Patent Publication Number: US-7899136-B2

Title: Frequency-offset estimation

Description:
FIELD OF THE INVENTION 
     The invention relates to the estimation of an overall frequency-offset on the basis of a plurality of frequency-offset estimates and further to the estimation of a quantity representative of a signal-to-noise ratio. In particular, the invention relates to communications systems and receiver. 
     BACKGROUND OF THE INVENTION 
     In mobile communication systems a mobile station may be connected to multiple base stations at the same time. In this case, frequency-offset correction in the mobile station is typically not done separately for each base station. Instead, frequency offset correction aims at correcting offsets of the frequency generating device. Usually, only a single device is used as a reference for frequency generation. Therefore, if frequency-offset estimates are obtained by measurement from a plurality of signal sources such as, for example, base stations to which the mobile station is connected, a strategy has to be devised of how to combine these multiple frequency-offset estimates into a single value, i.e. an overall frequency-offset estimate. As the reception performance and transmit frequency offset on the uplink of a mobile station sensitively depends on the compensation of frequency-offsets, an efficient strategy for combining the frequency-offset estimates into a single value is desirable. 
     Further, quantities representative of signal-to-noise ratios of signals in a radio receiver are known to be necessary for many applications and are used in a radio receiver for a variety of computations. Therefore, efficient algorithms and circuitry to generate signal-to-noise estimates in a radio receiver are desirable. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Aspects of the invention are made more evident by way of example in the following detailed description of embodiments when read in conjunction with the attached drawing figures, wherein 
         FIG. 1  is a block diagram showing basic functional blocks of a receiver; 
         FIG. 2  is a block diagram of the automatic frequency control unit shown in  FIG. 1 ; 
         FIG. 3  is a schematic illustration of an embodiment of the combiner shown in  FIG. 2 ; 
         FIG. 4  is a schematic diagram of a device for combining multiple frequency-offset estimates in a receiver; and 
         FIG. 5  is a schematic diagram of a device for calculating signal-to-noise ratio estimates. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the following description further aspects and embodiments of the present invention are disclosed. In addition, reference is made to the accompanying drawings, which form a part thereof, and in which is shown by way of illustration, one or more examples in which the invention may be practiced. The embodiments herein provide a better understanding of one or more aspects of the present invention. This disclosure of the invention is not intended to limit the features or key-elements of the invention to a specific embodiment. Rather, the different elements, aspects and features disclosed in the embodiments can be combined in different ways by a person skilled in the art to achieve one or more advantages of the present invention. It is to be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present invention. The elements of the drawing are not necessarily to scale relative to each other. Like reference numerals designate corresponding similar parts. 
     At a receiver, the actual frequency of the received signal may, for various reasons, be different from a local frequency used in the receiver to process the received signal, thereby causing a frequency-offset in the receive signal path of the mobile receiver. For instance, frequency shifts in the received radio signal or detuning of the local oscillator of the receiver may account for the generation of such frequency-offset in the receiver. A frequency-offset in the receiver significantly impairs the performance of the receiver and may lead to a transmit center-frequency offset that exceeds allowed tolerance levels. 
     In the following, according to a first embodiment, an improved combining of frequency-offset estimates in a receiver is described. The embodiments described below may be employed in various mobile communications systems, among them CDMA (Code Division Multiple Access) systems such as, for example, UMTS (Universal Mobile Telecommunications System) or mobile communications systems using other types of multiple access schemes, for example, GSM (Global System for Mobile Communications). Communications systems considered below may be, for example, multi-cell systems or single cell systems comprising multiple transmitters. 
       FIG. 1  illustrates basic functional blocks of a receiver, for example, a mobile receiver. The receive signal path of the receiver may comprise an amplification stage  1 , a first reception section (RX 1 )  2 , a received signal strength indicator (RSSI) unit  3 , an automatic gain control (AGC) unit  5 , a second reception section (RX 2 )  4 , an automatic frequency control (AFC) unit  6  and a data processing unit (DATA)  7 . 
     Amplification stage  1 , first reception section  2 , RSSI unit  3  and AGC unit  5  form a feedback loop used for received signal power control. More specifically, amplification stage  1  receives at input  10  an input signal provided by a receiver input. The receiver input may be an antenna (not shown) followed by optional circuitry such as filters and/or additional signal preprocessing units. The input signal is amplified (e.g., multiplied) by a power control signal connected to the second input  11  of the amplification stage  1 . An output of the amplification stage  1  is fed into the first reception section  2  of the receiver. The first reception section  2  typically comprises the RF (Radio Frequency) part of the receiver. Thus, as known in the art, the input signal is down-converted to an intermediate frequency (IF) band or the baseband. Down-conversion is typically done by a mixer (not shown) which is operated by a local oscillator  8  outputting an oscillator signal of frequency f os . Further, the first reception section  2  may comprise filter stages and other signal processing units as known in the art. 
     An output signal of the first reception section  2  is fed into the RSSI unit  3 . The RSSI unit  3  generates an output  12  which is representative of the signal strength or signal power of the received signal. The output  12  of the RSSI unit  3  is coupled to an input of the AGC unit  5 . The AGC unit  5  compares the output  12  of the RSSI unit  3  to a target value and generates an amplification control signal  13  in response to the comparison result. The amplification control signal  13  is fed into a control input  11  of the amplification stage  1  and thus is used to control the received signal power amplification of the receiver. In other words, the feedback loop comprising the amplification stage  1 , the first reception section  2 , the RSSI unit  3  and the AGC unit  5  establish a regulation circuit which is operative to adjust the signal power in the received signal data stream at the signal output  14  of the RSSI unit  3  to a fixed, known energy target level Pt′. 
     The signal output  14  of the RSSI unit  3  is fed into the second reception section  4 . The second reception section  4  of the receiver may comprise a demodulator for reconstructing data samples (also termed symbols in the following) contained in the received signal data stream. To this end, the second reception section  4  may for instance comprise parts of a RAKE receiver for detection and preprocessing of signal contributions received over different propagation paths of a radio channel. Further, the second reception section  4  may be equipped with a descrambling and a despreading stage used for extracting the wanted data and control/pilot signals from the received signal which is a superposition of all data and control signals picked up at the input. As known in the art, in CDMA communications systems, user signals (i.e. logical channels per base station and user) are separated by different spreading codes. Thus, user signal separation in the receiver may be performed by despreading the received signal. 
     Further, the second reception section  4  provides for separation of signals transmitted from different signal sources such as base stations. In CDMA communications systems, each signal source uses an individual scrambling code for coding signals to be transmitted. Therefore, separation of signals received from different signal sources in the receiver may be accomplished by descrambling the received signal. 
     In communications systems using other techniques for multi-user access and/or base station identification, it is likewise possible to distinguish between signals which are intended for different users and/or received from different signal sources (e.g., base stations), respectively. In other words, at an output  15  of the second reception section  4 , a user-specific and signal source-specific signal may be provided. Such signal may be represented by a stream of complex-valued symbols r i,m  associated with the particular mobile station, where i denotes the time index and m identifies the base station, m=1, . . . , M, from which the symbol r i,m  has been transmitted. 
     The output  15  of the second reception section  4  is coupled to an input  16  of the AFC unit  6  and an input  17  of the data processing unit  7 . Data processing in the data processing unit  7  may be accomplished according to known techniques in the art (e.g., may comprise de-interleaving, channel-decoding etc.) and will not be described in more detail in the following. In the AFC unit  6 , the symbols r i,m  are processed to calculate an overall frequency-offset estimate  Δf . The overall frequency-offset estimate  Δf  is used as input for a control unit  9  which generates a frequency control signal f c  for adjusting the frequency f os  generated by, for example, an oscillator  8 . Thus, the first reception section  2 , RSSI unit  3 , second reception section  4 , AFC unit  6 , control unit  9  and oscillator  8  form a frequency closed-loop control circuit which is operable to maintain  ΔA =0. The control unit  9  may be implemented by a look-up table or a conversion function and affects the control response of the frequency closed-loop control circuit, in one embodiment. In more general terms, the overall frequency-offset estimate  Δf  may be used to control the processing of the received signal in the mobile receiver. 
     Various modifications are feasible for implementing the frequency closed-loop control circuit according to the invention. For instance, the frequency control signal f c  may be input to a frequency correction stage (not shown) instead of oscillator  8 . The frequency correction stage may be arranged at any point in the receive signal path between the antenna and the input  17  of the data processing unit  7 . Such frequency correction stage may either be located in the analog part or in the digital part of the receiver. In the latter case, frequency correction may for instance be performed in the second reception section  4  by means of, for example, a digital frequency correction circuit (not shown). In this regard, it is to be noted that analog-to-digital conversion is typically performed in the first reception section  2  of the receiver but may generally be performed at any convenient point in the receive signal path shown in  FIG. 1 . 
       FIG. 2  illustrates by way of example the design of the AFC unit  6  according to one embodiment. The AFC unit  6  comprises a phasor generation unit  100 , an averaging unit (AVG)  101 , a unit  102  computing the squared magnitude of the complex phasors, a divider (DIV)  103 , a combiner  104  and an argument unit  105 . The phasor generation unit  100  computes on the basis of the input symbols r i,m  complex-valued phasors p i,m . Phasor p i,m  may be defined in one embodiment by
 
 p   i,m   =r   i,m   ·r   i−D,m ,  (1)
 
and is the product of symbol r i,m  and the conjugate complex of a preceding symbol r i−D,m  (associated with the same signal source m). D is an integer and may typically be chosen to be D=1. The argument of phasor p i,m , i.e. arg(p i,m ), is indicative of a phase shift between actual symbol r i,m  and preceding symbol r i−D,m .
 
     Phasors p i,m  are fed into the averaging unit  101 . In the averaging unit, phasors p i,m  are averaged or summed over an averaging length L avg  according to 
     
       
         
           
             
               
                 
                   
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     The averaged phasors p m   av  may be used twofold, namely for computing frequency-offsets Δf m  associated with the symbol streams r i,m  and for computing quantities representative of a signal-to-noise ratio associated with the symbol streams r i,m . 
     To generate an estimate of the frequency-offset Δf m , the averaged phasors p m   av  are fed into the argument unit  105 . Argument unit  105  calculates the argument—i.e. the phase or angle—of each averaged phasor p m   av , which is proportional to the frequency-offset Δf m  according to Δf m =arg(p m   av )/(2π·L avg ·T sym ). Note that normalizing by the factor (2π·L avg ·T sym ) −1  is not depicted in  FIG. 2 . Further note that for D≠1, D·T sym  has to be used instead of T sym . 
     To generate quantities representative of the signal-to-noise ratios, the averaged phasors p m   av  are fed into the square unit  102  followed by the divider  103 . At the output of the divider  103 , a quantity C m  which relates to the signal-to-noise ratio associated with the symbol stream r i,m  is output. 
     In the following, it is shown that a quantity related to the signal-to-noise ratio associated with the symbol stream r i,m  may be computed on the basis of phasors p i,m . A quantity related to the signal-to-noise ratio may be any quantity which is related to the signal-to-noise ratio as a meaningful metric, particularly a quantity which translates into the signal-to-noise ratio by a unique functional relationship. To simplify notation, the index m is dropped because the computation is identical for symbols from each signal source (e.g. base station) m. 
     The energy of the averaged phasor p av  is the square of the absolute value of the complex-valued averaged phasor p av  and can be written as the sum of the square of the averaged phasor&#39;s real and imaginary part, i.e.
 
 Q=|p   av | 2   =re ( p   av ) 2   +im ( p   av ) 2 .  (3)
 
     This energy relates to the signal-to-noise ratio of the signal. It is assumed that the receiver uses ideal automatic gain control based on RSSI measurements on chip level before base station separation and user separation (e.g., descrambling and despreading). To simplify matters, it is further assumed that all non-wanted signal parts contribute either orthogonally (e.g., are cancelled by despreading) or appear as white Gaussian random noise (such as, for example, signals from base stations on different scrambling codes). The following derivation uses the special case of a CDMA receiver. 
     The following notation is used below:
     E The wanted-signal energy per chip   N The noise energy per chip   SNR=E/N The signal-to-noise ratio on chip-level   L corr  Spreading factor (number of chips per symbol)   L avg  Averaging length for phasors   Δf frequency-offset   T sym  Symbol sampling time   Pt′ AGC energy target level per chip at the output of the AGC feedback loop   

     The signal energy at the output of the AGC feedback loop is the AGC energy target level, i.e.
 
Pt′=E+N  (4)
 
with
 
N=Pt′/(1+SNR)
 
E=Pt′−N  (5)
 
     A frequency-offset of Δf reduces the average energy per chip E after despreading over L corr  values (corresponding to T sym ) to a “degraded” average energy per chip E deg  according to
 
E deg *L corr   2 =E*|sinc(Δ f *T sym )| 2 *L corr   2   (6)
 
     For the quality indication of frequency-offset estimates, a degraded signal-to-noise ratio can be defined by
 
SNR deg =E deg /N with SNR deg &lt;SNR  (7)
 
     The squared averaged phasor energy Q can finally be expressed by 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     Pt takes into account any possible power scaling by the second reception section  4 , i.e. may be interpreted as the energy target level per chip downstream of the second reception section  4 . If the second reception section  4  does not introduce any power scaling, Pt=Pt′. 
     A first approximation of this term can be derived on the basis of the following assumptions: 
     SNR&lt;&lt;1 (  SNR deg &lt;&lt;1) 
     L*SNR deg &gt;&gt;2. 
     Under these assumptions, equation (8) yields
 
 Q= 4Pt 2 (SNR deg   2 L 2 +L).  (9)
 
     A second even simpler approximation is found on the basis of more stringent assumptions: 
     SNR&lt;&lt;1 (  SNR deg &lt;&lt;1) 
     L*SNR deg &gt;&gt;2 
     L*SNR deg   2 &gt;1 
     Under these assumptions, equation (8) yields
 
Q=4Pt 2 L 2 SNR deg   2 .  (10)
 
     As it is apparent from equation (10), the energy Q of the averaged phasor is proportional to the square of the degraded signal-to-noise ratio SNR deg  if L is large enough. As an example, in UMTS, when using the common pilot channel symbols as input symbol stream r i,m  from each base station m, the spreading factor has a fixed value of L corr =256. Thus, L avg  may be chosen such that equation (10) is roughly satisfied (note that in many cases not necessarily exact results are required). Using for instance an average length of L avg =150 corresponding to one UMTS frame, the approximation set out in equation (10) holds for about −34 dB&lt;SNR deg &lt;−10 dB. Translated from chip-level to symbol-level, the range of the degraded signal-to-noise ratio SNR deg  is from −10 dB to +14 dB. This range should be fully sufficient to provide differentiation between different signal-to-noise ratios of frequency-offset estimates. 
     The averaging length L avg  may be variable and be chosen to be different for different measurements. For this reason and to further limit the dynamic range of the results, the energy Q of the averaged phasor may be divided by L 2 . This is done in the divider  103  according to
 
 C=Q /L 2 .  (11)
 
     As the AGC energy target level Pt′ and thus the scaled energy target level Pt are likely to be fixed values, C is then a quantity representative of the signal-to-noise ratio of the processed signal irrespective of the used average length L avg . 
       FIG. 3  illustrates an exemplary embodiment of the combiner  104 . Combiner  104  may comprise an optional discarding unit (DISC)  200 , a weighting unit (WG)  210  and an averaging unit (AVG)  220 . 
     The discarding unit  200  is operable to discard frequency estimates Δf m  having a degraded signal-to-noise ratio SNR deg  lower than a required minimum SNR deg,min . To this end, the discarding unit  200  may comprise a multiplier  201 , a comparator  202  and a multiplexer  203 . The multiplier  201  is configured to compute a threshold value T according to
 
T=4SNR deg,min   2 Pt 2   (12)
 
in one embodiment, wherein C m  is compared to threshold value T in comparator  202 . If C m &lt;T, the corresponding frequency-offset Δf m  has a low confidence because it has been calculated on the basis of noisy data with a degraded signal-to-noise ratio SNR deg  (which is represented by C m ) lower than the minimum degraded signal-to-noise ration SNR deg,min . In this case, C m  is set to C m =0 by multiplexer  203 . It is to be noted that threshold values T different from the threshold value T indicated in equation (12) may be used.
 
     Values of C m  as output by the discarding unit  200  are input into the weighting unit  210 . The weighting unit  210  may comprise a first multiplier  211  and a second multiplier  212  connected in series. The (optional) first multiplier  211  multiplies each value C m  by a weighting factor J m , in one embodiment. Weighting factor J m  may provide for a source-importance weighting adjustment which introduces priorities with respect to the signal content. More specifically, a symbol stream r i,m  of one specific signal source (e.g. base station)  m  may be of higher importance for signal demodulation in the receiver because, for instance, base station  m  offers a specific service. As an example, base station  m  may provide HSDPA (High Speed Downlink Packet Access) in an UMTS communications system. Then, it may be desirable to optimize the frequency adjustment in the receiver such that the compensation of Δf   m    is favored over the compensation of frequency-offsets Δf m  of signals from other signal sources m≠  m  in order to better exploit the enhanced service HSDPA. To this end, J   m    is chosen to J   m   &gt;1, whereas J m =1 for m≠  m . Source importance weighting as explained above may be for instance accomplished in response to service indicators which are transmitted by the signal sources and which are translated in the receiver into service mode flags (e.g., a HSDPA-mode flag for a base station which offers HSDPA). Then, appropriate weighting values J m  are applied based on the activated flags in the receiver. As will be detailed further below, different weighting schemes may be used for J m . 
     The second multiplier  212  multiplies the output of the first multiplier  211  by Δf m . Thus, the weighting unit  210  generates at an output  213  of the second multiplier  212  values J m ·C m ·Δf m  and at an output  214  of the first multiplier  211  values J m ·C m . 
     These outputs  213 ,  214  of the weighting unit  210  are input to the averaging unit  220 . The averaging unit  220  comprises a first accumulator (AC)  221 , a second accumulator (AC)  222  and a divider (DIV)  223 . The accumulators  221 ,  222  accumulate their inputs over m=1, . . . , M and pass their respective results to the divider  223 . The divider  223  generates the overall frequency-offset  Δf  according to 
     
       
         
           
             
               
                 
                   
                     
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     Averaging schemes different from the averaging scheme exemplified above may be employed. 
     The overall frequency-offset estimate  Δf  may be output periodically at a time interval given by L avg . For instance, in an UMTS communications system, using as symbols r i,m  pilot symbols transmitted via the common pilot channel (CPICH), assuming L avg =150 yields one value of  Δf  per frame (frame duration is 10 ms). 
     Further, with regard to circuitry design, as signal processing upstream of the averaging unit  220  is accomplished separately for each signal source m, it is either possible to duplicate the components arranged upstream of the averaging unit  220  or to operate them in a time multiplex cycle running successively over m=1, . . . , M. 
     In the example described above, both the frequency-offsets Δf m  and the quantities C m  representative of a signal-to-noise ratio and used as weighting factors are computed on the basis of the same input data and on the basis of a differential phase estimation approach. That way, weighting factors C m  include all effects relevant for weighting but not known by external sources and exclude all effects external sources are subject to while the frequency-offset estimates Δf m  are not. Further, as the weighting factors C m  may be based on the same time interval as the frequency-offset estimates Δf m , errors introduced by non-synchronized weighting factor sources are excluded. Thus, the above scheme for generating weighting factors C m  frequency-offset estimates Δf m  may be beneficial in view of low hardware implementation expenditure and high accuracy. However, instead of computing the frequency-offsets Δf m  from the averaged phasors P m   av , frequency-offsets Δf m  as used by the combiner  104  may also be computed elsewhere in the receiver, i.e. by different algorithms using other signal processing devices not shown in the foregoing. In this case, the argument unit  105  may be omitted. 
     According to another embodiment, the concept of source-importance weighting may be implemented in virtually any combiner independent of how frequency-offset estimates Δf m  and quantities representative of the signal-to-noise ratios are established.  FIG. 4  illustrates a circuitry according to the general concept of source-importance weighting adjustment for an overall frequency-offset  Δf  calculation. Combiner  304  may be similar to combiner  104  as shown in  FIG. 3 . Optional discarding unit  200  may be omitted. Averaging unit  320  may be designed identical to averaging unit  220 . Weighting unit  310  may, for example, use signal-to-noise ratios SNR m  or values C m  for signal quality weighting purposes. Again, the signal source-specific frequency-offset estimates Δf m  may be provided by different circuitry than shown in  FIG. 2 . Additionally, signal source-specific signal-to-noise ratios SNR m  communicated to the weighting unit  310  may be computed in a conventional fashion, i.e. not on the basis of a differential phase estimation approach (by using phasors) as explained above, but elsewhere in the receiver. 
     Moreover, it is possible in one embodiment that weighting of the frequency-offset estimates Δf m  with the quantities representative of the signal-to-noise ratios is omitted. In this case, frequency-offset estimates Δf m  are simply weighted by the signal content dependent weighting factors J m . Then, the combiner  104  may not receive the quantities C m  representative of a signal-to-noise ratio. Thus, the discarding unit  200  and the multiplier  211  can be omitted and the signal content dependent weighting factors J m  may be coupled to the input of the multiplier  212  (which receives at the other input the frequency-offset estimates Δf m ). As to  FIG. 4 , in this case the combiner  304  must not receive the quantities SNR m  (which may be represented by the quantities C m  in  FIG. 3 ). 
     Register  330  contains a number of signal source service flags each associated with a specific signal source (e.g., base station) m and indicative of whether the respective signal source m provides a specific service, for instance HSDPA. If a flag has the value 1, the service is provided, and if the flag has the value 0, the service is not provided. Here, signal source  m  (and probably also other signal sources) provides this service. If the flag has the value 1, multiplexer  340  is controlled to output J&gt;1. Otherwise, if the flag has the value 0, multiplexer  340  outputs the value 1. Thus, if during a communication to multiple signal sources one signal source activates a specific service mode (e.g. HSDPA), the frequency-offset compensation in the receiver is improved for the signal transmitted by signal source  m . It is apparent from the above that for different services different values of J may be used in order to differentiate between the importance of a plurality of services. 
     Features relating to the concept of source-importance weighting explained in conjunction with the circuitry shown in  FIG. 4  may be applied in the aforementioned embodiments and vice versa. Further, features relating to the concept of estimating an overall frequency-offset  Δf  on the basis of a plurality of frequency-offset estimates Δf m  as presented in conjunction with  FIGS. 1 to 3  are applicable to the circuitry as shown in  FIG. 4  and vice versa. 
     According to another embodiment of the invention, circuitry for calculating a signal-to-noise ratio is shown in  FIG. 5 . Such circuitry may be used in virtually any kind of receiver in communications systems, i.e. its use is neither limited to mobile communications systems nor to radio systems. Concerning mobile communication systems, it may be implemented in a base station or in a mobile station or both. As known in the art, estimates of signal-to-noise ratio are used by various circuit parts in a receiver. For instance, in a RAKE receiver, outputs of single RAKE fingers can be combined in a combiner using signal-to-noise ratio estimates associated with each finger output (i.e. associated with a component of a signal which is transmitted via a specific propagation path of the radio channel). Thus, signal-to-noise ratio estimation according to this embodiment of the invention may, for example, also be used to provide signal-to-noise ratio estimates for a RAKE combiner. 
     The circuitry depicted in  FIG. 5  comprises a phase-shift estimation unit  400  operative to generate averaged phasors p av  from an incoming complex-valued data stream r i . The phase-shift estimation unit  400  comprises a phasor generation unit  100  and an averaging unit  101 , which may be designed according to the corresponding units explained above. The averaged phasor p av  is thus formed according to equation (2) (without index m). As already mentioned, the averaged phasor p av  is representative of a phase-shift that occurred in the input data signal r i  over a number L avg  of consecutive data samples. L avg  may be equal to 1 but typically, a greater averaging length is used. 
     The averaged phasors p av  are fed into a phase-shift processing unit  401 . Phase-shift processing unit  401  comprises a first square (SQR) unit  402 , a second square (SQR) unit  403 , an adder  404 , a root extraction unit  405  and a divider (DIV)  406 . The first square unit  402  receives the real part of the averaged phasor p av  and its output is connected to a first input of the adder  404 . The second square unit  403  receives the imaginary part of the averaged phasor p av  and its output is connected to a second input of the adder  404 . At an output of the adder  404 , quantity Q according to equation (3) is calculated. 
     In root extraction unit  405 , Q 1/2  is calculated. The square root of Q corresponds to the absolute value of the complex-valued averaged phasor p av  and is proportional to the signal-to-noise ratio SNR. 
     Provided that the energy level per data sample is Pt s , the signal-to-noise ration SNR is to be calculated according to 
     
       
         
           
             
               
                 
                   SNR 
                   = 
                   
                     
                       
                         Q 
                       
                       
                         2 
                         ⁢ 
                         
                           Pt 
                           s 
                         
                         ⁢ 
                         
                           L 
                           avg 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     To this end, the divider  406  divides the square root of Q by 2·Pt s ·L avg  and outputs one estimate of signal-to-noise ratio estimate SNR per L avg  data samples r i . 
     In many cases, it may not be necessary to calculate the signal-to-noise ratio but it may be sufficient to generate a quantity which is proportional to the signal-to-noise ratio SNR or even a quantity which is representative of the signal-to-noise ratio SNR according to a unique functional relationship. In such cases, the phase-shift processing unit  401  may e.g. output the result of the adder  404  (optionally divided by L avg   2 ) or the output of the root extraction unit  405  (optionally divided by L avg ), respectively. 
     Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art, that any arrangement which is calculated to achieve the same purpose may be substituted for the specific embodiments shown. It is to be understood, that the above description is intended to be illustrative and not restrictive. This application is intended to cover any adaptations or variations of the invention. Combinations of the above embodiments and many other embodiments will be apparent to those of skill in the art upon reading and understanding the above description. The scope of the invention includes any other embodiments and applications in which the above structures and methods may be used. The scope of the invention should, therefore, be determined with reference to the appended claims along with the scope of equivalents to which such claims are entitled. 
     It is emphasized that the Abstract is provided to comply with 37 C.F.R. section 1.72(b) requiring an abstract that will allow the reader to quickly ascertain the nature and gist of the technical disclosure. It is submitted with the understanding, that it will not be used to interpret or limit the scope or meaning of the claims.