Abstract:
A method of channel estimation used in an orthogonal frequency division multiplexing (OFDM) system. Firstly, a plurality of synchronized signals are received respectively from a plurality of sub-channels, and the channel responses of two sub-channels are known. Then, the channel responses of other channels are estimated by the statistical property derived from Jake&#39;s model according to two sub-channels whose channel responses are known.

Description:
This application claims the benefit of Taiwan application Serial No. 94136948, filed Oct. 21, 2005, the subject matter of which is incorporated herein by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The invention relates in general to a method of channel estimation, and more particularly to a method of channel estimation of an OFDM system. 
   2. Description of the Related Art 
   Orthogonal frequency division multiplexing (OFDM) has the advantage of anti-multi-path interference and is currently adopted as the specification of digital video broadcasting-terrestrial (DVB-T) transmission. 
   The OFDM system spread the data to several sub-channels to be transmitted by multi-carrier modulation. The sub-carrier frequency of each sub-channel is different and orthogonal to each other such that each sub-channel can apply a lower transmission rate. Since the sub-carrier frequency of each sub-channel is different, the influence that each sub-channel receives during transmission also differs. The influence that each sub-channel receives is estimated at the reception end. That is, the channel response of the sub-channel is estimated, whereby the received signal is compensated to obtain the correct signal. 
   There are several methods for estimating channel response such as pilot-based channel estimation for instance. Referring to  FIG. 1 , a pilot pattern of an OFDM system is shown. Each circle denotes the data transmitted by a sub-channel at a time point, the horizontal axis is sub-channel C, and the vertical axis is time t. At each time point, a group of synchronized signals S including a plurality of signals modulated to the sub-channels are received. The black circle denotes the response signal. The contents of the response signal and the position of the response signal on the frequency-time grid are known to both the transmission end and the reception end. Therefore, the reception end can obtains the channel response of the sub-channel transmitting the response signal by comparing the received response signal with the known response signal. 
   Other channel responses of the sub-channels transmitting data signals can be obtained by the linear interpolation of the channel response of the known sub-channels. Examples of linear interpolation include time-domain interpolation and frequency-domain interpolation. For example, the method of estimating the channel response of the sub-channel C ( 1 ) at time point t 2  is shown in  FIG. 2 . Referring to  FIG. 1 . The black points denote response signals, so the channel responses of the sub-channels are known. For example, the channel response of the sub-channel C ( 3 ) is A 31 *exp(jθ 31 ) at the time point t 1 , the channel response of the sub-channel C ( 3 ) is A 35 *exp(jθ 35 ) at the time point t 5 , wherein A is an amplitude response of the sub-channel, and θ is a phase response of the sub-channel. Firstly, the method begins at step  201 , since the ratio of the difference between the time point t 2  and the time point t 1  to the difference between the time point t 2  and the time point t 5  is 1:3, the amplitude response A 32  of the sub-channel C ( 3 ) at time point t 2  is expressed as A 32 =(A 31 *¾+A 35 *¼) and the phase response θ 32  of the sub-channel C ( 3 ) at time point t 2  is expressed as θ 32 =(θ 31 *¾+θ 35 *¼) by time-domain linear interpolation. 
   Next, proceed to step  203 , since the ratio of the sub-carrier frequency difference between the sub-channel C ( 1 ) and the sub-channel C ( 0 ) to the sub-carrier frequency difference between the sub-channel C ( 1 ) and the sub-channel C ( 3 ) is 1:2, the amplitude response of the sub-channel C ( 1 ) at time point t 2  is expressed as A 12 =(A 02 *⅔+A 32 *⅓) and the phase response of the sub-channel C ( 1 ) at time point t 2  is expressed as θ 12 =(θ 02 *⅔+θ 32 *⅓) by frequency-domain linear interpolation. 
   However, the above channel estimation obtained by linear interpolation is not actual channel response, so the estimation is not precise enough and the quality of the received signals is affected. 
   SUMMARY OF THE INVENTION 
   It is therefore an object of the invention to provide a method for precisely estimating channel response. 
   The invention achieves the above-identified object by providing a method of channel estimation used in an orthogonal frequency division multiplexing (OFDM) system. Firstly, a plurality of synchronized signals are received respectively from a plurality of sub-channels of the OFDM system, wherein the i th  and the j th  sub-channel responses are known, i+n=j, i, n and j are positive integers. Then, the channel response of the (i+k) th  sub-channel is estimated according to the statistical properties of the channel response derived from Jake&#39;s model and the channel responses of the i th  and the j th  sub-channels, wherein k&lt;n and k is a positive integer. 
   Other objects, features, and advantages of the invention will become apparent from the following detailed description of the preferred but non-limiting embodiments. The following description is made with reference to the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  (PRIOR ART) is a pilot pattern of an OFDM system; 
       FIG. 2  (PRIOR ART) is a method flowchart of a conventional channel estimation; and 
       FIG. 3  is a method flowchart of channel estimation according to a preferred embodiment of the invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The accuracy of conventional method of estimating the channel response by linear interpolation is insufficient. The amplitude correlation coefficient and the phase correlation coefficient of the channel responses of two sub-channels spaced by a predetermined frequency are derived from Jake&#39;s model. The amplitude correlation coefficient ρ c  of the channel response derived from Jake&#39;s model is expressed as: 
                     ρ   e     ⁡     (     s   ,   τ     )       =         J   0   2     ⁡     (       ω   m     ⁢   τ     )         1   +       s   2     ⁢     σ   2                   (   1   )               
wherein,
 
J 0  is a zeroth order Bessel function of first kind, ω m  is a Doppler frequency, τ is a time delay, s is the frequency difference between two carriers, and σ is a delay spread.
 
   The above parameters ω m , τ, σ which can be obtained by other methods are regarded as known and are not elaborated here. Therefore, the amplitude correlation coefficient ρ e  between two carriers can be obtained according to the frequency difference s 
   The phase correlation coefficient ρ θ  of the channel response derived from Jake&#39;s model is expressed as: 
   
     
       
         
           
             
               
                 
                   
                     
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   In the above expression, the phase correlation coefficient ρ θ  between two carriers can be obtained according to the frequency differences. The invention estimates the channel response of the channel by Jake&#39;s model. Examples of the channel response include amplitude response and phase response. 
   Referring to  FIG. 3 , a method flowchart of channel estimation according to a preferred embodiment of the invention is shown. The present embodiment is exemplified by the estimation of the channel response of sub-channel C ( 1 ) at time point t 2 . Referring to  FIG. 1 . The black points denote response signals, so the channel responses of the sub-channels are known. For example, the channel response of the sub-channel C ( 3 ) is A 31 *exp(jθ 31 ) at the time point t 1 , the channel response of the sub-channel C ( 3 ) is A 35 *exp(jθ 35 ) at the time point t 5 , wherein A is an amplitude response of the sub-channel, and θ is a phase response of the sub-channel. Firstly, the method begins at step  301 , the amplitude response A 32  of the sub-channel C ( 3 ) at time point t 2  is expressed as A 32 =(A 31 *¾+A 35 *¼) and the phase response θ 32  of the sub-channel C ( 3 ) at time point t 2  is expressed as θ 32 =(θ 31 *¾+θ 35 *¼) by time-domain linear interpolation. 
   Next, proceed to steps  310 - 322 , frequency-domain non-linear interpolation is applied according to Jake&#39;s model. Firstly, proceed to step  310 , the amplitude correlation coefficient ρ e10  of the sub-channel C ( 1 ) at time point t 2  and the sub-channel C ( 0 ) at time point t 2  is obtained according to formula (1). Next, proceed to step  312 , the amplitude correlation coefficient ρ e13  of the sub-channel C ( 1 ) at time point t 2  and the sub-channel C ( 3 ) at time point t 2  is obtained. Next, proceed to step  314 , the amplitude response of the sub-channel C ( 1 ) at time point t 2  is expressed as: A 12 =(A 02 *ρ e10 /(ρ e10 +ρ e13 )+A 32 *ρ e13 /(ρ e10 +ρ e13 )) 
   Next, proceed to step  316 , the phase correlation coefficient ρ θ10  of the channel C ( 1 ) at time point t 2  and the sub-channel C ( 0 ) at time point t 2  is obtained according to formula (2). Next, proceed to step  318 , the amplitude correlation coefficient ρ θ13  of the sub-channel C ( 1 ) at time point t 2  and the sub-channel C ( 3 ) at time point t 2  is obtained. Next, proceed to step  320 , the phase response of the sub-channel C ( 1 ) at time point t 2  is expressed as:
 
θ 12 =(θ 02 *ρ θ10 /(ρ θ10 +ρ θ13 )+θ 32 *ρ θ13 /(ρ θ10 +ρ θ13 ))
 
   Therefore, in step  322 , the estimation of the channel response of the sub-channel C ( 1 ) at time point t 2  is expressed as: A 12  exp(jθ 12 ). 
   The time-domain linear interpolation of step  301  does not have to be performed in practical application because the channel response of a channel does not vary with the time significantly under normal circumstances. Therefore, the channel response of the sub-channel C ( 3 ) at time point t 2  can be set to be equal to the channel response of the sub-channel C ( 3 ) at time point t 1  or t 5 . 
   The method of channel estimation disclosed in the above embodiment of the invention accurately estimates the channel response of the channel by Jake&#39;s model so as to improve the quality of signal reception. 
   While the invention has been described by way of example and in terms of a preferred embodiment, it is to be understood that the invention is not limited thereto. On the contrary, it is intended to cover various modifications and similar arrangements and procedures, and the scope of the appended claims therefore should be accorded the broadest interpretation so as to encompass all such modifications and similar arrangements and procedures.