Abstract:
A system and method for estimating the frequency offset experienced between carrier and local oscillator frequencies in communication systems using quadrature modulation. The invention exploits the geometry of the quadrature modulation constellation and estimates actual offset within a predefined carrier offset value without requiring data estimation.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates generally to digital communication systems using quadrature modulation techniques. More specifically, the invention relates to a system and method for blind detection of carrier frequency offsets in such systems. 
   2. Description of the Prior Art 
   A digital communication system typically transmits information or data using a continuous frequency carrier with modulation techniques that vary its amplitude, frequency or phase. After modulation, the signal is transmitted over a communication medium. The communication media may be guided or unguided, comprising copper, optical fiber or air and is commonly referred to as the communication channel. 
   The information to be transmitted is input in the form of a bit stream which is mapped onto a predetermined constellation that defines the modulation scheme. The mapping of each bit as symbols is referred to as modulation. 
   Each symbol transmitted in a symbol duration represents a unique waveform. The symbol rate or simply the rate of the system is the rate at which symbols are transmitted over the communication channel. A prior art digital communication system is shown in  FIG. 1 . While the communication system shown in  FIG. 1  shows a single communication link, those skilled in this art recognize that a plurality of multiple access protocols exist. Protocols such as frequency division multiple access (FDMA), time division multiple access (TDMA), carrier sense multiple access (CSMA), code division multiple access (CDMA) and many others allow access to the same communication channel for more than one user. These techniques can be mixed together creating hybrid varieties of multiple access schemes such as time division duplex (TDD). The type of access protocol chosen is independent of the modulation type. 
   One family of modulation techniques is known as quadrature modulation and is based on two distinct waveforms that are orthogonal to each other. If two waveforms are transmitted simultaneously and do not interfere with each other, they are orthogonal. Two waveforms generally used for quadrature modulation are sine and cosine waveforms at the same frequency. The waveforms are defined as
 
 s   1 ( t )= A  cos(2π f   c   t )  Equation 1
 
and
 
 s   2 ( t )= A  sin(2π f   c   t )  Equation 2
 
where f c  is the carrier frequency of the modulated signal and A is the amplitude applied to both signals. The value of A is irrelevant to the operation of the system and is omitted in the discussion that follows. Each symbol in the modulation alphabet are linear combinations generated from the two basic waveforms and are of the form a 1  cos(2πf c t)+a 2  sin(2πf c t) where a 1  and a 2  are real numbers. The symbols can be represented as complex numbers, a 1 +ja 2 , where j is defined as j=√−1.
 
   The waveforms of Equations 1 and 2 are the most common since all passband transmission systems, whether analog or digital, modulate the two waveforms with the original baseband data signal. Quadrature modulation schemes comprise various pulse amplitude modulation (PAM) schemes (where only one of the two basic waveforms is used), quadrature amplitude modulation (QAM) schemes, phase shift keying (PSK) modulation schemes, and others. 
   A prior art quadrature modulator is shown in  FIG. 2 . The modulator maps the input data as a pair of numbers {a 1 , a 2 } which belong to a set defined by the modulation alphabet. a 1  represents the magnitude (scaling) of the first waveform and a 2  represents the magnitude (scaling) of the second waveform. Each magnitude is modulated (i.e. multiplied) by the orthogonal waveforms. Each individual modulator accepts two signal inputs and forms an output signal at the carrier frequency. 
   A prior art quadrature demodulator is shown in  FIG. 3 . The demodulator generates sine and cosine waves at a carrier frequency [f c ]f LO  for demodulation. Ignoring channel effects, the received signal can be represented as
 
 r ( t )= a   1 ( t )cos(2π f   c   t+φ   0 )+ a   2 ( t )sin(2π f   c   t+φ   0 )  Equation 3
 
where a 1 (t) represents the plurality of amplitudes modulated on waveform s 1 (t) as defined by Equation 1 and a 2 (t) represents the plurality of amplitudes modulated on waveform s 2 (t) as defined by Equation 2. φ is an arbitrary phase offset which occurs during transmission.
 
   The cosine and sine demodulator signal components are defined as: 
                     r   c     ⁡     (   t   )       =           r   ⁡     (   t   )       *     ⁢     cos   ⁡     (     2   ⁢   π   ⁢           ⁢     f   LO     ⁢   t     )         =         1   2     ⁢     a   1     ⁢     cos   ⁡     (         (       f   c     -     f   LO       )     ⁢   t     +     ϕ   0       )         +       1   2     ⁢     a   2     ⁢     sin   ⁡     (         (       f   c     -     f   LO       )     ⁢   t     +     ϕ   0       )         +       1   2     ⁢     a   1     ⁢     cos   ⁡     (         (       f   c     +     f   LO       )     ⁢   t     +     ϕ   0       )         +       1   2     ⁢     a   2     ⁢     sin   ⁡     (         (       f   c     +     f   LO       )     ⁢   t     +     ϕ   0       )                     Equation   ⁢           ⁢   4               
and
 
   
     
       
         
           
             
               
                 
                   
                     r 
                     s 
                   
                   ⁡ 
                   
                     ( 
                     t 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       
                         r 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       * 
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         
                           2 
                           ⁢ 
                           π 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             f 
                             LO 
                           
                           ⁢ 
                           t 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         a 
                         2 
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   
                                     f 
                                     c 
                                   
                                   - 
                                   
                                     f 
                                     LO 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               ϕ 
                               0 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         a 
                         1 
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   
                                     f 
                                     c 
                                   
                                   - 
                                   
                                     f 
                                     LO 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               ϕ 
                               0 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         a 
                         2 
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   
                                     f 
                                     c 
                                   
                                   + 
                                   
                                     f 
                                     LO 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               ϕ 
                               0 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         a 
                         1 
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   
                                     f 
                                     c 
                                   
                                   + 
                                   
                                     f 
                                     LO 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               t 
                             
                             + 
                             
                               ϕ 
                               0 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 5 
               
             
           
         
       
     
   
   The carrier frequency components, f c +f LO , are suppressed by the lowpass filters. The signals after filtering are: 
                     y   c     ⁡     (   t   )       =         1   2     ⁢     a   1     ⁢     cos   ⁡     (         (       f   c     -     f   LO       )     ⁢   t     +     ϕ   0       )         +       1   2     ⁢     a   2     ⁢     sin   ⁡     (         (       f   c     -     f   LO       )     ⁢   t     +     ϕ   0       )                   Equation   ⁢           ⁢   6               
and
 
   
     
       
         
           
             
               
                 
                   
                     y 
                     s 
                   
                   ⁡ 
                   
                     ( 
                     t 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       a 
                       2 
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               ( 
                               
                                 
                                   f 
                                   c 
                                 
                                 - 
                                 
                                   f 
                                   LO 
                                 
                               
                               ) 
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             ϕ 
                             0 
                           
                         
                         ) 
                       
                     
                   
                   - 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       a 
                       1 
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               ( 
                               
                                 
                                   f 
                                   c 
                                 
                                 - 
                                 
                                   f 
                                   LO 
                                 
                               
                               ) 
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             ϕ 
                             0 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 7 
               
             
           
         
       
     
   
   If the local oscillator frequency in Equations 6 and 7 is equal to the carrier frequency, f LO =f c , and the phase offset is equal to zero, φ 0 =0, the right hand sides of Equations 6 and 7 become ½a 1 (t) and ½a 2 (t) respectively. Therefore, to effect precise demodulation, the local oscillator must have the same frequency and phase as that of the carrier waveform. However, signal perturbations occurring during transmission as well as frequency alignment errors between the local oscillators of the transmitter and receiver manifest a difference between the carrier and local oscillator frequencies which is known as carrier offset. A phase difference between the carrier and local oscillator frequency is created as well. However, if the difference in frequencies is corrected, the difference in phase is simple to remedy. Phase correction is beyond the scope of the present disclosure. 
   Carrier frequency offset is defined as:
 
Δ f=f   c   −f   LO .  Equation 8
 
   To synchronize either parameter, the frequency and phase offsets need to be estimated. In prior art receivers, frequency offset estimation is performed after a significant amount of data processing. Without correcting offset first, the quality of downstream signal processing suffers. 
   “Estimation of Frequency Offset in Mobile Satellite Modems” by Cowley et al. International Mobile Satellite Conference, 16-18 Jun. 1993, pp. 417-422, discloses a circuit for determining a frequency offsets in mobile satellite applications. The frequency offset estimation uses a low pass filter, an M th  power block, a square fast Fourier transform block and a peak search block. 
   “A method for Course Frequency Acquisition for Nyquist Filtered MPSK” by Ahmed IEEE Transactions on Vehicular Technology, vol. 5, no. 4, 1 Nov. 1996, pp. 720-731, discloses a frequency offset estimator for mobile satellite communications. The estimator uses a low pass filter, a decimator, a fast Fourier transform block and a search algorithm. 
   “Carrier and Bit Synchronization in Data Communication—A tutorial Review” by Franks IEEE Transactions on Communications, US, IEEE Inc. New York, vol. COM-28, no. 8, 1 Aug. 1980, pp. 1107-1121, discloses carrier phase recovery circuits using elementary statistical properties and timing recovery based on maximum-likelihood estimation theory. 
   What is needed is a system and method of detecting and estimating carrier frequency offset before any data signal processing is performed. 
   SUMMARY OF THE INVENTION 
   The present invention provides a system and method for estimating the frequency offset experienced between carrier and local oscillator frequencies in communication systems using quadrature modulation. The invention exploits the geometry of the quadrature modulation constellation and estimates actual offset within a predefined carrier offset value without requiring data estimation. 
   Accordingly, it is an object of the invention to provide a less-complex system and method for blindly estimating carrier frequency offset. 
   It is another object of the present invention to blindly estimate carrier offset in a communication system using quadrature modulation regardless of the access protocol. 
   Accordingly, it is an object of the invention to provide a less-complex system and method for blindly estimating carrier frequency offset. 
   It is another object of the present invention to blindly estimate carrier offset in a communication system using quadrature modulation regardless of the access protocol. 
   Other objects and advantages of the system and method will become apparent to those skilled in the art after reading a detailed description of the preferred embodiment. 

   
     BRIEF DESCRIPTION OF THE FIGURES 
       FIG. 1  is a simplified system diagram of a prior art digital communication system. 
       FIG. 2  is a system diagram of the prior art quadrature transmitter shown in  FIG. 1 . 
       FIG. 3  is a system diagram of the prior art quadrature receiver shown in  FIG. 1 . 
       FIG. 4  is a system diagram of the blind carrier offset estimator of the present invention. 
       FIG. 5  is a detailed system diagram of a blind digital carrier offset estimator of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The embodiments will be described with reference to the drawing figures where like numerals represent like elements throughout. 
   Shown in  FIG. 4  is an analog or digital blind carrier detector  33  of the present invention. A quadrature modulated signal r(t) is received from a communication channel (not shown) and is input  19  to a receiver  17 . One skilled in this art recognizes that additional conversion means may exist before the detector input  19  to convert the energy used in the transmission media to compatible signals and is beyond the scope of this disclosure. The received signal r(t) is coupled to a cosine mixer  21   c  and a sine mixer  21   s . Each mixer  21   c ,  21   s  has a first input  25   c ,  25   s  for coupling with the received signal r(t) and a second input  27   c ,  27   s  for coupling with the output of a local oscillator LO. The local oscillator LO is programmed to generate cosine and sine waves at the carrier frequency f c  (Equations 4 and 5) of the received signal r(t). 
   The carrier-frequency demodulated outputs r c (t), r s (t) from each mixer  21   c ,  21   s  are input to respective lowpass filters  29   c ,  29   s  which suppress high-frequency noise components impressed upon the received signal r(t) during transmission through the transmission media and mixer sum frequencies, f c +f LO , (Equations 6 and 7). As in prior art demodulators, the response characteristics of the lowpass filters  29   c ,  29   s  may be a bandwidth as narrow as Δf MAX —the maximum allowable carrier offset. The output y c (t), y s (t) from each lowpass filter  29   c ,  29   s  is coupled to inputs  31   c ,  31   s  of a carrier offset estimator  33 . 
   The carrier offset estimator  33  produces an estimate of the carrier offset  35  before data signal processing commences using a complex power processor  37  in conjunction with a complex Fourier transform processor  39 . The filtered, carrier frequency demodulated cosine and sine components of the quadrature signal y c (t) and y s (t) are coupled to the complex power processor  37  which performs an intermediate power calculation of each quadrature component in the form of x y  where the powers y comprise integer multiples of four; i.e. y=4, 8, 12, 16 . . . . In the preferred embodiment, the power y is 4. 
   The complex power processor  37  may be implemented to raise the input complex signal to a power which is any positive integer multiple of four. Carrier offset detection systems which use a complex power processor with a power of two or its positive integer multiples are known in the art. However, these prior art systems do not work in quadrature-modulated digital communication systems. To properly detect a carrier offset in a quadrature-modulated digital communication system demodulator, a complex power of four or its integer multiples are necessary. 
   The complex power processor  37  combines the lowpass filter outputs y c (t) and y s (t) into a single complex value signal y(t) defined as:
 
 y ( t )= y   c ( t )+ jy   s ( t )  Equation 9
 
where j is defined as j=√−1. The complex power processor  37  generates two power output signals
 
 q   c ( t )= Re {( y ( t )) 4 }  Equation 10
 
and
 
 q   s ( t )= Im {( y ( t )) 4 }  Equation 11
 
where Re{x} denotes the real part of a complex number x, and Im{x} denotes the imaginary part of the complex number x. The complex power processor  37  removes the modulation component from each received symbol leaving the carrier frequency. The real q c (t) and imaginary q s (t) signal components are output and coupled to the complex Fourier transform processor  39 .
 
   The complex Fourier transform processor  39  treats the real q c (t) and imaginary q s (t) signal components as a single complex input signal q(t)=q c (t)+jq s (t). The processor observes q(t) for a finite period of time T W  and computes a complex Fourier transform of the observed signal q(t) over this period of time. 
   The Fourier processor  39  performs a Fourier transform of the power processed signals from the observed period T W  and outputs a frequency at which the amplitude of the transform was measured to be maximal Δf MAX  during that time period T W . The output  35  represents an accurate estimate of Δf and is signed since the transform input signal is complex. The sign identifies whether the local oscillator LO frequency is less than or greater than the carrier frequency. 
   A detailed, low-complexity digital implementation of the present invention  53  is shown in  FIG. 5 . Lowpass filter  29   c ,  29   s  output signals y c (t) and y s (t) are sampled at a sampling rate f s  to produce discrete-time signals y c [n] and y s [n]. To ensure that all possible carrier frequency offsets up to Δf MAX  are detected, 2Δf MAX &lt;f s  must be satisfied. The passband of the low pass filters  29   c ,  29   s  must be wider than Δf MAX  to avoid suppressing the signal which contains the carrier offset information. 
   The sampled signals y c [n] and y s [n] are input  51   c ,  51   s  to a complex power processor  57  and combined as a single complex signal, y[n], where y[n]=y c [n]+jy s [n]. The power processor  57  produces a complex output defined by q[n]=(y[n]) 4 . The output q[n] is coupled to a buffer  59  for accumulating N outputs from the complex power processor  57 . 
   The accumulated block of complex numbers N is coupled to a digital Fourier transform (DFT) processor  61  which performs a transform from the time domain to the frequency domain for the N complex numbers. The DFT processor  61  outputs N complex numbers corresponding with the input N. Each number is associated with a particular frequency ranging from −f s /2 to (+f s /2−f s /N). Each frequency is fs/N away from a neighboring frequency. The frequency domain values output by the DFT  61  are assembled and compared with one another. The value having the largest magnitude represents the best estimate of the carrier frequency offset Δf. 
   The embodiment described in  FIG. 5  is capable of estimating all carrier frequency offsets smaller than f s /2. This follows from the restriction 2Δf MAX &lt;f s  imposed above. The carrier offset Δf is resolved to within a frequency uncertainty of ±f s /2N since the frequencies at the output of the DFT  61  are quantized to a grid with a spacing of fs/N. Since the frequencies are fs/N away from each other, the invention  53  renders precision within ±½ of the selected value. Therefore, the number of samples N accumulated for the Fourier processor  61  to transform determines the resolution of the carrier offset estimate Δf. An efficient implementation of the DFT  61  used in the present invention  53  can be achieved using the fast Fourier transforms (FFT) family of algorithms. 
   The present invention  33 ,  53  may be physically realized as digital hardware or as software. The lowpass filters shown in  FIG. 5  may be realized in digital hardware or software operating at a sampling rate faster than f s . In some communication systems, for example those employing CDMA protocols, the lowpass filters and downsamplers f s  may be replaced with accumulators and integrate-and-dump processes. 
   While the present invention has been described in terms of the preferred embodiments, other variations which are within the scope of the invention as outlined in the claims below will be apparent to those skilled in the art.