Patent Publication Number: US-2012039192-A1

Title: Interference cancellation

Description:
TECHNICAL FIELD 
     The invention relates to methods and apparatus for use in the cancellation of carrier frequency offset interference in communication systems, and in particular the cancellation of carrier frequency offset interference in orthogonal frequency division multiple access (OFDMA) communication systems, spatial division multiple access (SDMA) OFDMA communication systems and multiple-input multiple-output (MIMO) OFDMA communication systems. 
     BACKGROUND ART 
     In orthogonal frequency division multiplex (OFDM) systems, a number of orthogonal frequency carriers are used to carry respective streams of data. It is necessary for the frequencies used for the carriers to be synchronised in the transmitter and receiver, otherwise a frequency deviation will exist between the carriers, causing a loss of orthogonality and therefore inter-carrier interference. Synchronisation issues can arise from the oscillators in the transmitter and receiver being mismatched, or a Doppler shift caused by the movement of one or both of the transmitter and receiver. 
     To prevent the loss of orthogonality, it is necessary for the receiver to estimate the amount by which the frequency carriers used to transmit the signals are offset from the desired carriers, and to apply this carrier frequency offset (CFO) to the received signals. 
     Typically, a predefined sequence of symbols is transmitted in order to facilitate CFO estimation. Various methods are known, often based on some form of autocorrelation process. Any CFO estimation algorithm will be vulnerable to errors arising from distortion of the sequence by the communication channel. 
     Any errors in the estimation of the carrier frequency offset in a downlink direction (for example from a base station to a mobile station) will result in residual synchronisation errors in the uplink direction. These residual errors cause carrier frequency offset interference (CFOI), i.e. interference (loss of orthogonality) that results from errors in the CFO estimation. 
     A similar requirement to correct carrier frequency offset exists in orthogonal frequency division multiple access (OFDMA) systems, in which users are assigned a subset of the available carriers. 
     As above, in addition to correcting the frequency offset for a downlink from a base station to a mobile station (for example), it is necessary to correct the frequency offset in the uplink. In this case, however, the frequency deviation for each user in the uplink will be different, so the correction of the frequency of one user cannot be accomplished individually in the base station, since if the offset is corrected for one user, it misaligns the other users. 
     The situation is further complicated in the uplink direction of a spatial division multiple access OFDMA (SDMA-OFDMA) system, for example as shown in  FIG. 1 . Each mobile station/user  2  has a respective oscillator and pair of antennas, which means where mobile stations  2  share one or more frequency carriers for transmitting data to the base station  4 , there can be a different carrier frequency offset for each mobile station  2  using the carrier. Therefore, it is not possible to apply a single CFO to the signals received on each carrier. 
     The CFOI caused by the residual CFO from the downlink direction will include self-interference, interference on the shared carriers from the other mobile station(s)  2  using that carrier and interference from other mobile station(s)  2  using different carriers. 
     One known solution to this problem is described in “Frequency Offset Compensation Scheme Using Interference Cancellation in Reverse Link of OFDM/SDMA systems” by Naoto Egashira, Takahiko Saba,  IEICE TRANS, Fundamentals , Vol. E89-A, No. 10 October 2006 which proposes a frequency offset compensation scheme without feedback transmission by adapting the principle of parallel interference cancellation (PIC) and iteration of the cancellation and replica generation process after equalisation. 
     However the combination of PIC and iteration increases the computational complexity enormously. 
     Therefore, it is desirable to provide an alternative way of cancelling the carrier frequency offset interference, that does not substantially increase the computational complexity, and that is simple to implement in a receiver. 
     DISCLOSURE OF INVENTION 
     A first aspect of the invention provides a first device for use in a communication system, the communication system further comprising a plurality of second devices, the system having a plurality of orthogonal frequency carriers available for transmissions, each second device having a respective carrier frequency offset estimated from signals received from the first device, each of the second devices transmitting a respective stream of symbols using the respective estimated carrier frequency offset and one or more frequency carriers selected from the plurality of orthogonal frequency carriers, the first device comprising receiver circuitry for receiving respective signals from each of the second devices; a channel estimator for generating, from the received signals, an estimate of the channel over which the signals have been transmitted; an interference estimator for generating, from the received signals, an estimate of interference at the first device caused by errors in the carrier frequency offsets estimated by each second device; and circuitry for equalising the received signals using the estimate of the channel and the estimate of the interference. 
     According to a second aspect of the invention, there is provided a method for operating a first device in a communication system, the system further comprising a plurality of second devices, the system having a plurality of orthogonal frequency carriers available for transmissions, each second device having a respective carrier frequency offset estimated from signals received from the first device, each of the second devices transmitting a respective stream of symbols using the respective estimated carrier frequency offset and one or more frequency carriers selected from the plurality of orthogonal frequency carriers, the method in the first device comprising receiving respective signals from each of the second devices; generating, from the received signals, an estimate of the channel over which the signals have been transmitted; generating, from the received signals, an estimate of interference at the first device caused by errors in the carrier frequency offsets estimated by each second device; and equalising the received signals using the estimate of the channel and the estimate of the interference. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an exemplary SDMA-OFDMA system; 
         FIG. 2  is a block diagram of a first device in accordance with a first embodiment of the invention; 
         FIG. 3  is a flow chart illustrating the steps in a method in accordance with the first embodiment of the invention; 
         FIG. 4  is a block diagram of a first device in accordance with a second embodiment of the invention; 
         FIG. 5  is a flow chart illustrating the steps in a method in accordance with the second embodiment of the invention; and 
         FIG. 6  is a graph illustrating the performance of the first devices of  FIGS. 2 and 4  over conventional devices. 
     
    
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     The invention is concerned with the receipt of signals in an OFDMA communication system that is using SDMA as described above with reference to  FIG. 1 , or MIMO. 
     The problem solved by the invention is illustrated in more detail below. 
     Consider six users (MS 1 , MS 2 , MS 3 , MS 4 , MS 5 , MS 6  in  FIG. 1 )  2  each transmitting data to the base station  4 , with the users  2  being paired (e.g. MS 1  and MS 2 , MS 3  and MS 4 , MS 5  and MS 6 ) such that each user  2  in a pair uses the same bandwidth (carriers). The users  2  are divided into two groups, group  1  comprising MS 1 , MS 3  and MS 5  and group  2  comprising MS 2 , MS 4  and MS 6 , so there is no overlap in the carriers used within a group. 
     An interference matrix Π is constructed for each group which includes the estimates of the frequency offsets for each of the users  2  in that group. The interference matrix Π is given by: 
     
       
         
           
             
               
                 
                   Π 
                   = 
                   
                     
                       ∑ 
                       u 
                       
                         N 
                         u 
                       
                     
                      
                     
                       
                         F 
                         H 
                       
                        
                       
                         E 
                         u 
                       
                        
                       F 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where F is an inverse Discrete Fourier Transform matrix of dimension N×V (where N is the number of users and V is the number of sub-carriers for each user) and E defines the distortive effect of the carrier frequency offset on the signal of a particular user in the time domain. 
     The output of each antenna in the receiver in the base station  4  is given by 
         G   r1 =Π 1   S   11 +Π 2   S   21   (2)
 
         G   r2 =Π 1   S   12 +Π 2   S   22   (3)
 
     where G r1  and G r2  denote the outputs from the first and second antennas respectively, Π 1  and Π 2  denote the interference matrices for group  1  and group  2  respectively, and S xy  denotes the signal received at antenna y from antenna x in the absence of carrier frequency offset. “x” can also be used to index the two users sharing subcarriers in a SDMA-OFDMA system. 
     It can be seen that the interference matrices of the two groups are not the same, so it is not possible to cancel the multiuser access interference jointly for both groups at the same time. 
     It is desirable for the signals of the two groups to be split by demultiplexing and equalisation. However, if there is a residual frequency offset, it is not possible to make the equalisation accurate, and in turn the separated CFOI cancellation processes for the two groups cannot be achieved. 
       FIG. 2  shows an exemplary device  10  in accordance with a first embodiment of the invention. In this embodiment, there are two groups of users  2  transmitting signals to the device  10 , as described above with reference to  FIG. 1 . Although the invention is shown as a device for receiving signals, it will be appreciated that the device can also be adapted to transmit signals. 
     The device  10  comprises two antennas  12  that each receives signals over an air interface. The signals received by each antenna  12  are processed by a respective guard interval remover  16  for removing the guard interval or cyclic prefix in the received signals to give a signal G rm , (where m identifies the antenna) and a respective FFT block  18  for performing a fast Fourier transform on the signal G rm . 
     It will be appreciated that the receiver front end comprising the antennas  12 , guard interval removers  16  and FFT blocks  18  are well known in the art, and will not be described further herein. Moreover, it will be appreciated that the receiver front-end of the device  10  can be implemented in an alternative form to that illustrated. 
     The output of the FFT block  18  for each antenna  12  is provided to an equaliser  20 . 
     A channel estimator  22  is provided that generates a matrix H representing the effect of the channel on the signals transmitted from the users/transmitters  2 . Although not shown in  FIG. 2 , the channel estimator  22  receives copies of the signals received by each of the antennas  12  (with or without the guard interval). The output of the channel estimator  22  is the matrix H. Methods for determining the channel estimate matrix H are conventional, for example making use of a predefined sequence in the transmitted signals, and will not be described further herein. 
     In this embodiment of the invention, the cancellation or compensation of the carrier frequency offset interference (CFOI) is performed during equalisation. In particular, it is considered that the effect of the CFOI is part of the channel response. 
     Thus, the receiver architecture  10  comprises a carrier frequency offset estimator  24  that generates a matrix Π for each group of users that estimates the effect of the carrier frequency offset interference in the received signals for each of the users  2  in that group. Although not shown in  FIG. 2 , the carrier frequency offset estimator  24  receives copies of the signals received by each of the antennas  12  (with or without the guard interval). As with the channel estimate matrix H, the interference matrices Π can be determined by making use of predefined sequences in the transmitted signals. Again, methods for determining these matrices will be known to a person skilled in the art, and will not be described further herein. 
     A combiner  26  combines the CFOI estimate matrices Π 1  and Π 2  and the channel estimate matrix H to give a matrix Ĥ 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       ^ 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               
                                 Π 
                                 1 
                               
                                
                               
                                 H 
                                 11 
                                 u 
                               
                             
                           
                           
                             
                               
                                 Π 
                                 2 
                               
                                
                               
                                 H 
                                 21 
                                 u 
                               
                             
                           
                         
                         
                           
                             
                               
                                 Π 
                                 1 
                               
                                
                               
                                 H 
                                 12 
                                 u 
                               
                             
                           
                           
                             
                               
                                 Π 
                                 2 
                               
                                
                               
                                 H 
                                 22 
                                 u 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       H 
                       ^ 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               
                                 ∑ 
                                 
                                   
                                     u 
                                     = 
                                     1 
                                   
                                   , 
                                   3 
                                   , 
                                   5 
                                 
                               
                                
                               
                                 
                                   F 
                                   H 
                                 
                                  
                                 
                                   E 
                                   1 
                                   u 
                                 
                                  
                                 
                                   FH 
                                   11 
                                   u 
                                 
                               
                             
                           
                           
                             
                               
                                 ∑ 
                                 
                                   
                                     u 
                                     = 
                                     2 
                                   
                                   , 
                                   4 
                                   , 
                                   6 
                                 
                               
                                
                               
                                 
                                   F 
                                   H 
                                 
                                  
                                 
                                   E 
                                   2 
                                   u 
                                 
                                  
                                 
                                   FH 
                                   21 
                                   u 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ∑ 
                                 
                                   
                                     u 
                                     = 
                                     1 
                                   
                                   , 
                                   3 
                                   , 
                                   5 
                                 
                               
                                
                               
                                 
                                   F 
                                   H 
                                 
                                  
                                 
                                   E 
                                   1 
                                   u 
                                 
                                  
                                 
                                   FH 
                                   12 
                                   u 
                                 
                               
                             
                           
                           
                             
                               
                                 ∑ 
                                 
                                   
                                     u 
                                     = 
                                     2 
                                   
                                   , 
                                   4 
                                   , 
                                   6 
                                 
                               
                                
                               
                                 
                                   F 
                                   H 
                                 
                                  
                                 
                                   E 
                                   2 
                                   u 
                                 
                                  
                                 
                                   FH 
                                   22 
                                   u 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     which is provided to the equaliser  20 . 
     The equaliser  20  processes the signals from each FFT block  18  with Ĥ to give streams of output symbols for each antenna  12  which are provided to a processing block  28  for further processing. The processing block  28  is conventional, and its operation will not be described further herein. 
     In a MMSE detection algorithm, the operation of the equaliser  20  can be represented by: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             ~ 
                           
                           1 
                         
                          
                         
                           ( 
                           k 
                           ) 
                         
                       
                       
                         
                           
                             X 
                             ~ 
                           
                           2 
                         
                          
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 H 
                                 ^ 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             H 
                           
                            
                           
                             
                               H 
                               ^ 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             
                               n 
                               T 
                             
                             SNR 
                           
                            
                           
                             I 
                             
                               n 
                               T 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       
                         
                           H 
                           ^ 
                         
                          
                         
                           ( 
                           k 
                           ) 
                         
                       
                       [ 
                       
                         
                           
                             G 
                             
                               r 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                            
                           
                             ( 
                             k 
                             ) 
                           
                         
                         
                           
                             G 
                             
                               r 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                            
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     where {tilde over (X)} 1 (k) is the estimated transmitted signal from one of the users  2  of group  1  over a carrier k and {tilde over (X)} 2 (k) is the estimated transmitted signal from the corresponding user  2  in group  2  that is using the same carrier k, n T  is the number of transmit antennas and SNR is a signal-to-noise ratio. 
     A method of receiving a data transmission in accordance with the invention is shown in  FIG. 3 . In step  101 , the first (receiving) device  10  receives a respective set of signals from each of the second (transmitting) devices  2 . Each of the signals has been transmitted from the second devices  2  using a carrier frequency offset determined from signals previously received from the first device  2  and a frequency carrier selected from a set of frequency carriers (which are orthogonal). 
     The first device  10  generates an estimate of the channels over which the signals have been transmitted (step  103 ). 
     As discussed above, there will be interference between the transmissions from the second devices  2  caused by errors in the estimation of the frequency offset in the opposite link (i.e. from the first device  10  to the second devices  2 ). Therefore, the first device  10  generates an estimate of the interference in the received signals caused by errors in the carrier frequency offsets estimated by each second device  2  (step  105 ). 
     In step  107 , the first device equalises the received signals using the determined estimates to generate an output stream of data symbols. 
       FIG. 4  shows an exemplary device  30  in accordance with a second embodiment of the invention. In this embodiment, there are two groups of users  2  transmitting signals to the device  30  as shown in  FIG. 1 . Again, although the invention is shown as a device for receiving signals, it will be appreciated that the device  30  can also be adapted to transmit signals. 
     In this embodiment, the cancellation or compensation of the carrier frequency offset interference (CFOI) is performed in two steps. In the first step, the CFOI for devices within each of the groups (referred to as intra-group interference) is cancelled in parallel, and in the second step, the remaining interference from errors in the carrier frequency offset is performed jointly with equalisation. 
     The device  30  comprises two antennas  12 , guard interval removers  16  and FFT blocks  18  as described above with reference to  FIG. 1 . 
     In this embodiment, the output of each FFT block  18  is provided to a block  32  that cancels the interference (CFOI) within each of the groups caused by errors in the carrier frequency offsets of the second devices  2 . According to this embodiment, the cancellation for each group is performed in parallel. In alternative embodiments, the cancellation can be performed for one of the groups, followed by the cancellation for the other group. 
     The device  30  is provided with a CFOI estimator  34  as described above with reference to the first embodiment. In this embodiment, the CFOI estimator  34  generates two interference matrices Π 1  and Π 2 , one for each group of users, and provides these matrices to block  32 . Although not shown in  FIG. 4 , the CFOI estimator  34  receives copies of the signals received by each of the antennas  12  (with or without the guard interval). 
     The interference canceller  32  has two parallel processing branches, with each processing branch cancelling the interference for one of the two groups. The MMSE partial interference cancellation in block  32  is given by: 
     Parallel processing branch  1  (cancellation of the interference in group  1 ): 
     
       
         
           
             
               
                 
                   
                     E 
                     
                       r 
                        
                       
                           
                       
                        
                       1 
                     
                     1 
                   
                   = 
                   
                     
                       
                         
                           
                             Π 
                             1 
                             H 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   Π 
                                   1 
                                 
                                  
                                 
                                   Π 
                                   1 
                                   H 
                                 
                               
                               + 
                               
                                 
                                   1 
                                   SNR 
                                 
                                  
                                 I 
                               
                             
                             ) 
                           
                         
                         
                           - 
                           1 
                         
                       
                        
                       
                         G 
                         
                           r 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             
                               Π 
                               1 
                               H 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     Π 
                                     1 
                                   
                                    
                                   
                                     Π 
                                     1 
                                     H 
                                   
                                 
                                 + 
                                 
                                   
                                     1 
                                     SNR 
                                   
                                    
                                   I 
                                 
                               
                               ) 
                             
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           Π 
                           1 
                         
                          
                         
                           S 
                           11 
                         
                       
                       + 
                       
                         
                           
                             
                               Π 
                               1 
                               H 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     Π 
                                     1 
                                   
                                    
                                   
                                     Π 
                                     1 
                                     H 
                                   
                                 
                                 + 
                                 
                                   
                                     1 
                                     SNR 
                                   
                                    
                                   I 
                                 
                               
                               ) 
                             
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           Π 
                           2 
                         
                          
                         
                           S 
                           21 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     E 
                     
                       r 
                        
                       
                           
                       
                        
                       2 
                     
                     1 
                   
                   = 
                   
                     
                       
                         
                           
                             Π 
                             1 
                             H 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   Π 
                                   1 
                                 
                                  
                                 
                                   Π 
                                   1 
                                   H 
                                 
                               
                               + 
                               
                                 
                                   1 
                                   SNR 
                                 
                                  
                                 I 
                               
                             
                             ) 
                           
                         
                         
                           - 
                           1 
                         
                       
                        
                       
                         G 
                         
                           r 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             
                               Π 
                               1 
                               H 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     Π 
                                     1 
                                   
                                    
                                   
                                     Π 
                                     1 
                                     H 
                                   
                                 
                                 + 
                                 
                                   
                                     1 
                                     SNR 
                                   
                                    
                                   I 
                                 
                               
                               ) 
                             
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           Π 
                           1 
                         
                          
                         
                           S 
                           12 
                         
                       
                       + 
                       
                         
                           
                             
                               Π 
                               1 
                               H 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     Π 
                                     1 
                                   
                                    
                                   
                                     Π 
                                     1 
                                     H 
                                   
                                 
                                 + 
                                 
                                   
                                     1 
                                     SNR 
                                   
                                    
                                   I 
                                 
                               
                               ) 
                             
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           Π 
                           2 
                         
                          
                         
                           S 
                           22 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Parallel processing branch  2  (cancellation of the interference in group  2 ): 
     
       
         
           
             
               
                 
                   
                     E 
                     
                       r 
                        
                       
                           
                       
                        
                       1 
                     
                     2 
                   
                   = 
                   
                     
                       
                         
                           
                             Π 
                             2 
                             H 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   Π 
                                   2 
                                 
                                  
                                 
                                   Π 
                                   2 
                                   H 
                                 
                               
                               + 
                               
                                 
                                   1 
                                   SNR 
                                 
                                  
                                 I 
                               
                             
                             ) 
                           
                         
                         
                           - 
                           1 
                         
                       
                        
                       
                         G 
                         
                           r 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             
                               Π 
                               2 
                               H 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     Π 
                                     2 
                                   
                                    
                                   
                                     Π 
                                     2 
                                     H 
                                   
                                 
                                 + 
                                 
                                   
                                     1 
                                     SNR 
                                   
                                    
                                   I 
                                 
                               
                               ) 
                             
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           Π 
                           1 
                         
                          
                         
                           S 
                           11 
                         
                       
                       + 
                       
                         
                           
                             
                               Π 
                               2 
                               H 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     Π 
                                     2 
                                   
                                    
                                   
                                     Π 
                                     2 
                                     H 
                                   
                                 
                                 + 
                                 
                                   
                                     1 
                                     SNR 
                                   
                                    
                                   I 
                                 
                               
                               ) 
                             
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           Π 
                           2 
                         
                          
                         
                           S 
                           21 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     E 
                     
                       r 
                        
                       
                           
                       
                        
                       2 
                     
                     2 
                   
                   = 
                   
                     
                       
                         
                           
                             Π 
                             2 
                             H 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   Π 
                                   2 
                                 
                                  
                                 
                                   Π 
                                   2 
                                   H 
                                 
                               
                               + 
                               
                                 
                                   1 
                                   SNR 
                                 
                                  
                                 I 
                               
                             
                             ) 
                           
                         
                         
                           - 
                           1 
                         
                       
                        
                       
                         G 
                         
                           r 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             
                               Π 
                               2 
                               H 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     Π 
                                     2 
                                   
                                    
                                   
                                     Π 
                                     2 
                                     H 
                                   
                                 
                                 + 
                                 
                                   
                                     1 
                                     SNR 
                                   
                                    
                                   I 
                                 
                               
                               ) 
                             
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           Π 
                           1 
                         
                          
                         
                           S 
                           12 
                         
                       
                       + 
                       
                         
                           
                             
                               Π 
                               2 
                               H 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     Π 
                                     2 
                                   
                                    
                                   
                                     Π 
                                     2 
                                     H 
                                   
                                 
                                 + 
                                 
                                   
                                     1 
                                     SNR 
                                   
                                    
                                   I 
                                 
                               
                               ) 
                             
                           
                           
                             - 
                             1 
                           
                         
                          
                         
                           Π 
                           2 
                         
                          
                         
                           S 
                           22 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     where E rm   n  are vectors after partial interference cancellation for either the first group of users or the second group of users by 
     
       
         
           
             
               
                 ( 
                 
                   
                     
                       Π 
                       1 
                     
                      
                     
                       Π 
                       1 
                       H 
                     
                   
                   + 
                   
                     
                       1 
                       SNR 
                     
                      
                     I 
                   
                 
                 ) 
               
               
                 - 
                 1 
               
             
              
             
                 
             
              
             or 
              
             
                 
             
              
             
               
                 ( 
                 
                   
                     
                       Π 
                       2 
                     
                      
                     
                       Π 
                       2 
                       H 
                     
                   
                   + 
                   
                     
                       1 
                       SNR 
                     
                      
                     I 
                   
                 
                 ) 
               
               
                 - 
                 1 
               
             
           
         
       
     
     respectively, m is the receive antenna index and n is the index of parallel branches  14 . 
     As in the first embodiment, a channel estimator  36  is provided to generate a matrix H representing the effect of the channel on the signals transmitted from the second devices  2 . Although not shown in  FIG. 4 , the channel estimator  36  receives copies of the signals received by each of the antennas  12  (with or without the guard interval). The output of the channel estimator  36  is the matrix H, and this matrix is provided to a combiner  37 . 
     The combiner  37  also receives the interference matrices Π 1  and Π 2  from the CFOI estimator  34  and combines them with the channel estimate matrix H to give Ĥ for each of the parallel processing branches as shown below: 
     For parallel branch  1 : 
     
       
         
           
             
               
                 
                   
                     H 
                     ^ 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             H 
                             11 
                           
                         
                         
                           
                             
                               
                                 
                                   Π 
                                   1 
                                   H 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         Π 
                                         1 
                                       
                                        
                                       
                                         Π 
                                         1 
                                         H 
                                       
                                     
                                     + 
                                     
                                       
                                         1 
                                         SNR 
                                       
                                        
                                       I 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               Π 
                               2 
                             
                              
                             
                               H 
                               21 
                             
                           
                         
                       
                       
                         
                           
                             H 
                             12 
                           
                         
                         
                           
                             
                               
                                 
                                   Π 
                                   1 
                                   H 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         Π 
                                         1 
                                       
                                        
                                       
                                         Π 
                                         1 
                                         H 
                                       
                                     
                                     + 
                                     
                                       
                                         1 
                                         SNR 
                                       
                                        
                                       I 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               Π 
                               2 
                             
                              
                             
                               H 
                               22 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     For parallel branch  2 : 
     
       
         
           
             
               
                 
                   
                     H 
                     ^ 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               
                                 
                                   Π 
                                   2 
                                   H 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         Π 
                                         2 
                                       
                                        
                                       
                                         Π 
                                         2 
                                         H 
                                       
                                     
                                     + 
                                     
                                       
                                         1 
                                         SNR 
                                       
                                        
                                       I 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               H 
                               11 
                             
                           
                         
                         
                           
                             H 
                             21 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   Π 
                                   2 
                                   H 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         Π 
                                         2 
                                       
                                        
                                       
                                         Π 
                                         2 
                                         H 
                                       
                                     
                                     + 
                                     
                                       
                                         1 
                                         SNR 
                                       
                                        
                                       I 
                                     
                                   
                                   ) 
                                 
                               
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               H 
                               12 
                             
                           
                         
                         
                           
                             H 
                             22 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The outputs of the combiner  37  and intra-group interference cancellation block  32  are provided to the equaliser  38 . 
     The equaliser  38  multiplies the signals E rm   n  from each parallel processing branch by Ĥ, as defined above, to equalise the signals and to remove the residual CFOI. 
     As in the first embodiment, in a MMSE detection algorithm, the operation of the equaliser  38 , for each parallel processing branch, can be represented by: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             X 
                             ~ 
                           
                           1 
                         
                          
                         
                           ( 
                           k 
                           ) 
                         
                       
                       
                         
                           
                             X 
                             ~ 
                           
                           2 
                         
                          
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               
                                 H 
                                 ^ 
                               
                                
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             H 
                           
                            
                           
                             
                               H 
                               ^ 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         + 
                         
                           
                             
                               n 
                               T 
                             
                             SNR 
                           
                            
                           
                             I 
                             
                               n 
                               T 
                             
                           
                         
                       
                       ) 
                     
                      
                     
                       
                         
                           H 
                           ^ 
                         
                          
                         
                           ( 
                           k 
                           ) 
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               E 
                               
                                 r 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                               n 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                           
                             
                               E 
                               
                                 r 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                               n 
                             
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     where {tilde over (X)} 1 (k) is the estimated transmitted signal from one of the users  2  of group  1  over a carrier k and {tilde over (X)} 2 (k) is the estimated transmitted signal from the corresponding user  2  in group  2  that is using the same carrier k, n T  is the number of transmit antennas and SNR is a signal-to-noise ratio. 
     The symbols estimated from the first parallel processing branch for group  1  and the symbols estimated from the second parallel processing branch for group  2  can be applied to subsequent demapping, depuncturing and decoding processes in a processing block  40 . 
     In a simplified implementation of this embodiment of the invention, it is possible for the interference canceller  32  to cancel the interference in only one of the groups (i.e. only one of the processing branches needs to be implemented), and the remaining interference can be dealt with during the equalisation process. 
     A method of receiving a data transmission in accordance with this embodiment of the invention is shown in  FIG. 5 . In step  121 , the first (receiving) device  10  receives a respective set of signals from each of the second (transmitting) devices  2 . Each of the signals has been transmitted from the second devices  2  using a carrier frequency offset determined from signals previously received from the first device  2  and a frequency carrier selected from a set of frequency carriers (which are orthogonal). 
     The first device  10  generates an estimate of the channels over which the signals have been transmitted (step  123 ). 
     As there will be interference between the transmissions from the second devices  2  caused by errors in the estimation of the frequency offset in the opposite link (i.e. from the first device  10  to the second devices  2 ), the first device  10  generates an estimate of the interference in the received signals caused by errors in the carrier frequency offsets estimated by each second device  2  (step  125 ). 
     In step  127 , the interference from the errors in the carrier frequency offsets are cancelled for each of the second devices  2  within individual groups using the estimate of the CFOI. 
     In step  129 , the first device equalises the output of step  127  using the determined estimates to remove the remaining interference and to generate an output stream of data symbols. 
       FIG. 6  shows the performance of both embodiments (equalisation with interference cancellation (EIC) and partial interference cancellation and residual interference cancellation with equalisation (P-EIC)) of the invention in relation to perfect synchronisation (i.e. where there are no errors in the carrier frequency offsets), and where there is no synchronisation. Clearly, both embodiments provide an improvement in the performance of the first device (measured in terms of the bit error rate (BER)) over no synchronisation, and the second embodiment (partial interference cancellation) provides enhanced performance over the first embodiment. 
     It will be appreciated that although the first devices  10  and  30  are shown as having two antennas  12 , the invention can be applied to receiver architectures that include more than two antennas, and in particular architectures in which there are M antennas, where M is an integer greater than one. In this respect, it will be appreciated that the equations defined above are relevant to the two antenna embodiment, and are therefore included for illustrative purposes only. 
     It will also be appreciated that the invention can be applied to the cancellation or compensation of carrier frequency offset interference in communication systems other than OFDM, OFDMA and SDMA-OFDMA communication systems. 
     While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments. 
     Variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. 
     A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measured cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope. A computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.