Method for synchronizing symbol timing

Abstract

A method of synchronizing symbol timing in a digital device includes the steps of receiving complex data samples of one or more symbols, correlating the data samples with a complex conjugate of a preamble data set, selecting between real and imaginary samples and generating a complex number based on the result. The method then determines an angle in a complex plane that represents symbol synchronization for the digital device. Disclosed embodiments include applications to communications devices, and to carrier recovery in such devices. In such embodiments the resultant angle may represent a carrier phase offset for the device.

1 . In a digital device, a method of symbol timing synchronization, the method comprising the steps of: 
 (1) receiving complex data samples of one or more symbols;    (2) correlating said complex data samples with a complex conjugate of a preamble data set, resulting in correlated complex data samples, each correlated complex data sample represented by a real sample and an imaginary sample;    (3) selecting between said real samples and said imaginary samples, resulting in a set of selected samples;    (4) generating a complex number based on said set of selected samples; and    (5) determining an angle in a complex plane associated with said complex number, whereby said angle represents symbol synchronization for the digital device.    
   
   
       2 . The method of  claim 1 , further comprising the step of: 
 (6) multiplying said angle by π/2 to determine an offset μ that indicates symbol synchronization.    
   
   
       3 . The method of  claim 1 , wherein step (2) comprises the step of multiplying said received complex data samples with said preamble data set.  
   
   
       4 . The method of  claim 1 , wherein step (3) comprises the step of selecting the larger of said real samples and said imaginary samples.  
   
   
       5 . The method of  claim 1 , wherein step (4) comprises the steps of: 
 (a) determining a Fourier transform based on said set of selected data samples; and    (b) evaluating said Fourier transform at π/2.    
   
   
       6 . The method of  claim 1 , wherein step (4) comprises the steps of: 
 (a) determining which of said selected data samples has the largest magnitude;    (b) selecting n adjacent samples from the selected data samples that includes said largest magnitude sample;    (c) determining a Fourier transform of said n adjacent data samples; and    (d) evaluating said Fourier transform at π/2, resulting in said complex number.    
   
   
       7 . The method of  claim 1 , wherein said complex number is in a rectangular format, and wherein step (5) comprises the step of: 
 converting said complex number to polar format having a magnitude and said angle.    
   
   
       8 . The method of  claim 1 , where step (4) comprises the steps of: 
 (a) determining which of said selected data samples has the largest magnitude;    (b) selecting four adjacent samples from the selected data samples, represented by r(−1), r(0), r(1), and r(2), wherein said largest magnitude data sample is one of r(0) and r(1);    (c) determining a Fourier transform of said four adjacent data samples; and    (d) evaluating said Fourier transform at π/2, resulting in said complex number.    
   
   
       9 . The method of  claim 8 , wherein step (c) comprises the steps of: 
 (i) determining r(0)-r(2), to produce a real part of said complex number; and    (ii) determining r(−1)-r(1), to produce an imaginary part of said complex number.    
   
   
       10 . In a digital device, a method of carrier recovery, the method comprising the steps of: 
 (1) receiving complex data samples of one or more symbols;    (2) correlating said complex data samples with a complex conjugate of a preamble data set, resulting in correlated complex data samples;    (3) selecting one of said correlated complex data samples;    (4) determining an angle in said complex plane based on said selected correlated complex data sample, whereby said angle represents a carrier phase offset in the digital device.    
   
   
       11 . The method of  claim 10 , wherein step (3) comprises the step of selecting a largest of said correlated complex data samples.  
   
   
       12 . The method of  claim 10 , wherein said complex number is in a rectangular format, wherein step (4) comprises the step of converting said complex number to a polar format having a magnitude and said angle.