Abstract:
A simple and robust CTL is used for time tracking of multipath components of a spread spectrum signal transmitted over a wireless multipath fading channel. A digital code-tracking loop includes the implementations of despreading early and late data samples by use of a pseudonoise sequence, an error signal output generated by the despreading, and adjustment for a plurality of on-time, early and late samples, a data rate of a control signal provided as a fractional proportion of a data rate of error signals.

Description:
CROSS REFERENCE TO RELATED APPLICATION(S) 
   This application claims priority from U.S. Provisional Application No. 60/376,465, filed Apr. 29, 2002, which is incorporated by reference as if fully set forth. 

   FIELD OF INVENTION 
   The present invention relates to the field of wireless communications. More specifically, the present invention relates to an improved code tracking system and method for the field of spread spectrum communication systems. 
   BACKGROUND 
   Code division multiple access (CDMA) technology has been widely used in mobile cellular phone systems. One of the advantages of CDMA technology is that it is very robust in scenarios where multiple-path fading may be experienced. A rake receiver, which is commonly used for CDMA reception, consists of a bank of correlators and a combiner. Each correlator, or rake finger, is used to separately detect and demodulate one of the strongest multipath components (fingers) of the wideband fading channel and the combiner combines all correlator outputs to obtain the combined energy from these strongest multipath components. Since the number of the multipath signals and their positions vary in time, time tracking of each multipath component is required. For this timing tracking, a code-tracking loop (CTL), also called delay lock loop (DLL), is usually used. In previous CTL designs, either a voltage controlled oscillator (VCO) or a numerically controlled oscillator (NCO) was used. A CTL may be either coherent or noncoherent. Coherent and non-coherent relate to how the despread data is summed to generate an error signal. 
   SUMMARY 
   According to the present invention, a simple and robust code-tracking loop (CTL) is used for time tracking of multipath components of a spread spectrum signal transmitted over a wireless multipath fading channel. The CTL includes despreading early and late data samples using a pseudonoise sequence, outputting an error signal by the despreading, adjusting for a plurality of on-time, early and late samples, and determining a data rate of a control signal as a fractional proportion of a data rate of error signals. The CTL has a simple structure to implement. A joint CTL is also disclosed for canceling interference between two multipaths when two multipaths are very close to each other. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a diagram of a wireless communications link. 
       FIG. 2  is a block diagram of CTL using high sampling input data. 
       FIG. 3  is a block diagram of CTL using low sampling rate input data. 
       FIG. 4  is a block diagram of one CTL design for UMTS FDD system. 
       FIG. 5  is a graph showing simulated timing tracking at signal to noise ratio SNR=−24 dB. 
       FIG. 6  is a graph showing simulated timing tracking at SNR=−24 dB. 
       FIG. 7  is a graph showing simulated timing tracking at SNR=−24 dB. 
       FIG. 8  is a graph showing the interference between two adjacent CTLs when they are separated by less than one and half chip. 
       FIG. 9  is a block diagram of joint CTL scheme. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The present invention will be described with reference to the drawing figures wherein like numerals represent like elements throughout. 
     FIG. 1  is a diagram of a wireless communications link, which includes one or more base stations  11  (only one shown for simplicity) and one or more wireless transmit and receive units (WTRUs)  12  (only one shown for simplicity). The base station includes a transmitter (not shown) and receiver  13 , and the WTRU  12  includes a transmitter (not shown) and receiver  14 . At least one of the base stations  11  and WTRU  12  have transmit functions so that a communications link is established between the base station  11  and the WTRU  12 , as represented by antennas  17 ,  18 . It should be understood by those skilled in the art that the CTL  21  of the present invention is implemented within a receiver, such as receiver  13  or  14 . 
   A CTL uses the early and late signals (i.e. samples) to generate an error signal for timing tracking. The early and late samples are defined as the samples that are a half chip (half chip interval) earlier and a half chip (half chip interval) later than the on-time sample, respectively. A “chip” is a time interval to transmit one bit of spreading code and a half chip is half the time interval of a chip interval. The frequency of a chip time interval is called the “chip rate.” In UMTS CDMA and CDMA2000 standards, the chip rate is defined as 3.84 MHz/s. 
   Referring to  FIG. 2 , a block diagram of a CTL  21  in accordance with the present invention is shown. The inputs are data samples with the sampling rate of 16 times the chip rate. It should be noted that although specific data rates are set forth herein, these data rates are provided by way of example only. For example, although data sample rates may vary, sampling rates of 8 and 16 are typical sample rates. In another example using 16 times the rate of sampling, for every 16 samples one of the samples will be an “on-time” synchronized sample which will be used for despreading, demodulation and rake combining. The CTL  21  will track this timing and select the on-time sample. To achieve this goal, the CTL  21  will use early and late samples. 
   CTL  21  includes an input sample selector  23 , an early sample pseudonoise (PN) despreader  25 , a late sample PN despreader  26 , an early-late detector  27 , an integration and dump circuit  28 , a sign calculator  29  and a summer  30 . The input sample selector  23  provides early and late samples to the PN despreaders  25 ,  26  which, in turn, provide signals to the early-late detector  27 . The early-late detector  27  includes a late power calculator  27   a , an early power calculator  27   b  and a summer  27   c . The output of the early-late detector  27  is an error signal which is provided to the integrator and dump circuit  28 . The output of the integrator and dump circuit  28  is sent to the sign calculator  29 . The sign calculator  29  outputs a ±1 signal that is input to the summer  30 . The summer  30  converts the relative timing control signal (i.e. −1/+1) to an absolute timing control signal taking into account previous results. The output of the summer  30  is sent to the input sample selector  23  to form the loop. 
   The integration function that is performed by the integrator in the integration and dump circuit  28  accumulates the signal power and to improve the signal-to-noise ratio. After the signal is integrated for a defined or predetermined period of time, the integration value is output. In order to integrate the signal for the next time period, the signal in the integrator is first cleared. Accordingly, the procedure in which the integrator integrates signal discontinuously between different periods of time is called “integration and dump.” The integration interval is selected to be a pilot symbol interval. In a preferred embodiment, the pilot symbol interval is a predetermined number of chips, which in the exemplary embodiment is 256 chips. 
   The CTL  21  operates by first despreading the early samples and the late samples. The early and late samples are despread by a PN sequence that is known to the receiver. The despread data is denoted as S e (k) and S l (k) for early and late samples respectively, where S e (k) and S l (k) are complex numbers, and k represents kth data in the time domain. The early-late detector  27  uses despread data, or data symbols, to generate an error signal, which can be obtained noncoherently using Equation (1):
 
 E   r ( k )=| S   e ( k )| 2   −|S   l ( k )| 2 .  Equation (1)
 
   For each N error signals E r (k), where (N&gt;1), a control signal C 0  will be generated according to the sign of the sum of these N error signals E r (k), which can be expressed as: 
   
     
       
         
           
             
               
                 
                   C 
                   0 
                 
                 = 
                 
                   sign 
                   ⁢ 
                   
                     
                       { 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             1 
                           
                           N 
                         
                         ⁢ 
                         
                           
                             E 
                             r 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       } 
                     
                     . 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
   
   This control signal C 0  is used to adjust all on-time, early and late samples either forward or backward by M samples. Typically the adjustment is M=1 or 2, or M/16 chip, which is typically 1/16 chip or ⅛ chip. The data rate of this control signal C 0  is therefore N times lower than the data rate of error signals E r (k). 
   Still referring to  FIG. 2 , in some instances the transmitted data can be estimated. If this is the case (i.e., the transmitted data can be estimated), this is done by first removing the modulated data is from the despread early signal and despread late signal. This results in:
 
S e (k)*α(k)*and   Equation (3)
 
S l ( k )*α(k)*, respectively,  Equation (4)
 
where α(k) is the transmitted symbol or an estimate of transmitted signal, and ( )* represents the conjugate. Thereafter, N l  despread early and late signals with data removed are coherently summed to calculate the error signal Er(k) that can be expressed by:
 
   
     
       
         
           
             
               
                 
                   
                     E 
                     r 
                   
                   ⁡ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     
                        
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             1 
                           
                           
                             N 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             
                               S 
                               e 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           ⁢ 
                           
                             
                               a 
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             * 
                           
                         
                       
                        
                     
                     2 
                   
                   - 
                   
                     
                       
                          
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             
                               N 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               
                                 S 
                                 l 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                 a 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               * 
                             
                           
                         
                          
                       
                       2 
                     
                     . 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
   
   The despread data S e (k) or S l (k) contains a demodulating symbol a(k) that is {−1,+1} for BPSK modulation or {−1,+1,−j,+j} for QPSK modulation. When the despread data S e (k) or S l (k) is multiplied with the conjugate of a(k) as in Equations (3) and (4), the a(k) component in the despread data S e (k) or S l (k) will be “removed.” 
   The data rate of the error signal E r (k) is N l  times lower than that of the despread early or late signal since every N l  despread early or late signal generates one error signal. For every N error signals E r (k), where N&gt;1, a control signal C 0  is generated according to the sign of the sum of these N error signals, and the data rate of this control signal C 0  is N 1 ×N times lower than the data rate of error signals. 
   In either case, the error signal E r (k) is generated. Equation (1) uses one despread data symbol to generate one error signal E r (k). Equation (5) uses N l  despread data symbols to generate one error signal E r (k). Therefore the data rates of the error signals E r (k) are different by N l  times. 
   According to one embodiment of the present invention, both coherent and non-coherent approaches are used. Coherent detection adds signals coherently (i.e. sum the complex numbers directly) such as the sums in Equation 5 (or as will be explained in detail hereafter, the inner sum in Equation 7). Noncoherent detection adds signals noncoherently (i.e. sum the power of complex numbers) such as the sum which will be explained with reference to Equation 6. The difference between the two approaches is that coherent detection has better performance than noncoherent detection. However, in order to use coherent detection to obtain better performance, the transmitted signal a(k) has to be known or estimated as performed in Equation 5. 
   A second embodiment of a CTL  31  in accordance with the present invention using low sampling rate input data is shown in  FIG. 3 . This CTL  31  includes an interpolator  33 , an early sample PN despreader  35 , a late sample PN despreader  36 , an early-late detector  37 , an integration and dump circuit  38 , a sign calculator  39  and a summer  40 . The interpolator  33  provides early and late samples to the PN despreaders  35 ,  36 , which in turn provide signals to the early-late detector  37 . The early-late detector  37  includes a late signal power calculator  37   a , an early signal power calculator  37   b , and a summer  37   c . The output of the early-late detector  37  is an error signal E r (k) which is provided to the integrator and dump circuit  38 . The output of the integrator and dump circuit  38  is sent to the sign calculator  39 . 
   The sign calculator  39  outputs a ±1 signal that is supplied to the summer  40 . The summer  40  converts the relative timing control signal (i.e. −1/+1) to an absolute timing control signal taking into account previous results. The output of the summer  40  is sent to the interpolator  33  to form the loop in the same manner as depicted in  FIG. 2 . 
   For low sampling rate input data, the sampling rate is typically two samples per chip. In order to adjust the timing for on-time and early/late samples forward or backward by a fraction of chip (for example 1/16 chip or ⅛ chip), the interpolator  33  is used to generate all on-time samples, and early/late samples which are offset by such amount of time from the previous samples. 
   As can be seen, the input data rates are different for the input sample selector  23  shown in  FIG. 2  and the interpolator  33  shown in  FIG. 3 . The sample selector  23  selects which input samples to use according to the control signal C 0 . Since the interpolator  33  has only two input samples per chip, it has to regenerate or interpolate the desired samples according to a control signal input. 
   The CTL  21  of  FIG. 2  requires a high-speed analog-to-digital converter (ADC). The CTL  31  of  FIG. 3  uses a low-speed ADC, which is lower in cost, but CTL  31  also requires an extra interpolator to regenerate the desired samples. With CTL  21 , a high data rate (i.e. 16 samples/chip) is used and therefore a high speed ADC is required. With CTL  31 , a low data rate (i.e. 2 samples/chip) is used and therefore a low speed ADC is required. The different data rates are needed for different applications. For example, in  FIG. 4 , a low speed ADC is preferred because is uses 2 samples/chip and interpolator  53 . 
   In an exemplary embodiment corresponding to the UMTS FDD standard, for uplink transmissions every slot of the dedicated physical control channel contains ten symbols (including pilot, transmit power control and TFCI bits). Among these ten symbols, pilot symbols are known to the receiver, but the power control and TFCI bits are unknown to the receiver. Suppose that SE k,j  and SL k,j  denote the despread early and late signals for the jth symbol in the kth slot. If the CTL  31  is updated every two frames (there are 15 slots per frame and 30 slots per two frames), then the control signal C 0  at the output of the integration and dump circuit  38  using noncoherent combining can be expressed as: 
                   C   0     =     SIGN   ⁢       {       ∑     k   =   1     30     ⁢           ⁢       ∑     j   =   1     10     ⁢           ⁢     {              SE     k   ,   j            2     -            SL     k   ,   j            2       }         }     .               Equation   ⁢           ⁢     (   6   )                 
Alternatively CTL  31  coherently sums a number of early and late signals from one slot, and then calculates the power and the error signal E r (k). Again if the CTL  31  is updated every two frames, then the control signal C 0  at the integrator output can be expressed as:
 
                     C   0     =     SIGN   ⁢     {       ∑     k   =   1     30     ⁢     {                ∑     j   =   1       N   1       ⁢       SE     k   ,   j       ⁢     a     k   ,   j     *              2     -              ∑     j   =   1       N   1       ⁢       SL     k   ,   j       ⁢     a     k   ,   j     *              2       }       }         ;           Equation   ⁢           ⁢     (   7   )                 
where α k,j  is the known pilot bit or the estimated power control/TFCI bit in the jth symbol of the kth slot.
 
   Some further alternatives are possible by implementing various combinations of the following items: 1) using an input sample selector  23  (for the high speed ADC as shown in  FIG. 2 ) or interpolator  33  (for the low speed ADC as shown in  FIG. 3 ); 2) using a noncoherent error signal calculation as in Equations 1 and 6 or using coherent error signal calculation as in Equations 5 and 7; and 3) using error signal power as in Equations 1–5, 6 and 7 or using error signal absolute value as in Equation 9. As explained above,  FIG. 2  uses an input sample selector, noncoherent error signal calculation, and error signal power (Equation 1) and  FIG. 3  uses an interpolator, noncoherent error signal calculation and error signal power (Equation 1).  FIG. 4 , explained below, uses an interpolator, noncoherent error signal calculation and error signal absolute value. 
   As explained above Equations (6) and (7) represent two different methods to generate the error signal E r (k) as explained above. Equation (6) uses noncoherent detection and uses the error signal generation in Equation (1), and Equation (7) uses coherent detection and uses the error signal generation in Equation (5). The “SIGN” is used to adjust the timing forward or backward. When the sign of Equations (6) or (7) is positive, it will adjust the timing backward; whereas when the sign of Equations (6) or (7) is negative, it will adjust the timing forward. 
   An embodiment of a CTL for UMTS FDD in accordance with the present invention is shown in  FIG. 4 . The CTL circuit  51  includes an interpolator  53 , a delay circuit  54 , early and late PN despreaders  55 ,  56 , two magnitude calculation circuits  57 ,  58  which calculate absolute values of the respective signals, and a summer  59 . Also included is an integrator and dump circuit  63 , a sign calculator  64  and a second summer  65 . The interpolator  53  provides a single early/late output to delay circuit  54 , which provides an early signal to early PN despreader  55 . The output of interpolator  53  is provided directly to late PN despreader  56  and the outputs of the despreaders  55 ,  56  are provided to respective magnitude calculation circuits  57 ,  58 . 
   The circuit of  FIG. 4  uses the first error signal generation method described by Equations (1) and (6) because the early sample and late sample are separated by exactly one chip interval, and the early sample can be obtained from late sample by delaying one sample. Further, in  FIG. 4 , the square calculation performed by the early and late signal power calculators  37   a ,  37   b  is replaced with an absolute value calculation in order to simplify the hardware complexity. 
   If one compares Equation (9) with Equation (1), it will be noted that the integrator and dump circuit  63  performs the summing as described in Equation (6); and the sign calculator  64  resolves the sign (+ or −) as described in Equation (6). Since this sign generates a relative timing adjustment, a new absolute timing signal is generated by summing the previous absolute timing with the incoming relative adjustment. This is done in summer  65 . 
   The absolute values (of the early and late despreaders  55 ,  56  calculated in the magnitude calculation circuits  57 ,  58 ) are provided to the summer  59 , which provides an error signal E r (k) as its output to the integrator and dump circuit  63  which and, in turn, outputs to the sign calculator  64 . The output from the sign calculator  64  hard limited to a ±1 signal, which is supplied as a phase control signal to the interpolator  53 , to form the loop. 
   The error signal Δ k,j  is the difference of the absolute values of E k,j  and L k,j , which can be expressed as:
 
Δ k,j   =|E   k,j   |−|L   k,j |  Equation (9)
 
   The integrator and dump circuit  63  provides the magnitude of the error signals and its output is hard-limited by the sign calculator  64  to either +1 or −1 according to the sign of the summed error signals. This +1 or −1 is used to adjust the timings of all punctual, early and late samples by ⅛ chip forward or backward and is implemented by controlling the interpolator phase. This interpolator phase is updated by subtracting the previous phase with the new input data (+1 or −1). 
   The interpolator  53  uses four samples (with the sampling interval of a half chip) to generate the punctual and late samples. The relationship between the phase control signal (i.e. the interpolator output), the timing offset and the interpolator coefficients is shown in Table 1. The early sample is generated by delaying one sample of the previously generated late sample. If the punctual sample is on phase “0,” then the late sample will be on the phase “2.” If the punctual sample is on phase “x,” then the late sample will be on phase “x+2.” 
   
     
       
             
           
             
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Interpolator Phase, Timing Offset and Coefficients. 
             
           
        
         
             
                 
               timing 
                 
                 
                 
                 
             
             
               Interpolator 
               offset 
               coefficient 
               coefficient 
               coefficient 
               coefficient 
             
             
               Phase 
               (chips) 
               1 
               2 
               3 
               4 
             
             
                 
             
           
        
         
             
               −6 
               −0.7500 
               0.0000 
               0.0000 
               0.0000 
               1.0000 
             
             
               −5 
               −0.6250 
               0.0547 
               −0.2578 
               0.6016 
               0.6016 
             
             
               −4 
               −0.5000 
               0.0625 
               −0.3125 
               0.9375 
               0.3125 
             
             
               −3 
               −0.3750 
               0.0391 
               −0.2109 
               1.0547 
               0.1172 
             
             
               −2 
               −0.2500 
               0.0000 
               0.0000 
               1.0000 
               0.0000 
             
             
               −1 
               −0.1250 
               −0.0391 
               0.2734 
               0.8203 
               −0.0547 
             
             
               0 
               0.0000 
               −0.0625 
               0.5625 
               0.5625 
               −0.0625 
             
             
               1 
               0.1250 
               −0.0547 
               0.8203 
               0.2734 
               −0.0391 
             
             
               2 
               0.2500 
               0.0000 
               1.0000 
               0.0000 
               0.0000 
             
             
               3 
               0.3750 
               0.1172 
               1.0547 
               −0.2109 
               0.0391 
             
             
               4 
               0.5000 
               0.3125 
               0.9375 
               −0.3125 
               0.0625 
             
             
               5 
               0.6250 
               0.6016 
               0.6016 
               −0.2578 
               0.0547 
             
             
               6 
               0.7500 
               1.0000 
               0.0000 
               0.0000 
               0.0000 
             
             
                 
             
           
        
       
     
   
   The integrator and dump circuit  63  is reset every 30 slots during steady tracking mode, and is reset every ten slots during the initial pull-in mode. At the beginning, the CTL  51  is in a “rough” timing position. It is desirable for CTL  51  to react quickly to find the right timing position (initial pull-in mode), and then the CTL  51  will lock to this position and track any timing change (tracking mode). During the first five minutes after the finger is assigned to the CTL  51 , the CTL  51  is assumed to be in the pull-in mode, and from the sixth frame on, the CTL  51  is assumed to be in the tracking mode. 
   For the pull-in mode, the CTL  51  is updated every ten slots and all ten pilot and data symbols are used per dedicated physical control channel (DPCCH) slot. In this case the accumulator output Q can be expressed as: 
   
     
       
         
           
             
               
                 Q 
                 = 
                 
                   SIGN 
                   ⁢ 
                   
                     
                       { 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             1 
                           
                           10 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             10 
                           
                           ⁢ 
                           
                             Δ 
                             
                               k 
                               , 
                               j 
                             
                           
                         
                       
                       } 
                     
                     . 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
   
   For steady mode, the CTL  51  is updated every 30 slots (or two frames) and all ten pilot and data symbols are used per DPCCH slot. The integrator and dump circuit output  63  can be expressed as: 
   
     
       
         
           
             
               
                 
                   Q 
                   ′ 
                 
                 = 
                 
                   SIGN 
                   ⁢ 
                   
                     
                       { 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             1 
                           
                           30 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             10 
                           
                           ⁢ 
                           
                             Δ 
                             
                               k 
                               , 
                               j 
                             
                           
                         
                       
                       } 
                     
                     . 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
   
   Simulations of the results of CTL  51  tracking during a steady mode were performed, The simulation parameters were as follows:
     1) Both time and frequency drift is 0.613 ppm;   2) The channel is AWGN channel;   3) Target SNR=−24 dB;   4) The CTL  51  is updated every two frames (30 slots);   5) For each CTL  51  updating, ⅛ chip forward or backward adjustment is applied;   6) The maximum timing error is calculated;   7) The root-square of mean square timing error (RMSE) is calculated;   8) Both noncoherent and coherent combining are considered;   9) For noncoherent combining, ten symbols per slot are used, and the error signal calculation is same as Equation (6);   10) For coherent combining, only three pilot symbols per slot are used, and the error signal calculation is same as Equation (7) with N1=3;   11) A simplified scheme is simulated, which uses the absolute value instead of power of early and late signals.   

     FIG. 5  is a graph showing simulated timing tracking at SNR=−24 dB using coherent detection. By applying Equation (7), a noncoherent combining of ten pilot symbols per slot is achieved.  FIG. 6  is a graph showing simulated timing tracking at SNR=−24 dB using non-coherent detection. 
     FIG. 7  shows the results of a simplified error signal calculation in accordance with the present invention using Equation (11). Since the error signal calculation in both Equation (6) for noncoherent combining and Equation (7) for coherent combining need to calculate the power of complex numbers, this power calculation is very complicated in a hardware implementation. In order to reduce the hardware complexity, the magnitude calculation is used instead of the power calculation. 
   If all ten pilot and data symbols are used for noncoherent combining in each slot and the CTL is updated every two frames (30 slots), then the accumulator output can be expressed as: 
   
     
       
         
           
             
               
                 
                   Q 
                   ″ 
                 
                 = 
                 
                   SIGN 
                   ⁢ 
                   
                     
                       { 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             1 
                           
                           30 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             10 
                           
                           ⁢ 
                           
                             { 
                             
                               
                                  
                                 
                                   E 
                                   
                                     k 
                                     , 
                                     j 
                                   
                                 
                                  
                               
                               - 
                               
                                  
                                 
                                   L 
                                   
                                     k 
                                     , 
                                     j 
                                   
                                 
                                  
                               
                             
                             } 
                           
                         
                       
                       } 
                     
                     . 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
   
   If only first three pilot symbols are used for coherent combining in each slot and the CTL is updated every two frames (30 slots), then the accumulator output can be expressed as: 
   
     
       
         
           
             
               
                 Q 
                 = 
                 
                   SIGN 
                   ⁢ 
                   
                     
                       { 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             1 
                           
                           30 
                         
                         ⁢ 
                         
                           { 
                           
                             
                                
                               
                                 
                                   ∑ 
                                   
                                     j 
                                     = 
                                     1 
                                   
                                   3 
                                 
                                 ⁢ 
                                 
                                   E 
                                   
                                     k 
                                     , 
                                     j 
                                   
                                 
                               
                                
                             
                             - 
                             
                                
                               
                                 
                                   ∑ 
                                   
                                     j 
                                     = 
                                     1 
                                   
                                   3 
                                 
                                 ⁢ 
                                 
                                   L 
                                   
                                     k 
                                     , 
                                     j 
                                   
                                 
                               
                                
                             
                           
                           } 
                         
                       
                       } 
                     
                     . 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
   
   Table 2 is a set of performance comparisons of the RMSE of difference CTL schemes. In this table, three CTL schemes were compared. One is the noncoherent combining using ten symbols per slot; the second is the coherent combing using three pilot symbols per slot; and the third is the simplified noncoherent combining using ten symbols per slot. For the target SNR=24 dB, the three schemes perform closely. When the SNR is −34 dB, the coherent combining performs worst because fewer symbols are used. The simplified scheme is worse than the non-simplified version. 
   
     
       
             
           
             
             
             
             
           
             
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               The RMSE of difference CTL schemes 
             
           
        
         
             
                 
                 
                 
               Simplified 
             
             
                 
               Noncoherent 
               Coherent 
               noncoherent 
             
             
                 
               combining using 
               combining using 
               combining using 
             
             
                 
               10 symbols 
               3 symbols 
               10 symbols 
             
             
                 
               per slot 
               per slot 
               per slot 
             
             
                 
                 
             
           
        
         
             
               SNR = −24 dB 
               1.63 
               1.51 
               1.52 
             
             
               SNR = −30 dB 
               2.18 
               2.27 
               2.17 
             
             
               SNR = −34 dB 
               3.07 
               5.15 
               4.03 
             
             
                 
             
           
        
       
     
   
   Each CTL tracks one finger independently. When two multipaths (or fingers) are within one and half chip, the two CTLs for the two fingers will interfere with each other and therefore degrades the CTL tracking performance. According to a particular aspect of the invention, a joint CTL scheme is used to reduce the interference from each other. Without loss of generality, it is possible to take an approach that there are two multipaths. The received signal r(t) can be expressed as
 
 r ( t )= h   1 ( t ) s ( t )+ h   2 ( t ) s ( t−τ )  Equation (14)
 
where s(t) is the useful signal,
 
                     s   ⁡     (   t   )       =       ∑     k   =     -   ∞       ∞     ⁢       a   k     ⁢     g   ⁡     (     t   -   kT     )             ,                           
α k  is the information symbol and g(t) is the signal waveform. h 1 (t) is the channel gain of the first path and h 2 (t) is the channel gain of the second path. τ is the relative delay between the two fingers. Note that the additive white Gaussian noise is not considered in Equation (14).
 
   When the relative delay between two adjacent fingers is less than 1.5 chip, the two independent CTLs will interfere with each other as shown in  FIG. 8 . It should be noted that triangle waveform is used for demonstration only and is not necessarily used in practice. Due to the interference, the performance of the two CTLs will degrade. The sample of the late signal of the first finger will contain the interference h 2 g(τ−T/2) from the second finger, and the sample of the early signal of the second finger will contain the interference h 1 g(τ−T/2) from the first finger. The sample of the late signal of the first finger S l   1st (k) is: 
                     S   l     1   ⁢           ⁢   st       ⁡     (   k   )       =           h   1     ⁡     (   k   )       ⁢     g   ⁡     (     T   /   2     )         +         h   2     ⁡     (   k   )       ⁢     g   ⁡     (     τ   -     T   /   2       )                   Equation   ⁢           ⁢     (   15   )                 
and the sample of the early signal of the second finger S e   2nd (k) is:
 
   
     
       
         
           
             
               
                 
                   
                     S 
                     e 
                     
                       2 
                       ⁢ 
                       nd 
                     
                   
                   ⁡ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       
                         h 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     ⁢ 
                     
                       g 
                       ⁡ 
                       
                         ( 
                         
                           τ 
                           - 
                           
                             T 
                             / 
                             2 
                           
                         
                         ) 
                       
                     
                   
                   + 
                   
                     
                       
                         h 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         g 
                         ⁡ 
                         
                           ( 
                           
                             T 
                             / 
                             2 
                           
                           ) 
                         
                       
                       . 
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
   
     FIG. 9  is a block diagram of joint CTL scheme  100 . The components are similar to  FIG. 4 , but with a joint error signal calculator  102  operating as part of two CTL circuits  103 ,  104 . 
   CTL circuit  103  includes an interpolator  113 , a delay circuit  114 , early and late PN despreaders  115 ,  116 , to magnitude calculation circuits  117 ,  118  which calculate absolute values of the respective signals, and to a summer  119 . Also included is an integrator and dump circuit  123 , a sign calculator  124 , and a second summer  125 . The interpolator  113  provides a single early/late output to delay circuit  114 , which provides an early signal to early PN despreader  115 . The output of interpolator  113  is provided directly to late PN despreader  116  and the outputs of the despreaders  115 ,  116  are provided to respective magnitude calculation circuits  117 , 118 . CTL circuit  104  includes an interpolator  133 , a delay circuit  134 , early and late PN despreaders  135 ,  136 , to magnitude calculation circuits  137 ,  138  which calculate absolute values of the respective signals, and to a summer  139 . Also included is an integrator and dump circuit  143 , a sign calculator  144 , and a second summer  145 . The interpolator  133  provides a single early/late output to delay circuit  134 , which provides an early signal to early PN despreader  135 . The output of interpolator  133  is provided directly to late PN despreader  136  and the outputs of the despreaders  135 ,  136  are provided to respective magnitude calculation circuits  137 ,  138 . 
   As can be seen, the relative delay τ between the two fingers can be obtained from two CTLs. As is the case with the circuit of  FIG. 4 , the circuit of  FIG. 9  uses the first error signal generation method-described by Equations (1) and (6) because the early sample and late sample are separated by exactly one chip interval and the early sample can be obtained from late sample by delaying one sample. An absolute calculation is used in order to simplify the hardware complexity. 
   According to particular aspects of the present invention, the following two methods are effective to cancel interference:
     Method 1: If the channel gains h 1 (t) and h 2 (t), are known, the inference is cancelled by subtracting the interference from useful signal. The error signals are generated as   

   
     
       
         
           
             
               
                 
                   
                     E 
                     r 
                     
                       1 
                       ⁢ 
                       st 
                     
                   
                   ⁡ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     
                        
                       
                         
                           S 
                           e 
                           
                             1 
                             ⁢ 
                             st 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                        
                     
                     2 
                   
                   - 
                   
                     
                        
                       
                         
                           
                             S 
                             l 
                             
                               1 
                               ⁢ 
                               st 
                             
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         - 
                         
                           
                             
                               h 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           ⁢ 
                           
                             g 
                             ⁡ 
                             
                               ( 
                               
                                 τ 
                                 - 
                                 
                                   T 
                                   / 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                        
                     
                     2 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
           
             
               
                 
                   
                     E 
                     r 
                     
                       2 
                       ⁢ 
                       nd 
                     
                   
                   ⁡ 
                   
                     ( 
                     k 
                     ) 
                   
                 
                 = 
                 
                   
                     
                        
                       
                         
                           
                             S 
                             e 
                             
                               2 
                               ⁢ 
                               nd 
                             
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         - 
                         
                           
                             
                               h 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           ⁢ 
                           
                             g 
                             ⁡ 
                             
                               ( 
                               
                                 τ 
                                 - 
                                 
                                   T 
                                   / 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                        
                     
                     2 
                   
                   - 
                   
                     
                        
                       
                         
                           S 
                           l 
                           
                             2 
                             ⁢ 
                             nd 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                        
                     
                     2 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
   
   The control signal C 0  is calculated using Equation (2).
     Method 2: If the channel gains h 1  and h 2  are not known, but the power of the two fingers is known, which are the means of the channel gains |h 1 | 2  and |h 2 | 2 , E|h 1 | 2  and E|h 2 | 2 . Since:   

   
     
       
         
           
             
               
                 
                   
                     1 
                     N 
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         1 
                       
                       N 
                     
                     ⁢ 
                     
                       
                          
                         
                           
                             S 
                             l 
                             
                               1 
                               ⁢ 
                               st 
                             
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                          
                       
                       2 
                     
                   
                 
                 = 
                 
                   
                     E 
                     ⁢ 
                     
                       
                          
                         
                           h 
                           1 
                         
                          
                       
                       2 
                     
                     ⁢ 
                     
                       
                         g 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           T 
                           / 
                           2 
                         
                         ) 
                       
                     
                   
                   + 
                   
                     E 
                     ⁢ 
                     
                       
                          
                         
                           h 
                           2 
                         
                          
                       
                       2 
                     
                     ⁢ 
                     
                       
                         g 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           τ 
                           - 
                           
                             T 
                             / 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
           
             
               
                 
                   
                     1 
                     N 
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         1 
                       
                       N 
                     
                     ⁢ 
                     
                       
                          
                         
                           
                             S 
                             e 
                             
                               2 
                               ⁢ 
                               nd 
                             
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                          
                       
                       2 
                     
                   
                 
                 = 
                 
                   
                     E 
                     ⁢ 
                     
                       
                          
                         
                           h 
                           1 
                         
                          
                       
                       2 
                     
                     ⁢ 
                     
                       
                         g 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           τ 
                           - 
                           
                             T 
                             / 
                             2 
                           
                         
                         ) 
                       
                     
                   
                   + 
                   
                     E 
                     ⁢ 
                     
                       
                          
                         
                           h 
                           2 
                         
                          
                       
                       2 
                     
                     ⁢ 
                     
                       
                         g 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           T 
                           / 
                           2 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
   
   The control signal C 0  is calculated as follows with the interference removed. 
   
     
       
         
           
             
               
                 
                   C 
                   0 
                   
                     1 
                     ⁢ 
                     st 
                   
                 
                 = 
                 
                   sign 
                   ⁢ 
                   
                     { 
                     
                       
                         
                           1 
                           N 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             
                                
                               
                                 
                                   S 
                                   e 
                                   
                                     1 
                                     ⁢ 
                                     st 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                       - 
                       
                         
                           1 
                           N 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             
                                
                               
                                 
                                   S 
                                   l 
                                   
                                     1 
                                     ⁢ 
                                     st 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                       - 
                       
                         E 
                         ⁢ 
                         
                           
                              
                             
                               h 
                               2 
                             
                              
                           
                           2 
                         
                         ⁢ 
                         
                           
                             g 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               τ 
                               - 
                               
                                 T 
                                 / 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                     } 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
           
             
               
                 
                   C 
                   0 
                   
                     2 
                     ⁢ 
                     nd 
                   
                 
                 = 
                 
                   sign 
                   ⁢ 
                   
                     { 
                     
                       
                         
                           1 
                           N 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             
                                
                               
                                 
                                   S 
                                   e 
                                   
                                     2 
                                     ⁢ 
                                     nd 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                       - 
                       
                         
                           1 
                           N 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             
                                
                               
                                 
                                   S 
                                   l 
                                   
                                     2 
                                     ⁢ 
                                     nd 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                       - 
                       
                         E 
                         ⁢ 
                         
                           
                              
                             
                               h 
                               1 
                             
                              
                           
                           2 
                         
                         ⁢ 
                         
                           
                             g 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               τ 
                               - 
                               
                                 T 
                                 / 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                     } 
                   
                 
               
             
             
               
                 Equation 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
   
   The present invention is useful in cellular mobile systems. In one preferred embodiment, the invention is implemented in a base station transmission as controlled by a radio network controller or a Node B transmit controller. It is understood, however, that the invention can be used for a wide variety of spread spectrum communications transmissions.