Abstract:
A method for non-data aided frequency offset determination for MPSK demodulation is accomplished by receiving a stream of K symbols and providing the symbol stream to a delay line of L symbols in length with L greater than 1. The symbol stream and an output of the delay line is taken at each increment of L and then multiplied and the output of the multiplier is raised to the M power to remove modulation. The result is accumulated over K symbols and the argument of 1/K2πMLT times the accumulated result is determined as a frequency offset. L is then incremented and the calculation repeated. The calculated frequency offsets are then summed for a final frequency offset determination.

Description:
REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is a continuation-in-part of U.S. patent application Ser. No. 11/196,233 filed on Aug. 2, 2005 entitled A HIGH ACCURACY NON DATA-AIDED FREQUENCY ESTIMATOR FOR M-ARY PHASE SHIFT KEYING MODULATION having a common assignee as the present invention. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the Invention  
         [0003]     This invention relates generally to the field of telecommunications network transmission systems and, more particularly, to a non-data-aided iterative frequency estimator for use in demodulation of M-ary phase shift keying (M-PSK) modulated signals.  
         [0004]     2. Description of the Related Art  
         [0005]     M-ary phase shift keying (M-PSK) modulation is widely used in communication systems. Among the most widely used M-PSK modulation schemes are binary phase shift keying (BPSK), quadriphase shift keying (QPSK), and their variations such as π/4 QPSK, differential QPSK. A representative explanation of these systems is disclosed in Y. Okunev, Phase and Phase-difference Modulation in Digital Communications, Artech House, 1997  
         [0006]     For current exemplary systems, the second generation CDMA system uses BPSK while the third generation WCDMA system uses both BPSK and QPSK modulation. The PHS system uses π/4 differential QPSK.  
         [0007]     It is often impractical or economically infeasible to maintain exact frequency synchronization between the transmitter and the receiver, as a result, accurate frequency estimation of the difference between the transmitted and received signals is desirable. This is especially true for coherent demodulation, for which highly accurate estimation is essential. Most prior art systems employ data-aided frequency estimation using training sequences embedded in message bursts. However, this technique uses bandwidth and may require additional complexity in the demodulation algorithms and hardware.  
         [0008]     It is therefore desirable to provide non-data-aided frequency estimator for M-PSK demodulation with increased accuracy.  
       SUMMARY OF THE INVENTION  
       [0009]     The present invention provides a method for non-data aided iterative frequency offset determination for MPSK demodulation accomplished by receiving a stream of K symbols and providing the symbol stream to a delay line of L symbols in length with L greater than 1. The symbol stream and an output of the delay line are then multiplied and the output of the multiplier is raised to the M power to remove modulation. The result is accumulated over K symbols and the argument of 1/K times the accumulated result is determined as the frequency offset. At a first increment, a frequency offset is determined for L=1. This offset is then removed in a second iteration for L=2 to provide a second frequency offset estimation. The process is iterated for selected values of L up to L−1 with each subsequent frequency offset removed for the next iteration and each of the calculated frequency offsets summed to provide a final frequency offset output. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]     These and other features and advantages of the present invention will be better understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein:  
         [0011]      FIG. 1  is a block diagram of the elements acting on a symbol input stream for each iterative element of an embodiment of the invention;  
         [0012]      FIG. 2  is a block diagram of an exemplary hardware implementation of the embodiment of  FIG. 1 ; and,  
         [0013]      FIG. 3  is a block diagram of the iterative elements of  FIG. 1  to create a system according to the present invention.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0014]     This invention applies to all types of MPSK modulation. In what follows, it is described using a MPSK modulation signal model.  
         [0015]     Each symbol of a received M-PSK signal can be described in baseband complex format by the following equation: 
 
 S ( k )= C   k   e   j2π(f     c     +f     0     )kT+θ   +n ( k )  (1) 
 
         [0016]     Where k represents the sample index and k=0, 1, . . . K. f c  and f 0  are the carrier frequency and frequency offset respectively. T is the symbol duration. θ is the phase offset. n(k) is the white Gaussian noise, C k  is the data symbol belonging to the MPSK constellation  
               C   k     =     ⅇ     j   ⁢       2   ⁢   πⅈ     M                 (   2   )             
 
 where 0≦k≦M−1 
 
         [0017]     Many frequency estimation techniques have been developed for MPSK. Most are data-aided, i.e., some sort of training sequence is transmitted in addition to the information. On the receiver side, the known training sequence is used to estimate frequency offset.  
         [0018]     Non-data aided frequency estimation does not need a training sequence. It takes into account of the fact that (C k ) M =1 to effectively remove the modulation from a M-PSK signal. The modulation removed M-PSK signal can then be used for frequency estimation. Frequency estimation methods based on this concept are called none-data-aided frequency estimators. A non-data aided frequency offset estimator is highly desirable since it has high bandwidth efficiency due to the fact that it eliminates the need for a training sequence.  
         [0019]     One commonly used non data-aided frequency estimation method for M-PSK is proposed in J Chuang and N Sollenberger, Burst Coherent Demodulation with Combined Symbol Timing, Frequency Offset Estimation, and Diversity Selection, IEEE trans. Communications, pp 1157-1164, July 1991, which is described below.  
         [0020]     Raising Equation (1) to the Mth power yields 
 
[ S ( k )] M   =e   j[2π(f     c     +f     0     )kT+θ]M   +n ′( k )  (3) 
 
 n′(k) is the noise term resulting from signal multiplied by noise and noise multiplied by noise. Modulation is removed in the equation. Next, multiplying [S(k)] M  by [S(k−1)] M , provides 
 
[ S ( k )] M   ·[S *( k− 1)] M   =e   j2πMf     0     T   +n ″( k )  (4) 
 
         [0021]     Again n″ (k) is the noise term resulting from signal multiplied by noise and noise multiplied by noise.  
         [0022]     It is apparent that carrier frequency and phase are removed in Equation (4) so it can be used to estimate f 0 . The estimation accuracy can be further improved by smoothing out the noise  
                 1   K     ⁢       ∑     k   =   0       K   -   1       ⁢     (         [     S   ⁡     (   k   )       ]     M     ·       [       S   *     ⁡     (     k   -   1     )       ]     M       )         =       ⅇ     j2π   ⁢           ⁢     Mf   0     ⁢   T       +       1   K     ⁢       ∑     k   =   0       K   -   1       ⁢       n   ″     ⁡     (   k   )                     (   5   )             
 
         [0023]     In summary the frequency estimator is  
               f   0     =       1     2   ⁢   π   ⁢           ⁢   MT       ⁢   arg   ⁢     {       1   K     ⁢       ∑     k   =   0       K   -   1       ⁢     (         [     S   ⁡     (   k   )       ]     M     ·       [       S   *     ⁡     (     k   -   1     )       ]     M       )         }               (   6   )             
 
         [0024]     The estimator described above is good for applications where moderate accurate frequency estimation is required such as differential PSK. However, for application where more accurate estimation is needed, such as coherent demodulation of M-PSK signal, it is not accurate enough.  
         [0025]     A new frequency estimator, which is capable of estimating very small frequency offset is created by replacing S(k) and S(k−1) with S(k) and S(k−L), where L is larger than 1. The use of S(k) and S(k−L), when L is large, enables estimation of small frequency errors since the phase offset is accumulated over L symbol periods to 2πf 0 LT instead of 2πf 0 T.  
         [0026]     As shown in  FIG. 1 , the symbol input stream S(k)  10  is routed to a multiplier  12  and through delay line of up to L symbols  14  and conjugated  16 . The delayed signal is multiplied and the result is raised to the M power in multiplier  18  [S(k)] M  times [S(k−L)] M , to provide 
 
[ S ( k )] M   ·[S *( k−L )] M   =e   j2πMLf     0     T   +n″ ( k )  (7) 
 
 where n″ (k) is the noise term resulting from signal multiplied by noise and noise multiplied by noise. 
 
         [0027]     Similar to Equation (4), we can use Equation (7) to estimate f 0 . The estimation accuracy can be further improved by smoothing out the noise as well  
                 1   K     ⁢           ⁢       ∑     k   ⁢           =           ⁢   0       K   ⁢           -           ⁢   1       ⁢     (         [     S   ⁡     (   k   )       ]     M     ·           ⁢       [       S   *     ⁡     (     k   ⁢           -           ⁢   L     )       ]     M       )         =           ⁢       ⅇ     j2π   ⁢           ⁢     Mf   0     ⁢           ⁢   T       ⁢           +           ⁢       1   K     ⁢           ⁢       ∑     k   ⁢           =           ⁢   0       K   ⁢           -           ⁢   1       ⁢       n   ″     ⁡     (   k   )                     (   8   )             
 
         [0028]     The offset frequency is then estimated as  
               f   0     =       1     2   ⁢           ⁢   π   ⁢           ⁢   MLT       ⁢   arg   ⁢     {       1   K     ⁢           ⁢       ∑     k   ⁢           =           ⁢   0       K   ⁢           -           ⁢   1       ⁢     (         [     S   ⁡     (   k   )       ]     M     ·           ⁢       [       S   *     ⁡     (     k   ⁢           -           ⁢   1     )       ]     M       )         }               (   9   )             
 
         [0029]     An initial frequency offset  22  is obtained by operating on the output of the exponent multiplier with ½πMLT times the argument of 1/K times the sum over K symbols in accumulator  20 . The frequency offset determination is usually accomplished for each burst. Frequency change during each burst is usually very small, however, should situations arise where frequency change is anticipated during symbol bursts, this method can be used multiple times during a burst.  
         [0030]     The performance of this frequency estimation method depends on K, the number of samples, as well as the interval between the adjacent samples. The estimator of the present invention collapses to the estimator described in Chuang and Sollenberger by letting L equal 1.  
         [0031]     K and L of large value will give more accurate estimation. However, it should be noted that the frequency offset that can be estimated must satisfy 
 
 MLTf   0 &lt;1  (10) 
 
 otherwise the e j2πMLf     0     T  term in Equation (7) will wrap around and produce incorrect results. 
 
         [0032]     The frequency estimator of the present invention uses iterative structure as shown in  FIG. 3 . The received signal is processed through the first round of frequency estimation using the method as shown in  FIG. 1  in an estimator  46  for L=1, which produces f 00 , the first round of frequency offset estimation. S 1 (k) is then generated by removing f 00  from the initial estimate S(k) in block  48 . To be specific 
 
 S   1 ( k )= S ( k )· e   −j2πf     00     KT   (10) 
 
         [0033]     S 1 (k) has a smaller frequency offset than S(k). Next, the residual frequency offset in S 1 (k) is estimated based on a frequency estimator  50  again using the method steps to implement Equation (7) with L=2. The second iteration of the frequency estimator, as stated earlier, handles a narrower range of frequency offset but has higher accuracy. Expressing the method operation in equation form 
 
 S   2 ( k )= S   1 ( k )· e   −j2πf     01     KT   (11) 
 
         [0034]     S 3 (k) is then generated by removing f 02  from the second estimate S 2 (k) in block  52 . This set of process steps repeats until the required resolution of frequency estimation is reached.  
         [0035]     The frequency offset range this iterative estimator is capable of estimating is  
               f   0     &lt;     1   MT             (   12   )             
 
         [0036]     The accuracy is mainly determined by the last stage. Large L provides better accuracy.  
         [0037]     The final estimator is shown representatively as element  54 . The outputs of each iterative frequency offset estimator stages is summed  56  to provide the frequency offset estimate  
               f   0     =       ∑     i   =   0       L   -   1       ⁢     f     0   ⁢           ⁢   i                 (   13   )             
 
 as output  58 . 
 
         [0038]     For a practical implementation of this estimator, executing all the stages of estimation of 0, 1, . . . L−1, as shown in  FIG. 3  is usually not required. Except the first and last stages, many of the stages 1, . . . L−2 can be skipped. For example, if the residual frequency offset in S 1 (k) is bounded by f r , all 1, . . . , L r −1 stages are skipped, provided ML r Tf r  is much smaller than 1. For practical implementation purposes, an exemplary embodiment employs a test of  
                 ML   r     ⁢     Tf   r       =     1   4             (   14   )             
 
 and incrementing the estimation stage by L r  for obtaining the next incremental frequency offset estimate. 
 
         [0039]     An implementation of the stages of the frequency offset estimator according to the present invention is shown in  FIG. 2 . The frequency offset estimator for MPSK demodulation includes a buffer  30  for receiving a stream of K symbols. A delay line  32  of L symbol lengths where L is greater than 1 is connected to the buffer and a multiplier  34  receives a first input from the buffer and a second input from the delay line. The output of the multiplier is raised to the M power using a multiplier string  36  and an accumulator  38  receives the result for K symbols. A 1/K multiplier  40  acts on the output of the accumulator and the argument of the output of the 1/K multiplier is determined as the frequency offset. For the embodiment shown, the argument function is obtained using a look-up table  42 . A multiplier  44  on the output provides the required ½πMLT factor. The buffer symbol data is then adjusted by the frequency offset for demodulation of the symbol burst.  
         [0040]     Compared with existing non-data-aided frequency estimators, this method is capable of providing high accuracy estimation if the frequency offset is relatively small. This frequency estimator is applicable to all wireless standards using MPSK modulation, such as PHS, CDMA, WCDMA, CDMA2000 and other Phase Shift Keying methodologies.  
         [0041]     Having now described the invention in detail as required by the patent statutes, those skilled in the art will recognize modifications and substitutions to the specific embodiments disclosed herein. Such modifications are within the scope and intent of the present invention as defined in the following claims.