Abstract:
Described herein are various methods for a communication device (e.g., a mobile station) receiving an AQPSK modulated signal (e.g., a VAMOS signal) to estimate a subchannel power imbalance ratio (SCPIR). Advantageously, the methods are not computationally complex and do not suffer from poor numerical performance.

Description:
TECHNICAL FIELD 
       [0001]    The invention relates to methods for estimating a subchannel power imbalance ratio (SCPIR). 
       BACKGROUND 
       [0002]    The Global System for Mobile communication (GSM) is a popular communication system having more than 3 Billion subscribers world-wide. Each year there is a significant increase in the number of GSM subscribers, especially in China and India, where subscriber density is very high. Supporting a large number of simultaneous voice calls is problematic for GSM operators. As subscriber growth increases, especially in areas having a high population density, this problem will become more frequent. Accordingly, solutions have been devised to increase the capacity of GSM networks. 
         [0003]    One recent initiative to increase the capacity of GSM networks is known as Voice Services over Adaptive Multi-user channels on One Slot (VAMOS). VAMOS can double system capacity and help optimize spectrum efficiency and usage of scarce radio resource, while reducing radio base station power consumption. That is, VAMOS doubles the number of users served by a single radio resource. 
         [0004]    In VAMOS, the network assigns the same physical channel (frequency (f) and time-slot (T)) to two different mobile stations (e.g., MS 1  and MS 2 ). Therefore, in the downlink, the network assigns the same physical resources (e.g. frequency/time-slot combination) to two different mobile stations, but allocates to each mobile station one of a pair of a training sequences for their respective channel estimation, thereby doubling the system capacity in case of Traffic channels. The training sequence pair is known a priori to both the mobile stations. The network decides to which of the pair of mobile stations higher transmit power should be allocated based on, for example, the near-far position of paired mobile stations and uses the Adaptive Quadrature Phase Shift Keying (AQPSK) modulation technique to introduce power imbalance between the two paired mobiles stations. 
         [0005]    Thus, in VAMOS, to achieve the doubling of the system capacity, co-channel interference is introduced intentionally. Before decoding, each mobile station therefore has to use an interference cancellation technique to reject the signal energy corresponding to the signal intended for the other mobile station from the received AQPSK modulated signal. But, for better receiver performance, prior to applying the interference rejection technique, the mobile stations needs to detect the power imbalance introduced by the network. 
         [0006]    What is desired, therefore, are methods for use in a receiver for detecting this power imbalance. 
       SUMMARY 
       [0007]    Described herein are various methods for a communication device (e.g., a mobile station) receiving a single carrier signal on which two bit streams (i.e., a first bit stream intended for a first communication device and a second bit stream intended for a second communication device) are modulated to detect the power imbalance between the two bit streams (i.e., subchannels) and, thereby, estimate the subchannel power imbalance ratio (SCPIR). Advantageously, the methods are not computationally complex and do not suffer from poor numerical performance. The two bit streams may be modulated on the single carrier signal using the AQPSK modulation technique to produce, for example, a VAMOS signal. 
         [0008]    In some embodiments, the method helps determine the sign of the SCPIR, which helps in equalization and detection. In these embodiments, a received VAMOS signal is projected to the space spanned by a pair of training sequences included in the VAMOS signal. The ratio of the two parameters produced during the projection gives an estimate of the sign of the SCPIR. In some particular embodiments, the received VAMOS signal is projected to the joint vector space spanned by the training sequences, whereas in other particular embodiments, we assume the vector spaces to be orthogonal, which assumption leads to a slightly less computationally complex method. The process of parameter estimation for these methods may be seen as taking a dot product (inner product) of the received VAMOS signal and users&#39; original training sequences. 
         [0009]    In other embodiments, the methods help determine SCPIR and use a statistical estimation technique to determine the parameters associated with each sub-channel instead of the inner product. Reasonable number of parameters that must be estimated per sub-channel is 3 to 7. 
         [0010]    The choice of which method to employ is a trade-off between implementation complexity and performance. 
         [0011]    Accordingly, in one particular aspect, a method performed by a communication device for estimating a subchannel power imbalance ratio (SCPIR) between a pair of AQPSK subchannels consisting of a first subchannel and a second subchannel is provided. In some embodiments, this method begins with the step of receiving, at the communication device, an AQPSK modulated signal, where the AQPSK modulated signal includes a first signal intended for the communication device and a second signal intended for another communication device, and the first signal includes a first training sequence (TS 1 ) and the second signal includes a second training sequence (TS 2 ) that is paired with TS 1 . Next, the communication device produces from the received AQPSK modulated signal a sample sequence (r). The communication device then (a) uses TS 1  and r to estimate a channel impulse response of length K (K is greater than or equal to 1) for the first subchannel (let h 1  denote the estimated channel impulse response for the first subchannel) and (b) uses TS 2  and r to estimate a channel impulse response of length K for the second subchannel (let h 2  denote the estimated channel impulse response for the second subchannel). Next, the communication device estimates the SCPIR from h 1  and h 2 . 
         [0012]    In some embodiments, K is equal to 1. In these embodiments, the step of determining h 1  comprises determining a dot product of r and TS 1 , where c 1  denotes the determined dot product, and the step of determining h 2  comprises determining a dot product of the r and TS 2 , where c 2  denotes the determined dot product. For example, c 1  may determined using the following equation: 
         [0000]    
       
         
           
             
               
                 c 
                 1 
               
               = 
               
                 
                   ∑ 
                   
                     k 
                     = 
                     0 
                   
                   
                     N 
                     - 
                     1 
                   
                 
                  
                 
                     
                 
                  
                 
                   
                     
                       a 
                       1 
                       * 
                     
                      
                     
                       [ 
                       k 
                       ] 
                     
                   
                    
                   
                     r 
                      
                     
                       [ 
                       k 
                       ] 
                     
                   
                 
               
             
             , 
           
         
       
     
         [0000]    and c 2  may be determined using the following equation: 
         [0000]    
       
         
           
             
               
                 c 
                 2 
               
               = 
               
                 
                   ∑ 
                   
                     k 
                     = 
                     0 
                   
                   
                     N 
                     - 
                     1 
                   
                 
                  
                 
                     
                 
                  
                 
                   
                     
                       a 
                       2 
                       * 
                     
                      
                     
                       [ 
                       k 
                       ] 
                     
                   
                    
                   
                     r 
                      
                     
                       [ 
                       k 
                       ] 
                     
                   
                 
               
             
             , 
           
         
       
     
         [0000]    where a 1  represents TS 1 , a 2  represents TS 2 , r[k] is the kth value of sequence r, and N is the length of the TS 1 , which is equal to the length of TS 2 . In some embodiments where K=1, h 1  and h 2  are determined using the following equation: 
         [0000]    
       
         
           
             
               
                 [ 
                 
                   
                     
                       
                         h 
                         1 
                       
                     
                   
                   
                     
                       
                         h 
                         2 
                       
                     
                   
                 
                 ] 
               
               = 
               
                 D 
                  
                 
                   [ 
                   
                     
                       
                         
                           c 
                           1 
                         
                       
                     
                     
                       
                         
                           c 
                           2 
                         
                       
                     
                   
                   ] 
                 
               
             
             , 
           
         
       
     
         [0000]    where D is a matrix that allows combined energy estimation for the two subchannels. In other embodiments, where K=1, h 1  and h 2  are determined using the following equations, respectively: 
         [0000]    
       
         
           
             
               h 
               1 
             
             = 
             
               
                 c 
                 1 
               
               
                 
                   ∑ 
                   
                     k 
                     = 
                     0 
                   
                   
                     N 
                     - 
                     1 
                   
                 
                  
                 
                   
                      
                     
                       
                         a 
                         1 
                       
                        
                       
                         [ 
                         k 
                         ] 
                       
                     
                      
                   
                   2 
                 
               
             
           
         
       
     
         [0000]    and 
         [0000]    
       
         
           
             
               h 
               2 
             
             = 
             
               
                 c 
                 2 
               
               
                 
                   ∑ 
                   
                     k 
                     = 
                     0 
                   
                   
                     N 
                     - 
                     1 
                   
                 
                  
                 
                   
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                         a 
                         2 
                       
                        
                       
                         [ 
                         k 
                         ] 
                       
                     
                      
                   
                   2 
                 
               
             
           
         
       
     
         [0013]    In some embodiments, the step of estimating the SCPIR comprises determining a ratio of h 1  and h 2 . In other embodiments, the step of estimating the SCPIR includes the following steps: (a) setting an initial estimate of the SCPIR to 20 log 10 of ratio of |h 1 | and |h 2 |, (b) determining whether the value of the initial estimate of the SCPIR is equal to a valid SCPIR value, and (c) if it is determined that the initial estimate of the SCPIR is not equal to a valid SCPIR value, then determining the valid SCPIR value that is closest in value to the initial estimate and choosing this valid SCPIR value as the estimate of the SCPIR. 
         [0014]    In some embodiments K is greater than 1 and h 1  is a column vector having a length of K and h 2  is a column vector having a length of K. In these embodiments, the step of estimating the SCPIR comprises setting an initial estimate of the SCPIR equal to 
         [0000]    
       
         
           
             20 
              
             
                 
             
              
             log 
              
             
                 
             
              
             10 
              
             
                 
             
              
             
               1 
               K 
             
              
             
               
                 ∑ 
                 
                   k 
                   = 
                   0 
                 
                 
                   K 
                   - 
                   1 
                 
               
                
               
                 
                    
                   
                     
                       h 
                       1 
                     
                      
                     
                       [ 
                       k 
                       ] 
                     
                   
                    
                 
                 / 
                 
                   
                      
                     
                       
                         h 
                         2 
                       
                        
                       
                         [ 
                         k 
                         ] 
                       
                     
                      
                   
                   . 
                 
               
             
           
         
       
     
         [0015]    In the embodiments where K&gt;1, h 1  and h 2  may be determined using the following equation: 
         [0000]    
       
         
           
             
               
                 [ 
                 
                   
                     
                       
                         h 
                         1 
                       
                     
                   
                   
                     
                       
                         h 
                         2 
                       
                     
                   
                 
                 ] 
               
               = 
               
                 A 
                  
                 
                     
                 
                  
                 r 
               
             
             , 
           
         
       
     
         [0000]    where A=([A 1 |A 2 ] H [A 1 |A 2 ]) −1 [A 1 |A 2 ] H . In other embodiment where K&gt;1, h 1  and h 2  may be determined using the following equations, respectively: h 1 =((A 1   H A 1 ) −1 A 1   H )r, and h 2 =((A 2   H A 2 ) −1 A 2   H )r. In still other embodiments where K&gt;1, h 1  and h 2  may be determined using the following equations, respectively: h 1 =((A 1   A A 1 ) −1 A 1   H )r, and h 2 =((A 2   H A 2 ) −1 A 2   H )(r−(A 1 h 1 )). 
         [0016]    In another particular aspect, an improved communication device is provided. In some embodiments, the improved communication device includes: (a) an RF module for receiving a carrier signal on which two bit streams, a first bit stream intended for the communication device and a second bit stream intended for another communication device, are modulated and for producing a sample sequence (r) from the received carrier signal; and (b) a subchannel power imbalance ratio (SCPIR) estimator for estimating a ratio of the power used to transmit the first bit stream and the power used to transmit the second bit stream. The first bit stream includes a first training sequence (TS 1 ) and the second bit stream includes a second training sequence (TS 2 ) that is paired with TS 1 . In some embodiments, the SCPIR estimator is configured to: (a) use TS 1  and r to estimate a channel impulse response of length K for a first subchannel, where h 1  denotes the estimated channel impulse response for the first subchannel and K is greater than or equal to 1; (b) use TS 2  and r to estimate a channel impulse response of length K for a second subchannel, where h 2  denotes the estimated channel impulse response for the second subchannel; and (c) estimate the ratio from h 1  and h 2 . 
         [0017]    The above and other aspects and embodiments are described below with reference to the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    The accompanying drawings, which are incorporated herein and form part of the specification, illustrate various embodiments of the present invention and, together with the description, further serve to explain the principles of the invention and to enable a person skilled in the pertinent art to make and use the invention. In the drawings, like reference numbers indicate identical or functionally similar elements. 
           [0019]      FIG. 1  illustrates a communication system according to an embodiment. 
           [0020]      FIG. 2  is a functional diagram of a particular embodiment of a communication device. 
           [0021]      FIGS. 3-6  are flow charts illustrating various processes according to particular embodiments. 
           [0022]      FIG. 7  is a block diagram of a particular embodiment of a data processing system for use in a communication device. 
           [0023]      FIG. 8  is a block diagram illustrating example software components of a communication device. 
       
    
    
     DETAILED DESCRIPTION 
       [0024]    Referring now to  FIG. 1 ,  FIG. 1  illustrates a communication system  100  according to an embodiment. In this example, we will assume communication system  100  is part of a GSM system and that two VAMOS communication devices (communication device  102   a  and communication device  102   b ) are served by a single VAMOS signal  110  transmitted using a base station antenna  108 . That is devices  102   a  and  102   b  form a VAMOS pair.  FIG. 1  shows two bit streams ( 101   a  and  101   b ) and we shall assume that bit stream  101   a  is intended for communication device  102   a  and bit stream  101   b  is intended for communication device  102   b.  In this example, the two bit streams  101  a,b are AQPSK modulated on a single carrier by transmitter  106  to produce VAMOS signal  110 , which is then transmitted using base station antenna  108 . 
         [0025]    As described above, the multiplexing of the two bit streams causes a high level of interference at the input of each communication device  102 . Thus, each communication device  102  requires a robust interference mitigation algorithm for equalization and detection of the bit stream intended for the device. Several such algorithms have been proposed, such as: Successive Interference Cancellation (SIC), Single Antenna MIMO, and Joint Detection (JD). Each of these algorithms requires an estimation of the SCPIR for effective interference mitigation. 
         [0026]    Referring now to  FIG. 2 ,  FIG. 2  is a functional diagram of a particular embodiment of communication device  102   a.  Communication device  102   a  includes an antenna  202  for receiving VAMOS signal  110 , an RF module  204  coupled to antenna  202  for producing a sample sequence (r) from the received signal  110 , an SCPIR estimator  206  coupled to RF module  204  for receiving r and for estimating an SCPIR, and a receiver unit  208  coupled to RF module  204  and SCPIR estimator  206 . Receiver unit  208  receives r and an SCPIR estimate from SCPIR estimator  206 . Based on the SCPIR estimate, receiver unit  208  may select a receiver module to process r to reproduce the transmitted bit stream, which may be further processed by data processing system  220  coupled to an output device (e.g., speaker, display, or other output device). For example, if the SCPIR is a positive value, then receiver unit  208  may select a legacy Single Antenna Interference Cancellation (SAIC) receiver module  210  to detect the bit stream intended for device  102   a,  whereas if the SCPIR is a negative value, then receiver unit  208  may select a SIC or JD receiver module  212  to detect the bit stream. 
         [0027]    Referring now to  FIG. 3 ,  FIG. 3  is a flow chart illustrating a process  300 , according to some embodiments, that is performed by a communication device  102  (e.g., communication device  102   a ). 
         [0028]    Process  300  may begin in step  302 , where the communication device  102   a  receives a carrier signal on which two bit streams are modulated. We shall assume that communication device  102  receives VAMOS signal  110 . As described above, bit stream  101   a  and bit stream  101   b  are AQPSK modulated on a carrier to produce VAMOS signal  110 . 
         [0029]    In step  303 , communication device  102   a  receives VAMOS signal  110  and produces therefrom a sample sequence (r). 
         [0030]    In step  304 , communication device  102   a  determines the training sequence included in bit stream  101   a  (“TS 1 ”) and the training sequence included in bit stream  101   b  (“TS 2 ”). This information may have been signaled to communication device  102   a  before the base station antenna  108  transmitted signal  110 . 
         [0031]    In step  306 , the communication device  102   a  selects an SCPIR estimation method based on the training sequence pair included in VAMOS signal  110 . For example, SCPIR estimator  206  may be operable to perform a number of different SCPIR estimation algorithms and may be configured to select which of these algorithms to use based on which training sequence pair is being used and other system constraints. In some environments there is a limited number of possible training sequence pairs (e.g., 8 pairs) and each pair within this limited set has a different degree of orthogonality (i.e., some training sequence pairs are more orthogonal than others). 
         [0032]    In step  308 , the selected SCPIR estimation method is performed to produce an SCPIR estimate. In step  310 , communication device  102   a  may, based on the SCPIR estimate, select a receiver module to use to further process the received data. For example, as discussed above, if the SCPIR estimate is a positive value, then communication device  102   a  may select the legacy SAIC receiver module  210 , otherwise it may select the SIC or JD receiver module  212 . In step  312 , the selected receiver module is activated and processes the received data. 
         [0033]    Referring now to  FIG. 4 ,  FIG. 4  is flow chart illustrating a process  400  for performing step  308  (i.e., the step in which an estimate of the SCPIR is generated). Process  400  may be performed by SCPIR estimator  206  of communication device  102   a.    
         [0034]    Process  400  may begin in step  402 , where SCPIR estimator  206  receives from RF module  204  the sample sequence r. In step  408 , SCPIR estimator  206  estimates a first channel impulse response (h 1 ) using TS 1  and r, where TS 1  is the training sequence included in bit stream  101   a  (i.e., the bit stream intended for communication device  102   a ). In step  410 , estimator  206  estimates a second channel impulse response (h 2 ) using TS 2  and r, where TS 2  is the training sequence included in bit stream  101   b  (i.e., the bit stream intended for communication device  102   b ). In some embodiments, SCPIR estimator  206  maintains in a data storage system its own copy of each possible training sequence pair and transmitter  106  identifies to SCPIR estimator  206  the training sequences that are included in the bit streams modulated on the VAMOS signal  110 . 
         [0035]    In step  412 , SCPIR estimator  206  determines an initial estimate of the SCPIR using h 1  and h 2 . In step  414 , SCPIR estimator  206  determines whether the initial estimate of the SCPIR is a valid value. In some embodiments, there exists a predefined set of valid SCPIR values (e.g., −10 dB, −8 dB, −4 dB, 0 dB, and 4 dB). Thus, in these embodiments, SCPIR estimator stores all of the valid SCPIR values and determines whether the initial SCPIR estimate is included in this set of stored valid SCPIR values. If the initial SCPIR estimate is included in the set of valid SCPIR values, the SCPIR estimator  206  selects the initial SCPIR estimate as the final estimate (step  415 ). Otherwise, SCPIR estimator  206  determines which of the valid SCPIR values is closest to the initial estimate (step  416 ) and then selects the valid SCPIR value determined in step  416  as the final SCPIR estimate (step  418 ). 
         [0036]    The received VAMOS signal  110  may be modeled as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     r 
                      
                     
                       [ 
                       n 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           
                             - 
                             ∞ 
                           
                         
                         
                           + 
                           ∞ 
                         
                       
                        
                       
                         
                           
                             h 
                             ~ 
                           
                            
                           
                             [ 
                             k 
                             ] 
                           
                         
                          
                         
                           { 
                           
                             
                               
                                 β 
                                 
                                   2 
                                 
                               
                                
                               
                                 
                                   a 
                                   1 
                                 
                                  
                                 
                                   [ 
                                   
                                     n 
                                     - 
                                     k 
                                   
                                   ] 
                                 
                               
                             
                             + 
                             
                               j 
                                
                               
                                 
                                   
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                                     - 
                                     
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                     + 
                     
                       v 
                        
                       
                         [ 
                         n 
                         ] 
                       
                     
                     + 
                     
                       w 
                        
                       
                         [ 
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                   ( 
                   
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                     . 
                     
                         
                     
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         [0000]    where {tilde over (h)} is the channel impulse response (CIR) excluding AQPSK gain, a 1  is the training sequence (in NRZ form) of the first user (first sub-channel) (e.g., TS 1 ), a 2  is the training sequence (in NRZ form) of the second user (second sub-channel) (e.g., TS 2 ), v is the interference, and w is Additive White Gaussian Noise (AWGN). The quantity β determines the power imbalance in the sub-channels. SCPIR in dB (α) is defined in terms of β as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     SCPIR 
                      
                     
                         
                     
                      
                     α 
                   
                   = 
                   
                     10 
                      
                     
                       
                         
                           log 
                           10 
                         
                          
                         
                           ( 
                           
                             
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         [0037]    Eq. 1 can be rewritten in terms of matrices as follows: 
         [0000]        r=A   1   h+jLA   2   h+v+w    (eq. 3), where:
   A 1  is the toeplitz matrix of first user&#39;s training sequence;   A 2  is the matrix of second user&#39;s training sequence having K linearly independent columns, where K is the length of the channel impulse response (the matrices A 1  and A 2  can be constructed as follows:   
 
         [0000]    
       
         
           
             
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                           a 
                           2 
                         
                          
                         
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             ; 
           
         
       
     
         [0000]    h is a CIR, e.g., h is a column vector storing CIR parameters 
         [0000]    
       
         
           
             h 
             = 
             
               [ 
               
                 
                   β 
                    
                   
                     
                       h 
                       ~ 
                     
                      
                     
                       [ 
                       k 
                       ] 
                     
                   
                 
                 
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         [0000]    and v and w are column vectors of interference and AWGN respectively. SCPIR is related to b as follows: 
         [0000]    
       
         
           
             α 
             = 
             
               20 
                
               
                 
                   
                     log 
                     10 
                   
                    
                   
                     ( 
                     
                       1 
                       b 
                     
                     ) 
                   
                 
                 . 
               
             
           
         
       
     
         [0040]    Referring now to  FIG. 5 ,  FIG. 5  is a flow chart illustrating a process  500 , according to one embodiment, for performing steps  408 - 412  of process  400 . Process  500  may begin in step  502 , where SCPIR estimator  206  determines a dot product of r and TS 1 , where c 1  denotes the determined dot product. For example, in step  502 , SCPIR estimator  206  sets c 1  equal to 
         [0000]    
       
         
           
             
               ∑ 
               
                 k 
                 = 
                 0 
               
               
                 N 
                 - 
                 1 
               
             
              
             
               
                 
                   a 
                   1 
                   * 
                 
                  
                 
                   [ 
                   k 
                   ] 
                 
               
                
               
                 
                   r 
                    
                   
                     [ 
                     k 
                     ] 
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    In step  504 , SCPIR estimator  206  determines a dot product of r and TS 2 , where c 2  denotes the determined dot product. For example, in step  504 , SCPIR estimator  206  sets c 2  equal to 
         [0000]    
       
         
           
             
               ∑ 
               
                 k 
                 = 
                 0 
               
               
                 N 
                 - 
                 1 
               
             
              
             
               
                 
                   a 
                   2 
                   * 
                 
                  
                 
                   [ 
                   k 
                   ] 
                 
               
                
               
                 
                   r 
                    
                   
                     [ 
                     k 
                     ] 
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    r[k] is the kth value of sequence r, and N is the length of the TS 1 , which is equal to the length of TS 2 . 
         [0041]    In step  506 , SCPIR estimator  206  uses the following equation to determine h 1  and h 2 : 
         [0000]    
       
         
           
             
               
                 [ 
                 
                   
                     
                       
                         h 
                         1 
                       
                     
                   
                   
                     
                       
                         h 
                         2 
                       
                     
                   
                 
                 ] 
               
               = 
               
                 D 
                  
                 
                   [ 
                   
                     
                       
                         
                           c 
                           1 
                         
                       
                     
                     
                       
                         
                           c 
                           2 
                         
                       
                     
                   
                   ] 
                 
               
             
             , 
           
         
       
     
         [0000]    where D is a matrix that allows combined energy estimation for the two subchannels. 
         [0042]    For example, D can be computed using Least Square or oblique projection based method that allows combined energy estimation for communication devices  102   a  and  102   b.  For instance, in some embodiments: 
         [0000]    
       
         
           
             D 
             = 
             
               
                 
                   [ 
                   
                     
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                            
                           
                             
                                
                               
                                 
                                   a 
                                   1 
                                 
                                  
                                 
                                   [ 
                                   k 
                                   ] 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                            
                           
                             
                               
                                 a 
                                 2 
                                 * 
                               
                                
                               
                                 [ 
                                 k 
                                 ] 
                               
                             
                              
                             
                               
                                 a 
                                 1 
                               
                                
                               
                                 [ 
                                 k 
                                 ] 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                            
                           
                             
                               
                                 a 
                                 1 
                                 * 
                               
                                
                               
                                 [ 
                                 k 
                                 ] 
                               
                             
                              
                             
                               
                                 a 
                                 2 
                               
                                
                               
                                 [ 
                                 k 
                                 ] 
                               
                             
                           
                         
                       
                       
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                            
                           
                             
                                
                               
                                 
                                   a 
                                   2 
                                 
                                  
                                 
                                   [ 
                                   k 
                                   ] 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                     
                   
                   ] 
                 
                 
                   - 
                   1 
                 
               
               . 
             
           
         
       
     
         [0043]    In step  508 , SCPIR estimator  206  sets the initial SCPIR estimate equal to: 20 log 10(|h 1 |/|h 2 |). 
         [0044]    Referring now to  FIG. 6 ,  FIG. 6  is a flow chart illustrating a process  600 , according to another embodiment, for performing steps  408 - 412  of process  400 . In this embodiment, it is assumed that TS 1  and TS 2  are orthogonal. Process  600  may being with steps  502  and  504  (see above). In steps  606  and  608 , SCPIR estimator  206  determines h 1  and h 2  using the following equations, respectively: 
         [0000]    
       
         
           
             
               h 
               1 
             
             = 
             
               
                 c 
                 1 
               
               
                 
                   ∑ 
                   
                     k 
                     = 
                     0 
                   
                   
                     N 
                     - 
                     1 
                   
                 
                  
                 
                   
                      
                     
                       
                         a 
                         1 
                       
                        
                       
                         [ 
                         k 
                         ] 
                       
                     
                      
                   
                   2 
                 
               
             
           
         
       
     
         [0045]    and 
         [0000]    
       
         
           
             
               h 
               2 
             
             = 
             
               
                 c 
                 2 
               
               
                 
                   ∑ 
                   
                     k 
                     = 
                     0 
                   
                   
                     N 
                     - 
                     1 
                   
                 
                  
                 
                   
                      
                     
                       
                         a 
                         2 
                       
                        
                       
                         [ 
                         k 
                         ] 
                       
                     
                      
                   
                   2 
                 
               
             
           
         
       
     
         [0046]    Next, SCPIR estimator performs step  508 , thereby establishing the initial SCPIR estimate. 
         [0047]    In another embodiment, h 1  and h 2  are determined using the following equation: 
         [0000]    
       
         
           
             
               [ 
               
                 
                   
                     
                       h 
                       1 
                     
                   
                 
                 
                   
                     
                       h 
                       2 
                     
                   
                 
               
               ] 
             
             = 
             
               
                 [ 
                 
                   
                     
                       
                         ( 
                         
                           
                             
                               [ 
                               
                                 
                                   A 
                                   1 
                                 
                                 | 
                                 
                                   A 
                                   2 
                                 
                               
                               ] 
                             
                             H 
                           
                            
                           
                             [ 
                             
                               
                                 A 
                                 1 
                               
                               | 
                               
                                 A 
                                 2 
                               
                             
                             ] 
                           
                         
                         ) 
                       
                       
                         - 
                         1 
                       
                     
                      
                     
                       [ 
                       
                         
                           A 
                           1 
                         
                         | 
                         
                           A 
                           2 
                         
                       
                       ] 
                     
                   
                   H 
                 
                 ] 
               
                
               
                 r 
                 . 
               
             
           
         
       
     
         [0000]    In yet another embodiment, h 1  and h 2  are determined using the following equations: h 1 =((A 1   H A 1 ) −1 A 1   H )r, and h 2 =((A 2   H A 2 ) −1 A 2   H )r. In still another embodiment, h 1  and h 2  are determined using the following equations: h 1 =((A 1   H A 1 ) −1 A 1   H )r, and h 2 =((A 2   H A 2 ) −1 A 2   H )(r−(A 1 h 1 )). In each of these three embodiments the CIRs (i.e., h 1  and h 2 ) are of length K, where K&gt;1. Also, in each of these three embodiments, the initial SCPIR estimate (see step  412 ) is set equal to: 
         [0000]    
       
         
           
             20 
              
             log 
              
             
                 
             
              
             10 
              
             
               
                 ( 
                 
                   
                     1 
                     K 
                   
                    
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         0 
                       
                       
                         K 
                         - 
                         1 
                       
                     
                      
                     
                       
                          
                         
                           
                             h 
                             1 
                           
                            
                           
                             [ 
                             k 
                             ] 
                           
                         
                          
                       
                       / 
                       
                          
                         
                           
                             h 
                             2 
                           
                            
                           
                             [ 
                             k 
                             ] 
                           
                         
                          
                       
                     
                   
                 
                 ) 
               
               . 
             
           
         
       
     
         [0000]    In these embodiments, one may determine which of the two subchannels is stronger by comparing the energy of h 1  (the CIR for the first subchannel) with the energy of h 2  (the CIR for the second subchannel). For example, if we let e 1  denote the energy of h 1  and we let e 2  denote the energy of h 2  then we can compute e 1  and e 2  using the following equation: 
         [0000]    
       
         
           
             
               e 
               n 
             
             = 
             
               
                 ∑ 
                 
                   k 
                   = 
                   0 
                 
                 
                   K 
                   - 
                   1 
                 
               
                
               
                 
                    
                   
                     
                       h 
                       n 
                     
                      
                     
                       [ 
                       k 
                       ] 
                     
                   
                    
                 
                 2 
               
             
           
         
       
     
         [0000]    for n=1,2, and then compare e 1  with e 2 . If e 1  is greater than e 2 , then the first subchannel should be designated as the stronger subchannel, otherwise the second subchannel should be designated as the stronger subchannel. 
         [0048]    Referring now to  FIG. 7 ,  FIG. 7  illustrates a block diagram of SCPIR estimator  206  according to some embodiments of the invention. As shown in  FIG. 7 , SCPIR estimator  206  may include a data processing system  702 , which may include one or more microprocessors and/or one or more circuits, such as an application specific integrated circuit (ASIC), Field-programmable gate arrays (FPGAs), etc; and a data storage system  706 , which may include one or more non-volatile storage devices and/or one or more volatile storage devices (e.g., random access memory (RAM)). As shown, data storage system  706  may store training sequences (e.g., a set of training sequence pairs, such as, TS 1  and TS 2  described above). In embodiments where data processing system  702  includes a microprocessor, computer readable program code  743  may be stored in a computer readable medium  742 , such as, but not limited, to magnetic media (e.g., a hard disk), optical media (e.g., a DVD), memory devices (e.g., random access memory), etc. In some embodiments, computer readable program code  743  is configured such that when executed, code  743  causes SCPIR estimator  206  to perform steps described above (e.g., steps describe above with reference to the flow charts shown in  FIGS. 3-6 ). In other embodiments, SCPIR estimator  206  is configured to perform steps described above without the need for code  743 . That is, for example, data processing system  702  may consist merely of one or more ASICs. Hence, the features of the present invention described above may be implemented in hardware and/or software. For example, in particular embodiments, the functional components of SCPIR estimator  206  described above may be implemented by data processing system  702  executing computer instructions  743 , by data processing system  702  operating independent of any computer instructions  743 , or by any suitable combination of hardware and/or software. 
         [0049]    Referring now to  FIG. 8 ,  FIG. 8  illustrates an embodiment of computer readable program code (CRPC)  743 . In the embodiment shown, CRPC  743  includes: (1) a set of instructions  802  for determining the training sequences (TS 1  and TS 2 ) contained in a received signal, (2) a set of instructions  804  for estimating a first CIR (h 1 ) using TS 1  and r, (3) a set of instructions  806  for estimating a second CIR (h 2 ) using TS 2  and r, (4) a set of instructions  808  for determining an initial estimate the SCPIR from h 1  and h 2 , (5) a set of instructions  810  for determining whether the initial estimate of the SCPIR is a valid SCPIR value, (6) a set of instructions  812  for determining the valid SCPIR value that is closest to the initial estimate, and (7) a set of instructions  814  for selecting the determined valid SCPIR value as the SCPIR estimate. 
         [0050]    While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context. 
         [0051]    Additionally, while the processes described above and illustrated in the drawings are shown as a sequence of steps, this was done solely for the sake of illustration. Accordingly, it is contemplated that some steps may be added, some steps may be omitted, the order of the steps may be re-arranged, and some steps may be performed in parallel.