Figure 5. Window samples must be rearranged to obtain a maximum correlation function when the sliding windows coincide with the redundant samples and their corresponding symmetric extensions.
    one
    The STO temporary offset estimate, which we call 8SE, is obtained by calculating the maximum of the metric given by
    M LRE, [8] = ICLE [8f + ICRE [8f -E: ~ 8], (1)
    G
    or by
    (2)
    where
    (3)
    they are the correlation functions of sliding windows, and ESE [8] is a term that considers the energy of poisoned signals
    ESE [8] = E u: [8] + ERE [8].
    where
    with
    No -I E, / ([8] = L Jy [-1-1 + 8f 'P, LE 1 = 0 ,(5)
    No-I 2 Ew [8] = L Jy [I + 8], 'P, LE 1 = 0 (6)
    10 Y
    with
    (7)
    Na-I 2
    Ew [8] = L Jy [N +1 +8], (8)
    'S, RE 1 = 0
    15 with r = 1 for the HS extension (LE and RE in DCT2e, and LE in DCT4e) or r = -1 for the HA extension (RE in DCT4e). The parameter p takes into account the signal to noise ratio (SNR):
    (Y2 SNR p =, s 2 = - (Y; + (Yn SNR +1 '
    20 Cu definitions: take into account symmetry and specular antisymmetry
    and CRE
    introduced into the DCT systems described in Figure 3 [9].
    The second method estimates the temporal offset using the maximum of the function
    (9)
    25th function
    (10)
    Figure 6 shows the general block diagram of the proposed synchronization algorithms, and Figure 7 represents the implementation of block 25, 5 considering each of the metrics described in equations (1), (2), (9 ) or (10).
    Once the perfect synchronization of the temporary offset, 8A SE, has been obtained, the invention also allows an estimation of the frequency offset (CFO) for DCT-based transceivers by the following expression:
    10 ~ SE = -2 ~ G L (CLE [SSEJ + and · CRE [SSE], where L means the angle.
    MODE OF REALIZATION
    A description of the invention based on the previous figures is given below.
    Recipients need to know exactly what the initial sample of each
    symbol, because without that information it is not possible to discern between the samples of
    20 redundancy to be ruled out. It is therefore necessary a synchronization block that detects the start time of each of the transmitted symbols accurately.
    To detect the temporal offset of the symbols and to correct it, the
    25 redundancy introduced in the transmitted symbols, which in the procedure of the invention is specified in two symmetrical extensions HS as a prefix and suffix in each symbol (§ and §. In Figure 3a) in DCT2e systems or an HS prefix and a suffix HA in DCT4e systems (Z in Figure 3b). These redundant samples within each symbol are correlated with the corresponding samples of the symbols from which
    30 are obtained, so that the similarity between them makes their correlation high. Thus, two pairs of sliding windows (ª and ª in Figure 5) are used to detect the beginning and end of each symbol based on the maximum correlation between each pair of sliding windows.
    Figure 6 shows the block diagram of the synchronization scheme that describes the process of the invention and the corresponding apparatus. From the frame of received symbols, and [n], an exploration of the same is carried out with two sliding windows looking for the similarities introduced by the redundancies. He Window size, NG samples, may be different from the number of redundancy samples of the SE symmetric extensions, samples. In figure 5 it
    NR
    They consider the same. To detect the prefix LE the two windows are in adjacent positions, in the same way that two contiguous windows 10 of NG samples separated from the previous ones, the length of each symbol, N samples, are used to obtain the suffix RE.
    Therefore, the sync block first creates the sliding windows. For this, a delay block or buffer (block 10) of NG samples is used to establish the W 1s window followed by a block 11 that undoes the introduced symmetry HS (DCT2e)
    or HA (DCT4e), or followed by a block 16 that undoes the introduced symmetry HS (DCT2e or DCT4e); the block .12. perform the conjugate operation on each sample of the W 1s window to multiply it by the corresponding sample of the W 2s window in block 13. In block 14 the correlation between the two windows is calculated:
    where r = 1 for DCT2e (HS symmetry) and r = -1 for DCT 4e (HA symmetry).
    To obtain the two windows W 1p and W 2p of Figure 5 that detect the symmetry in the prefix, a delay block 1.§ of N samples is needed with respect to the previous case of the 25 prefix, obtaining at the exit of block 14 the correlation:
    The energy terms of the sliding windows defined in the metrics of the invention to obtain the temporary offset estimator are calculated with blocks 17 and 30 18, so that at their output the four energy terms necessary for block 25 are available offset estimator:
    No -I 2
    E ~ [0] = L ly [1 + o],
    I, .LE 1 = 0
    NG-L Ew [8] = L IY [-I-I + 8f,
    lp, LE 1 = 0
    NG-l 2
    Ew, [8] = L ly [N-l-I + 8],
    ! .r, RE 1 = 0
    Once we have available the values of the correlation terms and energy of the windows, obtained directly or through iterative calculations, we proceed to calculate the different offset estimators described in the invention and shown in Figures 7 (a ), 7 (b), 7 (c) and 7 (d), respectively, and described below,
    In Figure 7 (a), the offset estimator receives as inputs the two correlations, CLE and CRE, as well as the four energy terms corresponding to the sliding windows Ew, Ew, Ew and Ew. By blocks 17 and 19 you get a
    Ip.LE lp.L6 Iquot;., RE 2 •• RE -
    of the metrics defined in the invention:
    quot;
    15 The maximum value of this metric (block 20) is the 8sE estimator of the temporal offset of the symbol:
    Figure 7 (b) shows the block diagram of the offset estimator described in the invention as:
    Figures 7 (c) and 7 (d) show the corresponding block diagrams of the other two offset estimators described in the invention:
    TO
    From the bSE estimator, in the invention the frequency offset estimate is obtained in a simple way
    TO
    liSE =
    Full Bibliography
    [1] J. Cioffi, quot; Digital communications, field 4: Multichannel modulation, quot; 10 https://web.stanford.edu/group/cioffi/doc/booklchap4.pdf.
    [2] J. A. C. Bingham, "Multicarrier modulation for data transmission: An idea whose time has come,"; IEEE Communications Magazine, vol. 28, no. 5, pp. 5-14, May 1990.
    [3] Y.-P. Lin, S.-M. Phoong, and P. P. Vaidyanathan, Filter Bank Transceivers for 15 OFDM and DMT systems. Cambridge University Press, 2011.
    [4] J. J. van de Beek, M. Sandell, and P. O. Borjesson, "ML estimation of time and frequency offset in OFDM systems,"; IEEE Transactions on Signal Processing, vol. 45, no. 7, pp. 1800-1805, July 1997.
    [5] T. M. Schmidl and D. C. Cox, quot; Robust frequency and timing synchronization for
    20 OFDM, quot; IEEE Transactions on Communications, vol. 45, no. 12, pp. 1613-1621, December 1997.
    [6] A. A. Nasir, S. Durrani, H. Mehrpouyan, S. Blostein, and R. A. Kennedy, quot; Timing and carrier synchronization in wireless communication systems: A survey and classification of research in the last five years, quot; arXiv preprint arXiv: 1507.02032,
    25 2015.
    [7] N. AI-Dhahir, H. Minn, and S. Satish, "Optimum DCT-based multicarrier transceivers for frequency-selective channels,"; IEEE Transactions on Communications, vol. 54, no. 5, pp. 911-921, May 2006.
    [8] P. Tan and N. C. Beaulieu, quot; A comparison of DCT-based OFDM and DFT-based
    30 OFDM in frequency offset and fading channels, quot; IEEE Transactions on Communications, vol. 54, no. 11, pp. 2113-2125, November 2006.
    [9] F. Cruz-Roldán, M. Domínguez-Jiménez, G. Sansigre-Vidal, P. Amo-López, M. Blanco-Velasco, and Á. Bravo-Santos, quot; On the use of discrete cosine transforms
    for multicarrier communications, quot; IEEE Transactions on Signal Processing, vol. eleven ,
    no. 11, pp. 6085-6090, November 2012.
    [10] F. Cruz-Roldán, M. Domínguez-Jiménez, G. Sansigre-Vidal, J. Piñeiro-Ave, and
    M. Blanco-Velasco, quot; Single-carrier and multicarrier transceivers based on discrete
    5 cosine transform type-IV, quot; IEEE Transactions on Wireless Communications, vol.
    12 no. 12, pp. 6454-6463, December 2013.
    [eleven] C.-K. Jao, S.-S. Long, and M.-T. Shiue, "DHT-based OFDM system for passband
    transmission over frequency-selective channel, quot; IEEE Signal Processing Letters,
    vol. 17, no. 8, pp. 699-702, August 2010.
    10 [12]W. A. Martins and P. S. R.Diniz, "Memoryless block transceivers with minimum
    redundancy based on hartley transforms, quot; Signal Processing, vol. 91, no. 2, pp.
    240-251, February 2011.
    [13] R. K. Martin, K. Vanbleu, M. Ding, G. Ysebaert, M. Milosevic, B. L.Evans, M.
    Moonen, andC.R.J.Jr.,quot; Implementationcomplexityandcommunication
    fifteen performancetradeoffsindisagreemultitonemodulationequalizers, quot;IEEE
    Transactions on Signal Processing, vol. 54, no. 8, pp. 3216-3230, August 2006.
    权利要求:
    Claims (13)
    [1]
    1.-Procedure for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, with means to add and extract a prefix and a suffix by symmetric extension in the symbols to be transmitted; It is characterized in that the procedure comprises generating the symbols by means of symmetrical extension (Q and ª or D, which are transmitted periodically from the transmitter to the rest of the equipment, which detect said extensions in reception, and from them with blocks 10, .11, 12, .u, 14, .1.§ and 16 generate CLE using the following algorithms:
    and CRE
    where CLE [8]isthe correlationinthe instant 8, and [t + 8] isthe sample receivedinhe
    instant 1 + 8,and '[-1-1 + 8]istheconjugatedfromthesamplereceivedinhe instant
    -1-1 + 8, CRE [8]isthe correlationinheinstant8, and [N -1-1 + 8]isthesample
    fifteen received at the time N -1-1 + 8, and '[N +1 + 8] is the conjugate of the sample received in
    the instant N +1 + 8, the parameter r is a constant and takes the values r = 1 for DCT2e
    and r = - L for DCT 4e, NGis the size of the windows, and N is the number of subchannels or
    subcarriers
    twenty 2.-Procedure for synchronizationinapoint to point transmission systemor
    multipoint with multi-carrier or single-carrier modulation, with means to add and
    extract a prefix and a suffix by symmetric extension in the symbols to be transmitted; be
    characterized in that the procedure comprises generating the symbols by means of symmetric extension (2 and ª or D, which are transmitted periodically from the transmitter to the rest of
    ~ 5 equipment, which detect inreceiving these extensions, and from them withthe
    blocks 17 and 18 generate Ew. . And Ew. I p, Jj 1s, HE through the following algorithms:
    where Ew, p.1.E [8] is the energy at instant 8, and [t + 8] is the sample received at O instant 1+ 8, EWquot; .RE [8] is the energy at instant 8, and [N -1-1 + 8] is the sample
    N -1-1 + 8, NG is the size of the windows, and N is the number of subchannels or subcarriers.
    [3]
    3.-Procedure for synchronization in a point-to-point transmission system or
    5 multipoint with multi-carrier or single-carrier modulation, with means to add and extract a prefix and suffix by symmetric extension in the symbols to be transmitted; It is characterized in that the procedure includes generating the symbols by means of symmetric extension (§ and § or J, which are transmitted periodically from the transmitter to the rest of the equipment, which detects said extensions in reception, and from them with the
    10 blocks 17 and 18 generate Ew, p .1.E and EWquot; .Rf: using the following algorithms:
    NG-I 2
    Ew, [8] = L Iy [-I-I + 8],
    _P.LE 1 = 0
    where E W'P .IE [8] is the energy at time O, and [-l-1 + 8] is the sample received at the
    instant -1-1 + 8, Ewquot; .quot ;, [8] is the energy at instant O, and [N + 1+ 8] is the sample
    15 received at the moment N + 1+ 8, NG is the size of the windows, and N is the number of
    subchannels or subcarriers.
    [4]
    4. Procedure for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, according to claims 1 to 20 3, characterized in that the correlation calculations are performed iteratively, storing samples and partial products of samples by conjugate samples.
    [5]
    5.-Procedure for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, according to claims 1 to 4, characterized in that, starting from blocks I. 19 and 20 carries out the detection of the beginning of each symbol using the algorithm
    quot; . _ fu []} _ I [] 2 I [] 2 ESE [O]}
    8SI, -m; x quot; tY 'IJlE, 8 -m; x e LE 8 + e RE 8 -4N' G
    where m; x {} represents the maximum value of the MUIE metric, [8] for the instant O,
    e LE [O] and e RE [8] are the correlations at time O, ESE [O] is the term that
    30 considers the energy of the poisoned signals, and NG is the size of the windows.
    14
    [6]
    6. Procedure for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, according to claims 1 to 4, characterized in that starting blocks 19, 20 and 22 carry out the start detection of each symbol using the algorithm
    where m, F {} represents the maximum value of the metric M LP.f.i [o] for the instant or,
    e LE [o] and RE [o] are the correlations at the moment o, ESE [o] is the term that considers the energy of the poisoned signals, the parameter p takes into account the signal to noise ratio (SNR) p = SNRj (SNR + 1), and NG is the size of the windows.
    7-Procedure for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, according to claims 1 to 4, characterized in that from blocks 17, .ll !, 20, .f..1 , 23 and 24 carries out the detection of the beginning of each symbol using the algorithm
    where m, F {} represents the maximum value of the metric M U1E, [o] for the instant or,
    e LE [o] and e RE [o] are the correlations in the instant or, EW¡ p.LE [o] is the energy in the
    instant o, and EW¡ '.RE [o] is the energy in the instant o.
    [8]
    8. Procedure for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, according to claims 1 to 4, characterized in that from blocks 1I. 20, 21, 23 Y24 carries out the detection of the beginning of each symbol using the algorithm
    where max {} represents the maximum value of the M LRE metric, [o] for the instant or,
    <5
    e LE [o] and e RI, [O] are the correlations in the instant or, Ew¡ p.u. [o] is the energy in the instant or, and EW¡ '.RE [o] is the energy in the instant or.
    [9]
    9. Procedure for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, according to claims 1 to 5, characterized in that it performs frequency synchronization by calculating the following algorithm:
    where L means the angle, CLE [6SE] and CRE [6SE] are the correlations in the instant
    TO
    DSE, the parameter r is a constant and takes the values r = 1 for DCT2e and r = -1 for DCT4e, N is the number of subchannels or subcarriers, and N G is the size of the windows.
    [10]
    10.-Procedure for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, according to claims 1 to 4 and 6, characterized in that it performs frequency synchronization by calculating the following algorithm:
    ~ SE = -2 ~ G L (CLE [6SE J + r 'CRE [6SE],
    where L means the angle, CLE [6SEJ and CRE [6sEJ are the correlations in the instant
    TO
    DSE, the parameter r is a constant and takes the values r = 1 for DCT2e and r = -1 for DCT4e, N is the number of subchannels or subcarriers, and N G is the size of the windows.
    [11]
    11.-Procedure for synchronization in a point-to-point or multipoint transmission system with multi-carrier or single-carrier modulation, according to claims 1 to 4 and 7, characterized in that it performs frequency synchronization by calculating the following algorithm:
    ~ SE = -2: N L (CLE [6SE J + r 'Cw {6SE],
    G
    where L means the angle, CLE [6SE] and CRE [6SE] are the correlations in the instant
    TO
    DSE, the parameter r is a constant and takes the values r = 1 for DCT2e and r = -1 for
    16
    DCT4e, N is the number of subchannels or subcarriers, and NG is the size of the windows.
    [12]
    12.-Procedure for synchronization in a point-to-point transmission system or
    Multipoint with multi-carrier or single-carrier modulation, according to claims 1 to 4 and 8, characterized in that it performs frequency synchronization by calculating the following algorithm:
    where L means the angle, CLE [5SEJ and CRE [5sEJ are the correlations in the instant
    one
    10 OR, the parameter r is a constant and takes the values r = 1 for DCT2e and r = -1 for DCT4e, N is the number of subchannels or subcarriers, and N G is the size of the windows.
    [13]
    13.-Procedure for synchronization in a point-to-point transmission system or
    Multipoint with multi-carrier or single-carrier modulation, according to claims 1 to 12, because in the calculations the real or imaginary part of the data of each complex sample received is used and [n] at time n.
    [14]
    14.-Device for receiving a multi-carrier or single-carrier signal, configured 20 to implement the method according to any of claims 1 to 13.
     FIG. 1 (Prior art)
    ePi
     or N-l
    FIG. 2 (Prior Art)
    17
    5
     HS 
    x XRE
    ~~ --------------------. ~
    ! ~ 6
    .
    FIG. 3 (a) (Prior Art)
    -
    HS
    x
    ~~ -------------------- ~~
    ;
    ...
    '
    FIG. 3 (b) (Prior Art)
    18
    NR Svmbo ~ ~ Svmbol n + 1
    J
    ~. ~~~~ .------------ ~~
    / '
    SUdlnquot; wlndows
     FIG. 4 (Prior Art)
    Symbol n-1j + -I NN.:.:.._-------Sv-m-bo....:~.:...n__________N~R!!+II
    Symbol n + 1
    RR
    ~ Wi E: _: - :: tji: mmm
    FIG. 5
    19
    ---------------------------------- ~ -----------------------,
     EnerlYpart
    E .. quot; .RL
    Moving
    sum
    J
    -M
    EWquot; oAt
    1_12
    Offset
    estimator
    1 ~ L -___......
    [15 ]
    15. Q! ~ i, 10Hz-o} ~, and m ~ try ~. ______J
    ~ :: ~~~~ = - ~ :: _ ~ _: ~ -------- ~ ----------------------
    : Ener¡and pint I Moving
    I I
    sum
    I I I I
    I
    ,
    Movong I I
    sum
     L___________________________________________________________ _
    FIG. 6
    twenty
     -----eleven-------------------------------, 
    CLE
    ,
     1_12
    I
    I
    I
    17 19: +: '} ----_, I
    ,
    I
    E _____
    C R.;, ;;; ......... 1 ~ I '~
    Go.
    M: O SE
    19E ±: gt; LRE '.I argmax,.
    - one
    EJYU .RE
    ,
    ,
    I
     ------------------------------------_
    FIG. 7 (a)
    ------ ~ ------------------------------.
    ,
     quot;
    OR • SE
    AND
    Wquot ;, LE
    one
     I --------------------------------------
    FIG. 7 (b)
    --17 ----------------------------- ~ 1
    ------
    - ,
    eleven
    eleven
    FIG. 7 (e)
    .---------------------------------------- 111
    1 1 lA
    : 8SE
    1 1 1
    1 1 1 1 1
    ___one
    FIG. 7 (d)
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