Abstract:
Correlators categorize different combinations of code sequences and identify locations for which code elements for the code sequences are equivalent. Then, a dispreading operation is performed once for each equivalent combination. The equivalent combinations, for example, may be locations where the code elements are the same or locations where code elements are complements of one another.

Description:
RELATED APPLICATIONS 
     This application relates to an application by the same inventors entitled “Methods and Apparatus to Despread Dual Codes for CDMA Systems,” filed on the same date as this application. 
     BACKGROUND OF THE INVENTION 
     This invention relates generally to single code and multi-code receivers, and more particularly to CDMA receivers having correlators to detect received CDMA signals. 
     The growing importance of wireless communication has increased the demand for data transmission over mobile radio channels. Although GSM standards have become very popular and data service specifications are developing, most current mobile communications still use CDMA technologies. Future multimedia transmission, however, will require wide bandwidths and high data rates, which in turn will require complex and expensive hardware. 
     CDMA systems use a pseudonoise (PN) sequence to “spread” input data to resist data loss in a noisy wireless environment. The transmitted baseband signal is expressed as                  S   T     =       ∑   i              b   i          [   j   ]            C   i           ,           (   1   )                                
     where b i [j], a scalar value representing the jth bit of user i, is +1 or −1, and C i , a column vector representing the PN code sequence, also has values of +1 or −1. After the baseband signals are summed and transmitted, receivers despread the received signal back into an original input symbol by correlating the received signal and the same C i  used to spread the signal PN code as follows: 
     
       
         b k [k]=sign(C k   T S R ).  (2) 
       
     
     The sign function produces a “1” if the input is positive and a “−1” if the input is negative. 
     For example, assume that the transmitted signal can be represented as a series of elements as follows: 
     
       
         b[0]C 0 +b[0]C 1 +b[0]C 2 +b[0]C 3  +b[0]C 4 +b[0]C 5   (3) 
       
     
     Normally, demodulating would involve “multiplying” that signal by the same code used for modulating the signal, adding the products, and then dividing the resulting sum by the total number of elements. For example, multiplying the above received signal (3) by the code used for modulating the signal yields: 
     
       
         b[0](C 0 ) 2 +b[0](C 1 ) 2 +b[0](C 2 ) 2 +b[0](C 3 ) 2 +b[0](C 4 ) 2 +b[0](C 5 ) 2 .  (4) 
       
     
     Because C i  equals +1 or −1, equation (4) becomes 
     
       
         b[0]+b[0]+b[0]+b[0]+b[0]+b[0]=6b[0].  (5) 
       
     
     Dividing by the total number of elements in the modulating code, in this case six, yields the original signal b[0]. 
     Third-generation mobile systems seek to support various types of new services requiring efficient transmission technologies, high bandwidth, and variable data rates. To meet these requirements, many system designers have considered Direct Sequence CDMA (DS-CDMA). Usually, correlators with a sign inverter and integrator are used to detect the user data at the receiver. The correlator output can be expressed by the following equation:                d   k     =       ∑     n   =   0         N   c     -   1                (     -   1     )       c     n   +     kN   c                r     n   +     kN   c                     (   6   )                                
     To reduce power consumption, some have proposed an alternative correlator architecture based on sign-magnitude representation of an input signal. This architecture involves dividing the summation into two terms to avoid sign change.                d   k     =         ∑       n   =   0     ,       c     n   +     kN   c         =   0           N   c     -   1            r     n   +     kN   c           -       ∑       n   =   0     ,         c   n     +     kN   c       =   1           N   c     -   1            r     n   +     kN   c                     (   7   )                                
     A register stores the partial summation of each term. This design permits the use of a single adder because the evaluation of each term does not occur simultaneously. 
     Multi-code CDMA receivers require correlators with the same input signal but different codes. A similar technique divides the summation of correlator operation into several partial summation terms to reduce the complexity. Unfortunately, the required spreading factor in the limited bandwidth restricts the data rate for each CDMA code channel. 
     To address these concerns, some have used multi-code CDMA transmission to support a high bandwidth and variable data rate in a DS-CDMA system. Multi-code transmission splits a high-rate data stream into several parallel low-rate data streams and spreads them using different code sequences. Multi-code CDMA receivers use multiple parallel correlators to detect the parallel data streams. 
     When the modulating signal becomes very long, however, the complexity, whether measured by number of operations required in the demodulation or the amount of circuitry, becomes very high. Furthermore, the number of correlators can become significant when the receiver is also using a RAKE combining technique. For example, a wideband CDMA system supporting 2 Mbps over five CDMA code channels, requires forty correlators for a four-finger RAKE receiver and I/Q spreading. In such a high bandwidth case, correlator complexity dominates the system complexity. 
     Some researchers have proposed code sets to reduce the computational complexity of multi-code correlators. For example, a spreading code sequence using a Walsh code structure spread by a PN code can use a fast Hadamard transform (FHT). In such systems, the multi-code CDMA signal is first despread using the PN code and then an FHT is used to correlate the signal. These systems, however, limit the code size to the number of available Walsh codes. Furthermore, correlation operations for all Walsh codes must be done simultaneously, requiring calculation of the full FHT even when only partial results are needed. 
     Other schemes using dual gold codes have been proposed with some decrease in complexity and increase in flexibility. Unfortunately, the restrictions on code sets and full correlation operations still exist in these schemes. 
     DISCLOSURE OF THE INVENTION 
     A method consistent with this invention of demodulating an encoded signal comprises forming groups of code elements having one of a predetermined set of values, the groups of code elements representing a code used to encode the signal; 
     identifying locations for which a corresponding set of element values for all the codes are equivalent; 
     aggregating the portions of the signal at the locations identified as having equivalent element values; and performing correlation functions on the aggregated portions to demodulate the signal. 
     Another method consistent with this invention of demodulating a signal encoded with a modulation code, the demodulation using subcodes of code elements at sequential locations, each of the elements having one of a predetermined set of values and the subcodes collectively constituting the modulation code, comprises identifying locations for which a corresponding set of element values for all the subcodes are equivalent; aggregating the portions of the signal at the locations identified as having equivalent element values; and performing correlation functions on the aggregated portions to demodulate the signal. 
     Yet another method consistent with this invention of demodulating a signal encoded with a multiple modulation codes of code elements at sequential locations, each of the elements having one of a predetermined set of values, comprises identifying locations for which a corresponding set of element values for all the codes are equivalent; aggregating the portions of the signal at the locations identified as having equivalent element values; and performing correlation functions on the aggregated portions to demodulate the signal. 
     A system consistent with this invention demodulates an encoded signal using groups of code elements having one of a predetermined set of values, the groups of code elements representing a code used to encode the signal The system comprises means for aggregating portions of the signal at locations for which a corresponding set of elements of the groups of codes is equivalent; and means for correlating the aggregated portions to demodulate the signal. 
     Both the foregoing general description and the following detailed description are exemplary and explanatory only and do not restrict the invention claimed. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate some systems and methods consistent with the invention and, together with the description, explain the principles of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the drawings, 
     FIG. 1 is a flowchart showing a procedure consistent with the present invention; and 
     FIG. 2 is a block diagram of a correlator  200  consistent with the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A. Principles of Operation 
     Systems and methods consistent with the present invention can apply to both single-code and multi-code CDMA correlators. Single code correlators use one code divided into several subcodes. Multi-code correlators simultaneously demodulate a received signal composed of several spread signals each modulated by a different code. 
     Systems and methods consistent with this invention categorize different combinations of code sequences, which allow certain correlation operations to take place once for each combination. Single-code CDMA correlators effectively divide pseudonoise codes into several subcodes. For example, the following sixteen-element PN code 
     1,1,1,−1,1,−1,1,−1,−1,−1,−1,1,1,1,1,−1 
     can be divided into the following four subcodes 
     C 0 : 1, 1, 1, −1 
     C 1 : 1, −1, 1, −1 
     C 2 : −1, −1, −1, 1 
     C 3 : 1, 1, 1, −1 
     Multi-code correlators would extract elements from each spreading code that have the same index. Thus for example, if there were four spreading codes of length 16 as follows: 
     C 1.0  C 1.1  C 1.2  . . . C 1.15    
     C 2.0  C 2.1  C 2.2  . . . C 2.15    
     C 3.0  C 3.1  C 3.2  . . . C 3.15    
     C 4.0  C 4.1  C 4.2  . . . C 4.15    
     the codes could be 
     C 0 : C 1.0  C 2.0  C 3.0  C 4.0    
     C 1 : C 1.1  C 2.1  C 3.1  C 4.1    
     C 2 : C 1.2  C 2.2  C 3.2  C 4.2    
     . . . 
     C 15 : C 1.15  C 2.15  C 3.15  C 4.15    
     Normally, each of these code, or subcodes, would be multiplied by the corresponding portions of the received signal. Such operations require m×n multiplications, where m is the number of codes or subcodes and n is the number of elements in each code or subcode, and a like number of additions to tally the products. 
     Systems and methods consistent with the present invention, however, take advantage of the property that at several locations the sets of values of the codes or subcodes are the same. For example, the first and third positions have the pattern 1,1,−1,1. Adding the corresponding portions of the received signal together before multiplying reduces the number of multiplications. There are 2 m  different patterns for m codes or subcodes, so at most only 2 m  multiplication operations need take place. 
     The number of multiplications can be reduced even further by recognizing that each pattern has a complementary pattern. The first and fourth locations have complementary patterns (1, −1,1, −1 and −1,1, −1,1), and can be combined by adding the negative of one pattern (i. e., subtracting). By combining the results from the first and third positions with the complement of the results from fourth location, and doing so for other such pairs, further reduces the number of multiplications to 2 m−1 , yielding significant savings in complexity. 
     For multi-code CDMA applications, systems and methods consistent with this invention allow designers to reduce the complexity of correlators without restricting the number of code sets. Such systems and methods maintain flexibility for better code design and a wide range of applications without reducing performance. By first performing partial sums of the input sequence values corresponding to common groups, and then performing mathematical operations (addition or subtraction) on those sums, designers can create correlators with less hardware than conventional designs. 
     Moreover, because the code combinations are mutually exclusive, correlators consistent with this invention can use one core adder at the input sample rate for partial summation. As an added benefit, partial summation reduces the dynamic range of summation results, which in turn allows a smaller core adder. 
     The following description concentrates on multi-code CDMA correlators. Persons of ordinary skill, however, will be able to apply the principles to single-code correlators as well. 
     Generally, systems and methods consistent with this invention divide the required summations for each correlator into common partial summation terms. The ability to derive correlator outputs for multiple codes from these terms allows redundant computations to be eliminated. 
     Assume that the system uses M binary PN codes, C l , . . . C m , with spreading factor L for multi-code CDMA transmission, where C m =(C m.l  . . . C m.L ). Each correlator output d m  corresponding to input signal x n  is:                d   m     =       ∑   n              (     -   1     )       c     m   ,   n              x   n                 (   8   )                                
     B n =(C l.n , . . . C M.n ) is defined as the bit matrix with the n th  binary elements of the M PN codes that define the bit presentation matrix P i , the M-bit binary representation of the number i, e.g., P 0 =(0, 0, . . . 0) m , P l=( 0, 0, . . . 1) M , and P 2     M     −1 =(1, 1, . . . 1) M . Similarly, P i.j  is defined as the j th  binary element of P i . Accordingly, then d m  can be written as:                d   m     =         ∑       n   =   0     ,       c     m   ,   n       =   0         L   -   1            X   n       -       ∑       n   =   0     ,       c     m   ,   n       =   1         L   -   1            X   n                 (   9   )                                
     If          S   i     =       ∑       n   =   0     ,       B   n     =     P   i           L   -   1            x   n                              
     is defined as the i th  partial summation term for M multi-code correlation outputs d m , then                d   m     =         ∑       i   =   0     ,       P   im     =   0           2   M     -   l            S   i       -       ∑       i   =   0     ,       P   im     =   l           2   M     -   l            S   i                 (   10   )                                
     Equation 10 shows how 2 M  partial summation terms derive correlation outputs. Specifically, the correlation output of m th  code results from adding or subtracting all the terms, as indicated by the value of P i.m . As explained above, the number of partial summation terms can be further cut in half from 2 M  to 2 M−1 , because S i  and S 2     m     −i−1  are additive complements of each other, so they can be merged and evaluated as S i −S 2     m     −i−1 . 
     B. Methods of Operation 
     FIG. 1 is a flowchart of a procedure  100  consistent with the present invention for a multi-code correlator. Operations are similar for a single-code correlator, with the codes being replaced by subcodes. 
     To begin with, a counter, n, is set to 0 (Step  110 ) Next, 2 M  registers are reset to 0 (step  120 ), where M is the number of codes. The M codes are grouped into an M-bit number B n  (step  130 ). 
     Next, the contents of the corresponding register are increased by the corresponding value of the input signal (step  140 ). The value n is incremented by 1 (step  150 ) and compared to the value kL (step  160 ). L represents the code length. 
     If n does not equal kL, the process repeats with the next code. Otherwise, the kth correlation result is obtained by adding the contents of the registers and adjusting for their signs (step  170 ). If all the correlation results are calculated the process is over. Otherwise, the registers are reset (step  120 ) and the next correlation result is determined. 
     C. Receiver Design 
     FIG. 2 shows a correlator  200  consistent with the present invention. Core adder  210  in correlator  200  calculates partial sums of the input signals and the contents of the registers in register bank  230  selected by multiplexer  220  under control of multiplexer signal  225 . Register bank  230  has 2 m  or 2 m−1  registers, depending upon whether the additive complements are combined as well. Multiplexer  220  also routes the output of adder  210  to the register indicated by signal  225  to store a new partial result in that register. Adder/subtractor network  240  computes the correlator outputs from the partial results in the register bank  230 . 
     For example, for M=3, multiplexer  220  would be a 3-bit multiplexer, and register bank  230  would have eight registers. An example of the operation of such a system appears below: 
     
       
         
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Input 
                 x 0   
                 x 1   
                 x 2   
                 x 3   
                 x 4   
                 x 5   
                 x 6   
                 x 7   
               
               
                   
                   
               
             
             
               
                   
                 Code 1 
                 1 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
               
               
                   
                 Code 2 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                   
                 Code 3 
                 0 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 Group No. 
                 6 
                 5 
                 3 
                 1 
                 4 
                 5 
                 6 
                 0 
               
               
                   
                 Reduced 
                 1 
                 2 
                 3 
                 1 
                 3 
                 2 
                 1 
                 0 
               
               
                   
                 Group No. 
               
               
                   
                   
               
             
          
         
       
     
     The reduced partial sum results are: 
     s 0 =x 7    
     s 1 =−x 0 +x 3 −x 6    
     s 2 =−x 1 +x 5    
     s 3 =x 2 −x 4 . 
     The correlator outputs are as follows: 
     C 1 =s 0 +s 1 +s 2 +s 3    
     C 2 =s 0 +S 1 −s 2 −s 3    
     C 3 =s 0 −s 1 +s 2 −s 3 . 
     To obtain the correlation outputs for the three codes, data stored in eight registers are summed with the appropriate sign inversion. The computation of correlation outputs is similar to correlating eight partial terms with three codes of length 8. 
     D. Complexity and Optimization 
     To implement an M-code correlator with code length L, a traditional correlator architecture requires M*L add/subtraction operations to derive one correlation output for each code. The correlator design described in FIG. 2 requires L add operations to obtain 2 M  partial summation results and an additional 2 M  add operations to obtain correlation results for a code. As explained above, the number of add operations can be reduced to 2 M−1  because pairs of partial summation results can be merged into one term. This reduces the number of add operations to L+M*2 M−1 . 
     If the complexity ratio of the proposed architecture, R, equals (L+M*2 M−1 )/M*L, Table 1 shows the complexity ratio of a code of length  256  for different values of M. 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Complexity ratio of code length 256 for different values M 
               
             
          
           
               
                 M 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
               
               
                   
               
               
                 Complexity 
                 50.8% 
                 34.9% 
                 28.1% 
                 26.3% 
                 29.2% 
                 39.9% 
                 62.5% 
                 111.1% 
               
               
                 Ratio 
               
               
                   
               
             
          
         
       
     
     The optimum complexity ratio occurs when M=5. 
     Performance of the architecture is bounded due to the exponential growth of partial summation terms. When M is large, the number of terms is significant in comparison with the code length. Add operations required for correlator outputs dominate the complexity thus degrading performance. The optimum complexity ratio R opt ≅(M+1)/M 2  for a given code length L occurs when M 2 *2M M−1 =L. Thus the complexity is greatly reduced when code length is long, and is optimum when M is large. 
     The complexity ratio degrades when the number of codes exceeds M opt , although the complexity ratio can be improved for a large number of codes by using two or more multi-code correlators. For example, for the M-code correlation using M a *M b -code correlators, where M=M a *M b , the complexity ratio is R=(L+M b *2 M     b     −1 )/M b *L, which is independent of M a . Therefore, for a large M, using the optimum M b  for a given code length L will provide the optimum complexity ratio. In general, systems and methods consistent with this invention can reduce the computational complexity more than about a half without restricting the structure of spreading codes. 
     E. Conclusion 
     The specific hardware used to implement the correlators is not critical to this invention. Persons of ordinary skill in the art will know to use whatever technologies or circuit designs are appropriate for their particular needs while still taking advantage of the savings attendant the present invention. Therefore, the scope of the appended claims is not to be limited to these specific examples.