Abstract:
A receiver for an orthogonal frequency division multiplex radio signal in which a carrier frequency is modulated by sub-carrier signals (S 1 ) coded with data. Analogue signal processing means ( 3  to  12 ) produces base-band analogue signals (I-Rx, Q-Rx) in phase quadrature and analogue-to-digital converters ( 13, 14 ) convert the analogue signals to phase quadrature digital signals (xI(n), xq(n)). The digital signal processor includes the OFDM demodulator ( 15 ) and mismatch compensation ( 17, 18 ). The mismatch compensation ( 17, 18 ) combines each of the reproduced sub-carrier signals (RI) with a limited number of the reproduced sub-carrier signals (RI-Rk) according to respective frequency offset coefficient (I, k) that is a function of an estimated value of the offset (fc) of the reference frequency relative to the carrier frequency.

Description:
FIELD OF THE INVENTION 
     This invention relates to an orthogonal frequency division multiplex (‘OFDM’) receiver with compensation for frequency offset. As used herein, ‘receiver’ refers to apparatus capable of receiving a radio signal, whether or not it is also capable of transmitting a radio signal. 
     BACKGROUND OF THE INVENTION 
     OFDM transmissions are widely used. Examples of their use include Digital Video Broadcast (DVB), Digital Audio Broadcast (DAB), and wireless broadband transmission standards such as IEEE 802.11a, ETSI/BRAN/Hiperlan2 and ARIB/MMAC/HiSWAN. 
     An OFDM transmitter/receiver (‘transceiver’) includes an analogue signal processing part, the RF front-end, and a digital signal processing (DSP) part, also referred to as the base-band digital IC. In the reception direction, the function of the RF front-end is to convert the OFDM signal from the RF frequency (e.g. 5 GHz in IEEE802.11a) to base-band, and to generate the in-phase (I) and quadrature (Q) components of the base-band signal. The digitised I and Q signals are then processed by the DSP unit. There are two basic architectures to generate I and Q digital signals:
         The first architecture, which is not utilised by the present invention, is known as digital I/Q generation. In digital I/Q generation, the RF signal is converted to a low intermediate frequency (IF) (for example 20 MHz in IEEE802.11a) and sampled at a relatively high frequency (e.g. greater than 40 MHz in IEEE802.11a) by a single Analogue to Digital Converter (ADC). The single digitised signal is then processed by the DSP unit, which digitally generates the I and Q signals and processes them. A drawback of this architecture is that it is power consuming and increases the complexity of the DSP. Also, many I/Q compensation techniques only deal with a mismatch that remains constant over the whole frequency band of the signal and only give good results for narrow band signals.   The second architecture is called analogue I/Q generation. An example of a transceiver in conformity with the IEEE802.11a standards with this architecture as disclosed in our co-pending European Patent Application N° EP 01401631.5 filed 20 Jun. 2001 is shown in  FIG. 1  and the signals appearing in operation at various stages of the receiver are shown in  FIG. 2 .       

     An analogue I/Q receiver may include a first down-conversion stage, which converts the RF signal to an intermediate frequency, as shown in  FIGS. 1 and 2 . However it is also possible for the receiver to convert the RF signal directly down to base-band. 
     The transceiver illustrated in  FIGS. 1 and 2  comprises an analogue I/Q receiver section  1  and a transmitter section  2 . In the analogue receiver section  1 , the RF signal is filtered in a band-pass filter  3 , amplified in a low-noise amplifier  4 , converted down to intermediate frequency by mixing in a mixer  5  with an RF signal generated locally by a voltage controlled oscillator  6  and filtered in a band-pass filter  7 . The IF signal is then mixed in two mixers  8  and  9  with two sine waves produced by a voltage controlled oscillator  10  and which have the same IF frequency with a phase difference of 90 degrees, so as to generate the base-band I and Q signals. The I and Q signals are filtered by respective low-pass filters  11  and  12 . Then they are digitised using respective analogue-to-digital converters  13  and  14  and demodulated in an OFDM demodulator  15 . The two ADCs are typically clocked at a frequency that is at least a factor of two lower than in digital I/Q receivers, which reduces the circuit area and power consumption and also simplifies the base-band digital IC compared to a receiver using digital I/Q generation. 
     Analogue I/Q generation has been found to be more difficult to implement than digital I/Q generation, however, because avoiding signal impairment (such as cross-talk between the sub-carriers especially, for example) has required high quality matching between the I and Q signal paths. The analogue treatment of the I/Q signals is sensitive to mismatch. Such mismatch arises from slight differences in the values and behaviour of active and passive elements found in the I and Q signal paths, even though great care is taken in the design and layout of these elements in a symmetrical way during the design of the system and/or circuit. Mismatches are even more pronounced when the effects of thermal drift are taken into account. 
     The present invention enables signal impairments to be reduced without requiring such high quality matching between the I and Q signal paths. The overall solution combines the advantages of a high quality signal and a low power consumption and circuit area. 
     SUMMARY OF THE INVENTION 
     The present invention provides a receiver for an orthogonal frequency division multiplex radio signal as described in the accompanying claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of a transceiver including an OFDM receiver, 
         FIG. 2  is a graphical diagram of typical frequency distributions of signals appearing at different points in the receiver of  FIG. 1 , 
         FIG. 3  is a block schematic diagram of compensation circuits incorporated in the receiver of  FIG. 1  in accordance with one embodiment of the present invention, given by way of example, 
         FIG. 4  is a graphical diagram of typical frequency distributions of base-band sub-carrier signals in operation of the receiver of  FIG. 1  without compensation circuits, both without and with frequency offset, 
         FIG. 5  is a graphical diagram similar to  FIG. 4  showing I/Q mismatch cross-talk in operation of the receiver of  FIG. 1 , both without and with frequency offset, 
         FIG. 6  is a schematic diagram of a calibration configuration of the receiver of  FIG. 3 , 
         FIG. 7  is a schematic diagram of a compensation circuit in the receiver of  FIG. 3  in accordance with a preferred embodiment of the invention, and 
         FIG. 8  is a graphical diagram showing simulated packet error rates as a function of frequency offset for different compensation configurations. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Our co-pending European Patent Application N° EP 01401631.5 filed 20 Jun. 2001 describes a digital method for mismatch compensation of the I and Q paths of an OFDM transmitter or receiver implementing analogue I/Q generation.  FIGS. 1 and 2  (taken from our co-pending European Patent Application) show an OFDM transceiver system with the sources of the I/Q mismatch and the analogue signals in the receiver (in the context of an architecture with one IF frequency). 
     The method that is described in our co-pending European Patent Application allows the compensation of the I/Q mismatch in an OFDM receiver when there is no offset or a negligible offset between the transmitter and the receiver carrier frequency. However, when the carrier frequency offset becomes bigger, the data transmission quality degrades very quickly (i.e. higher bit error rate) and it becomes necessary to implement a different compensation method. 
     The embodiment of the present invention shown in  FIG. 3  is applicable to any OFDM receiver implementing analogue I/Q generation, compliant or not with the wireless broadband transmission standards such as IEEE 802.11a, ETSI/BRAN/Hiperlan2 and ARIB/MMAC/HiSWAN mentioned above. In this embodiment of the invention, the I and Q mismatch is compensated in the digital signal processor (‘DSP’) part of the OFDM receiver, taking advantage of the specific properties of OFDM signals. This compensation substantially reduces the signal impairments with little increase in DSP complexity. The overall solution combines the advantages of a high quality signal and a low power consumption and circuit area. 
       FIG. 3  is a block diagram of the processing section of an analogue I/Q receiver of the kind shown in  FIG. 1 , similar references being used to designate similar elements. The upper part of  FIG. 3  represents the RF front-end and the lower part represents the processing section of the DSP. 
     The two digital signals x I (n) and x Q (n) from the ADCs  13  and  14  are sent to the DSP which implements the functions described below:
         As in most OFDM systems, the receiver (and transmitter) generates its clock signals internally from its own crystal (not shown). During data transmission, the receiver is tuned nominally to the same channel as the transmitter from which it is receiving the signals but a frequency offset equal to the difference between the transmitter and the receiver carrier central frequency usually appears. When the digital I and Q signals enter the DSP, this carrier frequency offset is compensated in the time domain by a frequency offset compensation circuit  16 .   The OFDM demodulator  15  performs a fast Fourier transform (‘FFT’) by converting the time domain signals to the frequency domain and recovers the sub-carriers that were transmitted.   An I/Q mismatch compensation block  17  removes cross-talk between sub-carriers, which is generated by the mismatch between the analogue components of the I and Q channels, especially the IF mixers, the low pass filter and the analogue to digital converter. The I/Q mismatch compensation method is described in more detail below.   The signals then pass to a phase offset compensation and equalisation circuit  18 .   Finally, the data is decoded from the compensated sub-carriers in a circuit  19 .       

     Cross-talk between sub-carriers is generated In operation of an OFDM receiver without compensation after the conversion from IF to base-band by the mismatch between the analogue components of the I and Q channels and increases the data transmission error rate. This cross-talk will now be described by equations and the method to remove this cross-talk in order to improve the data transmission quality will then be analysed. 
     In the time domain, an OFDM signal is the sum of K sinusoidal waveforms, that is to say the sub-carriers that carry the data to be transmitted. Each sub-carrier&#39;s amplitude and phase is represented by the complex element S k  with k=[−K/2, −1, . . . , +1, +K/2]. 
     The OFDM signal is transmitted after being up converted with a central carrier frequency f c . Then, each sub-carrier is sent at the frequency f c +kf s /N, with N being the size of the inverse fast Fourier transform (‘IFFT’) being used for the OFDM modulation and f s  the sampling frequency. The signal at the transmitter antenna is represented by the following equation: 
     
       
         
           
             
               
                 
                   
                     x 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     Re 
                     ⁡ 
                     
                       ( 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             
                               - 
                               
                                 K 
                                 2 
                               
                             
                           
                           
                             k 
                             = 
                             
                               K 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           
                             S 
                             k 
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               ( 
                               
                                 
                                   j2π 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         f 
                                         c 
                                       
                                       + 
                                       
                                         
                                           k 
                                           N 
                                         
                                         ⁢ 
                                         
                                           f 
                                           s 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
           
         
       
     
     In the receiver, after down conversion to base-band, the sub-carriers are placed symmetrically around the DC frequency if there is no carrier frequency offset as shown in the upper part of  FIG. 4 . With the presence of a carrier frequency offset Δf c  between the transmitter and the receiver, the sub-carriers are shifted by Δf c , as shown in the lower part of  FIG. 4 . 
     In a receiver system working with analogue I/Q generation, the essential path mismatch originates from the analogue part imperfections. Putting G k  as the common gain for the I and Q path, α k  and θ k  as the low pass filter and A/D converter amplitude mismatch and phase mismatch, they are function of the sub-carrier k frequency. The IF mixers have an amplitude mismatch α and a phase mismatch θ that are independent of the sub-carrier frequency. Then, the I and Q samples at the output of the receiver A/D converters are modelled as follows: 
                 x   I     ⁡     (   n   )       =     Re   (         ∑               k   =     -     K   2           k   =     K   2         ⁢       (     1   +   α     )     ⁢     (     1   +     α   k       )     ⁢     ⅇ     (     j   ⁢           ⁢     (     θ   +     θ   k       )           ⁢     G   k     ⁢     S   k     ⁢     ⅇ     (     j   ⁢           ⁢   2   ⁢   π   ⁢       n   .   k     N       )       ⁢     ⅇ     j   ⁡     (       2   ⁢   π   ⁢       Δ   ⁢           ⁢     f   c         f   s       ⁢   n     +     φ   0       )             )                     x   Q     ⁡     (   n   )       =     Im   ⁡     (         ∑               k   =     -     K   2           k   =     K   2         ⁢     (     1   -   α     )     ⁢     (     1   -     α   k       )     ⁢     ⅇ     (       -   j     ⁢           ⁢     (     θ   +     θ   k       )           ⁢     G   k     ⁢     S   k     ⁢     ⅇ     (     j   ⁢           ⁢   2   ⁢   π   ⁢       n   .   k     N       )       ⁢     ⅇ     j   ⁡     (       2   ⁢   π   ⁢       Δ   ⁢           ⁢     f   c         f   s       ⁢   n     +     φ   0       )           )             
We consider α and α k  to be small compared to 1. Then, for sub-carrier k, the overall amplitude mismatch can be represented by a k  and the overall phase mismatch by φ k , with a k =α+α k  and φ k =θ+θ k . The I and Q samples at the output of the receiver A/D converters can be described as follows:
 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       I 
                     
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     Re 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             ∑ 
                             
                                 
                             
                           
                           
                             k 
                             = 
                             
                               - 
                               
                                 K 
                                 2 
                               
                             
                           
                           
                             k 
                             = 
                             
                               K 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               1 
                               + 
                               
                                 α 
                                 k 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               ( 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ϕ 
                                   k 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             G 
                             k 
                           
                           ⁢ 
                           
                             S 
                             k 
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               ( 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                   
                                     n 
                                     . 
                                     k 
                                   
                                   N 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               j 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                       
                                         Δ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           f 
                                           c 
                                         
                                       
                                       
                                         f 
                                         s 
                                       
                                     
                                     ⁢ 
                                     n 
                                   
                                   + 
                                   
                                     φ 
                                     0 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
             
               
                 
                   
                     
                       x 
                       Q 
                     
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     Im 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             ∑ 
                             
                                 
                             
                           
                           
                             k 
                             = 
                             
                               - 
                               
                                 K 
                                 2 
                               
                             
                           
                           
                             k 
                             = 
                             
                               K 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 α 
                                 k 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               ( 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ϕ 
                                   k 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             G 
                             k 
                           
                           ⁢ 
                           
                             S 
                             k 
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               ( 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                   
                                     n 
                                     . 
                                     k 
                                   
                                   N 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               j 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                       
                                         Δ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           f 
                                           c 
                                         
                                       
                                       
                                         f 
                                         s 
                                       
                                     
                                     ⁢ 
                                     n 
                                   
                                   + 
                                   
                                     φ 
                                     0 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
         
         
           
             where n=−E . . . −1,0,1 . . . N−1, E being the length of the cyclic extension and φ 0  the phase offset for the first sample. 
           
         
       
    
     The complex signal before the frequency offset compensation is: 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       ⁡ 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             x 
                             I 
                           
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                         + 
                         
                           j 
                           · 
                           
                             
                               x 
                               Q 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         
 
                       
                       ⁢ 
                       
                           
                       
                       = 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             
                               - 
                               
                                 K 
                                 2 
                               
                             
                           
                           
                             k 
                             = 
                             
                               K 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 
                                   I 
                                   k 
                                 
                                 ⁢ 
                                 
                                   G 
                                   k 
                                 
                                 ⁢ 
                                 
                                   S 
                                   k 
                                 
                                 ⁢ 
                                 
                                   C 
                                   n 
                                 
                               
                               + 
                               
                                 
                                   J 
                                   k 
                                 
                                 ⁢ 
                                 
                                   
                                     G 
                                     _ 
                                   
                                   
                                     - 
                                     k 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     S 
                                     _ 
                                   
                                   
                                     - 
                                     k 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     C 
                                     _ 
                                   
                                   n 
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               j 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               
                                 
                                   n 
                                   . 
                                   k 
                                 
                                 N 
                               
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   where 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         I 
                         k 
                       
                       = 
                       
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               ϕ 
                               k 
                             
                             ) 
                           
                         
                         - 
                         
                           
                             j 
                             · 
                             
                               a 
                               k 
                             
                           
                           ⁢ 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 ϕ 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         J 
                         k 
                       
                       = 
                       
                         
                           
                             
                               
                                 
                                   a 
                                   k 
                                 
                                 · 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       ϕ 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 j 
                                 · 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       ϕ 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                             &amp; 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             C 
                             n 
                           
                         
                         = 
                         
                           
                             ⅇ 
                             
                               j 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                       
                                         Δ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           f 
                                           c 
                                         
                                       
                                       
                                         f 
                                         s 
                                       
                                     
                                     ⁢ 
                                     n 
                                   
                                   + 
                                   
                                     φ 
                                     0 
                                   
                                 
                                 ) 
                               
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
           
         
       
     
     The offset frequency compensation is implemented in the time domain by multiplying the received samples by 
               ⅇ     -     j   ⁡     (       2   ⁢   π   ⁢       Δ   ⁢           ⁢     f   c         f   S       ⁢   n     +     φ   1       )           ,         
where n=0,1 . . . N−1.
 
     The demodulation is performed by a fast Fourier transform on the useful samples. The received sub-carrier R I  is described by the following equations: 
     
       
         
           
             
               
                 
                   
                     R 
                     l 
                   
                   = 
                   
                     
                       
                         I 
                         l 
                       
                       ⁢ 
                       
                         G 
                         l 
                       
                       ⁢ 
                       
                         S 
                         l 
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁡ 
                           
                             ( 
                             
                               
                                 φ 
                                 0 
                               
                               + 
                               
                                 φ 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                     
                     + 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ⅇ 
                         
                           - 
                           
                             j 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   φ 
                                   0 
                                 
                                 + 
                                 
                                   φ 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             
                               - 
                               
                                 K 
                                 2 
                               
                             
                           
                           
                             k 
                             = 
                             
                               K 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           
                             λ 
                             
                               l 
                               , 
                               k 
                             
                           
                           ⁢ 
                           
                             
                               J 
                               k 
                             
                             
                               I 
                               k 
                             
                           
                           ⁢ 
                           
                             
                               I 
                               _ 
                             
                             
                               - 
                               k 
                             
                           
                           ⁢ 
                           
                             
                               G 
                               _ 
                             
                             
                               - 
                               k 
                             
                           
                           ⁢ 
                           
                             
                               S 
                               _ 
                             
                             
                               - 
                               k 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
             
             
               
                 
                   with 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       λ 
                       
                         l 
                         , 
                         k 
                       
                     
                     = 
                     
                       
                         1 
                         N 
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             π 
                             ⁡ 
                             
                               ( 
                               
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 
                                   k 
                                   - 
                                   l 
                                 
                                 N 
                               
                               - 
                               
                                 2 
                                 ⁢ 
                                 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       f 
                                       c 
                                     
                                   
                                   
                                     f 
                                     s 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 N 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       
                                         k 
                                         - 
                                         l 
                                       
                                       N 
                                     
                                     - 
                                     
                                       2 
                                       ⁢ 
                                       
                                         
                                           Δ 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             f 
                                             c 
                                           
                                         
                                         
                                           f 
                                           s 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     
                                       k 
                                       - 
                                       l 
                                     
                                     N 
                                   
                                   - 
                                   
                                     2 
                                     ⁢ 
                                     
                                       
                                         Δ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           f 
                                           c 
                                         
                                       
                                       
                                         f 
                                         s 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     Equation 5 shows that each received sub-carrier R I  is the sum of the transmitted sub-carrier S I  multiplied by the coefficient I I  and the channel gain G I  plus a cross-talk (right-hand term), which is dependent on all the other sub-carriers. 
     Since the phase φ 1  is known, it can be set to zero for simplification. Furthermore, it is known that the effect of a clock frequency offset on the frequency domain symbol is a rotation of sub-carrier k by a phase that depends on the sub-carrier frequency and is denoted by φ VPE (k). It can be verified that in the presence of I/Q imbalance, carrier and clock frequency offset, Equation 5 is modified as follows: 
     
       
         
           
             
               
                 
                   
                     R 
                     l 
                   
                   = 
                   
                     
                       
                         I 
                         l 
                       
                       ⁢ 
                       
                         G 
                         l 
                       
                       ⁢ 
                       
                         S 
                         l 
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             φ 
                             0 
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               φ 
                               VPE 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     + 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           
                             - 
                             
                               K 
                               2 
                             
                           
                         
                         
                           k 
                           = 
                           
                             K 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         
                           λ 
                           
                             l 
                             , 
                             k 
                           
                         
                         ⁢ 
                         
                           
                             J 
                             k 
                           
                           
                             I 
                             k 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             
                               ⅇ 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   φ 
                                   0 
                                 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     φ 
                                     VPE 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       - 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           _ 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             I 
                             
                               - 
                               k 
                             
                           
                           _ 
                         
                         ⁢ 
                         
                           
                             G 
                             _ 
                           
                           
                             - 
                             k 
                           
                         
                         ⁢ 
                         
                           
                             S 
                             _ 
                           
                           
                             - 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   7 
                 
               
             
           
         
       
     
     The I/Q mismatch that is represented in these equations is compensated as follows in this embodiment of the present invention. 
     Based on equation 7, and the assumption that the cross-talk term remains small compared to the left-hand term, the compensation is implemented by subtracting the cross-talk from the received signal. Then, the corrected signal Z I  is defined by the equation below: 
     
       
         
           
             
               
                 
                   
                     Z 
                     l 
                   
                   = 
                   
                     
                       
                         R 
                         l 
                       
                       - 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             
                               - 
                               
                                 K 
                                 2 
                               
                             
                           
                           
                             k 
                             = 
                             
                               K 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           
                             λ 
                             
                               l 
                               , 
                               k 
                             
                           
                           ⁢ 
                           
                             
                               J 
                               k 
                             
                             
                               I 
                               k 
                             
                           
                           ⁢ 
                           
                             
                               R 
                               _ 
                             
                             
                               - 
                               k 
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     = 
                     
                       
                         R 
                         l 
                       
                       - 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             
                               - 
                               
                                 K 
                                 2 
                               
                             
                           
                           
                             k 
                             = 
                             
                               K 
                               2 
                             
                           
                         
                         ⁢ 
                         
                           
                             λ 
                             
                               l 
                               , 
                               k 
                             
                           
                           ⁢ 
                           
                             A 
                             k 
                           
                           ⁢ 
                           
                             
                               R 
                               _ 
                             
                             
                               - 
                               k 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
             
               
                 
                   
                     S 
                     l 
                   
                   = 
                   
                     
                       
                         Z 
                         l 
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           
                             - 
                             j 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               ϕ 
                               VPE 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         I 
                         l 
                       
                       ⁢ 
                       
                         G 
                         l 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   9 
                 
               
             
           
         
       
         
         
           
             where R I  is the received signal and S I  is the original transmitted signal. As shown in equation 9, the transmitted sub-carrier S I  is recovered by calculation from Z I  by doing a phase shift of −φ VPE  followed by a division by I I G I . The phase compensation and the equalisation digital treatments in the circuit  18  that follows the I/Q mismatch compensation block  17  in the base-band digital IC implement these calculations. 
           
         
       
    
     If we assume that the amplitude and phase mismatch a k  and φ k  are small compared to 1, the second order term in I k  can be neglected and the ratio J k /I k  can be simplified as follows: 
     
       
         
           
             
               
                 I 
                 k 
               
               = 
               
                 
                   
                     cos 
                     ⁡ 
                     
                       ( 
                       
                         ϕ 
                         k 
                       
                       ) 
                     
                   
                   - 
                   
                     
                       j 
                       · 
                       
                         a 
                         k 
                       
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         
                           ϕ 
                           k 
                         
                         ) 
                       
                     
                   
                 
                 ≈ 
                 
                   cos 
                   ⁡ 
                   
                     ( 
                     
                       ϕ 
                       k 
                     
                     ) 
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   J 
                   k 
                 
                 
                   I 
                   k 
                 
               
               = 
               
                 
                   
                     
                       a 
                       k 
                     
                     · 
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         
                           ϕ 
                           k 
                         
                         ) 
                       
                     
                   
                   + 
                   
                     j 
                     · 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         
                           ϕ 
                           k 
                         
                         ) 
                       
                     
                   
                 
                 
                   cos 
                   ⁡ 
                   
                     ( 
                     
                       ϕ 
                       k 
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 =&gt;   
               
               ⁢ 
               
                 A 
                 k 
               
             
             = 
             
               
                 
                   J 
                   k 
                 
                 
                   I 
                   k 
                 
               
               = 
               
                 
                   a 
                   k 
                 
                 + 
                 
                   j 
                   · 
                   
                     tan 
                     ⁡ 
                     
                       ( 
                       
                         ϕ 
                         k 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     The corrected signal Z I  can then be rewritten as: 
     
       
         
           
             
               
                 
                   
                     Z 
                     l 
                   
                   = 
                   
                     
                       R 
                       l 
                     
                     - 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           
                             - 
                             
                               K 
                               2 
                             
                           
                         
                         
                           k 
                           = 
                           
                             K 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         
                           
                             λ 
                             
                               l 
                               , 
                               k 
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 a 
                                 k 
                               
                               + 
                               
                                 j 
                                 · 
                                 
                                   tan 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       ϕ 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             R 
                             _ 
                           
                           
                             - 
                             k 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   10 
                 
               
             
           
         
       
     
     When there is negligible carrier frequency offset (Δf C ˜0) the coefficient λ I,k  is equal to 1 for k equal to I and 0 otherwise. Then Equation 8 can be simplified and we obtain the same compensation as in the receiver described in our co-pending European Patent Application N° EP 01401631.5:
 
 Z   k   =R   k −( a   k   +j .tan (φ k ))   R     −k   Equation 11
 
     The complex term A k  or the simplified terms a k  and tan(φ k ) are called the I/Q mismatch coefficients and are calculated during a calibration procedure; various calibration procedures are available and a suitable procedure is described below. 
     As shown in the upper part of  FIG. 5 , each received sub-carrier is compensated for the I/Q mismatch by removing the cross-talk that is generated by a single symmetric sub-carrier when there is no carrier frequency offset. 
     When the carrier frequency offset becomes significant cross-talk is generated by all the other sub-carriers. However, since the function |sin (πN.x)/sin (πx)| decreases quickly when |x| increases, |λ I,k | also decreases quickly with increasing values of 
                        k   -   l     N     -     2   ⁢       Δ   ⁢           ⁢     f   c         f   s                .         
It has been shown by simulation that it is possible to obtain sufficient compensation while reducing the complexity of the implementation by compensating the cross-talk of a limited number of sub-carriers only. For instance, three or even two sub-carriers (out of 64 in Hiperlan 2) are enough in some cases.
 
     As shown in the lower part of  FIG. 5 , the cross-talk to be subtracted from each received sub-carrier is calculated from a selected number k of other sub-carriers which have the highest λ I,k  values (see equation 6) which corresponds to 
             N   ⁢              k   -   l     N     -     2   ⁢       Δ   ⁢           ⁢     f   c         f   s                      
being smaller than a chosen maximum value. For instance the criterion
 
               N   ⁢              k   -   l     N     -     2   ⁢       Δ   ⁢           ⁢     f   c         f   s                  ≤   2         
can be selected.
 
     The corrected signal Z I  becomes: 
     
       
         
           
             
               
                 
                   
                     
                       Z 
                       l 
                     
                     = 
                     
                       
                         R 
                         l 
                       
                       - 
                       
                         
                           ∑ 
                           k 
                         
                         ⁢ 
                         
                           
                             
                               λ 
                               
                                 l 
                                 , 
                                 k 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   a 
                                   k 
                                 
                                 + 
                                 
                                   j 
                                   . 
                                   
                                     tan 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         ϕ 
                                         k 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             
                               R 
                               _ 
                             
                             
                               - 
                               k 
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           with 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       N 
                       ⁢ 
                       
                          
                         
                           
                             
                               k 
                               - 
                               l 
                             
                             N 
                           
                           - 
                           
                             2 
                             ⁢ 
                             
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   f 
                                   c 
                                 
                               
                               
                                 f 
                                 s 
                               
                             
                           
                         
                          
                       
                     
                     ≤ 
                     max_value 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   12 
                 
               
             
           
         
       
     
     A calibration procedure is used to calculate the mismatch coefficients a k  and tan (φ k ), for each sub-carrier k that are used to implement the I/Q mismatch compensation. The calibration procedure is preferably executed once only, after power up of the system and is carried out before normal data transmission in order to avoid adding any overhead to the normal operation. The calibration method may be changed depending on the actual values of the analogue components mismatch in the various components of the RF front-end. The calibration method described below is similar to that described in our co-pending European Patent Application N° EP 01401631.5. 
     In  FIG. 6 , we illustrate by way of example a preferred configuration of the OFDM transceiver enabling the calibration of the I and Q paths. In addition to the receiver section, the transceiver comprises a transmitter section including digital-to-analogue converters (‘DACs’)  20  and  21  that normally convert digital I and Q transmission signals from the base-band DSP to analogue I and Q signals, transmitter low pass filters  22  and  23  that filter the I and Q transmission analogue signals respectively and IF mixers  8 ′ and  9 ′ that shift the transmitted signal from baseband to an intermediate frequency. During the calibration mode of operation of the transceiver, two training signals S t1  and S t2  are generated by the base-band DSP and sent through I and Q calibration paths  24 ,  25  and  25 ′ (shown in thick lines in  FIG. 6 ), which are different from the normal data signal path and are created using switches S 1 , S 2 , S 3  S 4 , S 5  and S 6 . This structure is sufficient for the training of the receiver if the transmitter DACs  20  and  21  and the IF mixers  8 ′ and  9 ′ are well matched. However, as described in our co-pending European Patent Application N° EP 01401631.5, further calibration paths (not shown) are preferably provided to invert periodically the route of the I and Q training signals S t1  and S t2  so as to compensate for residual mismatch of the transmitter DACs  20  and  21  and IF mixers  8 ′ and  9 ′. 
     The first training signal S t1  is used to measure the crosstalk coefficient for the negative sub-carriers (k=−1 to −K:2). S t1  is a time domain signal made of at least one symbol. It can either be stored as a set of time domain samples or be obtained by OFDM modulation of a plurality of stored frequency domain components D k =B k e jP     k    mapped on sub-carriers of frequency (f c +k f s /N). In a preferred embodiment, S t1  comprises a single OFDM symbol corresponding to the modulation of K/2 non-zero components D 1  to D K/2  such that B k =1, P k =0, and thus D k =1 for all k from 1 to K/2. 
     After insertion of the cyclic extension, the I and Q components are obtained and, for the purposes of this embodiment of the present invention, are used to train the receive path (although it would also be possible to use them to train the transmit path). Denoting by R k  and R −k  the FFT outputs corresponding to sub-carriers k and −k as described above, the crosstalk coefficients for sub-carrier −k, a −k  and tan (φ k ) are obtained by the following complex operations: 
               a     -   k       =         ℜ   ⁡     (       R     -   k         R   k   *       )       ⁢           ⁢   and   ⁢           ⁢     tan   ⁡     (     ϕ     -   k       )         =         ??   ⁡     (       R     -   k         R   k   *       )       ⁢           ⁢   with   ⁢           ⁢   k     =     1   ⁢           ⁢   to   ⁢           ⁢     K   /   2                 
and where the asterisk * denotes complex conjugation.
 
     The second training signal S t2  is used to measure the crosstalk coefficient for the positive sub-carriers (k=1 to K:2). S t2  comprises a single OFDM symbol corresponding to the modulation of K/2 non-zero components D −1  to D −K/2  such that B −k =1, P −k =0, and thus D −k =1 for all k from −1 to −K/2. In the same way as the first training signal, the crosstalk coefficients for sub-carrier k, a k  and tan (φ k ) are obtained by the following complex operations: 
     
       
         
           
             
               a 
               
                 - 
                 k 
               
             
             = 
             
               
                 
                   ℜ 
                   ⁡ 
                   
                     ( 
                     
                       
                         R 
                         k 
                       
                       
                         R 
                         
                           - 
                           k 
                         
                         * 
                       
                     
                     ) 
                   
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 and 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   tan 
                   ⁡ 
                   
                     ( 
                     
                       ϕ 
                       k 
                     
                     ) 
                   
                 
               
               = 
               
                 
                   
                     ?? 
                     ⁡ 
                     
                       ( 
                       
                         
                           R 
                           k 
                         
                         
                           R 
                           
                             - 
                             k 
                           
                           * 
                         
                       
                       ) 
                     
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   with 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   k 
                 
                 = 
                 
                   1 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   to 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     K 
                     / 
                     2. 
                   
                 
               
             
           
         
       
     
       FIG. 7  illustrates a preferred implementation of the compensation with the chosen maximum value of 1. In this case, the interference from only 2 sub-carriers is removed from each sub-carrier of index I, although it will be appreciated that this implementation can readily be extended to compensation of the cross-talk from a greater number of sub-carriers. The indexes k 1  and k 2  of these sub-carriers are directly computed for each value of I since the frequency offset and the chosen maximum value are known. 
     In more detail, the sub-carriers numbers of indexes I, k 1  and k 2  from the OFDM demodulation FFT circuit  17  are selected by a selection circuit  26  for each value of the index I in turn as defined by a counter  27 . In this preferred implementation, the values λ I,k1  and λ I,k2  (see equation 6) are pre-computed and stored in a look-up table  28  for the various values of/and of the frequency offset, although it would also be possible to compute them directly as and when needed. The complex numbers A(k)=J k /I k =a k +j tan (φ k ) have also been computed during the calibration phase and are stored in another look-up table  29 . Then for each FFT sub-carrier output of index I, complex multiplications are performed of A k1  by λ I,k1  in a multiplier  30  and of A k2  by λ I,k2  in a multiplier  31 . Complex conjugations of R k1  and R k2  are performed in circuits  32  and  33  and the results are multiplied by the outputs of multipliers  30  and  31  in multipliers  34  and  35  respectively. Two complex subtractions of R k1  and R k2  from R I  are performed in a sum circuit  36  to obtain the compensated symbol Z I . 
     The number of operations per symbol depends on the chosen maximum value, but the resulting complexity is typically small compared to other blocks like FFT  15  and in any case much smaller than digital I/Q generation complexity. 
     In order to evaluate the effect of the I/Q mismatch compensation of the above embodiments of the invention, simulations of packet error rate (PER) were performed on a Hiperlan2 simulator with a carrier frequency offset ranging from −310 kHz to +310 kHz, which is a range wider than the ETSI specifications (40 PPM between transmitter and receiver clock, corresponding to +/− 200 kHz with a 5 GHz channel central frequency). 
     The results from simulations that implement the I/Q mismatch compensation algorithm described by Equation 12 (with max_value equal to 1) are shown in  FIG. 8 . For comparison, the results from simulations without I/Q mismatch compensation and from simulations implementing the algorithm described by Equation 11 are shown in the same Figure. 
     It will be noted that when the carrier frequency offset is close to zero, the algorithm described by Equation 12 and that described by Equation 11 produce the same improvement in data transmission and the PER is substantially lower than that obtained without I/Q mismatch compensation. 
     However, when the carrier frequency offset becomes bigger (more than a few tens of kHz) the data transmission quality becomes much better for the algorithm described by Equation 12 than that described by Equation 11. Above a frequency offset of 70 kHz, it can be seen that the algorithm described by Equation 11 can even degrade the data transmission quality compared to no I/Q mismatch compensation at all. This is explained by the fact that the compensation method calculates the cross-talk to be removed from the received sub-carrier using a single symmetric sub-carrier despite the fact that the cross-talk was generated by several other sub-carriers.