# Patent

## Title
Method for demodulating UWB pulse sequences encoded according to an on-off keying modulation scheme

## Abstract

The present invention relates to a method for transmitting data in the form of at least one pulse sequence Tsgk (for k=1 to K). The method according to the invention includes at least one symbol decoding step in the course of which at least one modulation value Pwk representative of an amount of power carried by each pulse sequence Tsgk is computed and compared to at least one predetermined threshold value Thvk, which will be computed beforehand by equating a first and a second probability density function representing a likelihood for the transmitted signal to carry a first symbol and a likelihood for the transmitted signal to carry a second symbol, respectively. The method according to the invention enables to limit the processing time and power needed for performing the demodulation of a power-modulated UWB signal.

## Background
BACKGROUND OF THE INVENTION
The present invention relates to a method for transmitting data in a telecommunication system including at least one transmitter and one receiver, said transmitter being intended to transmit a signal formed by at least one sequence of Ns pulses over Ns time windows, each pulse being enclosed within a time chip whose position within its relevant time window is defined by a chip number.
Such data transmission methods are currently studied with the aim of assessing the relevance of so-called Ultra-Wide Band telecommunication systems (further referred to as UWB systems). In such a system each transmitter may be identified by a signature formed by the above-mentioned chip numbers, which signature is in itself quite sturdy and may thus be reliably and accurately communicated to all potential receivers.
The pulses used in UWB systems are very short, having for example a duration lower than 0.1 nanosecond, which offers to such systems bandwidths at least as large as 10 GigaHertz, entailing high flexibility and hence numerous possible applications for such systems.
The above-described signal may form a carrying signal on which information can be encoded by modulation of said carrying signal. The inventors have observed that, because of the shortness of the pulses involved, a precise synchronization with a given pulse sequence will be difficult to perform at the receiver end, so that the chosen modulation scheme should involve as few time-related parameters as possible in order to be cost-efficient.
SUMMARY
The present invention thus aims at providing a modulation/demodulation scheme according to which the information carried by pulse sequences may be recovered at the receiver end without said receiver having to map precisely, with respect to time, the received pulse sequences.
Indeed, a method for transmitting data as described in the opening paragraph is characterized according to the invention in that it includes at least one symbol decoding step to be executed at the receiver end, in the course of which symbol decoding step at least one modulation value representative of an amount of power carried by each pulse sequence is computed and compared to at least one predetermined threshold value, which threshold value will have been computed beforehand by equating a first and a second probability density function representing a likelihood for the transmitted signal to carry a first symbol and a likelihood for the transmitted signal to carry a second symbol, respectively.
The symbol decoding step according to the invention enables to achieve a demodulation of a modulated UWB symbol in a very straightforward manner, by quantifying the power of the received signal and performing simple comparisons with one or several threshold values, which comparisons are easy to implement. Such a demodulation scheme does not require the receiver to perform a precise mapping, with respect to time, of the received signal, which in turn enables to manufacture adapted receivers at a relatively low cost.
Furthermore, though each predetermined threshold value may be predefined and for example set at 1⁄2 or 3⁄4 if Vki is to be chosen among integer values 0 and 1. The inventors have observed, however, that such fixed thresholds, which do not take into account communication conditions between the transmitter end the receiver may generate decoding errors. The inventors thus have designed a thresholding scheme based on an equalization of two probability densities, each taking into account real-time communication conditions, so that neither gray zone nor overlap will exist between two interpreting conditions.
According to a particular embodiment of the invention, the threshold value is defined by a polynom of a variable M1/2, where M is defined by M=(2.B.Ns.Ti+1)/2, B being a bandwidth of the pulse sequence for which the threshold value is computed, and Ti a time duration over which an integration of each pulse belonging to said pulse sequence is performed in order to compute the amount of power carried by said pulse sequence.
As will be explained hereinafter, the polynom defining the threshold value will preferably be limited to the second order in order to achieve a suitable balance between computing complexity and decoding efficiency.
According to a preferred embodiment of the invention, a first-order coefficient of the polynom defining the threshold value is given by an ordinate of a curve whose abcissis is formed by an energy ratio related to the transmission of the relevant pulse sequence.
The modulation of the UWB signals to be demodulated by carrying out such a symbol decoding step may result from various modulation schemes.
According to a particular embodiment of the invention, a method as described hereinbefore further includes at least one symbol encoding step to be executed before transmission of said pulse sequence, in the course of which symbol encoding step each pulse sequence is multiplied by an integer value representative of a symbol to be carried by said pulse sequence.
By virtue of this modulation scheme, the information carried by signals transmitted in Ultra-Wide Band telecommunication systems according to the invention will essentially be related to the power carried by these signals, which power is related to the amplitude of the pulses included within such a signal. Such a modulation scheme is easy to implement, which in turn enables to manufacture adapted transmitters at a relatively low cost.
According to a variant of the invention, each signal to be transmitted is constituted by a superimposition of a predetermined number of pulse sequences, each pulse sequence having been subjected to a symbol encoding step and corresponding to one of several sub-bands into which a total bandwidth available for transmission has previously been divided.
This variant of the invention enables to transmit simultaneously several symbols through a same communication channel, and thus to significantly increase the throughput of a telecommunication system in which such a variant of the invention is embodied.
According to one of its hardware-oriented aspects, the invention also relates to a telecommunication system including at least one transmitter and one receiver, said transmitter being intended to transmit a signal formed by at least one pulse sequence of Ns pulses over Ns time windows, each pulse being enclosed within a time chip whose position within its relevant time window is defined by a chip number, system in which the receiver includes symbol decoding means intended to compute at least one modulation value representative of an amount of power carried by each pulse sequence and to compare said modulation value to at least one predetermined threshold value obtained by equating a first and a second probability density function representing the likelihood for the transmitted signal to carry a first symbol and the likelihood for the transmitted signal to carry a second symbol, respectively.
According to a particular embodiment of this hardware-related aspect, the transmitter includes symbol encoding means intended to multiply each pulse sequence by one of two integer values representative of a symbol to be carried by said pulse sequence.
According to a variant of this hardware-related aspect, the transmitter further includes signal combination means intended to receive a predetermined number of pulse sequences, each pulse sequence having been generated by symbol encoding means and corresponding to one of several sub-bands into which a total bandwidth available for transmission has previously been divided, said signal combination means being intended to combine all said pulse sequences into a signal to be transmitted.
According to another of its hardware-oriented aspects, the invention also relates to a device intended to receive a signal formed by at least one sequence of Ns pulses over Ns time windows, each pulse being enclosed within a time chip whose position within its relevant time window is defined by a chip number, which receiver includes symbol decoding means intended to compute at least one modulation value representative of an amount of power carried by each pulse sequence and to compare said modulation value to at least one predetermined threshold value obtained by equating a first and a second probability density function representing the likelihood for the transmitted signal to carry a first symbol and the likelihood for the transmitted signal to carry a second symbol, respectively.
According to yet another of its hardware-oriented aspects, the invention also relates to a device intended to transmit a signal formed by at least one sequence of Ns pulses over Ns time windows, each pulse being enclosed within a time chip whose position within its relevant time window is defined by a chip number, which transmitter includes symbol encoding means intended to multiply each pulse sequence by one of two integer values representative of a symbol to be carried by said pulse sequence.



BRIEF DESCRIPTION OF DRAWING
The characteristics of the invention mentioned above, as well as others, will emerge more clearly from a reading of the following description given in relation to the accompanying figures, amongst which:
FIG. 1 is a functional diagram depicting a telecommunication system in which the invention is used;
FIG. 2 is a chronogram depicting a pulse sequence constituting a carrying signal transmitted in such a telecommunication system;
FIG. 3 is a chronogram depicting a pulse model which may be used for generating such a sequence;
FIG. 4 is a chronogram depicting a data frame including a plurality of pulse sequences;
FIG. 5 is a block diagram depicting symbol decoding means included in a receiver in which a variant of the invention is embodied;
FIG. 6 is a diagram depicting how a threshold value may be dynamically computed according to the invention; and
FIG. 7 is a diagram depicting a tabulated function which may be used for computing such a threshold value according to a preferred embodiment of the invention.



DETAILED DESCRIPTION
FIG. 1 depicts a telecommunication system SYST in which the present invention is embodied. This system SYST includes at least one transmitter TRD and one receiver RCD, which may for example be both constituted by devices such as mobile phones. The transmitter TRD is intended to transmit a signal Tsg formed by at least one sequence of Ns pulses pj (for j=1 to Ns) over Ns time windows, each pulse being enclosed within a time chip whose position within its relevant time window is defined by a chip number cj (for j=1 to Ns). The number Ns of pulses included in this sequence may, for example, be chosen equal to 128, while the width of each time window may be chosen equal to 100 nanoseconds, with a width of 1 nanosecond for each time chip.
According to the present invention, the transmitter TRD includes symbol encoding means ENC intended to multiply each pulse sequence by an integer value representative of a symbol to be carried by said pulse sequence.
The information carried by the transmitted signal Tsg will thus essentially be related to the power carried by this signal Tsg, which power is related to the amplitude of the pulses included within said signal Tsg. This information may then be recovered by the receiver RCD without said receiver RCD having to map precisely, with respect to time, the received pulse sequences.
To this end, the receiver RCD includes symbol decoding means DEC intended to compute at least one modulation value representative of an amount of power carried by each pulse sequence and to compare said modulation value to at least one predetermined threshold value. As will be explained hereinafter, the result of such a comparison will automatically point to the demodulated value of the symbol originally encoded within the transmitted signal Tsg by the symbol encoding means ENC.
FIG. 2 depicts such a transmitted signal Tsg in the form of a chronogram, according to which each pulse sequence has a total duration Ts divided into time windows having each a duration Tf, each time window being sub-divided into time chips Tc, a single time chip within each window being intended to enclose a pulse pj (for j=1 to Ns), which single time chip is identified by means of a chip number cj. The transmitter of this transmitted signal Tsg will thus be identified by a signature Sg=(c1, c2 . . . cNs) jointly formed by all above-mentioned chip numbers cj (for j=1 to Ns), which signature Sg is in itself quite sturdy and may thus be reliably and accurately communicated to all potential receivers.
In accordance with the invention, each pulse pj (for j=1 to Ns) belonging to the pulse sequence shown in this picture has been multiplied by a same integer value Vi representative of a symbol to be carried by said pulse sequence, in the form of the power carried by this sequence, the reference “i” being indicative of a reference number allocated to the pulse sequence under consideration.
Furthermore, the pulses pj (for j=1 to Ns) are multiplied by values aj which are randomly chosen equal to +1 or −1 in the course of the symbol encoding step, so that in the example shown here, the second pulse p2 is negative.
Such a random distribution of positive and negative pulses, which does not affect the information carried by said pulses because said information is related to a square form of said pulses, allows to prevent appearance of high-amplitude peaks in the spectral domain, which peaks could interfere with equipment not included in the telecommunication system. Such frequency interference should be limited as a rule, and is targeted by a European Commission Directive 83/336 CEE, as well as by regulation of the USA's Federal Communications Commission.
All pulses pj (for j=1 to Ns) of the pulse sequence shown here may additionally be submitted to a time jitter dti in the course of the symbol encoding step.
This time-jitter, introduced by time-delaying means, will be kept small with respect to a delay spread induced by a communication channel through which the modulated signal will be transmitted. The delay spread may have, for example, a value of 100 nanoseconds. Such a time-jitter won't affect the information carried by each pulse sequence, and mainly adds an optional degree of flexibility to the modulation scheme according to the invention.
The transmitted signal Tsg may thus be expressed in the following form




  
    Tsg
    ⁡
    
      (
      t
      )
    
  
  =
  
    
      ∑
      
        i
        ,
        j
      
    
    ⁢
    
      
        Vi
        ·
        α
      
      ⁢
      
        
      
      ⁢
      
        j
        ·
        
          pj
          ⁡
          
            (
            
              t
              -
              cj
              -
              
                j
                ·
                Tf
              
              -
              dti
            
            )
          
        
      
    
  




In the present application, the information to be carried by the transmitted signal Tsg will be of a binary nature, so that the integer value Vi representative of a bit to be carried by said pulse sequence will either be equal to 1 or to 0.
FIG. 3 is another chronogram which depicts a possible shape p(t) which may be chosen for constituting the above-mentioned pulses. Pulses pj(t) (for j=1 to Ns) of a same sequence may have different shapes, provided that they all have essentially a same width and carry a same quantity of energy. All pulses pj(t) (for j=1 to Ns) belonging to a same sequence may, however, have a same shape such as the shape p(t) depicted here, which is defined as a derivative of the second order of a Gaussian function, which may be expressed mathematically as:

p(t)=A·[1−4π(t/Tw)2]·exp(−2π(t/Tw)2).

Other pulse shapes known to those skilled in the art may, of course, be used in this same purpose.
FIG. 4 is yet another chronogram which depicts a dataframe DF formed by successive pulse sequences such as the one described above, each having a total duration Ts, a guard interval GI being periodically inserted between two such sequences in order to prevent alteration of a given sequence by a following one, which alterations could be caused, for example, by intermodulation products between said pulse sequences. This dataframe DF is thus constituted by successive frames having each a duration Tr, with Tr=Ts+GI, and including each a pulse sequence as described above.
A device intended to receive such a data frame DF must thus only be able to measure quantities representative of the successive amounts of power carried by the successive pulse sequences in order to identify the informational content of the dataframe DF, without having to map precisely, with respect to time, the received pulse sequences.
FIG. 5 depicts symbol decoding means DEC included in a receiver according to an alternative embodiment of the invention, in which embodiment the transmitted signal Tsg is a composite signal including a combination of K pulse sequences as described hereinbefore, each pulse sequence having thus been subjected to a symbol encoding step at the transmitting end. This receiver includes an antenna device ANT intended to receive such a composite signal Tsg. The decoding means DEC include an array of K band-pass filters PBFk (for k=1 to K) intended to separate from each other K sub-bands into which a total bandwidth used for transmitting the composite signal Tsg has been divided in order to define K different pulse sequences intended each to carry a specific symbol.
This variant of the invention enables to transmit simultaneously several symbols through a same communication channel, and thus to significantly increase the throughput of a telecommunication system in which such a variant of the invention is embodied.
In such an embodiment, each pulse sequence corresponding to a given sub-band of rank k (with k=1 to K) will be expressed as:



  
    
      
        Tsgk
        ⁡
        
          (
          t
          )
        
      
      =
      
        
          ∑
          
            i
            ,
            j
          
        
        ⁢
        
          
            Vki
            ·
            α
          
          ⁢
          
            
          
          ⁢
          
            kj
            ·
            
              pkj
              ⁡
              
                (
                
                  t
                  -
                  ckj
                  -
                  
                    j
                    ·
                    Tf
                  
                  -
                  dtki
                
                )
              
            
          
        
      
    
    ,
    with
  




  
    
      Tsg
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        ∑
        k
      
      ⁢
      
        Tsgk
        ⁡
        
          (
          t
          )
        
      
    
  



In the embodiment of the invention depicted here, the symbol decoding means DEC include an array of K squaring modules SQMk (with k=1 to K), each of which being connected to one of the band-pass filters BPFk and intended to receive a pulse sequence Tsgk (with k=1 to K) and to deliver a signal Sqsk constituted by a square of said signal Tsgk.
The symbol decoding means DEC further include an array of K integrating modules INTk (with k=1 to K), each of which being connected to one of the squaring modules SQMk and intended to deliver a modulation value Pwk representative of an amount of power carried by the corresponding pulse sequence Tsgk. Such a modulation value Pwk may for example be computed as the integral, on the duration of the channel delay, of the square signal Sqsk delivered by the related squaring module SQMk.
The symbol decoding means DEC also include an array of K comparing modules CMPMk (with k=1 to K), each of which being connected to one of the integrating modules INTk and intended to compare the modulation value Pwk to be delivered by said integrating module INTk with a predetermined threshold value Thvk, which may be different from one comparing module to another.
The symbol carried by a given pulse sequence Tsgk will thus be identified in a very straightforward manner, according to a simple decoding grid which may be expressed as follows:

    
    
        If Pwk<Thvk, then the symbol carried by pulse sequence Tsgk is S0; and
        If Thvk<Pwk, then the symbol carried by pulse sequence Tsgk is S1.
    
    


Each squaring module SQMk may be formed by a Gilbert cell fed with identical input signals. Each integrating module INTk may be formed by an operational amplifier provided with an RC feedback. Each comparing module CMPMk may be formed by an operational amplifier intended to receive a given modulation value Pwk and the predetermined threshold value Thvk assigned to this comparing module CMPMk. The symbol decoding means DEC may thus be formed by off-the-shelf analog circuits, which analog circuits are known for their high processing speed and do not require any sampling, as opposed to digital solutions, which will enable to further reduce the processing power and the time required for performing a signal decoding step according to this embodiment of the invention.
Each predetermined threshold value may be predefined and for example set at 1⁄2 or 3⁄4 if Vki is to be chosen among integer values 0 and 1. The inventors have observed, however, that such fixed thresholds, which do not take into account communication conditions between the transmitter end the receiver may generate decoding errors. The inventors thus have designed a thresholding scheme based on an equating of two probability densities, each taking into account real-time communication conditions, so that neither gray zone nor overlap will exist between two interpreting conditions.
Several expressions of first and second probability densities can be derived from existing art in the field of mathematics applied to optics. The inventors have, more specifically, singled out probability densities yielded by a so-called “Chi-square” theory, which gives, when applied by the inventors to the field of UWB transmission, the following expressions for a first probability density p0 representing a likelihood for the transmitted signal to carry a value Vki equal to 0 and a second probability density p1 representing a likelihood for the transmitted signal to carry a value Vki equal to 1:




   
  
    {
    
      
        
          
            
              p
              ⁢
              
                
              
              ⁢
              0
              ⁢
              
                (
                x
                )
              
            
            =
            
              
                1
                
                  Γ
                  ⁡
                  
                    (
                    M
                    )
                  
                
              
              ⁢
              
                
                  
                    (
                    
                      x
                      N
                    
                    )
                  
                  
                    M
                    -
                    1
                  
                
                ·
                
                  exp
                  ⁡
                  
                    (
                    
                      -
                      
                        x
                        N
                      
                    
                    )
                  
                
              
            
          
        
      
      
        
          
            
              p
              ⁢
              
                
              
              ⁢
              1
              ⁢
              
                (
                x
                )
              
            
            =
            
              
                
                  (
                  
                    x
                    E
                  
                  )
                
                
                  
                    (
                    
                      M
                      -
                      1
                    
                    )
                  
                  /
                  2
                
              
              ·
              
                
                  I
                  
                    M
                    -
                    1
                  
                
                ⁡
                
                  (
                  
                    2
                    ⁢
                    
                      
                        
                          x
                          ·
                          E
                        
                      
                      N
                    
                  
                  )
                
              
              ·
              
                exp
                ⁡
                
                  (
                  
                    -
                    
                      
                        x
                        +
                        E
                      
                      N
                    
                  
                  )
                
              
            
          
        
      
    
  




where Γ denotes the Euler function and Ij the jth Bessel function of the first kind, E being an energy carried by the pulse sequence and computed by integrating the transmitted signal over a given time period Ti, N being a noise intensity adversely affecting the transmission of said signal, and M being defined by M=(2·B·Ns·Ti+1)/2, B being a bandwidth of the pulse sequence for which the threshold value is computed.
FIG. 6 illustrates the equating p0=p1 of the probability densities defined in the above equation system, to which a threshold value Thvk will provide an optimal solution or, depending on the embodiment chosen for implementing the invention, an approximated solution.
According to a particular embodiment of the invention, the threshold value is defined by a polynom of a variable M1/2, which is an approximation of the solution of the above equation system and enables to avoid the computation of an optimal solution to said system. This polynom will preferably be limited to the second order in order to achieve a suitable balance between computing complexity and decoding efficiency, and may be expressed as:




  
    Thvk
    =
    
      N
      ·
      
        [
        
          
            L
            4
          
          +
          
            
              φ
              ⁡
              
                (
                L
                )
              
            
            ·
            
              
                M
                -
                1
              
            
          
          +
          M
        
        ]
      
    
  
  ,
  
    
      where
      ⁢
      
        
      
      ⁢
      L
    
    =
    
      E
      /
      
        N
        .
      
    
  




This formula has been singled out by the inventors as providing the best results in terms of computing costs with respect to decoding precision.
This expression has been derived by the inventors from the above mentioned equation system by using K.x−1/2.exp(x) as asymptotic equivalent of IM−1(x) for a fixed positive value of K and a large value of x. The term −1 included in the first order variable of the polynom of M1/2 stems from the mathematical manipulations of the above described equation system and may be dispensed with in other, sub-optimal embodiments of the invention. This expression enables a relatively simple dynamic update of the predetermined threshold value, which will allow to take into account possible variations of communication conditions expressed by variations of the values of M and L.
According to the preferred embodiment of the invention described above, the first-order coefficient of the polynom defining the threshold value Thvk, i.e. the coefficient in front of the (M−1)1/2 term, is given by an ordinate of a tabulated curve whose abcissis is formed by an energy ratio L=E/N related to the transmission of the relevant pulse sequence, which curve is shown on FIG. 7.

## Claims

1. A method for demodulating data transmitted in a telecommunication system including at least one transmitter and one receiver, said transmitter being configured to transmit a signal formed by at least one pulse sequence of Ns pulses over Ns time windows, each pulse being enclosed within a time chip whose position within its relevant time window is defined by a chip number, which method comprises:
decoding during at least one symbol decoding executed in said receiver to compute at least one modulation value representative of an amount of power carried by each pulse sequence; and
comparing the modulation value to at least one predetermined threshold value, wherein
the predetermined threshold value has previously been determined by equating a first and a second probability density function representing a likelihood for the transmitted signal to carry a first symbol and a likelihood for the transmitted signal to carry a second symbol, respectively, so that information carried by pulse sequences may be recovered at the receiver without said receiver having to precisely map the pulse sequences, and
each signal to be transmitted is constituted by a superimposition of a predetermined number of pulse sequences, each pulse sequence having been subjected to symbol encoding and corresponding to one of several sub-bands into which a total bandwidth available for transmission has previously been divided.

2. The method as claimed in claim 1, according to which the threshold value is defined by a polynom of a variable M1/2, where M is defined by M=(2.B.Ns.Ti+I)/2, B being a bandwidth of the pulse sequence for which the threshold value is computed, and Ti a time duration over which an integration of each pulse belonging to said pulse sequence is performed in order to compute the amount of power carried by said pulse sequence.

3. The method as claimed in claim 2, according to which the polynom defining the threshold value is limited to the second order.

4. The method as claimed in claim 2, according to which a first-order coefficient of the polynom defining the threshold value is given by an ordinate of a curve whose abcissis is formed by an energy ratio related to the transmission of the relevant pulse sequence.

5. The method as claimed in any one of claims 1 to 4, further including at least one symbol encoding to be executed before transmission of said pulse sequence, in the course of which symbol encoding each pulse sequence is multiplied by one of two integer values representative of a symbol to be carried by said pulse sequence.

6. A telecommunication system including at least one transmitter and one receiver, said transmitter being configured to transmit a signal formed by at least one pulse sequence of Ns pulses over Ns time windows, each pulse being enclosed within a time chip whose position within its relevant time window is defined by a chip number in which the receiver comprises:
a symbol decoder configured to compute at least one modulation value representative of an amount of power carried by each pulse sequence; and
a comparator configured to compare said modulation value to at least one predetermined threshold value obtained by equating a first and a second probability density function representing the likelihood for the transmitted signal to carry a first symbol and the likelihood for the transmitted signal to carry a second symbol, respectively, wherein
the transmitter further includes a signal combiner configured to receive a predetermined number of pulse sequences, each pulse sequence having been generated by the symbol encoder and corresponding to one of several sub-bands into which a total bandwidth available for transmission has previously been divided, said signal combiner being configured to combine all said pulse sequences into a signal to be transmitted.

7. The telecommunication system as claimed in claim 6, in which the transmitter includes a symbol encoder configured to multiply each pulse sequence by one of two integer values representative of a symbol to be carried by said pulse sequence.

8. A receiver configured to receive a signal formed by at least one sequence of Ns pulses over Ns time windows, each pulse being enclosed within a time chip whose position within its respective time window is defined by a chip number, which receiver comprises:
a symbol decoder configured to compute at least one modulation value representative of an amount of power carried by each pulse sequence; and
a comparator configured to compare said modulation value to at least one predetermined threshold value obtained by equating a first and a second probability density function representing the likelihood for the transmitted signal to carry a first symbol and the likelihood for the transmitted signal to carry a second symbol, respectively, wherein
each signal to be received is constituted by a superimposition of a predetermined number of pulse sequences, each pulse sequence having been subjected to the symbol encoding and corresponding to one of several sub-bands into which a total bandwidth available for transmission has previously been divided.