Abstract:
An apparatus and method of an OFDM system for compensating IQ imbalance. The apparatus includes a mixer module for mixing a wireless signal to generate a pair of in-phase and quadrature-phase analog signals; an in-phase and quadrature-phase imbalance parameter estimation unit coupled to the mixer module for estimating a gain compensation value and a phase compensation value; and a signal compensation module coupled to the in-phase and quadrature-phase imbalance parameter estimation unit for compensating the pair of in-phase and quadrature-phase analog signals for gain imbalance and phase imbalance, according to the gain compensation value and the phase compensation value respectively.

Description:
BACKGROUND 
   The invention relates to an apparatus and method for compensating IQ imbalance, and more particularly, to an apparatus and method for compensating IQ imbalance in an OFDM system when a carrier frequency offset exists. 
   In a normal communication system, in order to increase utilization efficiencies of the communication bandwidth, the communication bandwidth is often divided into several sub-channels and the orthogonal frequency division multiplexing (OFDM) technique is utilized to perform the signal transmissions and receptions. The above-mentioned communication system is called as OFDM communication system. For example, in the digital video broadcasting-terrestrial (DVB-T) standard, the radio signal received by the antennas of the receiver is a time-domain sequential signal composed of a plurality of OFDM symbols. In addition, the OFDM symbols can be transformed into an OFDM frequency-domain signal by a well-known Fourier transformation unit. As is known by those of average skill in the art, the OFDM frequency-domain signal is composed of a plurality of sub-carriers. 
   Please refer to  FIG. 1 , which is a diagram of an OFDM receiver  100 . As shown in  FIG. 1 , the OFDM receiver  100  comprises an antenna  102 , a low noise amplifier (LNA)  104 , an in-phase mixer  106 , a quadrature-phase mixer  108 , a plurality of low-pass filters (LPF)  110  and  112 , a plurality of analog-to-digital converters (ADC)  116  and  118 , and a compensation module  114 . First, the antenna  102  is utilized to receive a radio signal R 1 (t). The LNA  104  is utilized to amplify the radio signal R 1 (t) received by the antenna  102  to output a radio signal R 2 (t). And then, the in-phase mixer  106  is utilized to mix the radio signal R 2 (t) and an in-phase carrier 2 cos(2πf C t) to generate an in-phase analog signal R I (t). Next, the quadrature-phase mixer  108  is utilized to mix the radio signal R 2 (t) and a quadrature-phase carrier 2 sin(2πf C t) to generate a quadrature-phase analog signal R Q (t). Please note that the amplitude coefficient 2 of the in-phase carrier 2 cos(2πf C t) and the quadrature-phase analog signal 2 sin(2πf C t) is only utilized for simply illustrating the following equations. In other words, the amplitude parameter is possible to be any other values. This is not a limitation of the present invention. Next, the LPFs  110  and  112  are respectively utilized to filter out the high-frequency parts of the in-phase analog signal R 1 (t) and the quadrature-phase analog signal R Q (t) to output the filtered in-phase analog signal R′ I (t) and filtered quadrature-phase analog signal R′ Q (t). Finally, the ADCs  116  and  118  are respectively utilized to convert the in-phase analog signal R′ 1 (t) and the quadrature-phase analog signal R′ Q (t) into digital signals R′ I [n] and R′ Q [n]. The digital signals R′ I [n] and R′ Q [n] are inputted into the compensation module  114  to perform related signal processing. 
   As known by those skilled in the art, the above-mentioned in-phase carrier 2 cos(2πf C t) and the quadrature-phase carrier 2 sin(2πf C t) ideally correspond to a 90-degree phase difference such that the mixed in-phase analog signal R I  and the mixed quadrature-phase analog signal R Q  can be orthogonal. However, in the actual circuit, some factors such as, temperature, manufacturing procedure, and the supplying voltage shift, may cause a gain imbalance and a phase imbalance of the in-phase carrier 2 cos(2πf C t) and the quadrature-phase carrier 2 sin(2πf C t). This also causes a gain imbalance and a phase imbalance of the mixed in-phase analog signal R I  and the mixed quadrature-phase analog signal R Q . In general, omitting the influences caused by the gain of the LNA  104  and related noises, the radio signal R 2 (t) input into the in-phase mixer  106  and the quadrature mixer  108  can be represented by the following equation as:
 
 R   2 ( t )= Re{[r   I ( t )+ jr   Q ( t )] e   j2πf     C     t }  Equation (1)
 
   In equation (1), r I (t) represents an in-phase analog signal transmitted by a transmitter (not shown), and r Q (t) represents a quadrature-phase analog signal transmitted by the transmitter. At this time, please consider the influences of a gain imbalance ε and a phase imbalance θ on the OFDM receiver  100  when the in-phase mixer  106  receives an in-phase carrier 2 cos(2πf C t) and the quadrature-phase mixer  108  receives the quadrature-phase mixer −2(1+ε)sin(2πf C t+θ). Therefore, the in-phase analog signal R I (t) and the quadrature-phase R Q (t) generated by the OFDM receiver  100  can be represented by the following equation as: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
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   It can be determined utilizing the equations (2) and (3) that after the LPFs  110  and  112  filter out the high-frequency parts of the in-phase analog signal R I (t) and the quadrature-phase R Q (t), that the in-phase analog signal R′ I (t) and the quadrature-phase analog signal R′ Q (t) can be represented by the following equation as:
 
 R′   I ( t )= r   I ( t )  Equation (4)
 
 R′   Q ( t )=(1+ε)[ r   Q ( t )cos θ− r   I ( t )sin θ]  Equation (5)
 
   Furthermore, after being digitized by the ADCs  116  and  118 , the in-phase digital signal R′ I [n] and the quadrature-phase digital signal R′ Q [n] can be represented by the following equations as:
 
 R′   I   [n]=r   I   [n]   Equation (6)
 
 R′   Q   [n ]=(1+ε)[ r   Q   [n ] cos θ− r   I   [n ] sin θ]  Equation (7)
 
   In the related art, methods utilized in the OFDM receiver to compensating for the IQ imbalance comprise: (1) Utilize an adaptive frequency-domain equalizer (AFEQ). This reference can be found in the paper by A. Schuchert, R. Hasholzner, “A Novel IQ Imbalance Compensation Scheme for the Reception of OFDM Signals,” IEEE Trans. On Consumer Electronics, Vol. 43, No. 3, August 1998. (2) Utilize an adaptive time-domain compensator (ATDC). This can be referred to as a paper S. Fouladifard, H. Shafiee, “On Adaptive cancellation of IQ Mismatch in OFDM Receivers,” Proc. ICASSP 2003 IEEE International Conference on, Vol. 4, 6-10 April 2003 Pages: IV-564-7. (3) Utilize a decision feedback correction scheme (DFCS). This can be refer to as a paper J. Tubbax, B. Come, L. Van der Perre, L. Deneire, S. Donnay, M. Engels, “Compensation of IQ imbalance in OFDM systems,” Communications, 2003. ICC &#39;03. IEEE International Conference on, Volume: 5, 11-15 May 2003 Pages: 3403-3407. 
   Because the above-mentioned mechanisms for compensating IQ imbalance are well-known by those skilled in the art, descriptions of the detailed circuit and operations are omitted here. However, the above-mentioned mechanisms for compensating IQ imbalance never mention the negative influences of the carrier frequency offset. In fact, the carrier frequency offset and the IQ imbalance both contribute to ruining the orthogonal properties of sub-carriers in the OFDM system. A main reason that the carrier frequency offset exists is the imbalance between the oscillator of the transmitter and the mixer of the receiver. A secondary cause of the carrier frequency offset is the Doppler shift generated because of the corresponding movements between the transmitter and the receiver. 
   While considering the carrier frequency offset and the IQ imbalance individually, the compensation of the carrier frequency offset and the IQ imbalance each requires its own method. However, while the two effects both exist, there is no one method to simultaneously solve the two problems. As a result, the compensation performance is degraded. The above-mentioned three IQ imbalance compensation mechanisms can be utilized to solve only the IQ imbalance, however, they cannot solve the carrier frequency offset imbalance. Therefore, if the characteristic of the circuit further comprises the carrier frequency offset, the above-mentioned three IQ imbalance compensation mechanisms are insufficient. Therefore, when the in-phase carrier of the in-phase mixer  106  and the quadrature-phase carrier of the quadrature-phase mixer  108  have the carrier frequency offset, according to related experiments, the OFDM  100  cannot compensate the gain imbalance ε and the phase imbalance θ by utilizing the above-mentioned three ways of compensation. In other words, if the carrier frequency offset exists, the efficiency of the above-mentioned three ways of compensation will be decreased enormously. 
   SUMMARY 
   It is therefore one of the primary objectives of the claimed invention to provide an apparatus and method for compensating IQ mismatch in an OFDM system while a carrier frequency offset exists at the same time, to solve the above-mentioned problem. 
   According to an exemplary embodiment of the claimed invention, a method for compensating IQ imbalance is disclosed. The method is utilized for compensating a phase imbalance and a gain imbalance between an in-phase carrier and a quadrature-phase carrier, and the method comprises: respectively mixing a ratio frequency signal according to the in-phase carrier and quadrature-phase carrier to generate an in-phase analog signal and a quadrature-phase analog signal, wherein a frequency offset is between a carrier frequency of the RF signal and a frequency of the in-phase carrier and the frequency offset is also between the carrier frequency of the RF signal and a frequency of the RF signal; calculating a gain compensation value and a phase compensation value according to the in-phase analog signal and the quadrature-phase signal; and utilizing the gain compensation value to compensate the gain imbalance and utilizing the phase compensation value to compensate the phase imbalance. 
   According to another exemplary embodiment of the claimed invention, a receiver capable of compensating IQ imbalance is disclosed. The receiver is utilized for compensating a gain imbalance and a phase imbalance between an in-phase carrier and a quadrature-phase carrier, and the receiver comprises: a mixer module respectively mixing an RF signal according to the in-phase carrier and the quadrature-phase carrier in order to generate an in-phase analog signal and a quadrature-phase analog signal, wherein a frequency offset is between a carrier frequency of the RF signal and a frequency of the in-phase carrier, and the frequency offset is between the carrier frequency of the RF signal and a frequency of the quadrature-phase carrier; an in-phase and quadrature-phase imbalance parameter estimation unit, coupled to the mixer module, for estimating a gain compensation value and a phase compensation value according to the in-phase analog signal and the quadrature-phase analog signal; and a signal compensation module, coupled to the in-phase and quadrature-phase imbalance parameter estimation unit, for utilizing the gain compensation value to compensate the gain imbalance and for utilizing the phase compensation value to compensate the phase imbalance. 
   The present invention method and receiver capable of compensating the IQ imbalance effectively estimates a gain imbalance and a phase imbalance when a carrier frequency offset exists. Furthermore, the present invention method and receiver capable of compensating the IQ imbalance utilizes an inverse matrix to multiply an in-phase analog signal and a quadrature-phase analog signal output by a mixer module in order to eliminate the IQ imbalance. 
   These and other objectives of the present invention will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment that is illustrated in the various figures and drawings. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
       FIG. 1  is a diagram of an OFDM receiver according to the related art. 
       FIG. 2  is a diagram of a receiver capable of compensating IQ imbalance of an embodiment according to the present invention. 
       FIG. 3  is a diagram of an in-phase and quadrature-phase parameter estimation unit according to the present invention. 
   

   DETAILED DESCRIPTION 
   Please refer to  FIG. 2  a functional diagram of the present invention, which is a receiver  400  capable of compensating IQ imbalance while at the same time a carrier frequency offset also exists. As shown in  FIG. 2 , the receiver  400  comprises an antenna  402 , an LNA  404 , a mixer module  406 , a plurality of ADCs  408  and  410 , an in-phase and quadrature-phase imbalance parameter estimation unit  422 , and a compensation module  412 . The antenna  402  is utilized to receive a radio signal R 1 (t), and the LNA  404  is utilized to amplify the radio signal R 1 (t) received by the antenna  402  in order to output a radio signal R 2 (t). Next, the mixer module  406  generates an in-phase analog signal V I (t) and a quadrature-phase analog signal V Q (t) according to the radio signal R 2 (t). After the in-phase analog signal V I (t) and the quadrature-phase analog signal V Q (t) are digitized by the ADCs  408  and  410 , an in-phase digital signal V I [n] and a quadrature-phase digital signal V Q [n] are generated respectively. In this embodiment, the in-phase and quadrature-phase imbalance parameter estimation unit  422  estimates a gain compensation value ε′ and a phase compensation value θ′ according to the in-phase digital signal V I [n] and the quadrature-phase digital signal V Q [n]. Finally, the compensation module  412  compensates the gain imbalance and the phase imbalance of the in-phase digital signal V I [n] and the quadrature-phase digital signal V Q [n] according to the gain compensation value ε′ and the phase compensation value θ′. 
   As shown in  FIG. 2 , the mixer module  406  comprises an in-phase mixer  414 , a quadrature-phase mixer  416 , and a plurality of LPFs  418  and  420 . Consider that the receiver  400  compensates the IQ imbalance while the carrier frequency offset Δf also exists at the same time. Assuming that the carrier frequency offset Δf and the IQ imbalance (including the gain imbalance ε and the phase imbalance θ) both exist, the system model is illustrated as follows. First, the in-phase mixer  414  receives an in-phase carrier 2 cos [2π(f C +Δf)t], and the quadrature-phase mixer  414  receives a quadrature-phase carrier −2(1+ε)sin [2π(f C +Δf)t+θ]. In this embodiment, the in-phase mixer  414  mixes the radio signal R 2 (t) and the in-phase carrier 2 cos [2π(f C +Δf)t] to generate an in-phase analog signal R I (t), and the quadrature-phase mixer  416  mixes the radio signal R 2 (t) and the quadrature-phase carrier −2(1+ε)sin [2π(f C +Δf)t+θ] to generate a quadrature-phase analog signal R Q (t). Please note that in the following description, an exemplary amplitude coefficient 2 of the in-phase carrier 2 cos [2π(f C +Δf)t] and the quadrature-phase carrier −2(1+ε)sin [2π(f C +Δf)t+θ] is only for simplifying the description, which in fact could be any other values. This is not a limitation of the present invention. Finally, the LPFs  418  and  420  are respectively utilized to filter out the high-frequency parts of the in-phase analog signal R I (t) and the quadrature-phase analog signal R Q (t) in order to output filtered in-phase analog signal V I (t) and filtered quadrature-phase analog signal V Q (t). And after the filtered in-phase analog signal V I (t) and filtered quadrature-phase analog signal V Q (t) are digitized by the ADCs  408  and  410 , the in-phase digital signal V I [n] and the quadrature-phase digital signal V Q [n] are generated. 
   As in usual cases, the noise induced by the LNA  404  is omitted in the following analysis. The radio signal R 2 (t) input to the mixer module  406  can be represented by the above-mentioned equation (1). Therefore, the in-phase analog signal R I (t) and the quadrature-phase analog signal R Q (t) output by the in-phase mixer  414  and the quadrature-phase mixer  416  can be represented by the following equations: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
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                                 ] 
                               
                               ⁢ 
                               
                                 ⅇ 
                                 
                                   j2π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     f 
                                     c 
                                   
                                   ⁢ 
                                   t 
                                 
                               
                             
                             } 
                           
                           · 
                           2 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   f 
                                   c 
                                 
                                 + 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   f 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           2 
                           ⁢ 
                           
                             
                               r 
                               I 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 f 
                                 c 
                               
                               ⁢ 
                               t 
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     f 
                                     c 
                                   
                                   + 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     f 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                             ) 
                           
                         
                         - 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         2 
                         ⁢ 
                         
                           
                             r 
                             Q 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               c 
                             
                             ⁢ 
                             t 
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   f 
                                   c 
                                 
                                 + 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   f 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           
                             
                               r 
                               I 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               πΔ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ft 
                             
                             ) 
                           
                         
                         + 
                         
                           
                             
                               r 
                               I 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                       f 
                                       c 
                                     
                                   
                                   + 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     f 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                             ) 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             
                               r 
                               Q 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               πΔ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ft 
                             
                             ) 
                           
                         
                         - 
                         
                           
                             
                               r 
                               Q 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                       f 
                                       c 
                                     
                                   
                                   + 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     f 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
           
             
               
                 
                   
                     
                       
                         
                           R 
                           Q 
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         Re 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             { 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       r 
                                       I 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                   + 
                                   
                                     jr 
                                     Q 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 ⅇ 
                                 
                                   j2π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     f 
                                     c 
                                   
                                   ⁢ 
                                   t 
                                 
                               
                             
                             } 
                           
                           · 
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         ( 
                         
                           
                             - 
                             2 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               1 
                               + 
                               ɛ 
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       f 
                                       
                                         
                                             
                                         
                                         ⁢ 
                                         c 
                                       
                                     
                                     + 
                                     
                                       Δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       f 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 t 
                               
                               + 
                               θ 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             + 
                             ɛ 
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 - 
                                 
                                   
                                     r 
                                     I 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     f 
                                     c 
                                   
                                   ⁢ 
                                   t 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           f 
                                           c 
                                         
                                         + 
                                         
                                           Δ 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           f 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   θ 
                                 
                                 ) 
                               
                             
                             + 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             r 
                             Q 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             2 
                             ⁢ 
                             π 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               c 
                             
                             ⁢ 
                             t 
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     f 
                                     c 
                                   
                                   + 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     f 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               t 
                             
                             + 
                             θ 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             ɛ 
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 - 
                                 
                                   
                                     r 
                                     I 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     πΔ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     ft 
                                   
                                   + 
                                   θ 
                                 
                                 ) 
                               
                             
                             - 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             
                               r 
                               
                                 
                                     
                                 
                                 ⁢ 
                                 I 
                               
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                         f 
                                         
                                           
                                               
                                           
                                           ⁢ 
                                           c 
                                         
                                       
                                     
                                     + 
                                     
                                       Δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       f 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 t 
                               
                               + 
                               θ 
                             
                             ) 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             
                               r 
                               Q 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 πΔ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ft 
                               
                               + 
                               θ 
                             
                             ) 
                           
                         
                         - 
                         
                           
                             
                               r 
                               Q 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                         f 
                                         c 
                                       
                                     
                                     + 
                                     
                                       Δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       f 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 t 
                               
                               + 
                               θ 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
   
   From the above-mentioned equations (8) and (9), it can be seen that after the LPFs  418  and  420  filtering out the high-frequency parts of the in-phase analog signal R I (t) and the quadrature-phase analog signal R Q (t), the in-phase analog signal V I (t) and the quadrature-phase analog signal V Q (t) can be respectively represented by the following equations: 
   
     
       
         
           
             
               
                 
                   
                     V 
                     I 
                   
                   ⁡ 
                   
                     ( 
                     t 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       
                         r 
                         I 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         2 
                         ⁢ 
                         πΔ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ft 
                       
                       ) 
                     
                   
                   + 
                   
                     
                       
                         r 
                         Q 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         2 
                         ⁢ 
                         πΔ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ft 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
           
             
               
                 
                   
                     
                       
                         
                           V 
                           Q 
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             ɛ 
                           
                           ) 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   r 
                                   Q 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     πΔ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     ft 
                                   
                                   + 
                                   θ 
                                 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   r 
                                   I 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     πΔ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     ft 
                                   
                                   + 
                                   θ 
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             ɛ 
                           
                           ) 
                         
                         [ 
                         
                           
                             
                               
                                 r 
                                 Q 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 πΔ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ft 
                               
                               ) 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               θ 
                               ) 
                             
                           
                           - 
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             
                               r 
                               
                                 
                                     
                                 
                                 ⁢ 
                                 Q 
                               
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               πΔ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ft 
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             θ 
                             ) 
                           
                         
                         - 
                         
                           
                             
                               r 
                               I 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               πΔ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ft 
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             θ 
                             ) 
                           
                         
                         - 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             r 
                             I 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             2 
                             ⁢ 
                             πΔ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ft 
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                       ] 
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             ɛ 
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         r 
                                         Q 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         t 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       cos 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           2 
                                           ⁢ 
                                           πΔ 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           ft 
                                         
                                         ) 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         r 
                                         I 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         t 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     sin 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         2 
                                         ⁢ 
                                         πΔ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         ft 
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 θ 
                                 ) 
                               
                             
                             - 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             V 
                             
                               
                                   
                               
                               ⁢ 
                               I 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
   
   In equations (8)-(11), r I (t) represents an in-phase analog signal transmitted by a transmitter (not shown), and r Q (t) represents a quadrature-phase analog signal transmitted by the transmitter. 
   In this embodiment, the in-phase and quadrature-phase imbalance parameter estimation unit  422  estimates the gain compensation value ε′ according to a first predetermined functional relationship between (1+ε) 2  and a power value (V I   2 [n]) of the in-phase digital signal V I [n] and a power value (V Q   2 [n]) of the quadrature-phase digital signal V Q [n]. Furthermore, the in-phase and quadrature-phase imbalance parameter estimation unit  422  estimates the desired phase compensation value θ′ according to a second predetermined functional relationship between −(1+ε)·E(V I   2 [n])·sin θ and a product of the in-phase digital signal V I [n] and the quadrature-phase digital signal V Q [n]. 
   Generally speaking, the in-phase analog signal r I (t) and the quadrature-phase analog signal r Q (t) transmitted by the transmitter are uncorrelated in statistic characteristic. Furthermore, the power of the in-phase analog signal r I (t) and the quadrature-phase analog signal r Q (t) transmitted by the transmitter are equal. Therefore, the equations (12) and (13) can be obtained as follows:
 
 E ( r   I ( t )· r   Q ( t ))=0   Equation (12)
 
 E ( r   I   2 ( t ))= E ( r   Q   2 ( t ))  Equation (13)
 
In equations (12) and (13), E(x) represents the expectation value of X.
 
   From the equations (10), (11), (12), and (13), we can determine that: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               V 
                               I 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       r 
                                       I 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       2 
                                       ⁢ 
                                       πΔ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       ft 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       r 
                                       Q 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       2 
                                       ⁢ 
                                       πΔ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       ft 
                                     
                                     ) 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   r 
                                   I 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   cos 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     πΔ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     ft 
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   r 
                                   Q 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   sin 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     πΔ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     ft 
                                   
                                   ) 
                                 
                               
                             
                             + 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         2 
                         ⁢ 
                         
                           
                             r 
                             I 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             r 
                             Q 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             2 
                             ⁢ 
                             πΔ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ft 
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             2 
                             ⁢ 
                             πΔ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ft 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           E 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 r 
                                 I 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           E 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 cos 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   πΔ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ft 
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           E 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 r 
                                 
                                   
                                       
                                   
                                   ⁢ 
                                   Q 
                                 
                                 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           E 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   πΔ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ft 
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         2 
                         ⁢ 
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 r 
                                 I 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 r 
                                 Q 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   πΔ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ft 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 πΔ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ft 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               r 
                               I 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
           
             
               
                 
                   
                     
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               V 
                               Q 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   ɛ 
                                 
                                 ) 
                               
                               2 
                             
                             [ 
                             
                               
                                 
                                   
                                     r 
                                     Q 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       2 
                                       ⁢ 
                                       πΔ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       ft 
                                     
                                     + 
                                     θ 
                                   
                                   ) 
                                 
                               
                               - 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                             
                           ⁢ 
                           
                             
                               
                                 r 
                                 I 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   πΔ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ft 
                                 
                                 + 
                                 θ 
                               
                               ) 
                             
                           
                           ] 
                         
                         2 
                       
                       ) 
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               ɛ 
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               r 
                               I 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
   
   The following equation is derived according to the equations (14) and (15): 
                     E   ⁢           ⁢     (       V   Q   2     ⁡     (   t   )       )         E   ⁢           ⁢     (       V   I   2     ⁡     (   t   )       )         =       (     1   +   ɛ     )     2             Equation   ⁢           ⁢     (   16   )                 
Therefore, from the equation (16), the gain imbalance ε is:
 
   
     
       
         
           
             
               
                 ɛ 
                 = 
                 
                   
                     
                       [ 
                       
                         
                           E 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 V 
                                 Q 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ) 
                           
                         
                         
                           E 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 V 
                                 I 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       2 
                     
                   
                   - 
                   1 
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
   
   In addition, according to the above-mentioned equations (10), (11), and (13), the cross-correlation between the in-phase analog signal V I (t) and the quadrature-phase analog signal V Q (t) is: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 V 
                                 I 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                 V 
                                 Q 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             ( 
                             
                               
                                 
                                   
                                     r 
                                     I 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     πΔ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     ft 
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   
                                     r 
                                     Q 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 sin 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     πΔ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     ft 
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             ɛ 
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   r 
                                   Q 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     πΔ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     ft 
                                   
                                   + 
                                   θ 
                                 
                                 ) 
                               
                             
                             - 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               r 
                               I 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 πΔ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ft 
                               
                               + 
                               θ 
                             
                             ) 
                           
                         
                         ) 
                       
                       ) 
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             ɛ 
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 - 
                                 E 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       r 
                                       I 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       2 
                                       ⁢ 
                                       πΔ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       ft 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     sin 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           πΔ 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           ft 
                                         
                                         + 
                                         θ 
                                       
                                       ) 
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 r 
                                 Q 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 πΔ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ft 
                               
                               ) 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   πΔ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ft 
                                 
                                 + 
                                 θ 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             ɛ 
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               r 
                               I 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             E 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   - 
                                   cos 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     πΔ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     ft 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                           
                         ⁢ 
                         
                           ( 
                           
                             
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   πΔ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ft 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             + 
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   πΔ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ft 
                                 
                                 ) 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                           
                           ) 
                         
                         ) 
                       
                       + 
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 πΔ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ft 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       2 
                                       ⁢ 
                                       πΔ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       ft 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   θ 
                                 
                                 - 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                             
                           ⁢ 
                           
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 πΔ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ft 
                               
                               ) 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             θ 
                           
                           ) 
                         
                         ) 
                       
                       ) 
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             ɛ 
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               r 
                               I 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 - 
                                 E 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       cos 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         2 
                                         ⁢ 
                                         πΔ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         ft 
                                       
                                       ) 
                                     
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   θ 
                                 
                                 ) 
                               
                             
                             - 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         E 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 sin 
                                 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   2 
                                   ⁢ 
                                   πΔ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ft 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             θ 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           - 
                           
                             ( 
                             
                               1 
                               + 
                               ɛ 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           E 
                           ⁡ 
                           
                             ( 
                             
                               
                                 r 
                                 I 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
   
   Therefore, the phase imbalance θ can be obtained as follows: 
   
     
       
         
           
             
               
                 θ 
                 = 
                 
                   
                     
                       sin 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             - 
                             E 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   V 
                                   I 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               · 
                               
                                 
                                   V 
                                   Q 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                         
                           
                             ( 
                             
                               1 
                               + 
                               ɛ 
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           E 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 r 
                                 I 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       sin 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             - 
                             E 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   V 
                                   I 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               · 
                               
                                 
                                   V 
                                   Q 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                         
                           
                             ( 
                             
                               1 
                               + 
                               ɛ 
                             
                             ) 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           E 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 V 
                                 I 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
   
   Please note that the value of E(r I   2 (t)) is equal to E(V I   2 (t), in this embodiment, the phase compensation module  410  uses the equation (19), wherein E(r I   2 (t)) is substituted by E(V I   2 (t)), to calculate the phase compensation value θ′. 
   After the gain imbalance ε and the phase imbalance θ both obtained, the influences of the gain imbalance ε and the phase imbalance θ on the in-phase analog signal V I (t) and the quadrature-phase analog signal V Q (t) are eliminated accordingly. Signals without the influences of the gain imbalance ε and the phase imbalance θ are expressed as following:
 
 S   I ( t )= r   I ( t )cos(2 πΔft )+ r   Q ( t )sin(2 πΔft )  Equation (20)
 
 S   Q ( t )= r   Q ( t )cos(2 πΔft )− r   I ( t )sin(2 πΔft )  Equation (21)
 
   From the equations (10) and (11), the signals S I (t), S Q (t) and V I (t), V Q (t) have the following relationship:
 
 V   I ( t )= S   I ( t )   Equation (22)
 
 V   Q ( t )=(1+ε)( S   Q ( t )cos(θ)− S   I ( t )sin(θ))  Equation (23)
 
   The following equations (24) and (25) can be obtained from equations (22) and (23): 
   
     
       
         
           
             
               
                 
                   
                     S 
                     I 
                   
                   ⁡ 
                   
                     ( 
                     t 
                     ) 
                   
                 
                 = 
                 
                   
                     V 
                     I 
                   
                   ⁡ 
                   
                     ( 
                     t 
                     ) 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
           
             
               
                 
                   
                     S 
                     Q 
                   
                   ⁡ 
                   
                     ( 
                     t 
                     ) 
                   
                 
                 = 
                 
                   
                     1 
                     
                       cos 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             V 
                             Q 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         
                           1 
                           + 
                           ɛ 
                         
                       
                       + 
                       
                         
                           
                             V 
                             I 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                     ) 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
   
   Please refer to  FIG. 3 , which is a diagram of the in-phase and quadrature-phase imbalance parameter estimation unit  422  shown in  FIG. 2  The in-phase analog signal V I (t) and the quadrature-phase analog signal V Q (t) are digitized by the ADCs to generate an in-phase digital signal V I [n] and a quadrature-phase digital signal V Q [n]respectively, then input to the in-phase and quadrature-phase imbalance parameter estimation unit  422 . The average power estimation units  512  and  510 , respectively, estimates the power (V I   2 [n]) of the in-phase digital signal V I [n] and the power (V Q   2 [n]) of the quadrature-phase digital signal V Q [n] and outputs to the calculation unit  516 . The calculation unit  516  calculates the gain compensation value ε′according to the first predetermined functional relationship between (1+ε) 2  and the above-mentioned power values of the two signals V I [n] and V Q [n]. Furthermore, the cross-correlation estimation unit  514  estimates the product of the in-phase digital signal V I [n] and the quadrature-phase digital signal V Q [n] and outputs the product to the calculation unit  518 . The calculation unit  518  calculates the desired phase compensation value θ′ according to a second predetermined functional relationship between −(1+ε)·E(r I   2 (t))·sinθ and the product. 
   The equations (26) and (27) respectively show the equations for obtaining the gain compensation value ε′ and the phase compensation value θ′ which is performed by the in-phase and quadrature-phase imbalance parameter estimation unit  422 : 
   
     
       
         
           
             
               
                 
                   ɛ 
                   ′ 
                 
                 = 
                 
                   
                     
                       [ 
                       
                         
                           E 
                           ⁢ 
                           
                               
                           
                           [ 
                           
                             
                               V 
                               Q 
                               2 
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           ] 
                         
                         
                           E 
                           ⁢ 
                           
                               
                           
                           [ 
                           
                             
                               V 
                               I 
                               2 
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           ] 
                         
                       
                       ] 
                     
                     
                       1 
                       2 
                     
                   
                   - 
                   1 
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
           
             
               
                 
                   θ 
                   ′ 
                 
                 = 
                 
                   
                     sin 
                     
                       - 
                       1 
                     
                   
                   ⁡ 
                   
                     ( 
                     
                       
                         - 
                         
                           E 
                           ⁢ 
                           
                               
                           
                           [ 
                           
                             
                               
                                 V 
                                 I 
                               
                               ⁡ 
                               
                                 [ 
                                 n 
                                 ] 
                               
                             
                             · 
                             
                               
                                 V 
                                 Q 
                               
                               ⁡ 
                               
                                 [ 
                                 n 
                                 ] 
                               
                             
                           
                           ] 
                         
                       
                       
                         
                           ( 
                           
                             1 
                             + 
                             
                               ɛ 
                               ′ 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           E 
                           ⁢ 
                           
                               
                           
                           [ 
                           
                             
                               V 
                               I 
                               2 
                             
                             ⁡ 
                             
                               [ 
                               n 
                               ] 
                             
                           
                           ] 
                         
                       
                     
                     ) 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
   
   Finally, the compensation unit  412  compensates the in-phase digital signal V I [n]and the quadrature-phase digital signal V Q [n] according to the gain compensation value ε′ and the phase compensation value θ′ estimated by the in-phase and quadrature-phase imbalance estimation unit  422  to generate the compensated signals which eliminates the influence of the gain imbalance ε and the phase imbalance θ . The equations for the above compensation are shown as following: 
   
     
       
         
           
             
               
                 
                   
                     S 
                     I 
                   
                   ⁡ 
                   
                     [ 
                     n 
                     ] 
                   
                 
                 = 
                 
                   
                     V 
                     I 
                   
                   ⁡ 
                   
                     [ 
                     n 
                     ] 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
           
             
               
                 
                   
                     S 
                     Q 
                   
                   ⁡ 
                   
                     [ 
                     n 
                     ] 
                   
                 
                 = 
                 
                   
                     1 
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         
                           θ 
                           ′ 
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             V 
                             Q 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         
                           1 
                           + 
                           
                             ɛ 
                             ′ 
                           
                         
                       
                       + 
                       
                         
                           
                             V 
                             I 
                           
                           ⁡ 
                           
                             [ 
                             n 
                             ] 
                           
                         
                         ⁢ 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               θ 
                               ′ 
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
   
   In contrast to the related art, the present invention of the receiver and method capable of compensating IQ imbalance effectively estimates a gain imbalance and a phase imbalance while at the same time a carrier frequency offset also exists. Furthermore, the present invention method and receiver capable of compensating the IQ imbalance can utilize an inverse matrix to multiply an in-phase analog signal and a quadrature-phase analog signal output by a mixer module in order to eliminate the IQ imbalance. 
   Those skilled in the art will readily observe that numerous modifications and alterations of the device and method may be made while retaining the teachings of the invention. Accordingly, the above disclosure should be construed as limited only by the metes and bounds of the appended claims.