Abstract:
An effective data sequence based timing error detector (EDS-TED) for baseband transmission system using Tomlinson-Harashima Precoder is disclosed. The EDS-TED extracts timing error information embedded in the received signal to build up autocorrelation between the ESD signals and minimize the mean square error between the received and desired EDS so as to improve the performance of the TED in terms of Peak-to-Peak Jitter and TED gain. Thus the quality of the received signal increases and the error rate decreases.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to a timing error detector and a method thereof, and more particularly, to a timing error detector for a baseband transmission system using a Tomlinson-Harashima precoder. 
     2. The Prior Arts 
     In a transmission channel of a high speed digital transmission system, there are many unavoidable noise sources, which provide noises interfering clock signals recovered by the receiver side. Such noise interferences may cause large jitters, and therefore the receiver side cannot recover information transmitted from the transmitter side. As such, correct timing error information is very important for a high speed digital transmission system, such as a 10 GBASE-T baseband transmission system. Accordingly, an effective technology of extracting the timing error information is very much desired by a receiver, for overcoming the problem caused by the noise contained in the correct timing error information, thus obtaining the correct timing error information as desired. 
     Nowadays, data transmission rates are developed to be higher and higher. As such, the system unit interval becomes much shorter. When the system is in operation with a higher data transmission rate, the timing margins of the system are closer to each other. Therefore, the performance of a timing recovery (TR) loop plays a critical role hereby. Typically, a decision feedback equalizer (DFE) includes two parts, a feedforward equalizer (FFE), and a feedback equalizer (FBE). To solve the error propagation problem, a Tomlinson-Harashima precoder (THP), which is known as a transmitter side pre-equalization technique, has been proposed to move the FBE of the DFE to the transmitter side. The THP is not only capable of avoiding the error propagation problem, but also compatible with the low density parity check (LDPC) codes, thus reducing the impact to the system and lowering the operation risk of the system. 
     One of the most important blocks in a TR loop is the timing error detector (TED), such as a Mueller and Muller TED (MM-TED) or an equalizer-based TED (EQ-TED). The MM-TED has been widely used in many TR systems. In a typical MM-TED, the output of the TED is determined according to the sampled data and estimated data values. The EQ-TED estimates the timing error information according to the coefficients of the FFE. The EQ-TED does not need any decision results for estimating the timing error, and therefore it can be applied in a receiver for a baseband transmitter using THP. 
     The present invention is provided as a solution to problems of the conventional MM-TED. In a THP of a baseband transmitter, the THP employs a modular element for restricting the output within a predetermined range, which causes a non-linear effect, and therefore the MM-TED of the baseband communication system using the DFE cannot detect the correct timing error information. Moreover, the conventional EQ-TED has the following disadvantages. Firstly, an optimal first precursor tap weight obtained at an optimal sampling phase is assumed to be known, in that only when an optimal coefficient of the FFE is known, the system can obtain the correct timing error information. Otherwise, the EQ-TED would be biased. Secondly, the estimated timing error is related to the algorithm for dynamically adjusting the FFE coefficient, and accordingly different estimated values of the timing error may be obtained in accordance with different adaptive algorithms. 
     As such, a timing error detector and a method thereof are desired to provide a solution to the problems associated with the conventional technologies, and thus improving the performance of the entire communication system. 
     SUMMARY OF THE INVENTION 
     A primary objective of the present invention is to provide a timing error detector, adapted for a non-linear Tomlinson-Harashima precoder of a transmitter in a baseband communication system, e.g., a 10 GBASE-T system, for extracting correct timing error information from the received signals. In accordance with the present invention, an autocorrelation between effective data sequences (EDS) is constructed, and a mean square error (MSE) between the received and the desired EDS, thus reducing the peak-to-peak jitter of the recovered clock pulse and enhancing the timing error detection gain, and further improving the quality of the received signals at the input of slicers and reducing the error rate thereof. 
     Another primary objective of the present invention is to provide a method for detecting a timing error, for incorporating with a non-linear Tomlinson-Harashima precoder of a baseband transmitter, and extracting the correct timing error information according to the timing error instant estimation value signals, so as to bypass the non-linear effect caused by the Tomlinson-Harashima precoder, thus improving the signal-to-noise ratio at the input of the slicer. 
     Further, the preset invention is adapted for a variety of modulation techniques, such as pulse amplitude modulation, and 128-points double square mapping. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be apparent to those skilled in the art by reading the following detailed description of a preferred embodiment thereof, with reference to the attached drawings, in which: 
         FIG. 1  is a schematic diagram illustrating an effective data sequence timing error detection (EDS-TED) according to an embodiment of the present invention; 
         FIG. 2  is a schematic diagram illustrating a baseband communication system having a transmitter side using a THP and a receiver side employing the EDS-TED according to an embodiment of the present invention; 
         FIG. 3  is a schematic diagram illustrating an equivalent model of a baseband communication system using THP according to an embodiment of the present invention; and 
         FIG. 4  is a flow chart illustrating a method for detecting a timing error according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. 
       FIG. 1  is a schematic diagram illustrating an effective data sequence based timing error detection (EDS-TED)  10  according to an embodiment of the present invention. Referring to  FIG. 1 , the EDS-TED  10  includes a first subtractor  12 , a first delayer  14 , a second delayer  16 , a third delayer  17 , a second subtractor  18 , and a multiplier  19 . The EDS-TED  10  is adapted for processing an EDS c 1 [ n ] of the receiver side and an error signal e[n], and generating an output value X EDS . The EDS c 1 [ n ] of the receiver side is provided from a feedforward equalizer (FFE)  20 , and the error signal e[n] is provided by a posterior subtractor  30 . The output value X EDS  is received by a loop filter (LPF)  40 . As such, the EDS-TED  10  of the present invention is provided mainly for performing a logical calculation to the EDS c 1 [ n ] at the receiver side and the error signal e[n], so as to obtain an output signal of the output value X EDS . 
     The first subtractor  12  subtracts the error signal e[n] from the EDS c 1 [ n ] of the receiver side and generates an EDS estimation value c 2 [ n ] of the transmitter side. The EDS estimation value c 2 [ n ] of the transmitter side is then provided to the first delayer  14  and the second subtractor  18 . The EDS estimation value c 2 [ n ] of the transmitter side is then delayed by the first delayer  14  and the second delayer  16 , thus generating a delayed EDS estimation value c 2 [ n− 2] at the receiver side. The second subtractor  18  subtracts the delayed and EDS estimation value c 2 [ n− 2] of the transmitter side from the EDS estimation value c 2 [ n ], thus obtaining a difference signal c 2 [ n ]−c 2 [ n− 2], and transmitting the difference signal to the first multiplier  19 . The third delayer  17  delays the error signal e[n] and generates a delayed error signal e[n−1]. The first multiplier  19  then multiplies the difference signal with the delayed error signal e[n−1], and obtains the output value X EDS . Therefore, the output value X EDS  can be represented as:
 
 X   EDS   =e[n− 1]( c 2 [n]−c 2 [n− 2]).
 
       FIG. 2  is a schematic diagram illustrating a baseband communication system with a receiver side employing the EDS-TED of  FIG. 1  according to an embodiment of the present invention. Referring to  FIG. 2 , it illustrates a baseband communication including a Tomlinson-Harashima precoder (THP)  50 . The THP  50  is positioned at the transmitter side for precoding information baud-rate signals a[n] (a modulation signal of which has M levels), to generate a precoded channel input signal v[n]. After passing through the transmission channel, the precoded channel input signal v[n] is then received by the receiver side, and therefore a received signal y(t) is generated thereby. As shown in  FIG. 2 , the adder  58  of the receiver side represents that the transmission channel  56  causes a white Gaussian noise N(t) to be added in the received signal y(t). It should be noted that the adder  58  is used to show that the effect affection applied by the transmission channel to the transmitted signal is equivalent to an adder  58  employed at the receiver side, instead of restricting that the receiver side of the communication system should include such an adder. 
     The received signal y(t) at the receiver side is converted into a digital input signal y(t k ) by an analog-to-digital converter (ADC)  70 . It should be noted that the received signal y(t) is a continuous signal, and the digital input signal y(t k ) is a discrete signal, and therefore y[k] is employed for substituting y(t k ). The ADC  70  requires an external clock signal for sampling to generate y[k]. The sampling period t k  of the ADC can be represented as: t k =kTs+φ, in which k is a timing subscript, Ts represents a sampling period, φ represents a sampling phase, while Ts=T/2, and T represents a baud-rate time of the transmission system. 
     Then, the signal y[k] is operated by a down-sampler  74  having a reduction factor of 2, and a modulation reduction sampled signal y[n] is thus generated. After performing the equalization, the FFE  20  generates the receiver side EDS, c 1 [ n ], and at the same time, the receiver side EDS, c 1 [ n ], is provided to the EDS-TED  10  and a 2M module (2MM)  76 . The EDS-TED  10  executes the foregoing operations to generate the output value X EDS , while the modulo-2M device  76  executes a 2M module process to remove the precoding sequence contained therein to obtain a received baud-rate signal a 1 [ n ]. In other words, the 2M module  76  is a decoding module. The slicer  78  then receives the received baud-rate signal a 1 [ n ], and generates a decision a 2 [ n ]. Then, the posterior subtractor  30  subtracts the decision a 2 [ n ] from the received baud-rate signal a 1 [ n ], and obtains the error signal e[n]. 
     The output value X EDS  of the EDS-TED  10  is sequentially processed by the LPF  40 , a digital-to-analog converter (DAC)  42 , a voltage control oscillator (VCO)  44 , and finally the VCO  44  outputs a clock signal t k  to the ADC  70 . Accordingly, the EDS-TED  10 , the LPF  40 , the DAC  42 , and the VCO  44  constitute a timing loop in the receiver side for the baseband communication system. 
     As such, the EDS-TED  10  according to the present invention can extract a suitable difference signal from the timing loop in the receiver side for the baseband communication system, i.e., the output value X EDS , so that the timing loop can more effectively output the correct clock signal t k , and therefore the signal-to-noise ratio at the slicer  78  input is maximized. 
     For further illustrating the improvement made by the EDS-TED  10  of the present invention to the baseband communication system, please refer to  FIG. 3 .  FIG. 3  is a schematic diagram illustrating an equivalent model of a baseband communication system using THP according to an embodiment of the present invention. As shown in  FIG. 3 , the equivalent model of the THP is represented by a first adder  92 , a fourth subtractor  93 , and a feedback loop  94 . A precoding sequence d[n] is added by the first adder  92  to an original information baud-rate a[n], thus generating an EDS sequence c[n]. The fourth subtractor  93  and the feedback loop  94  are provided for generating the precoded channel input signal v[n]. According to the simplified model of the THP, the non-linear precoding sequence d[n] is distinguished from other linear blocks, so as to illustrate the advantages of the present invention. The fifth subtractor  96  subtracts a precoding sequence d 1 [ n ] from the receiver side EDS, c 1 [ n ], so as to generate the received baud-rate signal a 1 [ n ] at the input of the slicer  78 . The precoding sequence at the transmitter side d[n] and the received precoding sequence at the receiver side d 1 [ n ] are both random signals, and therefore they are non-linear physical quantities. The equivalent system to which the original information baud-rate a[n] is inputted, as shown in  FIG. 3  and directed by the arrow NLR, is a non-linear system, i.e., the non-linear block  100  as shown in  FIG. 3  is a non-linear system. However, the equivalent system to which the EDS c[n] is inputted, as shown in  FIG. 3  and directed by the arrow LNR, i.e., the linear block  101  as shown in  FIG. 3 , is a linear system. 
     Assuming that the error signal e[n] inputted to the EDS-TED  10  according to the present invention is defined as:
 
 e[n]=c 1 [n]−c[n],  
 
because the EDS c[n] is only available at the transmitter side, the receiver side has to estimate the EDS c[n]. In case the decision is correct, i.e., a 2 [ n ]=a[n], then:
 
 c[n]=a 2 [n]+d 1 [n] 
 
and therefore
 
                           e   ⁡     [   n   ]       =       ⁢       c   ⁢           ⁢     1   ⁡     [   n   ]         -     (       a   ⁢           ⁢     2   ⁡     [   n   ]         +     d   ⁢           ⁢     1   ⁡     [   n   ]           )                   =       ⁢       c   ⁢           ⁢     1   ⁡     [   n   ]         -     a   ⁢           ⁢     2   ⁡     [   n   ]         -     (       c   ⁢           ⁢     1   ⁡     [   n   ]         -     a   ⁢           ⁢     1   ⁡     [   n   ]           )                     =       ⁢       a   ⁢           ⁢     1   ⁡     [   n   ]         -     a   ⁢           ⁢     2   ⁡     [   n   ]             ,                 
in which d 1 [ n ]=c 1 [ n ]−a 2 [ n ], i.e., the received precoding sequence d 1 [ n ] can be obtained by subtracting an output signal of a 2M module  76  from its input signal, which is also subtracting the received baud-rate signal a 1 [ n ] from the receiver side EDS c 1 [ n ]. Comparing with the definition given to e[n] as shown in  FIG. 2 , the foregoing assumption is coincident with the structure shown in  FIG. 2 , i.e., e[n]=a 1 [ n ]−a 2 [ n ]=c 1 [ n ]-c[n]. Because the linear block  101  between the receiver side EDS c 1 [ n ] and the precoding information baud-rate signal c[n] is a linear system, a system configuration of the EDS-TED  10  of the present invention can be deducted in accordance with the minimum square error criteria, in which the delay elements are provided for the causality considerations. As such, the design of the timing loop is not affected by the nonlinearity introduced by the THP, and therefore the present invention provides a solution to the nonlinear distortion error introduced by the conventional THP, thus improving the performance of the communication system in its entirety.
 
     It should be noted that the transmitter illustrated in the foregoing embodiments are given for exemplifying the features of the present invention. As such, the present invention is also adapted for other THP transmitter for solving the nonlinearity problem of the THP. 
     In another embodiment, the present invention further provides a timing error detection method, for providing a solution to the nonlinear distortion problem of the conventional nonlinear THP transmitter, thus allowing the receiver side obtaining the correct data as desired. 
       FIG. 4  is a flow chart illustrating a method for detecting a timing error according to an embodiment of the present invention. Referring to  FIG. 4 , first at step S 10 , a transmitter side EDS estimation value c 2 [ n ] is obtained by subtracting an error signal from a receiver side EDS. Then, at step S 20 , a delayed transmitter side EDS estimation value by performing two times of delaying processes. At step S 30 , a difference signal is obtained by subtracting the double delayed signal from the original transmitter side EDS estimation value. Then, at step S 40  a delayed error signal is obtained by performing a once delaying process to the difference signal. At step S 50 , a timing error instant estimation value is obtained by multiplying the difference signal with the delayed error signal. A timing error detector constructed according to the method for detecting a timing error can be employed incorporating with a THP for constructing a communication system having a linear timing loop, thus providing a solution to the nonlinear distortion problem of the conventional nonlinear THP transmitter, and improving the communication performance thereof. 
     Table 1 shows a comparison of the performance of the EDS-TED of the present invention with the conventional MM-TED and EQ-TED. As shown in Table 1, the resulting peak-to-peak jitter, decision-point signal-to-noise ratio (DP-SNR) and the symbol error rate (SER) for the TH precoded system with the EDS-TED of the present invention, the conventional MM-TED and the EQ-TED, respectively, are listed for comparison. Referring to Table 1, when there is no residual frequency offset Δf s , the MM-TED operates well. Further, when the residual frequency offset Δf s  is too high, the EQ-TED will fail to work since it cannot provide a correct timing error data. On the contrary, when the residual frequency offset Δf s  is lower than 20 ppm, the EDS-TED of the present invention can still work well. As such, the TH precoded system with the EDS-TED of the present invention achieves an improved performance in terms of peak-to-peak jitter, DP-SNR, and SER, comparing with the conventional MM-TED and EQ-TED. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Loop Performance Comparison 
               
             
          
           
               
                 Performance 
                 Δf s   
                 MM-TED 
                 EQ-TED 
                 proposed 
               
               
                 metrics 
                 (ppm) 
                 [3] 
                 [6] 
                 EDS-TED 
               
               
                   
               
             
          
           
               
                 Peak-to-peak 
                 0 
                 35.10 
                 17.40 
                 8.81 
               
               
                 jitter (ps) 
                 10 
                 1249.98 
                 76.50 
                 8.49 
               
               
                   
                 20 
                 1249.98 
                 1249.98 
                 9.72 
               
               
                 DP-SNR 
                 0 
                 30.35 
                 30.44 
                 30.49 
               
               
                 (dB) 
                 10 
                 22.42 
                 29.65 
                 30.33 
               
               
                   
                 20 
                 22.41 
                 22.42 
                 30.14 
               
               
                 SER 
                 0 
                 1.42 * 10 −3   
                 1.42 * 10 −3   
                 1.42 * 10 −3   
               
               
                   
                 10 
                 8.58 * 10 −1   
                 1.82 * 10 −3   
                 1.43 * 10 −3   
               
               
                   
                 20 
                 9.00 * 10 −1   
                 7.73 * 10 −1   
                 1.44 * 10 −3   
               
               
                   
               
             
          
         
       
     
     Although the present invention has been described with reference to the preferred embodiments thereof, it is apparent to those skilled in the art that a variety of modifications and changes may be made without departing from the scope of the present invention which is intended to be defined by the appended claims.