Abstract:
A communications signal is received through a propagation channel, down-converted in frequency and then converted into a digital signal. The samples of the digital signal are processed to estimate the information conveyed by the communications signal. The estimated information is then used with knowledge about the propagation channel to model the samples of the digital signal. The modeled samples are compared with actual samples of the digital signal to deduce phase errors in the digital signal. The phase errors are then used to deduce a frequency error in the digital signal that can be used to correct the samples of the digital signal and to correct the down-conversion process.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a National Phase Application of PCT/GB2005/003486, which claims priority to GB 0420186.9, which is hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     For most types of mobile communication system to operate satisfactorily, it is required that the receiver is locked in time and frequency to the transmitter. Traditionally, the receiver achieve-frequency synchronism with the transmitter by controlling the frequency of a local oscillator used to down-convert the signal from RF to base-band (or IF depending on the radio architecture). 
       FIG. 1  depicts various processing stages that form part of such an approach. Indeed,  FIG. 1  can be taken to represent a view into the signal processing chain of a mobile telephone or a cellular communications network base station. It should be noted that the blocks shown in  FIG. 1  represent processing operations performed on a received signal but do not necessarily correspond directly to physical units that may appear within a practical implementation of a receiver. The first stage  101  corresponds to the radio frequency processing. During the radio frequency processing, the received signal is down-converted to base-band using a mixer  103 . The reference frequency used to drive the mixer is generated by an oscillator  104 . Following this carrier down-conversion, the signal is low-pass filtered  102  and then passed to the mixed-signal processing stage  108 . The mixed signal processing includes Analogue-to-Digital Conversion (ADC)  105 , sampling  106  and low pass filtering  107 . The resulting signal, which is now digital, is supplied to the digital signal processing stage  109  where it is buffered in preparation for processing. The demodulation stage  110  produces estimates of the transmitted information bits. As part of the digital signal processing, estimates of the residual frequency offset in the digital signal are produced. Those frequency error estimates are filtered at  111  in order to improve their accuracy and used to control the frequency reference produced by the oscillator  104 . 
     This frequency locking mechanism is typical of mobile communication receivers and achieves synchronism through a feedback loop. Such an approach is very effective in conditions where the frequency reference of the transmitter is stable over time. However, such stability cannot always be achieved. For example in cellular communication systems, the hand-over of a user between different base-stations will result in a short term offset in the frequency of the received signal. This frequency offset will usually be relatively low (0.1 parts per million is a typical value) but can negatively impact on the performance of the demodulation of the signal within the receiver, especially when a high order modulation scheme is used. For example, the performance of the 8PSK modulation used by the E-GPRS (Enhanced General Packet Radio Service) system will be affected by such a small residual frequency offset. In order to limit the performance degradation that such a residual frequency offset causes to the information link, a correction of the receiver frequency reference should be made as quickly as possible. The mechanism described in  FIG. 1  is therefore not suitable since the feedback loop introduces a delay in the correction made to the signal. 
     One possible mechanism to correct this residual frequency offset is depicted in  FIG. 2 . It can be seen that this approach is similar to the one presented in  FIG. 1 . However, an extra processing stage has been introduced in the digital signal processing section  209 . The digital signal produced by the mixed-signal processing stage  208  is buffered and first processed by the ‘estimate and correct frequency error’ unit  211 . The resulting signal, from which the residual frequency offset will have ideally been removed, is then demodulated  210 . The ‘estimate and correct frequency error’ unit uses the buffered received signal to first estimate the residual frequency offset. Once this frequency offset has been estimated, a phase correction to the received signal is performed in order to remove it. The residual frequency offset in the received signal can be estimated using frequency component analysis techniques. However, because the residual frequency offset is low compared to the sampling frequency, a large number of samples is usually required in order to obtain an accurate estimate. 
     BRIEF SUMMARY OF THE INVENTION 
     According to one aspect, the invention provides apparatus for analysing a digital signal representing a communications signal, comprising a series of information symbols, that has been acquired by a receiver through a propagation channel, the apparatus comprising symbol estimation means for processing samples of the digital signal to estimate symbols of the communications signal, sample simulation means for modelling at least one sample of the digital signal using estimated symbols and knowledge about the propagation channel and phase error estimation means for comparing a modelled sample of the digital signal with an actual sample of the digital signal to estimate a phase error in the latter sample. 
     The invention also relates to a method of analysing a digital signal representing a communications signal, comprising a series of information symbols, that has been acquired by a receiver through a propagation channel, the method comprising a symbol estimation step comprising processing samples of the digital signal to estimate symbols of the communications signal, a sample simulation step comprising modelling at least one sample of the digital signal using estimated symbols and knowledge about the propagation channel, and a phase error estimation step comprising comparing a modelled sample of the digital signal with an actual sample of the digital signal to estimate a phase error in the latter sample. 
     Thus, the invention provides a way of quantifying phase errors in a communications signal acquired by a receiver. Such errors may be attributable, at least in part, to imperfect frequency conversion of the acquired communications signal within the receiver. 
     If desired, estimated phase errors can be used to correct the digital signal representing the acquired communications signal. In certain embodiments, a phase error that is estimated from an actual sample of the digital signal and a modelled sample of the digital signal is used to correct the sample of the digital signal that follows the sample that was used to produce the phase error estimate. 
     In certain embodiments, phase error estimates are used to produce estimates of a frequency error in the digital signal representing the acquired communications signal. A frequency error estimate so produced may be used to correct phase errors in the digital signal and/or correct a frequency conversion process involved in the production of the digital signal. 
     As mentioned earlier, the invention involves the estimation of symbols of the communications signal. These estimated symbols can, for example, be in the form of modulated symbols having complex values or demodulated symbols represented by groups of bits. 
     The invention can be implemented by hardware or by software running on a processor or by a combination of both. The invention can be employed in a participant of a mobile communications network, such as a base station or a hand set. In particular, the invention is suited to use in a EGPRS system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       By way of example only, certain embodiments of the invention will now be described with reference to the accompanying drawings, in which: 
         FIG. 1  presents a general mechanism for achieving frequency synchronism of a receiver with a transmitter; 
         FIG. 2  presents a mechanism for achieving frequency synchronism of a receiver with a transmitter in the case where a large number of received samples are available; 
         FIG. 3  presents a decision-directed approach for the phase correction of a received signal; and 
         FIG. 4  describes various computations performed in the approach shown in  FIG. 3 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 3  gives an overview of a digital signal processing unit  301  that can be used in place of unit  109  to implement an embodiment of the invention. As in  FIGS. 1 and 2 , the signal generated by the mixed-signal processing is buffered within the digital signal processing unit  301  in preparation for processing. Each decision produced by demodulation unit  306  (analogous to unit  110 ) is compared with the corresponding received sample to produce an estimate of the latter&#39;s phase error, and hence current frequency offset, using unit  303 . Because the demodulation unit  306  will introduce a delay in the generated decisions, a delay unit  302  is required for the received samples. Filtering, or averaging, of those frequency estimates is then performed by unit  304  in order to improve the accuracy of those estimates. This filtered frequency offset estimate is then used by unit  305  to correct the phase of the received samples. Each decision produced by the demodulation unit  306  is used as soon as available rather than at the end of the whole information block. Hence, the frequency correction can be applied to the received signal as soon as decisions are made by the demodulation unit  306 . The accuracy of this frequency correction is then improved as more samples from the received signal are processed. 
     In order to describe the computations performed by digital signal processing stage  301 , it is first useful to present the model of the transmission link. 
     A transmission block {d k } kε(1, . . . , D)  is made of D information bits d k ε{0,1}. These information bits are first grouped into C sets of M bits (it is assumed that D=M×C):
 
Δ k   ={d   M×k   , . . . ,d   (M×k)+(M−1) }
 
     Each set of M information bits Δ k  is modulated onto the complex plane using a modulation scheme M that maps sets of M bits on to the complex plane. For example, in the case of an 8PSK modulation, the modulation M can be expressed as: 
     
       
         
           
             
               
                 
                   
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     A slightly modified version of the 8PSK modulation described by the above equation is used in the E-GPRS system. 
     The C modulated symbols c k =M (Δ k ) are then transmitted over the air and in the process are distorted by the propagation channel. Assuming a general model with memory for the propagation channel, the samples {s k } kε(1, . . . , C)  at the input of the receiver can be expressed as: 
             {             s   k     =     F   ⁡     (       c   k     ,     ξ     k   -   1         )                     ξ   k     =     S   ⁡     (       c   k     ,     ξ     k   -   1         )                         
ξ k  represents the state (memory) of the propagation channel when the k th  modulated symbol is transmitted. Note that any filtering performed by either the transmitter and/or the receiver can be incorporated in the propagation channel model. The mappings F and S used to model the propagation channel can be time varying. However, to simplify the notations, it is assumed in this document that those mappings do not depend on time.
 
     At the receiver, the signal will be corrupted by noise and by the effect of the residual frequency offset between the transmitter and the receiver. Taking into account these effects, the signal which is input to the digital signal processing unit  301  can be expressed as:
 
 r   k   =e   j×θ     k     ×s   k   +n   k  
 
where {n k } kc(1, . . . , C)  denotes the sequence of additive noise samples and the e j×θ     k    multiplicative term models the effect of the residual frequency offset on the received signal. The phase offset on the k th  sample can be expressed as:
 
θ k =( k ×           )+θ 0  
 
where           denotes the residual angular frequency offset and is related to frequency error through:

             f   =       Θ     2   ⁢   π       ·     f   s             
where f s  is the sampling frequency.
 
     The operation of the digital signal processing stage  301  in correcting the residual phase offset in a received data stream will now be described with the aid of  FIGS. 3 and 4 , the latter Figure showing in more detail the operations that occur within the digital signal processing stage  301 . 
     After the reception of the k th  complex sample r k , the demodulator  306 / 401  produces an estimate of the transmitted symbol Δ k−δ . The delay δ in the symbol decisions produced by the demodulator  306 / 401  can be explained by the fact that the propagation channel between the transmitter and the receiver has memory. Hence, the transmitted information is spread over multiple received symbols and the demodulator  306 / 401  will usually combine the information in those different symbols in order to improve its performance. The symbol decision produced by the demodulation unit  306 / 401  is denoted {circumflex over (Δ)} k−δ . 
     Using knowledge of the modulation used by the transmitter, the digital signal processing stage  301  can then generate an estimate of the transmitted complex symbol c k−δ . This estimated complex symbol is denoted ĉ k−δ . It should be noted that the digital signal processing stage  301  may not have prior knowledge of the modulation scheme M being used by the transmitter and hence may have to deduce the modulation scheme from the signal stream arriving from the mixed signal unit  108 . This is the case in, for example, the EGPRS system where the transmitter can select between the GMSK and 8PSK modulation schemes without explicitly providing this format information to the receiver. 
     Assuming that the digital signal processing stage  301  has knowledge of the propagation channel conditions, modelled by the mappings F and S, it is possible for the digital signal processing stage to generate an estimate of the complex symbol s k−ε . This estimate is denoted ŝ k−δ . 
     It should be noted that the digital signal processing stage  301  will usually not have prior knowledge of the propagation channel conditions. However, it may be possible for the digital signal processing stage  301  to generate an estimate of the channel mappings. In this case, the digital signal processing stage  301  can generate the complex symbol ŝ k−δ  using those estimates rather than the true mappings. For example, in the EGPRS system, the sequence of transmitted symbols includes a pattern, referred to as training sequence, which is known to the receiver. The receiver can use this training sequence to generate an estimate of the propagation channel conditions. 
     If one assumes that the channel estimation is perfect, then the symbol ŝ k−δ  corresponds to the received symbol r k−δ  a without additive noise or residual frequency offset. This means that, if the noise in the received sample r k−δ  is ignored, the phase difference between the two samples is equal to θ k−δ . This relation can be used to estimate the residual frequency offset. 
     One possible way to produce an estimate {circumflex over (θ)} k−δ  of the phase difference is through the complex multiplication of the received symbol r k−δ  with the complex conjugate of the re-modulated symbol ŝ k−δ . This modulation produces the following complex symbol:
 
 p   k   =r   k−δ   ×ŝ   k−δ   =e   j×θ     k−δ   ×( s   k−δ   ×ŝ   k−δ )+( n   k−δ   ×ŝ   k−δ )
 
     If one ignores the noise term and assumes that the symbol ŝ k−δ  was generated perfectly, the symbol p k  can be expressed as:
 
 p   k   =e   j×θ     k−δ     ∥s   k−δ ∥ 2  
 
     Hence, the estimate {circumflex over (θ)} k−δ  can be generated by computing the phase of the complex sample p k . 
     It should be noted that a different set of computations could be performed to estimate the phase difference {circumflex over (θ)} k−δ  from the received symbol r k−δ  and the re-modulated symbol ŝ k−δ . 
     One such alternative method will now be described in detail. In this method, it is assumed that the phase error is small such that the sine of the phase error can taken to be an approximation of the phase error. Thus: 
                 θ   ^       k   -   δ       ≅       Im   ⁡     (     p   k     )               Re   ⁡     (     p   k     )       2     +       Im   ⁡     (     p   k     )       2                 
where Re(p k ) and Im(p k ) are the real and imaginary part of p k . Within the digital signal processing stage  301 , the preceding equation can be implemented as a form of Taylor series expansion as follows:
 
{circumflex over (θ)} k−δ ≅Im( p   k )(1+0.25 ×Z+ 0.09375 ×Z   2 +0.0390625 ×Z   3 +0.017089844 ×Z   4 +0.00769043 ×Z   5 +0.00352478 ×Z   6 +0.001636505 ×Z   7 +0.000767112 ×Z   8 )
 
where Z is defined as:
 
 Z= 2×(1−(Re( p   k ) 2 +Im( p   k ) 2 ))
 
     An estimate of the residual frequency offset can then be generated from the phase difference estimates for a series of demodulated symbols ĉ k−δ . This estimate is denoted as {circumflex over (Θ)} k . The estimated residual frequency offset and the estimated phase difference are linked through the following equation:
 
{circumflex over (θ)} k−δ =(( k −δ)×           )+{circumflex over (θ)} 0  

     Hence the residual frequency offset can be estimated by performing a linear regression on the phase difference estimates {circumflex over (θ)} k−δ . If, for example, the linear regression minimises the mean square error, the residual frequency offset can be computed using the following equation 
                 Θ   ^     k     =         12   ×     (       ∑     i   =   0       k   -   δ       ⁢     i   ·       θ   ^     i         )       -     6   ×     (     k   -   δ     )     ×     (       ∑     i   =   0       k   -   δ       ⁢       θ   ^     i       )               (     k   -   δ   +   1     )     3     -     (     k   -   δ   +   1     )               
where i=0 to k−δ and denotes all of phase difference estimates calculated so far for the current burst.
 
     The initial phase {circumflex over (θ)} 0  can be estimated using the following equation: 
     
       
         
           
             
               
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     It is to be noted that this initial phase is re-estimated for each new sample {circumflex over (θ)} i  produced by the demodulation unit  306 / 401 . 
     The estimates of the residual frequency offset             and the initial phase {circumflex over (θ)} 0  are then used to correct the phase of the next received symbol to be processed by the demodulation unit  306 / 401 . This is achieved by arranging that the next received symbol r k+1  to be processed by the demodulation unit  306 / 401  is multiplied by the complex phasor:
 
 e   −j×(((k+1)×             )+{circumflex over (θ)}     0     )  

     At that point, assuming that the linear regression estimated perfectly the residual frequency offset             and the initial phase {circumflex over (θ)} 0 , the modified symbol to be processed by the demodulation unit does not have any phase error.
     For communication systems where the channel conditions are estimated using a sequence of known transmitted symbols, it is possible to improve the accuracy of the estimates of the residual frequency offset             and the initial phase {circumflex over (θ)} 0  by performing the linear regression using symbols close to this training sequence first. In this case, the initial phase {circumflex over (θ)} 0  will be incorporated in the model of the propagation channel. Moreover, because the initial phase {circumflex over (θ)} 0  does not need to be estimated, the computational complexity is also reduced.
     For example, in the EGPRS system, a sequence of 26 known symbols is inserted in the middle of a burst of information. When symbols close to the training sequence are used, the residual frequency error             can be estimated using the following equation:
     
       
         
           
             
               
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     The phasor used to correct the phase of the next symbol to be processed by the demodulation unit is then equal to:
 
 e   −j×(((k+1)×               ))  

     It should be noted that the quality of the samples {circumflex over (θ)} i  which are processed by the linear regression is degraded by the noise that is present in the received signal data stream. It is therefore possible to improve the accuracy of the estimate             by ignoring samples {circumflex over (θ)} i  that are deemed too noisy. For example,           can be calculated using the following equation:
                 Θ   ^     k     =       (       ∑     i   =   0       k   -   δ       ⁢     i   ·     λ   i     ·       θ   ^     i         )       (       ∑     i   =   0       k   -   δ       ⁢       i   2     ·     λ   i         )             
where λ i {0,1} is a weight indicating whether the phase sample {circumflex over (θ)} i  is excised or not. The preceding equation is based on the a priori assumption that {circumflex over (θ)} 0  is zero.
 
     Different approaches can be taken to decide whether a phase sample should be excised. For example, a sample {circumflex over (θ)} i  could be discarded (i.e., λ i  set to 0) if it is more than a given distance away from the line fitted to the {circumflex over (θ)} i  data by the linear interpolation. Another option is to use any prior knowledge that the receiver may have about the maximum that is possible for the residual frequency error. For example, if the receiver knows that            ≦          then it is possible to check that the current phase sample {circumflex over (θ)} i  lies within the region defined by          . Given a priori limits          ≦          it is possible to calculate the line (of phase error versus received sample index) with the highest allowable gradient (since the phase error for a given sample is proportional to the sample index and the frequency offset—hence the use of the linear regression to estimate the frequency error). If the phase were estimated perfectly, the phase for the k th  sample would never be larger than (k×         )+θ 0 . Hence, samples for which the phase estimate is larger than that can be excised. It should be noted, however, that since in practice the phase estimates will be noisy, only the samples which are larger than the ideal maximum value plus a statistical margin should be removed. It will also be understood that, since the frequency error can be positive or negative, the region corresponding to valid phase estimates needs to contain both positive and negative phase estimates. Finally, the check on the phase error being lower than the expected (k×         )+θ 0  requires the knowledge of θ 0 . One solution is to use an up to date estimate of θ 0  from the linear regression. Another solution is to use a fixed, pre-defined, value.
       FIG. 4  describes how the various computations described above are put together in order to correct the residual frequency offset in the received signal. The demodulation unit  401  provides estimates of the transmitted information symbols {circumflex over (Δ)} k−δ . Those information symbols are then modulated through unit  402 . The channel mapping performed by unit  403  is then applied to those modulated symbols. This produces estimates of the received symbols ŝ k−δ . Those symbols are combined with the received symbols s k−δ . The time synchronism of those two data streams is achieved by the delay unit  404 . The phase difference samples {circumflex over (θ)} k−δ  are computed by unit  405  and are then processed by unit  406 . Unit  406  performs the linear regression on the phase difference samples (including, if desired, sample excision) and produces an estimate of the residual frequency error             and, depending on the variant, the initial phase {circumflex over (θ)} 0 . This information is then used by the phase correction unit  408  to de-rotate the received symbol stream.
     It should be noted that, in some cases, the modulation unit  402  and the channel mapping unit  403  may not be required. This is the case when the demodulation unit  401  outputs not only estimates of the transmitted information symbols {circumflex over (Δ)} k−δ  but also estimates of the modulated symbols ŝ k−δ . For example, if the demodulation technique used within unit  401  is based on the Viterbi algorithm, the samples ŝ k−δ  are usually required during the computations performed to derive the information symbols {circumflex over (Δ)} k−δ . In such circumstances it is then not necessary to replicate those computations in the modulation unit  402  and the channel mapping unit  403 . 
     It should also be noted that the residual frequency offset estimate             used to perform the phase correction on the received symbols in unit  408  can also be used to drive the feedback loop controlling the local oscillator (unit  111  in  FIG. 1 ).