Abstract:
A receiver includes a first mixer configured to provide an in-phase (I) component of a radio frequency (RF) signal to an I channel by down-converting the RF signal, a second mixer configured to provide a quadrature (Q) component of the RF signal to a Q channel by down-converting the RF signal, amplification means, arranged on the I and Q channels, configured to amplify the I and Q components, a mismatch estimator configured to convert the amplified I and Q components into a frequency domain, and estimate a gain mismatch value and a phase mismatch value on the basis of the converted components, and a mismatch compensator configured to compensate for mismatch of the received signal on the basis of the estimated gain and phase mismatch values.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority to and the benefit of Korean Patent Application No. 10-2010-0099729, filed on Oct. 13, 2010, the disclosure of which is incorporated herein by reference in its entirety. 
       BACKGROUND 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to a radio receiver for estimating and compensating for in-phase/quadrature (IQ) mismatch. 
         [0004]    2. Discussion of Related Art 
         [0005]    In recent communication systems, a direct conversion reception method capable of reducing the number of components and having low complexity and low power consumption has been preferred. The direct conversion reception method converts a signal of a radio frequency (RF) band into a baseband by use of one mixer without involving an intermediate frequency. The mixer receives the RF signal and outputs signals of an in-phase (I) component and a quadrature (Q) component. Each signal is input to an analog-to-digital (A/D) converter through an amplifier and an analog filter. In this process, mismatch occurs in the signals of the I and Q components due to an analog circuit including a local oscillator, a mixer, an amplifier, and an analog filter. This mismatch reduces a signal to noise ratio of a received signal, thereby increasing a bit error rate (BER) and degrading the performance of a wireless communication receiver. To reduce the mismatch, errors of the I and Q components should be minimized when the analog circuit is designed. Also, when the analog circuit is designed, more precision is required and cost of the analog circuit increases. 
         [0006]    To avoid these disadvantages, methods of estimating and compensating for the mismatch in a digital stage have been proposed. For example, there is a method using a pilot signal in an orthogonal frequency division multiplexing (OFDM) system or a method using a known signal in a system including a transmitter and a receiver. The method of estimating the mismatch by use of a specific pilot signal in a system supporting the OFDM scheme cannot be applied to a system with no pilot signal. There is a disadvantage in that the performance of estimating the mismatch is degraded due to a pilot signal estimation error. In the method proposed in a transceiver structure including both of the transmitter and the receiver, mismatch of the receiver is estimated by generating a specific signal through the transmitter and receiving the specific signal by the receiver in an RF stage. This method additionally requires a signal generator in a system only having a receiver such as a mobile broadcast receiver, and has a disadvantage in that the mismatch is not compensated for in real time during communication. Mismatch compensation methods proposed in the related art have a disadvantage in that time mismatch occurring due to a group delay difference of an analog filter between I and Q components or a circuit length difference in a broadband system having a high sampling frequency is not processed. 
       SUMMARY OF THE INVENTION 
       [0007]    The disclosed technology is directed to a receiver capable of estimating and compensating for IQ mismatch using an unknown received signal. For example, the unknown received signal may be a general data signal rather than a pilot signal. 
         [0008]    The disclosed technology is directed to a receiver capable of estimating and compensating for mismatch of the receiver, regardless of a type of modulation signal, and estimating and compensating for mismatch of a received signal while the signal is received. 
         [0009]    The disclosed technology is also directed to a receiver capable of effectively estimating and compensating for mismatch when there is a time delay between I and Q components in a receiver having a high sampling frequency such as a broadband system by estimating mismatch using some bands of a received signal. 
         [0010]    According to a first aspect of the disclosed technology, there is provided a receiver including: a first mixer configured to provide an I component of an RF signal to an I channel by down-converting the RF signal; a second mixer configured to provide a Q component of the RF signal to a Q channel by down-converting the RF signal; amplification means, arranged on the I and Q channels, configured to amplify the I and Q components; a mismatch estimator configured to convert the amplified I and Q components into a frequency domain, and estimate a gain mismatch value and a phase mismatch value on the basis of the converted components; and a mismatch compensator configured to compensate for mismatch of the received signal on the basis of the estimated gain and phase mismatch values. 
         [0011]    According to a second aspect of the disclosed technology, there is provided a receiver using a direct conversion method, including: a mismatch estimator configured to transform signals including I and Q components of a received signal into frequency domain values, and estimate a gain mismatch value and a phase mismatch value on the basis of the frequency domain values; and a mismatch compensator configured to compensate for gain mismatch and phase mismatch of the received signal on the basis of the estimated gain and phase mismatch values. 
         [0012]    According to a third aspect of the disclosed technology, there is provided a receiver using a direct conversion method, including: a mismatch compensator configured to compensate for gain mismatch and phase mismatch of a received signal; a mismatch estimator configured to transform signals including I and Q components of the received signal for which the gain mismatch and the phase mismatch have been compensated into frequency domain values, and estimate a gain mismatch value and a phase mismatch value on the basis of the frequency domain values; and a loop filter configured to filter the estimated gain and phase mismatch values and feed back the filtered values to the mismatch compensator. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    The above and other objects, features and advantages of the present invention will become more apparent to those of ordinary skill in the art by describing in detail exemplary embodiments thereof with reference to the accompanying drawings, in which: 
           [0014]      FIG. 1  is a diagram illustrating a general structure of a receiver using a direct conversion reception method; 
           [0015]      FIG. 2  is a block diagram showing a receiver according to an exemplary embodiment of the disclosed technology; 
           [0016]      FIG. 3  is a block diagram showing a receiver according to another exemplary embodiment of the disclosed technology; 
           [0017]      FIG. 4  is a diagram showing mathematical modeling of distortion of a signal input to an A/D converter when phase mismatch and gain mismatch occur in the receiver of  FIGS. 2 and 3 ; 
           [0018]      FIG. 5  is a diagram showing an IQ mismatch compensator of  FIGS. 2 and 3 ; 
           [0019]      FIG. 6  is a circuit diagram showing an example of an IQ mismatch estimator of  FIGS. 2 and 3 ; 
           [0020]      FIG. 7  is a circuit diagram showing another example of the IQ mismatch estimator of  FIGS. 2 and 3 ; 
           [0021]      FIG. 8  is a circuit diagram showing another example of the IQ mismatch estimator of  FIGS. 2 and 3 ; 
           [0022]      FIG. 9  is a circuit diagram showing another example of the IQ mismatch estimator of  FIGS. 2 and 3 ; and 
           [0023]      FIG. 10  is a circuit diagram showing a loop filter of  FIGS. 2 and 3 . 
       
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0024]    Exemplary embodiments of the disclosed technology are disclosed herein. However, specific structural and functional details disclosed herein are merely representative for purposes of describing exemplary embodiments of the disclosed technology, however, exemplary embodiments of the disclosed technology may be embodied in many alternate forms and should not be construed as limited to exemplary embodiments of the disclosed technology set forth herein. 
         [0025]    The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. 
         [0026]    As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and/or “including,” when used herein, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
         [0027]    Unless the context clearly indicates a specific order, steps may occur out of the noted order. That is, the steps may be executed in the same order as noted, the steps may be executed substantially concurrently, or the steps may be executed in the reverse order. 
         [0028]    Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
         [0029]      FIG. 1  is a diagram illustrating a general structure of a receiver using a direct conversion reception method. 
         [0030]    Referring to  FIG. 1 , a signal received by an antenna  110  is input to mixers  114   a  and  114   b  through a low noise amplifier (LNA)  112 . The mixers  114   a  and  114   b  divide the input signal into I and Q components, and down-convert the I and Q components into baseband signals. The signals after the down-conversions are input to A/D converters  120   a  and  120   b  through variable gain amplifiers (VGAs)  116   a  and  116   b  and low pass filters  118   a  and  118   b . After digital conversion, the signals are transferred to a demodulator  122 . A signal output from a local oscillator  124  is input to the I component mixer  114   a  and a phase shifter  126 . The phase shifter  126  shifts a phase of the input signal by 90 degrees and provides the phase-shifted signal to the Q component mixer  114   b . Here, a phase difference between the signal input to the I component mixer  114   a  and the signal input to the Q component mixer  114   b  should be ideally 90 degrees. However, if the phase difference is not 90 degrees, phase mismatch occurs. Outputs of the mixers  114   a  and  114   b  pass through the VGAs  116   a  and  116   b  and the low pass filters  118   a  and  118   b . If there is a signal amplification gain difference between two circuits, gain mismatch occurs. 
         [0031]      FIG. 2  is a block diagram showing a receiver according to an exemplary embodiment of the disclosed technology. As compared to the receiver of  FIG. 1 , the receiver of  FIG. 2  further includes an IQ mismatch estimator  230  and an IQ mismatch compensator  232 . 
         [0032]    The IQ mismatch estimator  230  receives digital signals from the A/D converters  120   a  and  120   b , and estimates IQ mismatch values from the digital signals. Here, the IQ mismatch values include a phase mismatch value and a gain mismatch value. 
         [0033]    The IQ mismatch compensator  232  compensates for IQ mismatch of digital signals received from the A/D converters  120   a  and  120   b  on the basis of the estimated IQ mismatch values, and transfers IQ mismatch-compensated signals to a demodulator  122 . 
         [0034]      FIG. 3  is a block diagram showing a receiver according to another exemplary embodiment of the disclosed technology. As compared to the receiver of  FIG. 1 , the receiver of  FIG. 3  further includes an IQ mismatch estimator  330 , an IQ mismatch compensator  332 , and a loop filter  334 . 
         [0035]    The IQ mismatch estimator  330  estimates IQ mismatch values from signals passing through the IQ mismatch compensator  332 , and outputs the estimated IQ mismatch values to the IQ mismatch compensator  332 . 
         [0036]    The IQ mismatch compensator  332  compensates for IQ mismatch of the digital signals received from the A/D converters  120   a  and  120   b  on the basis of the estimated IQ mismatch values, and transfers the IQ mismatch-compensated signals to the demodulator  122 . For stable convergence, the loop filter  334  is inserted between the IQ mismatch estimator  330  and the IQ mismatch compensator  332 . 
         [0037]      FIG. 4  is a diagram showing mathematical modeling of distortion of a signal input to the A/D converter when phase mismatch and gain mismatch occur in the receiver of  FIGS. 2 and 3 . 
         [0038]    In  FIG. 4 , x in (t) corresponds to a signal input to the mixers  114   a  and  114   b  through the antenna  110  and the LNA  112 , and 2 cos(2πf LO t+θ/2) and −2 sin(2πf LO t−θ/2) correspond to signals input to the mixers  114   a  and  114   b  for the I and Q components as an output of the local oscillator  124 . f LO  corresponds to a frequency of the local oscillator  124 , and corresponds to a center frequency of a transmitted signal in a structure based on the direct conversion method. θ corresponds to a phase mismatch value between the I and Q components, and E corresponds to a gain mismatch value between the I and Q components. Here, when a transmitted signal, which is a baseband signal transmitted from a transmission stage, is x BB (t)=a(t)+jb(t), a signal x in (t) input to the mixers  114   a  and  114   b  is x in (t)=a(t)cos(2πft)−b(t)sin(2πft). 
         [0039]    When there is IQ mismatch, the following Equation (1) is given if signals I and Q output through the mixers  114   a  and  114   b , the VGAs  116   a  and  116   b , and the low pass filters  118   a  and  118   b  are expressed as a(t) and b(t), which are I and Q components of the transmitted signal. 
         [0000]    
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           I 
                         
                       
                       
                         
                           Q 
                         
                       
                     
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                   = 
                   
                     
                       
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                       · 
                       
                         [ 
                         
                           
                             
                               
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                       · 
                       
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         [0040]    Accordingly, an inverse matrix of a mismatch matrix M should be multiplied by 
         [0000]    
       
         
           
             
               [ 
               
                 
                   
                     I 
                   
                 
                 
                   
                     Q 
                   
                 
               
               ] 
             
               
           
         
       
     
         [0000]    so as to recover a transmitted signal x BB (t) from the signals I and Q. The inverse matrix of M is defined as the following Equation (2). 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                     
                       - 
                       1 
                     
                   
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                                   · 
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         [0041]    Here, w=−θ/2, γ=(2+ε)/(2−ε), and A=(cos θ)/{(1+ε)cos θ}. 
         [0042]      FIG. 5  is a diagram showing the IQ mismatch compensator of  FIGS. 2 and 3 . 
         [0043]    The IQ mismatch compensator of  FIG. 5  corresponds to a circuit implemented for the inverse matrix of the mismatch matrix M shown in Equation (2). In Equation (2), A is a scale common between the I and Q components, and may be omitted if its value is close to 1. Therefore, when the phase mismatch value θ and the gain mismatch value ε can be estimated, it is possible to remove the IQ mismatch on the basis of the circuit shown in  FIG. 5 . 
         [0044]    Referring to  FIG. 5 , the IQ mismatch compensator includes a first operator  510 , a second operator  514 , multipliers  512 ,  516 , and  520 , and adders  518  and  522 . 
         [0045]    The first operator  510  carries out a tan(−θ) operation from the phase mismatch value θ, and outputs a phase mismatch compensation value to the first multiplier  512  and the third multiplier  520 . The first multiplier  512  multiplies an output of the first operator  510  by an I component of the received signal, and outputs a result of multiplication to the first adder  518 . The second operator  514  carries out an operation of (2+ε)/(2−ε) from the gain mismatch value ε, and outputs a gain mismatch compensation value to the second multiplier  516 . The second multiplier  516  multiplies an output of the second operator  514  by a Q component of the received signal, and outputs a result of multiplication to the first adder  518  and the third multiplier  520 . The first adder  518  adds an output of the second multiplier  516  to an output of the first multiplier  512 , and outputs a mismatch-compensated Q component. The third multiplier  520  multiplies the output of the second multiplier  516  by the output of the first operator  510 , and outputs a result of multiplication to the second adder  522 . The second adder  522  adds an output of the third multiplier  520  to the I component of the received signal, and outputs a mismatch-compensated I component. 
         [0046]    The IQ mismatch estimator of  FIGS. 2 and 3  can estimate IQ mismatch according to the following method. 
         [0047]    First, if a signal input to the mixers  114   a  and  114   b  corresponds to a tone signal having a single frequency, the IQ mismatch can be calculated through the following method. A transmitted signal x BB (t), which is a baseband signal, corresponds to the following Equation (3). 
         [0000]        X   BB ( t )= a ( t )+ jb ( t )= Xe   j(2πf     τ     t+φ)   =X (cos(2 πf   τ   t +φ)+ j  sin(2 πf   τ   t +φ))  (3)
 
         [0048]    The transmitted signal x BB (t) is distorted by mismatch characteristics of the receiver, and input to the A/D converters  120   a  and  120   b . Therefore, if a signal r BB (t) input to the A/D converters  120   a  and  120   b  is derived using Equation (1), the following Equation (4) is given. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       r 
                       BB 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       I 
                       + 
                       
                         j 
                          
                         
                             
                         
                          
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                     = 
                     
                       
                         
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         [0049]    Here, a tone frequency f τ  is an integer multiple of an intercarrier frequency Δf of a fast Fourier transform (FFT), and is f τ =τ·Δf if the integer multiple is τ. If r BB (t) is transformed by the FFT, a τ-th index and a −τ-th index respectively have values corresponding to the following Equations (5) and (6) on the basis of a DC carrier index value “0.” 
         [0000]    
       
         
           
             
               
                 
                   
                     R 
                      
                     
                       [ 
                       τ 
                       ] 
                     
                   
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                        
                       
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                               2 
                             
                           
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                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
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                      
                     
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                         τ 
                       
                       ] 
                     
                   
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                              
                             
                                 
                             
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                               θ 
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                   6 
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         [0050]    The following Equation (7) can be derived from Equations (5) and (6). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       R 
                        
                       
                         [ 
                         
                           - 
                           τ 
                         
                         ] 
                       
                     
                     · 
                     
                       R 
                        
                       
                         [ 
                         τ 
                         ] 
                       
                     
                   
                   = 
                   
                     
                       X 
                       2 
                     
                      
                     
                       ( 
                       
                         
                           ɛ 
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   ε 
                                   2 
                                 
                                 4 
                               
                             
                             ) 
                           
                            
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                            
                           
                               
                           
                            
                           
                             
                               sin 
                                
                               
                                   
                               
                                
                               θ 
                             
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0051]    If Equation (7) is rewritten for the gain mismatch value ε, the gain Mismatch value can be derived as shown in the following Equation (8). 
         [0000]    
       
         
           
             
               
                 
                   ɛ 
                   = 
                   
                     
                       2 
                       
                         X 
                         2 
                       
                     
                      
                     Re 
                      
                     
                       { 
                       
                         
                           R 
                            
                           
                             [ 
                             τ 
                             ] 
                           
                         
                         · 
                         
                           R 
                            
                           
                             [ 
                             
                               - 
                               τ 
                             
                             ] 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0052]    A phase mismatch value θ as shown in the following Equation (9) can be derived from the gain mismatch value ε derived by Equation (8). 
         [0000]    
       
         
           
             
               
                 
                   θ 
                   = 
                   
                     
                       sin 
                       
                         - 
                         1 
                       
                     
                     ( 
                     
                       
                         
                           2 
                           
                             X 
                             2 
                           
                         
                         · 
                         
                           ( 
                           
                             1 
                             
                               1 
                               - 
                               
                                 
                                   ɛ 
                                   2 
                                 
                                 4 
                               
                             
                           
                           ) 
                         
                         · 
                         Im 
                       
                        
                       
                         { 
                         
                           
                             R 
                              
                             
                               [ 
                               τ 
                               ] 
                             
                           
                           · 
                           
                             R 
                              
                             
                               [ 
                               
                                 - 
                                 τ 
                               
                               ] 
                             
                           
                         
                         } 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0053]    Here, if the magnitude of the phase mismatch value is small, the phase mismatch value of Equation (9) can be approximated as shown in the following Equation (10). 
         [0000]    
       
         
           
             
               
                 
                   θ 
                   ≈ 
                   
                     
                       2 
                       
                         X 
                         2 
                       
                     
                      
                     Im 
                      
                     
                       { 
                       
                         
                           R 
                            
                           
                             [ 
                             τ 
                             ] 
                           
                         
                         · 
                         
                           R 
                            
                           
                             [ 
                             
                               - 
                               τ 
                             
                             ] 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0054]    Accordingly, when a tone signal having a single frequency is received, the received signal is transformed by the FFT. A mismatch value according to Equations (8) to (10) can be calculated from an FFT value, and mismatch can be eliminated using the calculated mismatch value. 
         [0055]    Next, if signals input to the mixers  114   a  and  114   b  correspond to arbitrary modulation signals, not single frequencies, the signals input to the mixers  114   a  and  114   b  are transformed by the FFT. The following Equation (11) can be derived by extending and rewriting Equations (5) to (7). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ∑ 
                         
                           τ 
                           = 
                           1 
                         
                       
                       
                         
                           N 
                           2 
                         
                         - 
                         1 
                       
                     
                      
                     
                       
                         R 
                          
                         
                           [ 
                           
                             - 
                             τ 
                           
                           ] 
                         
                       
                       · 
                       
                         R 
                          
                         
                           [ 
                           τ 
                           ] 
                         
                       
                     
                   
                   ≈ 
                   
                     
                       ( 
                       
                         
                           ɛ 
                           2 
                         
                         + 
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 
                                   ε 
                                   2 
                                 
                                 4 
                               
                             
                             ) 
                           
                            
                           j 
                            
                           
                               
                           
                            
                           
                             
                               sin 
                                
                               
                                   
                               
                                
                               θ 
                             
                             2 
                           
                         
                       
                       ) 
                     
                     · 
                     
                       
                         ∑ 
                         
                           τ 
                           = 
                           1 
                         
                         
                           
                             N 
                             2 
                           
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                                
                               
                                 r 
                                 τ 
                               
                                
                             
                             2 
                           
                           + 
                           
                             
                                
                               
                                 r 
                                 
                                   - 
                                   τ 
                                 
                               
                                
                             
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0056]    Here, N is the total number of carriers, and r τ  is a value output in a τ-th carrier position after the FFT and is independent according to each carrier. A sum of powers of all carrier signals on a frequency axis corresponds to a power value of the received signal. Accordingly, the following Equations (12) and (13) can be derived from Equation (11) if 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ∑ 
                         
                           τ 
                           = 
                           1 
                         
                         
                           
                             N 
                             2 
                           
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                                
                               
                                 r 
                                 τ 
                               
                                
                             
                             2 
                           
                           + 
                           
                             
                                
                               
                                 r 
                                 
                                   - 
                                   τ 
                                 
                               
                                
                             
                             2 
                           
                         
                         ) 
                       
                     
                     = 
                     P 
                   
                    
                   
                     
 
                   
                    
                   ɛ 
                   = 
                   
                     
                       2 
                       P 
                     
                      
                     Re 
                      
                     
                       { 
                       
                         
                           ∑ 
                           
                             τ 
                             = 
                             1 
                           
                           
                             
                               N 
                               2 
                             
                             - 
                             1 
                           
                         
                          
                         
                           
                             R 
                              
                             
                               [ 
                               
                                 - 
                                 τ 
                               
                               ] 
                             
                           
                           · 
                           
                             R 
                              
                             
                               [ 
                               τ 
                               ] 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   θ 
                   = 
                   
                     
                       sin 
                       
                         - 
                         1 
                       
                     
                     ( 
                     
                       
                         
                           2 
                           P 
                         
                         · 
                         
                           ( 
                           
                             1 
                             
                               1 
                               - 
                               
                                 
                                   ɛ 
                                   2 
                                 
                                 4 
                               
                             
                           
                           ) 
                         
                         · 
                         Im 
                       
                        
                       
                         { 
                         
                           
                             ∑ 
                             
                               τ 
                               = 
                               1 
                             
                             
                               
                                 N 
                                 2 
                               
                               - 
                               1 
                             
                           
                            
                           
                             
                               R 
                                
                               
                                 [ 
                                 
                                   - 
                                   τ 
                                 
                                 ] 
                               
                             
                             · 
                             
                               R 
                                
                               
                                 [ 
                                 τ 
                                 ] 
                               
                             
                           
                         
                         } 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0057]    If the magnitude of the phase mismatch value is small, the phase mismatch value of Equation (13) can be approximated as shown in the following Equation (14). 
         [0000]    
       
         
           
             
               
                 
                   θ 
                   ≈ 
                   
                     
                       
                         2 
                         P 
                       
                       · 
                       Im 
                     
                      
                     
                       { 
                       
                         
                           ∑ 
                           
                             τ 
                             = 
                             1 
                           
                           
                             
                               N 
                               2 
                             
                             - 
                             1 
                           
                         
                          
                         
                           
                             R 
                              
                             
                               [ 
                               
                                 - 
                                 τ 
                               
                               ] 
                             
                           
                           · 
                           
                             R 
                              
                             
                               [ 
                               τ 
                               ] 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0058]    Accordingly, when an arbitrary modulation signal is received, the received signal is transformed by the FFT. A mismatch value according to Equations (12) to (14) can be calculated from an FFT value, and mismatch can be eliminated using the calculated mismatch value. 
         [0059]      FIG. 6  is a circuit diagram showing an example of the IQ mismatch estimator of  FIGS. 2 and 3 , and  FIG. 7  is a circuit diagram showing another example of the IQ mismatch estimator of  FIGS. 2 and 3 . The IQ mismatch estimator of  FIG. 6  corresponds to a circuit implemented from Equations (12) and (13), and the IQ mismatch estimator of  FIG. 7  corresponds to a circuit implemented from Equations (12) and (14). 
         [0060]    The IQ mismatch estimator of  FIG. 6  transforms signals input from the A/D converters  120   a  and  120   b  by the FFT, and calculates a sum of all output values after multiplying two output values positioned symmetrically with respect to a direct current (DC) component. The IQ mismatch estimator can derive the gain mismatch value c by multiplying a real part of the sum value by 2/P, and derive the phase mismatch value θ by carrying out a sin −1  operation after multiplying an imaginary part of the sum value by 
         [0000]    
       
         
           
             
               2 
               P 
             
             · 
             
               
                 ( 
                 
                   1 
                   
                     1 
                     - 
                     
                       
                         ɛ 
                         2 
                       
                       4 
                     
                   
                 
                 ) 
               
               . 
             
           
         
       
     
         [0000]    sin −1  corresponds to a non-linear function. When the non-linear function is actually implemented, complexity may be increased. Because a mismatch value to be compensated for is generally small, the IQ mismatch estimator can be implemented as shown in  FIG. 7  according to Equation (14) instead of Equation (13). 
         [0061]    Referring to  FIG. 6 , the IQ mismatch estimator includes an FFT unit  610 , first multipliers  612 , a summer  614 , a second multiplier  616 , a third multiplier  618 , an amplifier  620 , a squarer  622 , a subtractor  624 , a reciprocal output unit  626 , a fourth multiplier  628 , and an arcsin operator  630 . 
         [0062]    The FFT unit  610  transforms signals including I and Q components of a received signal into frequency domain values. The first multipliers  612  multiply transformed values by values positioned symmetrically with respect to a DC component. The summer  614  produces a sum of outputs of the first multipliers  612 . The second multiplier  616  multiplies a real part of an output of the summer  614  by a preset value, thereby deriving a gain mismatch value. The third multiplier  618  multiplies an imaginary part of the output of the summer  614  by a preset value. The amplifier  620  reduces the derived gain mismatch value by ½. The squarer  622  squares an output of the amplifier  620 . The subtractor  624  subtracts an output of the squarer  622  from a constant “1.” The reciprocal output unit  626  outputs a reciprocal of an output of the subtractor  624 . The fourth multiplier  628  multiplies an output of the reciprocal output unit  626  by an output of the third multiplier  618 . The arcsin operator  630  derives a phase mismatch value by carrying out an arcsin operation on an output of the fourth multiplier  628 . 
         [0063]    Referring to  FIG. 7 , the IQ mismatch estimator includes an FFT unit  710 , first multipliers  712 , a summer  714 , a second multiplier  716 , and a third multiplier  718 . 
         [0064]    The FFT unit  710  transforms signals including I and Q components of a received signal into frequency domain values. The first multipliers  712  multiply the frequency domain values by values positioned symmetrically with respect to a DC component. The summer  714  produces a sum of outputs of the first multipliers  712 . The second multiplier  716  derives a gain mismatch value by multiplying a real part of an output of the summer  714  by a preset value. The third multiplier  718  multiplies an imaginary part of the output of the summer  714  by a preset value. Although a mismatch is derived using signals of all bands as described above, a mismatch may be derived using only some bands, rather than all of the bands. In this case, Equations (12), (13), and (14) may be respectively modified to the following Equations (15), (16), and (17). 
         [0000]    
       
         
           
             
               
                 
                   ɛ 
                   = 
                   
                     
                       2 
                       
                         P 
                          
                         
                             
                         
                          
                         ′ 
                       
                     
                      
                     Re 
                      
                     
                       { 
                       
                         
                           ∑ 
                           
                             t 
                             = 
                             a 
                           
                           b 
                         
                          
                         
                           
                             R 
                              
                             
                               [ 
                               
                                 - 
                                 τ 
                               
                               ] 
                             
                           
                           · 
                           
                             R 
                              
                             
                               [ 
                               τ 
                               ] 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   θ 
                   = 
                   
                     
                       sin 
                       
                         - 
                         1 
                       
                     
                     ( 
                     
                       
                         
                           2 
                           
                             P 
                              
                             
                                 
                             
                              
                             ′ 
                           
                         
                         · 
                         
                           ( 
                           
                             1 
                             
                               1 
                               - 
                               
                                 
                                   ɛ 
                                   2 
                                 
                                 4 
                               
                             
                           
                           ) 
                         
                         · 
                         Im 
                       
                        
                       
                         { 
                         
                           
                             ∑ 
                             
                               τ 
                               = 
                               a 
                             
                             b 
                           
                            
                           
                             
                               R 
                                
                               
                                 [ 
                                 
                                   - 
                                   τ 
                                 
                                 ] 
                               
                             
                             · 
                             
                               R 
                                
                               
                                 [ 
                                 τ 
                                 ] 
                               
                             
                           
                         
                         } 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   θ 
                   ≈ 
                   
                     
                       
                         2 
                         
                           P 
                            
                           
                               
                           
                            
                           ′ 
                         
                       
                       · 
                       Im 
                     
                      
                     
                       { 
                       
                         
                           ∑ 
                           
                             τ 
                             = 
                             a 
                           
                           b 
                         
                          
                         
                           
                             R 
                              
                             
                               [ 
                               
                                 - 
                                 τ 
                               
                               ] 
                             
                           
                           · 
                           
                             R 
                              
                             
                               [ 
                               τ 
                               ] 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0065]    Here, P′ corresponds to the following Equation (18). 
         [0000]        P′=Σ   τ=a   b (| r   τ | 2   +|r   −τ | 2 )  (18)
 
         [0066]      FIG. 8  is a circuit diagram showing another example of the IQ mismatch estimator of  FIGS. 2 and 3 , and  FIG. 9  is a circuit diagram showing another example of the IQ mismatch estimator of  FIGS. 2 and 3 . The IQ mismatch estimator of  FIG. 8  is a circuit diagram corresponding to Equations (15) and (16), and the IQ mismatch estimator of  FIG. 9  is a circuit diagram corresponding to Equations (15) and (17). The IQ mismatch estimators according to  FIGS. 8 and 9  estimate mismatch by use of some bands. 
         [0067]    Referring to  FIG. 8 , the IQ mismatch estimator includes an FFT unit  810 , first multipliers  812 , a summer  814 , a second multiplier  816 , a third multiplier  818 , an amplifier  820 , a squarer  822 , a subtractor  824 , a reciprocal output unit  826 , a fourth multiplier  828 , and an arcsin operator  830 . As compared to the IQ mismatch estimator of  FIG. 6 , the IQ mismatch estimator of  FIG. 8  is different in that the first multipliers  912  multiply values corresponding to some bands by values positioned symmetrically with respect to a DC component, and output multiplication results to the summer  814 . The other components are the same as in  FIG. 6 . 
         [0068]    Referring to  FIG. 9 , the IQ mismatch estimator includes an FFT unit  910 , the first multipliers  912 , a summer  914 , a second multiplier  916 , and a third multiplier  918 . As compared to the IQ mismatch estimator of  FIG. 7 , the IQ mismatch estimator of  FIG. 9  has a difference in that the first multipliers  812  multiply values corresponding to some bands by values positioned symmetrically with respect to a DC component, and output multiplication results to the summer  914 . The other components are the same as in  FIG. 7 . 
         [0069]    Because a sampling frequency is high in a broadband communication system, there may be a time delay between I and Q components. Here, in the time delay, a time difference may occur due to a group delay difference while signals pass through analog circuits in paths of the I and Q components, and a time difference between the I and Q components may occur due to sampling timings of the A/D converters  120   a  and  120   b . The time difference may lead to an error in phase mismatch estimation. Because distortion by the time difference is not observed in a low frequency domain, it is possible to estimate mismatch by use of a signal of a low frequency band. The circuits of  FIGS. 8 and 9  estimate mismatch by use of some bands of a signal, for example, a low band in a broadband system. 
         [0070]      FIG. 10  is a circuit diagram showing the loop filter of the  FIG. 3 . Referring to  FIG. 10 , the loop filter includes a first amplifier  1010 , an adder  1012 , a memory  1014 , a second amplifier  1016 , and a third amplifier  1018 . After a value obtained by multiplying an input signal by a gain of μ 1  is added to a value obtained by multiplying a value stored in the memory by a gain of μ 2 , a value of an addition result is multiplied by μ 3  and a result of multiplication is output. 
         [0071]    The exemplary embodiments of the present disclosure have the following advantages. However, since this does not mean that all the exemplary embodiments of the present disclosure include the advantages, the scope of the present disclosure is not limited to the advantages. 
         [0072]    According to an exemplary embodiment, a receiver can estimate and compensate for mismatch of the receiver, regardless of a type of modulation signal, and estimate and compensate for mismatch of a received signal while the signal is received. 
         [0073]    According to an exemplary embodiment, a receiver can effectively estimate and compensate for mismatch when there is a time delay between I and Q components in a receiver having a high sampling frequency such as a broadband system by estimating mismatch by use of some bands of a received signal. 
         [0074]    It will be apparent to those skilled in the art that various modifications can be made to the above-described exemplary embodiments of the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the disclosed technology covers all such modifications provided they come within the scope of the appended claims and their equivalents.