# Patent

## Title
Frequency error estimation and correction

## Abstract

Counter-clockwise and clockwise quadrant transitions are detected and accumulated with respect to a received complex signal over a certain time period. These transitions may then be compared in order to obtain information indicative of both a magnitude and phase of a frequency offset error. Additionally, zero-crossings of the received complex signal over the same certain time period are detected and accumulated. The accumulated crossings provide information indicative of frequency offset magnitude. The determined magnitude and phase of the frequency offset error may then be used to adjust a local oscillator frequency to provide for improved receiver performance.

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This application is a continuation of U.S. patent application Ser. No. 10/154,233, filed May 22, 2002 (the disclosure of which is hereby incorporated by reference), now U.S. Pat. No. 7,075,948 issued Jul. 11, 2006.


BACKGROUND OF THE INVENTION
1. Technical Field of the Invention
The present invention relates to radio receivers and, in particular, to a system and method for frequency offset estimation.
2. Description of Related Art
The process for radio frequency transmission and reception is well known to those skilled in the art. Basically, at a transmitter, a carrier frequency is generated by a local oscillator and is modulated by a baseband signal. More specifically, two sinusoidal carriers of the same frequency, but having a ninety-degree phase offset, are modulated by the real (I) and imaginary (Q) parts of a complex valued baseband signal. At the receiver, coherent demodulation requires exactly the same carrier frequency and phase. In some radio communication systems, however, a frequency offset error appears in the demodulated baseband signal for one reason, or a combination of several reasons. For example, the local oscillator frequency used in the receiver generally may not exactly match the frequency used by the local oscillator transmitter. Also, if the transmitter or receiver is mobile, the received signal may be affected by a Doppler spread.
When the demodulating frequency generated by the local oscillator at the receiver is not precisely equal to the received frequency of the transmitted signal, the demodulated in-phase and quadrature components (I′ and Q′) of the baseband signal differ from the transmitted components (I and Q) by a variable phase offset. This results in a steady rotation of the whole I-Q constellation diagram which can adversely impact the accuracy of baseband signal reception and detection. In many mobile communication systems, a predefined word (often referred to as a pilot) signal provides a reference that can be used for frequency offset measurement. Once the offset is measured, the local oscillator at the receiver can be tuned to correct for that offset.
SUMMARY OF THE INVENTION
The present invention is directed to a computationally efficient system and method for measurement of frequency error. More specifically, the present invention utilizes measurements made on a demodulated signal (for example, a pilot signal) to determine both a direction and magnitude of the frequency error. A receiver frequency control loop responds to the error sign and magnitude to correct for the frequency error. The pilot signal may comprise a PSK signal.
In accordance with one aspect of the present invention, a sign and magnitude of a frequency error in a received complex signal is measured by detecting at least one quadrant transition of the received complex signal in both directions. The detected transitions are separately accumulated over a time period. By comparing the accumulated quadrant transitions, a difference value is obtained. The sign of that difference value provides the frequency error sign, and the magnitude of that difference value provides information indicative of the frequency error magnitude. A receiver frequency control loop responds to the error sign and magnitude to correct for the frequency error.
In accordance with another aspect of the present invention, a sign and magnitude of a frequency error in a received complex signal is measured by detecting at least one quadrant transition of the received complex signal as well as at least one zero-crossing transition. The detected transitions are separately accumulated over a time period. By comparing the accumulated net number of quadrant transitions, information indicative of frequency error sign may be obtained. Furthermore, the accumulated zero-crossing transitions provide information indicative of the frequency error magnitude. A receiver frequency control loop responds to the error sign and magnitude to correct for the frequency error.



BRIEF DESCRIPTION OF THE DRAWINGS
A more complete understanding of the method and apparatus of the present invention may be acquired by reference to the following Detailed Description when taken in conjunction with the accompanying Drawings wherein:
FIG. 1 is a timing diagram illustrating in-phase and quadrature components;
FIG. 2 is a diagram synthetically illustrating one bit counting of characteristic events (such as, for example, quadrant transitions);
FIGS. 3A-3D are logic diagrams illustrating single sign bit counter-clockwise transition detection;
FIGS. 4A-4D are logic diagrams illustrating single sign bit clockwise transition detection;
FIG. 5 is a block diagram of a frequency offset detector in accordance with a first embodiment of the present invention;
FIG. 6 is a block diagram of a frequency offset detector in accordance with a second embodiment of the present invention;
FIG. 7 is a block diagram of a frequency offset detector in accordance with a third embodiment of the present invention;
FIG. 8 is a block diagram of a frequency offset detector in accordance with a fourth embodiment of the present invention; and
FIG. 9 is a block diagram of UMTS-FDD cell searcher implementing the frequency offset detector of the present invention.



DETAILED DESCRIPTION OF THE DRAWINGS
Consider an input signal y(k) represented in the following format:

y(k)=b(k)Aej(φ(k)+Φ(k)+ωek+η(k)

wherein: Aejφ(k) is the pilot sequence;

    
    
        A is a real scalar value;
        ejΦ(k) is the channel phase distortion;
        b(k) the channel amplitude distortion;
        ωe is the frequency error offset; and
        η(k) is a complex noise term including all interferences, plus additive white Gaussian noise (AWGN), and has low power compared to the total power of y(k).

Typically, the pilot sequence symbols used are all identical. For example, in UMTS-FDD, each of the pilot QPSK components carry all ones, and hence Aejφ(k) can be expressed as:

    
    






  
    2
  
  ⁢
  
    e
    
      j
      ⁢
      
        π
        4
      
    
  




The QPSK components contain a phase error that is, in the case of a frequency error ω1−ω, variable and amounts to (ω1−ω)t+φ. Here, ω1 the local oscillator angular frequency and ω=2πFc, where Fc is the center frequency of the received signal. The consequence is that the received phase components I′ and Q′ contain variable mixtures of original QPSK components I and Q where:

I′(k)=Re{y(k)}=0.5A{I(k)cos{(ω1−ω)k+φ}−Q(k)sin{(ω1−ω)k+φ}}; and

Q′(k)=Im{y(k)}=0.5A{I(k)sin{(ω1−ω)k+φ}+Q(k)cos{(ω1−ω)k+φ}}

and further where I′(k) and Q′(k) vary in time. The mixing of original phase components is irrelevant in this case because of trivial information carried by each of them (for example, all ones in the case of a UMTS-FDD pilot signal). The time variation is to be analyzed, however, because the all-ones components of the pilot that are impaired by a constant frequency error behave as sine waves whose frequency is equal to the frequency offset that must be determined. Thus, the frequency offset estimation comprises the finding the (ω1−ω) term.

The system and method of the present invention for frequency offset determination is based on an event counting technique. Namely, a frequency offset causes the above-referenced phase components I′(k) and Q′(k) to fluctuate as sine waves. Each 0 to 2π cycle can be characterized by a characteristic event. In one aspect of the present invention, the characteristic event is a simultaneous appearance of a zero crossing on one component (for example, I′(k)) and of an extremum on the other component (for example, Q′(k)), as shown in FIG. 1. In another aspect of the present invention, the characteristic event is a zero crossing on one (or both) component (s). Due to the π/2 phase delay between the I′(k) and Q′(k) components, the extremum can be assumed to be detected on one component when both (1) the sign of this component does not change, and (2) a zero crossing is detected on the other component. It is thus recognized that both events (1) and (2) can be tracked simply from detection of possible sign changes. Additionally, for purposes of the frequency offset detection operation, the I′(k) and Q′(k) components can be quantized with only one bit (i.e., the sign bit). The one bit and sign change characteristics lead to several efficient designs for offset detection and measurement.
Reference is now made to FIG. 2 wherein there is shown a diagram synthetically illustrating one bit event counting. The arrows 10 pointing in a counterclockwise direction correspond to a sequence of events caused by a positive frequency offset, while the arrows 12 pointing in the clockwise direction mark a sequence of events caused by a negative frequency offset. For example, the top arrow 10 corresponds to a transition (or crossing) from a first quadrant to a second quadrant of the I′-Q′ QPSK constellation due to a positive frequency offset, while the top arrow 12 corresponds to a transition from the second to the first quadrant due to a negative frequency offset, each arrow being characterized by a zero crossing for the I′ component and no sign change for the Q′ component. Similar relationships can be identified for each of the other quadrant transitions.
Remembering now that the I′(k) and Q′(k) components can be quantized with only one bit (i.e., the sign bit), it will be recognized that each of the transitions can be detected by applying an appropriate logical analysis of events (1) and (2) described above against that bit. Consider first, for example, the arrows 10 defining the transitions in the counter-clockwise direction, and assume complementary logic (where the most significant bit (MSB) of a non-negative number is “1”, and otherwise “0”). In this context, the transition from the first to the second quadrant is detected if the following logical expression is true (i.e., “1”):

{I′(k−1) AND NOT(I′(k))} AND {Q′(k−1) AND Q′(k)};

wherein “k” is the current sample and “k−1” is the immediately preceding sample. Thus, if the MSB of the immediately preceding I′ sample is “1”, AND the MSB of current I′ sample is “0”, AND if the MSB of the immediately preceding Q′ sample is “1”, AND the MSB of current Q′ sample is “1”, THEN the I′-Q′ QPSK constellation is rotating in the counter-clockwise direction (due to a positive frequency offset condition) and has just crossed from the first quadrant to the second quadrant. A logic circuit implementing this logical expression is shown in FIG. 3A. The transition from the second to the third quadrant is detected if the following logical expression is true (i.e., “1”):

{Q′(k−1) AND NOT(Q′(k))} AND {NOT(I′(k−1)) AND NOT(I′(k))}.

A logic circuit implementing this logical expression is shown in FIG. 3B. The transition from the third to the fourth quadrant is detected if the following logical expression is true (i.e., “1”):

{NOT(I′(k−1)) AND I′(k)} AND {NOT(Q′(k−1)) AND NOT(Q′(k))}.

A logic circuit implementing this logical expression is shown in FIG. 3C. Lastly, the transition from the fourth to the first quadrant is detected if the following logical expression is true (i.e., “1”):

{NOT(Q′(k−1)) AND Q′(k)} AND {I(k−1) AND I′(k)}.

A logic circuit implementing this logical expression is shown in FIG. 3D. For each of the logical expressions recited above for detecting counter-clockwise direction transitions, the first {--} part of the expression reflects the zero crossing event (2) on one component, and the second {--} part of the expression reflects the no-sign-change event (1) on the other component.

Consider now, for example, the arrows 12 defining the transitions in the clockwise direction, and again assume complementary logic. In this context, the transition from the first to the fourth quadrant is detected if the following logical expression is true (i.e., “1”):

{Q′(k−1) AND NOT(Q′(k))} AND {I′(k−1) AND I′(k)};

wherein “k” is the current sample and “k−1” is the immediately preceding sample. Thus, if the MSB of the immediately preceding Q′ sample is “1”, AND the MSB of current Q′ sample is “0”, AND if the MSB of the immediately preceding I′ sample is “1”, AND the MSB of current I′ sample is “1”, THEN the I′-Q′ QPSK constellation is rotating in the clockwise direction (due to a negative frequency offset condition) and has just crossed from the first quadrant to the fourth quadrant. A logic circuit implementing this logical expression is shown in FIG. 4A. The transition from the fourth to the third quadrant is detected if the following logical expression is true (i.e., “1”):

{I′(k−1) AND NOT(I′(k))} AND {NOT(Q′(k−1)) AND NOT(Q′(k))}.

A logic circuit implementing this logical expression is shown in FIG. 4B. The transition from the third to the second quadrant is detected if the following logical expression is true (i.e., “1”):

{NOT(Q′(k−1)) AND Q′(k)} AND {NOT(I′(k−1)) AND NOT(I′(k))}.

A logic circuit implementing this logical expression is shown in FIG. 4C. Lastly, the transition from the second to the first quadrant is detected if the following logical expression is true (i.e., “1”):

{NOT(I′(k−1)) AND I′(k)} AND {Q′(k−1) AND Q′(k)}.

A logic circuit implementing this logical expression is shown in FIG. 4D. For each of the logical expressions recited above for detecting clockwise direction transitions, the first {--} part of the expression reflects the zero crossing event (2) on one component, and the second {--} part of the expression reflects the no-sign-change event (1) on the other component.

By detecting the occurrences of these transitions, information relating to the cycling of the I′-Q′ QPSK constellation due to a frequency offset may be obtained (i.e., the existence of an offset is identified by detecting any transition, and the detection of a certain transition provides an indication of direction of rotation). More specifically, by counting the number and type of these transitions over a certain time period information concerning the magnitude and direction of the frequency offset may be obtained. For example, the count of the net number of transitions (N) provides direction and is proportional, after a measurement interval (t), to the residual frequency offset (Δf) where:




  
    Δ
    ⁢
    
      
    
    ⁢
    f
  
  =
  
    
      N
      t
    
    =
    
      
        N
        *
        
          R
          b
        
      
      
        N
        bits
      
    
  




wherein: Rb is the bit rate on a single QPSK component; and

    
    
        Nbits is the number of processed I′ or Q′ bits, on a single component, during the measurement interval (i.e., the data block length in samples).
    
    


Reference is now made to FIG. 5 wherein there is shown a block diagram of a frequency offset detector 100 in accordance with a first embodiment of the present invention. The detector 100 includes a counter-clockwise transition detector 102 and a clockwise transition detector 104. The counter-clockwise transition detector 102 implements one or more of the counter-clockwise transition detection logical expressions noted above (and discussed in connection with the logical implementations of FIGS. 3A-3D, or their equivalents). The clockwise transition detector 104 implements a corresponding one or more of the clockwise transition detection logical expressions noted above (and discussed in connection with the logical implementations of FIGS. 4A-4D, or their equivalents). By “corresponding” it is meant that which ever one or more of the transition detection expressions that is implemented by the counter-clockwise transition detector 102, the clockwise transition detector 104 should preferably implement the corresponding opposite transition detection expressions. For example, if the counter-clockwise transition detector 102 implements the logical expression for detecting a first to second quadrant transition, the clockwise transition detector 104 should preferably implement the corresponding opposite logical expression for detecting a second to first quadrant transition.
The input to the counter-clockwise transition detector 102 and the clockwise transition detector 104 comprises a single quantization bit for each of the received I′ and Q′ signals. More specifically, in a preferred embodiment of the detector 100, the input comprises the sign bit (the most significant bit in this instance) of the received I′ and Q′ signals. Although the expressions recited above assume complementary logic, it will be understood that the input and the detection expressions may implement other equivalent formatting.
The output from each of the counter-clockwise transition detector 102 and the clockwise transition detector 104 is a signal D (Dccw for the detector 102 and Dcw for the detector 104) that when active indicates a detected occurrence of a transition event for the received signal. Active in this case could comprise either active high (i.e., logical “1”) or active low (i.e., logical “0”) as desired for a given implementation.
The signals D are accumulated in a counter 108 that includes a counter-clockwise accumulator 108(1) (counting the active signals Dccw over a given time period) and a clockwise accumulator 108(2) (counting the active signals Dcw over the same given time period). A reset signal 110 is used to reset the counter 108 at the start of each new time period. The output from the counter 108 at the expiration of each time period is a count N (Nccw for the counter-clockwise accumulator 108(1) and Ncw for the clockwise accumulator 108(2)) that represents the sum number of occurrences of a detected transition event in each direction for the received signal during the given time period.
A processing component 112 receives the counts N and mathematically operates on those counts to determine information that is at least indicative of, if not explicitly defining, the magnitude and sign of the frequency offset. With respect to the sign, the processing component 112 includes a subtractor 116 that subtracts the count Ncw of the clockwise accumulator 108(2) from the count Nccw of the counter-clockwise accumulator 108(1). The processing component then examines the sign portion 118 (i.e, the most significant bit) of the subtractor 116 output to identify the sign of the frequency offset. For example, if the sign 118 is positive, then the sign of the frequency offset is also positive. Conversely, if the sign 118 is negative, then the sign of the frequency offset is negative.
With respect to magnitude, the processing component 112 examines the value portion 120 (i.e., the numerical result of the subtraction Ndif=Nccw−Ncw) of the subtractor 116 output. The difference value Ndif is indicative of the offset magnitude (see, dotted line in FIG. 5) and may be used directly for other operations such as. frequency offset correction. If desired, the difference value may be converted 122 by the processing component 112 into a frequency magnitude by recognizing that the net number of transitions during the given time period is proportional to the frequency offset in accordance with:




  
    Δ
    ⁢
    
      
    
    ⁢
    f
  
  =
  
    
      
        
          N
          dif
        
        /
        n
      
      t
    
    =
    
      
        
          N
          dif
        
        *
        
          R
          b
        
      
      
        n
        *
        
          N
          bits
        
      
    
  




wherein: Rb is the bit rate on a single QPSK component (I′ or Q′);

    
    
        Nbits is the number of processed I′ or Q′ bits during the time period; and
        n is the number of corresponding quadrant transitions monitored by the detectors 102 and 104 (for example, if only a first to second transition and corresponding second to first transition were monitored, then n=1). This conversion 122 thus comprises the multiplication of the value 120 by a chosen constant to produce the frequency offset magnitude.
    
    


A noted benefit concerning the operation of the embodiment of FIG. 3 is its behavior in the presence of pure noise. Since pure noise may be characterized by a relatively equal number of clockwise and counter-clockwise transitions, these cancel out in the comparator 116 operation (Ndif=Nccw−Ncw), and the result more accurately reflects the frequency offset alone when averaged over time.
There is, however, a drawback with this operation in that the maximum frequency offset that is capable of detection is limited to 1/n of the sampling rate. This can be better understood by reference to a specific example. It is recognized that the maximum frequency offset occurs when Ndif increases by one for each signal sample. Take an implementation of the present invention in a UMTS-FDD common pilot channel (C-PICH) scenario where sampling occurs at a rate of 15 kHz. Thus, the time period t contains Ns number of symbols (Ns=t*15,000). The maximum rate of change of Ndif is thus Ns quadrant transitions in one direction over the time period t. By replacing Ndif by Ns=t*15,0000 in the frequency offset formula set forth above, the following maximum measurable frequency offset (Maxf) calculation results:




  Maxf
  =
  
    
      
        Ns
        /
        n
      
      t
    
    =
    
      
        
          t
          *
          15
          ⁢
          
            ,
          
          ⁢
          000
        
        
          n
          *
          t
        
      
      =
      
        
          15
          ⁢
          
            ,
          
          ⁢
          000
        
        n
      
    
  




showing the 1/n of the sampling rate limitation of the FIG. 3 implementation. Any frequency offset above this relationship is erroneously measured, and suffers from the so-called “aliasing effect.” It is recognized that in some instances, due to the use of more inexpensive local oscillators in the receiver, an initial frequency offset often times exists that exceeds the (sampling rate)/n limitation.

Reference is now made to FIG. 6 wherein there is shown a block diagram of a frequency offset detector 200 in accordance with a second embodiment of the present invention. The detector 200 includes a counter-clockwise transition detector 202 and a clockwise transition detector 204. The counter-clockwise transition detector 202 implements one or more of the counter-clockwise transition detection logical expressions noted above (and discussed in connection with the logical implementations of FIGS. 3A-3D, or their equivalents). The clockwise transition detector 204 implements a corresponding one or more of the clockwise transition detection logical expressions noted above (and discussed in connection with the logical implementations of FIGS. 4A-4D, or their equivalents). By “corresponding” it is meant that which ever one or more of the transition detection expressions that is implemented by the counter-clockwise transition detector 202, the clockwise transition detector 204 should preferably implement the corresponding opposite transition detection expressions. For example, if the counter-clockwise transition detector 202 implements the logical expression for detecting a first to second quadrant transition, the clockwise transition detector 204 should preferably implement the corresponding opposite logical expression for detecting a second to first quadrant transition.
The detector 200 still further includes a zero-crossing detector 206. The zero-crossing detector 206 may implement a zero-crossing detection portion (for example, the first {--} portion shown above) of any one or more of the transition detection logical expressions noted above (or their equivalents). For example, the expressions for the transitions in the counter-clockwise direction are as follows:
first to second: I′(k−1) AND NOT(I′(k))
second to third: Q′(k−1) AND NOT(Q′(k))
third to fourth: NOT(I′(k−1)) AND I′(k)
fourth to first: NOT(Q′(k−1)) AND Q′(k).
Conversely, the expressions for the transitions in the clockwise direction are as follows:
fourth to third: I′(k−1) AND NOT(I′(k))
first to fourth: Q′(k−1) AND NOT(Q′(k))
second to first: NOT(I′(k−1)) AND I′(k)
third to second: NOT(Q′(k−1)) AND Q′(k). It will be noted from a review of the above zero-crossing expressions that the same expressions are used in both the clock-wise and counter-clockwise directions, but are reshuffled (for example, first to second and fourth to third are both satisfied when I′(k−1) AND NOT(I′(k)) is logically true). In this scenario, if a given expression is used within the zero-crossing detector, its satisfaction is counted twice (for the same example as above, once as a first to second zero-crossing and again for its matching fourth to third zero-crossing).
The input to the counter-clockwise transition detector 202, the clockwise transition detector 204 and the zero-crossing detector 206 comprises a single quantization bit for each of the received I′ and Q′ signals. More specifically, in a preferred embodiment of the detector 200, the input comprises the sign bit (the most significant bit in this case) of the received I′ and Q′ signals. Although the expressions recited above assume complementary logic, it will be understood that the input and the detection expressions may implement other equivalent formatting.
The output from each of the counter-clockwise transition detector 202, the clockwise transition detector 204 and zero-crossing detector 206 is a signal D (Dccw for the detector 202, Dcw for the detector 204, and Dzero for the detector 206) that when active indicates a detected occurrence of a transition/zero-crossing event for the received signal. Active in this case could comprise either active high (i.e., logical “1”) or active low (i.e., logical “0”) as desired for a given implementation.
The signals D are accumulated in a counter 208 that includes a counter-clockwise accumulator 208(1) (counting the active signals Dccw over a given time period), a clockwise accumulator 208(2) (counting the active signals Dcw over the same given time period), and a zero-crossing accumulator 208(3) (counting the active signals Dzero over the same given time period). A reset signal 210 is used to reset the counter 208 at the start of each new time period. The output from the counter 208 at the expiration of each time period is a count N (Nccw for the counter-clockwise accumulator 208(1), Ncw for the clockwise accumulator 208(2), and Nzero for the zero-crossing accumulator 208(3)) that represents the sum number of occurrences of a detected transition event in each direction and zero-crossing event for the received signal during the given time period.
A processing component 212 receives the counts N and mathematically operates on those counts to determine information that is at least indicative of, if not explicitly defining, the magnitude and sign of the frequency offset. With respect to the sign, the processing component 212 includes a comparator 216 that compares the count Ncw of the clockwise accumulator 208(2) with the count Nccw of the counter-clockwise accumulator 208(1) (a subtractor may alternatively be used, with the sign of the value resulting from the subtraction being indicative of offset sign). The processing component then examines the sign output 218 of the comparator 216 output to identify the sign of the frequency offset. For example, if the sign 218 is positive, then the sign of the frequency offset is also positive. Conversely, if the sign 218 is negative, then the sign of the frequency offset is negative.
With respect to magnitude, the sign is disregarded because the zero-crossing detector is detecting an event and counting it twice as both a clockwise zero-crossing and a counter-clockwise zero-crossing (note the example recited above). The count Nzero of the zero-crossing accumulator 208(3) is indicative of offset magnitude (see dotted line in FIG. 6) and may be directly used in other operations such as offset correction. Alternatively, the processing component 212 may convert 222 the count Nzero of the zero-crossing accumulator 208(3) into a frequency magnitude by recognizing that the number of zero-crossings during the given time period is proportional to the frequency offset in accordance with:




  
    Δ
    ⁢
    
      
    
    ⁢
    f
  
  =
  
    
      
        
          
            N
            zero
          
          /
          2
        
        ⁢
        n
      
      t
    
    =
    
      
        
          N
          zero
        
        *
        
          R
          b
        
      
      
        2
        ⁢
        n
        *
        
          N
          bits
        
      
    
  




wherein: Rb is the bit rate on a single QPSK component (I′ or Q′);

    
    
        Nbits is the number of processed I′ or Q′ bits during the time period;
        2 reflects that one crossing is counted twice; and
        n is the number of matching zero-crossing transitions monitored by the detector 206 (for example, if only a first to second crossing and matching fourth to third crossing were monitored, then n=1).

Again, this conversion comprises the multiplication by a constant.

    
    


Using the zero-crossing implementation discussed above provides for an improvement in the maximum measurable frequency offset (in comparison to the embodiment of FIG. 5). Since sign is ignored by the zero-crossing detector 206, each crossing counts twice (once for clockwise (of one transition) and again for counter-clockwise (of a different transition)). More specifically, it is possible that during one sample change, both I′ and Q′ may change their sign. Such a change would reflect at least a π phase change in FIG. 2. This would give a Nyquist frequency that is twice as high as that provided with the embodiment of FIG. 5 (where an event was measured by the combination of (1) and (2) which precludes both I′ and Q′ from changing). The higher Nyquist frequency in essence doubles the maximum frequency offset that can be detected. This can be better understood by reference to a specific example. It is recognized that the maximum frequency offset occurs when Nzero increases by n for each signal sample (where n is the number of matching zero-crossing detections that are utilized). Take an implementation of the present invention in a UMTS-FDD common pilot channel (CPICH) scenario where sampling occurs at a rate of 15 kHz. Thus, the time period t contains Ns number of symbols (Ns=t*15,000). The maximum rate of change of Nzero is thus 2*Ns zero-crossings in any direction over the time period t (“2” because both I′ and Q′ change sign with the zero-crossing). By replacing Nzero by Ns=2*t*15,0000 in the frequency offset formula set forth above, the following maximum frequency offset (Maxf) calculation results:




  Maxf
  =
  
    
      
        2
        *
        
          Ns
          /
          n
        
      
      t
    
    =
    
      
        
          2
          *
          t
          *
          15
          ⁢
          
            ,
          
          ⁢
          000
        
        
          n
          *
          t
        
      
      =
      
        
          
            30
            ⁢
            
              ,
            
            ⁢
            000
          
          n
        
        =
        
          7.5
          ⁢
          
            
          
          ⁢
          kHz
        
      
    
  




when n=4 (where all four zero crossings are detected).

There is, however, a drawback with this operation in that for smaller frequency offsets, sign is still detectable using the detectors 202 and 204, but the measured magnitude will be more adversely affected by noise than with the implementation of FIG. 5. The reason for this is that, although the clockwise and counter-clockwise rotations for noise are equally likely, they all sum up in the same sense with the zero-crossing detector 206 and have a greater contribution to the detected magnitude in comparison to the actual magnitude.
Reference is now made to FIG. 7 wherein there is shown a block diagram of a frequency offset detector 300 in accordance with a third embodiment of the present invention. In this implementation, the detectors 202 and 204, and processor 212 operation for sign determination, are the same as with FIG. 6. The detector 300, however includes a modified, non-redundant counting, zero-crossing detector 306. The zero-crossing detector 306 implements a zero-crossing detection portion (for example, the first {--} portion shown above) of any one or more of the transition detection logical expressions noted above (or their equivalents). More specifically, the detection is implemented in a non-redundant manner. It will be remembered the same zero-crossing expressions are used in both the clock-wise and counter-clockwise directions, but are reshuffled. These expressions are, therefore, directionally-independent, and the zero-crossing detector 306 counts just once (instead of twice as in the implementation of FIG. 6) for each crossing. For example, the expressions for the crossing transitions are as follows:
a): I′(k−1) AND NOT(I′(k))
b): Q′(k−1) AND NOT(Q′(k))
c): NOT(I′(k−1)) AND I′(k)
d): NOT(Q′(k−1)) AND Q′(k).
With respect to magnitude, the count Nzero of the zero-crossing accumulator 208(3) is indicative of offset magnitude and may be directly used for other operations such as offset correction. Alternatively, the processing component 312 may convert 322 the count Nzero of the zero-crossing accumulator 208(3) into a frequency magnitude by recognizing that the number of zero-crossings during the given time period is proportional to the frequency offset in accordance with:




  
    Δ
    ⁢
    
      
    
    ⁢
    f
  
  =
  
    
      
        
          N
          zero
        
        /
        n
      
      t
    
    =
    
      
        
          N
          zero
        
        *
        
          R
          b
        
      
      
        n
        *
        
          N
          bits
        
      
    
  




wherein: Rb is the bit rate on a single QPSK component I′ or Q′ (i.e., the symbol rate, or the sampling rate);

    
    
        Nbits is the number of processed I′ or Q′ bits during the time period (i.e., the number of processed symbols); and
        n is the number of zero-crossing transitions monitored by the detector 306 (for example, if only the a) crossing was monitored, then n=1).

Again, the conversion to produce the frequency offset comprises a multiplication by a constant.

    
    


This implementation likewise provides an improvement in the maximum measurable frequency offset (in comparison to the embodiment of FIG. 5). In this case, however, each crossing counts only once. It is still possible, however, that during one sample change, both I′ and Q′ may change their sign, which would give a Nyquist frequency that is twice as high as that provided with the embodiment of FIG. 5 (where an event was measured by the combination of (1) and (2) which precludes both I′ and Q′ from changing). The higher Nyquist frequency in essence doubles the maximum frequency offset that can be detected. This can be better understood by reference to a specific example. It is recognized that the maximum frequency offset occurs when Nzero increases by n/2 for each signal sample (where n is the number of matching zero-crossing detections that are utilized). Take an implementation of the present invention in a UMTS-FDD common pilot channel (C-PICH) scenario where sampling occurs at a rate of 15 kHz. Thus, the time period t contains Ns number of symbols (Ns=t*15,000). The maximum rate of change of Nzero is thus n*Ns/2 zero-crossings in one direction over the time period t. By replacing Nzero by n*Ns/2=n*t*15,0000/2 in the frequency offset formula set forth above, the following maximum frequency offset (Maxf) calculation results:




  
    max
    ⁢
    
      
    
    ⁢
    f
  
  =
  
    
      
        
          
            n
            *
            Ns
          
          2
        
        /
        n
      
      t
    
    =
    
      
        
          n
          *
          t
          *
          15
          ⁢
          
            ,
          
          ⁢
          000
        
        
          2
          ⁢
          n
          *
          t
        
      
      =
      
        
          
            15
            ⁢
            
              ,
            
            ⁢
            000
          
          2
        
        =
        
          7.5
          ⁢
          
            
          
          ⁢
          kHz
        
      
    
  




showing that the maximum frequency offset is still no longer tied to the value of n as with the FIG. 5 implementation and provides equivalent range performance to the implementation of FIG. 6.

Reference is now made to FIG. 8 wherein there is shown a block diagram of a frequency offset detector 400 in accordance with a fourth embodiment of the present invention. The detector 400 essentially combines the functionality of the first and third embodiments (see, FIGS. 5 and 7). The detector 400 includes a counter-clockwise transition detector 102 and a clockwise transition detector 104 as described above in FIG. 3. The detector 400 still further includes a modified, non-redundant counting, zero-crossing detector 306 as described above in FIG. 7.
The output from each of the counter-clockwise transition detector 102, the clockwise transition detector 104 and zero-crossing detector 306 is a signal D (Dccw for the detector 102, Dcw for the detector 104, and Dzero for the detector 306) that when active indicates a detected occurrence of a transition/zero-crossing event for the received signal. Active in this case could comprise either active high (i.e., logical “1”) or active low (i.e., logical “0”) as desired for a given implementation.
The signals D are accumulated in a counter 408 that includes a counter-clockwise accumulator 408(1) (counting the active signals Dccw over a given time period), a clockwise accumulator 408(2) (counting the active signals Dcw over the same given time period), and a zero-crossing accumulator 408(3) (counting the active signals Dzero over the same given time period). A reset signal 410 is used to reset the counter 408 at the start of each new time period. The output from the counter 408 at the expiration of each time period is a count N (Nccw for the counter-clockwise accumulator 408(1), Ncw for the clockwise accumulator 408(2), and Nzero for the zero-crossing accumulator 408(3)) that represents the sum number of occurrences of a detected transition event in each direction and zero-crossing event for the received signal during the given time period.
A processing component 412 receives the counts N and mathematically operates on those counts to determine information that is at least indicative of, if not explicitly defining, the magnitude and sign of the frequency offset. With respect to the sign, the processing component 412 includes a subtractor 416 that subtracts the count Ncw of the clockwise accumulator 408(2) from the count Nccw of the counter-clockwise accumulator 408(1). The processing component then examines the sign portion 418 (i.e., the most significant bit) of the subtractor 416 output to identify the sign of the frequency offset. For example, if the sign 418 is positive, then the sign of the frequency offset is also positive. Conversely, if the sign 418 is negative, then the sign of the frequency offset is negative.
With respect to magnitude, the processing component 412 includes a comparator 430 that compares the value portion 420 (i.e., the numerical result of the subtraction Ndif=Nccw−Ncw) of the subtractor 416 output against a threshold value (T). The threshold T may be an selected value, and is preferably set to a small percentage of the number of symbol samples Ns during the time period. More specifically, in accordance with a preferred implementation of the present invention, the threshold T is set to 3% of Ns.
If Ndif is less than T, this is indicative of the frequency offset being relatively low. In this scenario, the frequency offset determination scheme of FIG. 5 is implemented. More specifically, the difference value Ndif is taken as being indicative of offset magnitude (see, dotted line in FIG. 8) and may be directly used for other operations such as offset correction. Alternatively, the difference value may be converted 422 by the processing component 412 into a frequency magnitude by recognizing that the net number of transitions during the given time period is proportional to the frequency offset in accordance with:




  
    Δ
    ⁢
    
      
    
    ⁢
    f
  
  =
  
    
      
        
          N
          dif
        
        /
        n
      
      t
    
    =
    
      
        
          N
          dif
        
        *
        
          R
          b
        
      
      
        n
        *
        
          N
          bits
        
      
    
  




wherein: Rb is the bit rate on a single QPSK component (I′ or Q′);

    
    
        Nbits is the number of processed I′ or Q′ bits during the time period; and
        n is the number of corresponding quadrant transitions monitored by the detectors 102 and 104 (for example, if only a first to second transition and corresponding second to first transition were monitored, then n=1).

Again, this conversion to produce the frequency offset comprises a multiplication by a constant.

    
    


Conversely, if Ndif equals or exceeds T, this is indicative of the frequency offset being relatively high. In this scenario, the frequency offset determination scheme of FIG. 7 is implemented. More specifically, the count Nzero of the zero-crossing accumulator 408(3) is taken as indicative of the offset magnitude (see dotted line in FIG. 8) and may be directly used for other operations such as offset correction. Alternatively, the processing component 412 then converts 424 the count Nzero of the zero-crossing accumulator 408(3) into a frequency magnitude by recognizing that the number of zero-crossings during the given time period is proportional to the frequency offset in accordance with:




  
    Δ
    ⁢
    
      
    
    ⁢
    f
  
  =
  
    
      
        
          N
          zero
        
        /
        n
      
      t
    
    =
    
      
        
          N
          zero
        
        *
        
          R
          b
        
      
      
        n
        *
        
          N
          bits
        
      
    
  




wherein: Rb is the bit rate on a single QPSK component I′ or Q′ (the symbol rate);

    
    
        Nbits is the number of processed I′ or Q′ bits during the time period (number of processed symbols); and
        n is the number of zero-crossing transitions monitored by the detector 306 (for example, if only the a) crossing was monitored, then n=1).

Again, this conversion comprises a multiplication by a constant.

    
    


The logical expressions for detecting transitions and zero-crossings may be implemented by the counter-clockwise transition detector, the clockwise transition detector and the zero-crossing detector (of any embodiment shown herein) in any suitable technological manner (for example, in hardware, software, firmware, or the like, including combinations thereof). For example, the logic circuit implementations illustrated in FIGS. 3A-3D and 4A-4D (or equivalents, or simplifications, or combinations) may be utilized if appropriate for the detector application. Alternatively, the logical expressions may be coded in software running as an application, or implemented through the use of a digital signal processor or programmable array. Furthermore, it should be recognized, as discussed above, that the logical expressions for detecting transitions (event (1) AND event (2)) incorporate the logical expressions for zero-crossings (event (2)), and thus a separate physical implementation for zero-crossing detection is not required (this is graphically illustrated by the dotted line functionality within the clockwise and counter-clockwise transition detectors in FIGS. 6-8).
The detection of a corresponding pair of transitions (for example, first to second and second to first, as mentioned above) is sufficient to provide information for making a frequency offset magnitude and direction determination. By increasing the number of transition pairs detected, however, the accuracy of the magnitude determination improves. Thus, if a given implementation of the detector requires a high degree of accuracy in the measured magnitude of the determined frequency offset, the counter-clockwise transition detector and the clockwise transition detector should implement plural (up to the maximum of four if possible) pairs of transition detections.
Reference is now made to FIG. 9 wherein there is shown a block diagram of UMTS-FDD cell searcher 500 implementing the frequency offset detector of the present invention. The cell searcher 500 performs signal acquisition in three steps. In a first step (often referred to in the art as “step 1”), slot acquisition (or slot synchronization) 502 is performed. In this step 1 process, the cell searcher 500 synchronizes itself to the time slots of the received signal by detecting the beginnings of each slot through a correlation process where the received signal is correlated against a primary synchronization code. In the second step (often referred to in the art as “step 2”), frame acquisition (or frame synchronization) 504 is performed. In this step 2 process, the cell searcher 500 synchronizes itself to the frame alignment (where a frame comprises 15 consecutive slots) through a correlation process where the received signal at each slot location is correlated against a secondary synchronization code. This frame alignment process not only detects the beginning of the frame, but also detects which sequence of codes are present in the received signal (and thus identifies the scrambling code used by the base station). In the third step (often referred to in the art as “step 3”), base station identification (or scrambling code acquisition) 506 is performed. In this step 3 process, the cell searcher 500 identifies the unique code used by the base station to scramble its transmitted data.
The frequency offset detector (100, 200, 300 and 400) of the present invention is particularly useful in connection with the performance of the step 3 process for base station identification 506. Although any of the detectors shown in FIGS. 5-8 may be used in the cell searcher 500, as a practical matter the detector 400 provides the best accuracy and would be preferred for a UMTS-FDD application. The I and Q (more specifically, the I′ and Q′) components of the primary common pilot channel (P-CPICH) are retrieved. Although the I and Q components have identical data contents (e.g., all ones), they are different because the scrambling code is complex in nature. So, the CPICH is actually the same as the scrambling code (during one frame). Although the I and Q components differ, they do not need to be retrieved separately, since this is the final step of the signal acquisition phase. Actually, the correct scrambling code is identified by correlating the complex input signal with the conjugate of one of the eight assumed scrambling codes (where this group of eight candidate codes for the actual scrambling code is an outcome of the step 2 process in addition to the frame synchronization). Correlating the complex input signal with the conjugate of an assumed scrambling codes is performed as follows:

E(I′+jQ′)T(Is−jQs)

wherein: I′ is the “in-phase” signal vector I′;

    
    
        Is is the real part of the assumed scrambling code;
        Q′ is the “quadrature” signal vector;
        Qs is the imaginary part of the assumed scrambling code;
        E is the “energy” (i.e., the correlation result); and
        T refers to a transposition.

In the presence of phase error (Φ), I′ and Q′ are:

I′=I*cos(Φ)/2−Q*sin(Φ)/2; and

Q′=I*sin(Φ)/2+Q*cos(Φ)/2,

where I and Q are the original phase components, respectively, and Φ is the phase offset. In the case of a pilot signal, I and Q contain Is and Qs, respectively. The energy E will have the largest peak when the CPICH (I′+jQ′) is matched with the true scrambling code candidate (Is_true-j Qs_true), which is the goal of the base station identification 506 (or scrambling code acquisition step). Recognizing again that the CPICH is equal to the scrambling code, this means that I=Is and also that Q=Qs. Thus:

    
    





  
    E
    =
    
      
        
          I
          ′
        
        ⁢
        Is
      
      +
      
        
          Q
          ′
        
        ⁢
        Qs
      
      +
      
        j
        ⁡
        
          (
          
            
              
                Q
                ′
              
              ⁢
              Is
            
            -
            
              
                I
                ′
              
              ⁢
              Qs
            
          
          )
        
      
    
  




  
    E
    =
    
      
        
          1
          2
        
        ⁢
        
          (
          
            
              
                I
                2
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              Φ
            
            +
            
              
                Q
                2
              
              ⁢
              cos
              ⁢
              
                
              
              ⁢
              Φ
            
          
          )
        
      
      +
      
        
          j
          2
        
        ⁢
        
          (
          
            
              
                I
                2
              
              ⁢
              sin
              ⁢
              
                
              
              ⁢
              Φ
            
            +
            
              
                Q
                2
              
              ⁢
              sin
              ⁢
              
                
              
              ⁢
              Φ
            
          
          )
        
      
    
  



recognizing that Is=I and Qs=Q, and further:




  
    
      
        I
        T
      
      ·
      Q
    
    =
    
      
        
          I
          T
        
        ·
        Qs
      
      =
      
        
          
            Q
            T
          
          ⁢
          I
        
        =
        
          
            
              Q
              T
            
            ⁢
            Is
          
          =
          0
        
      
    
  




  
    
      
        Thus
        :
        
          

        
        ⁢
        
          
          E
          
        
      
      =
      
        
          
            1
            2
          
          ⁢
          
            (
            
              
                I
                2
              
              +
              
                Q
                2
              
            
            )
          
        
        =
        Const
      
    
    ,
  



recognizing that cos2Φ+sin2Φ=1. The CPICH information can then be considered as retrieved where it is constant on observed intervals. Nonetheless, in the presence of a frequency offset this supposedly constant value varies with time. The frequency offset process of the present invention (references 100, 200, 300 and 400 in FIGS. 5-8)) takes into account the phase components I′Is_true and Q′Qs_true, referred to herein as I′ and Q′, respectively, which already had to be computed for finding the correlation peak (value E). By estimating the number of “sector crossings” in I′ and Q′ (more precisely, I′Is and Q′Qs), the present invention computes the frequency offset (solid line) or information indicative of the frequency offset (dotted line). This information (sign and magnitude) can then be fed back 508 to the automatic frequency control loop 510 of the receiver to improve its operation.

Although preferred embodiments of the method and apparatus of the present invention have been illustrated in the accompanying Drawings and described in the foregoing Detailed Description, it will be understood that the invention is not limited to the embodiments disclosed, but is capable of numerous rearrangements, modifications and substitutions without departing from the spirit of the invention as set forth and defined by the following claims.

## Claims

1. A frequency error system for measuring a sign and magnitude of a frequency error in a received complex signal, comprising:
a first detector operating to detect at least one quadrant transition of the received complex signal;
a first accumulator that accumulates a net number of quadrant transitions detected by the first detector during a time period;
a second detector operating to detect at least one zero-crossing of the received complex signal;
a second accumulator that accumulates a number of zero-crossings detected by the second detector during the same time period; and
a processing unit which determines the frequency error sign from a sign of the accumulated net number of quadrant transitions detected by the first detector, and determines the frequency error magnitude from a value of the accumulated zero-crossings.

2. The system as in claim 1 further including a processing component that calculates a value proportional to the frequency error magnitude by dividing the accumulated zero-crossings value by the time period.

3. The system as in claim 2 wherein the zero-crossing detector detects two separate zero-crossings, and wherein the processing component calculates a value proportional to the frequency error magnitude by dividing the accumulated zero-crossings by two times the time period.

4. The system as in claim 2 wherein the zero-crossing detector detects four separate zero-crossings, and wherein the processing component calculates a value proportional to the frequency error magnitude by dividing the accumulated zero-crossings by four times the time period.

5. The system as in claim 2 wherein the processing component resets the first and second accumulators at the end of each time period.

6. The system as in claim 1 wherein the received complex signal is quantized by a single I bit and a single Q bit, and wherein the first and second detectors each operate to make detections by examining the single bits.

7. The system as in claim 6 wherein the quantized single I and Q bits are sign bits of the I and Q components of the received complex signal.

8. The system as in claim 1 wherein the zero-crossing detector operates to detect zero-crossings in a non-redundant manner.

9. The system as in claim 1 wherein the zero-crossing detector operates to detect zero-crossings in either direction of rotation.

10. The system as in claim 1 wherein the second detector is incorporated within the first detector.

11. The system of claim 1, further comprising:
wherein the net number of quadrant transitions is a difference value between counter-clockwise quadrant transitions and clockwise quadrant transitions, a sign of that difference value being indicative of the frequency error sign; and
a comparator that compares the difference value to a threshold, a magnitude of that difference value being indicative of the frequency error magnitude if the threshold is not exceeded, and the accumulated zero-crossings being indicative of the frequency error magnitude if the threshold is exceeded.

12. The system of claim 1 wherein the received complex signal is a PSK signal.

13. The system of claim 12 further comprising a receiver frequency control loop responsive to the frequency error sign and frequency error magnitude for correcting the frequency error in the received complex PSK signal.

14. The system as in claim 1 wherein determination of the frequency error magnitude from the value of the accumulated zero-crossings comprises calculating the frequency error magnitude as a function of the value of the accumulated zero-crossings multiplied by a constant is derived from a number of bits in the time period.

15. The system of claim 14 where in the constant is a ratio of a bit rate and the number of bits in the time period.

16. A method for measuring a sign and magnitude of a frequency error in a received complex signal, comprising:
detecting at least one quadrant transition of the received complex;
accumulating a number of quadrant transitions during a time period;
detecting at least one zero-crossing of the received complex signal;
accumulating a number of zero-crossings detected during the same time period;
determining the frequency error sign from a sign of the accumulated net number of quadrant transitions, and
determining the frequency error magnitude from a value of the accumulated zero-crossings.

17. The method as in claim 16 further including the step of adjusting frequency of a receiver frequency control loop to correct for the frequency error in accordance with the provided sign and magnitude.

18. The method of claim 17 wherein the received complex signal is a PSK signal.

19. The method as in claim 16 wherein the step of providing comprises the step of calculating a value proportional to the frequency error magnitude by dividing the accumulated zero-crossings by the time period.

20. The method as in claim 16 wherein the received complex signal is quantized by a single I bit and a single Q bit, and wherein the detecting steps detect quadrant transitions and zero-crossings by examining the single bits.

21. The method as in claim 20 wherein the quantized single I and Q bits are sign bits of the I and Q components of the received complex signal.

22. The method of claim 16, further comprising:
wherein the net number of quadrant transitions is a difference value between counter-clockwise quadrant transitions and clockwise quadrant transitions, a sign of that difference value being indicative of the frequency error sign; and
comparing the difference value to a threshold, a magnitude of that difference value being indicative of the frequency error magnitude if the threshold is not exceeded, and the accumulated zero-crossings being indicative of the frequency error magnitude if the threshold is exceeded.

23. The method as in claim 22 further including the step of adjusting frequency of a receiver frequency control loop to correct for the frequency error in accordance with the provided sign and magnitude.

24. The method of claim 23 wherein the received complex signal is a PSK signal.

25. The method as in claim 16 wherein determining the frequency error magnitude from the value of the accumulated zero-crossings comprises calculating the frequency error magnitude as a function of the value of the accumulated zero-crossings multiplied by a constant is derived from a number of bits in the time period.

26. The method of claim 25 where in the constant is a ratio of a bit rate and the number of bits in the time period.

27. A frequency error system for measuring a sign and magnitude of a frequency error in a received complex signal, comprising:
a first detector operating to detect at least one quadrant transition of the received complex signal;
a first accumulator that accumulates a net number of quadrant transitions detected by the first detector during a time period;
a second detector operating to detect at least one zero-crossing of the received complex signal;
a second accumulator that accumulates a number of zero-crossings detected by the second detector during the same time period; and
a processing unit which determines the frequency error sign from a sign of the accumulated net number of quadrant transitions detected by the first detector, and determines the frequency error magnitude by multiplying a numerical value of the accumulated number of zero-crossings by a constant number.

28. A method for measuring a sign and magnitude of a frequency error in a received complex signal, comprising:
detecting at least one quadrant transition of the received complex;
accumulating a number of quadrant transitions during a time period;
detecting at least one zero-crossing of the received complex signal;
accumulating a number of zero-crossings detected during the same time period;
determining the frequency error sign from a sign of the accumulated net number of quadrant transitions, and
determining the frequency error magnitude from a multiplication of a numerical value of the accumulated number of zero-crossings by a constant number.