Patent Publication Number: US-7711035-B2

Title: Method and apparatus for suppressing communication signal interference

Description:
BACKGROUND OF THE INVENTION 
   The present invention generally relates to wireless communication systems, and particularly relates to interference suppression in wireless communication receivers. 
   Direct-sequence spread-spectrum modulation is commonly used in CDMA systems (such as W-CDMA, IS-95, and IS-2000). Data to be transmitted via a spread spectrum carrier is mapped into information symbols, and each information symbol is transmitted as a sequence of chips, which gives rise to bandwidth spreading. The sequence of chips used to spread the transmit symbols is referred to as the spreading code. 
   At the receiver, the received signal is despread using a despreading code, which typically is the conjugate of the spreading code. RAKE receivers represent a traditional approach to demodulating CDMA signals. RAKE receivers capitalize on the multipath propagation that typically exists between the transmitter and the receiver. Multipath propagation of the transmitted signal can lead to time dispersion, which causes multiple resolvable echoes (or rays) of the signal to be received at the receiver. A RAKE receiver aligns different ones of its “fingers” (correlators) with different ones of the signal echoes, and each finger outputs despread values at the symbol rate. These despread values are then weighted by the conjugate of the respective channel coefficient and then summed to produce a soft estimate of the transmitted symbol. This weighting and summing process is commonly referred to as RAKE combining. 
   Combining multipath echoes in the above manner yields an improved Signal-to-interference Ratio (SIR) when white noise is the dominant received signal impairment term at the receiver. However, RAKE combining is less than optimal when colored noise is the dominant impairment term. Colored noise arises from self-interference (Inter-Symbol Interference or ISI) and Multi-user Access Interference (MAI). As wireless networks crowd more and more users onto the same spectrum, and as the signal data rates increase, colored noise may become more problematic. 
   Thus, receiver structures capable of colored noise suppression represent an area of increasing interest. Unfortunately, the conventional approaches to interference suppression in colored noise environments entail potentially significant receiver complexity. For the typical portable communication device, such as a cellular radiotelephone, Portable Digital Assistant (PDA) or wireless pager, that complexity adds cost and undesirably affects cost, design time, and battery life. 
   SUMMARY OF THE INVENTION 
   The present invention comprises a method and apparatus for calculating whitening filters in communication signal processing applications, such as in wireless communication receivers. As a simplifying construction, a frequency domain representation of a whitening filter is made to depend on essentially one unknown, namely, a scaling factor that is based on an estimated ratio of total base station power to the power spectral density (PSD) of inter-cell interference plus noise. An exemplary method reduces the computational complexity of calculating the scaling factor by computing it based on the modeling terms used in a parametric model of the impairment correlations for a received communication signal. Preferably, the model comprises an interference impairment term scaled by a first model fitting parameter, and a noise impairment term scaled by a second model fitting parameter. Alternatively, the scaling factor can be computed by direct estimation, for example. 
   Thus, in an exemplary embodiment, the present invention comprises a method of generating a whitening filter for a communication signal transmitted from a wireless communication network base station comprising estimating a ratio of total base station transmit power to the PSD of inter-cell interference plus noise, calculating a scaling factor based on the estimated ratio of total base station transmit power to the PSD of inter-cell interference plus noise, and determining a whitening filter for whitening the communication signal. That whitening filter determination can be a function of the scaling factor, a frequency response associated with a transmit pulse shaping filter used at the base station, and a frequency response of a propagation channel through which the communication signal is received. 
   With the above basis for filter determination, the whitening filter determination can be made using a stored or calculated value for the transmit pulse shaping filter&#39;s frequency response, the medium channel coefficients calculated for the propagation channel, and the scaling factor. Because the filter response can be stored at the receiver based on a priori knowledge and the medium channel coefficient calculation can be made directly from pilot channel measurements, whitening filter determination reduces to the task of scaling factor determination. Basing scaling factor determination on the model fitting parameters of a parametric impairment correlation model offers one method of simplifying determination of the scaling factor. Using individualized signals—i.e., base-station-specific signals—from each of the base stations contributing to the inter-cell interference, if such signals are available, represents another simplified approach to calculating the scaling factor. 
   In a circuit embodiment, a receiver circuit is configured to generate a whitening filter for a communication signal transmitted from a wireless communication network base station. The exemplary receiver circuit comprises a calculation circuit configured to calculate a scaling factor based on an estimated ratio of total base station transmit power to the PSD of inter-cell interference plus noise, and a filter circuit configured to determine a whitening filter for whitening the communication signal as a function of the scaling factor, a frequency response associated with a transmit pulse shaping filter used at the base station, and a frequency response of a propagation channel through which the communication signal is received. 
   In one embodiment, the whitening filter is implemented as a receiver circuit that generates a filtered signal for input to a RAKE receiver. In this manner, colored interference in the communication signal is suppressed in advance of RAKE processing, which then provides multipath channel compensation and RAKE combining. In another embodiment, the whitening filter is implemented as part of a chip equalizer filter that also includes channel compensation filtering. In general, the whitening filter determination can be separate from, or part of, channel compensation filtering. Likewise, whitening filter circuit implementations can be separate from, or part of, channel compensation filter circuits. 
   Thus, the advantageous whitening filter determination of the present invention may be practiced as part of two-step signal processing method, wherein whitening is applied to a received communication signal, and then channel compensation is applied, or a combined-step method wherein whitening and channel compensation are performed together. Those skilled in the art will appreciate that because such filtering processes are linear, the filtering order for channel compensation and whitening may be reversed as needed or desired. 
   Of course, the present invention is not limited to the above features and advantages. Those skilled in the art will recognize additional features and advantages of the present invention upon reading the following detailed description and upon viewing the accompanying figures, in which like or similar elements are assigned like reference numbers. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a diagram of an exemplary wireless communication device that is configured according to one or more embodiments of the present invention. 
       FIG. 2  is a diagram of an exemplary communication signal flow between a remote transmitter and the device receiver depicted in  FIG. 1   
       FIG. 3  is a diagram of a receiver circuit for whitening filter determination in accordance with the present invention. 
       FIG. 4  is a diagram of exemplary processing logic embodying the circuit functionality of  FIG. 3 . 
       FIG. 5  is a diagram of an exemplary RAKE-based receiver in accordance with the present invention. 
       FIG. 6  is a diagram of an exemplary chip equalizer-based receiver in accordance with the present invention. 
       FIG. 7  is a diagram of a Single-Input-Multiple-Output (SIMO) receiver embodiment in accordance with the present invention. 
       FIG. 8  is a diagram of exemplary receiver details for the receiver of  FIG. 7 . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The present invention addresses suppression of colored noise, and offers simplified whitening filter generation. By way of non-limiting example, then, the present invention can be implemented to significant advantage in the wireless communication device  10  of  FIG. 1 . Device  10  comprises a receiver  12 , a transmitter  14 , one or more antennas  16 , a switch/duplexer  18 , a system controller  20 , and a user interface  22 . Those skilled in the art will appreciate that the actual architecture of device  10  can be varied without departing from the scope of the present invention, and that the illustrated architecture provides a non-limiting basis for discussing exemplary receiver operations. 
   With that in mind,  FIG. 2  illustrates a fundamental signal flow for the wireless transmission of data from a remote transmitter  24  to the receiver  12  of device  10 . Transmitter  24  can be, for example, a base station transmitter in a wireless communication network. The received signal, r(t), comprises the transmitted signal, s(t), but with channel distortions caused by propagation through the transmission medium channel, G(ω), and with additive white noise. The medium channel imparts phase and attenuation distortions that generally must be compensated for at the receiver  12  via some form of channel compensation filter that applies the conjugate medium channel, represented as G*(ω), to the received communication signal. However, application of the channel compensation filter leaves the colored noise problem unaddressed. Colored noise in the received signal generally arises in the form of ISI and MAI. 
   Therefore,  FIG. 2  illustrates an optimal conceptual implementation of filtering at receiver  12  that addresses the “matched filter in colored noise” by providing a signal-whitening step followed by a matching step (matching to the composite of the true channel and the whitening filter). The whitening filter, W(ω), compensates the received communication signal for colored noise and the present invention provides an advantageous method and apparatus for determining it in a computationally efficient manner. 
     FIG. 3  broadly illustrates an exemplary receiver circuit  30  that is configured to determine a whitening filter according to the present invention, and it may be configured to determine a channel compensation filter, as well. Indeed, the two filters may be determined together in some embodiments as a composite filter. It should be understood that receiver circuit  30  can be implemented as part of the receiver processing circuitry comprising receiver  12  of device  10 , and that it can be embodied in hardware, software, or some combination thereof. For example, receiver circuit  30  may be implemented as a computer program comprising stored program instructions for execution by a microprocessor, digital signal processor, or some other digital processor, or the like. Alternatively, receiver circuit  30  may comprise all or part of an Application Specific Integrated Circuit (ASIC), Field Programmable Gate Array (FPGA), Complex Programmable Logic Device (CPLD), or the like. 
   Regardless, receiver circuit  30  can be implemented as part of the signal processing chain for the communication signal(s) received by receiver  12  of device  10 . In particular, receiver circuit  30  can be configured to generate a filtered signal from the received communication signal, wherein the filtered signal serves as the input to a subsequent demodulation processor that demodulates/decodes the filtered signal to recover transmitted data bits, for example. 
     FIG. 4  broadly illustrates exemplary whitening filter determination. While whitening may be done in either the time or frequency domains, a frequency domain representation of the desired whitening filter serves as the advantageous basis for reducing its calculation essentially to the determination of one unknown. In an exemplary Single-Input-Single-Output (SISO) context, this process is best understood by forming an exemplary composite filter as, 
                   H   ⁡     (   ω   )       =           kP   *     ⁡     (   ω   )       ⁢       G   *     ⁡     (   ω   )               I   or     ⁢              P   ⁡     (   ω   )       ⁢     G   ⁡     (   ω   )              2       +     Φ   ⁡     (   ω   )                   (   1   )               
where P(ω) equals the frequency response of the transmit pulse shaping filter associated with transmission of the received communication signal, P*(ω) equals the conjugate of that frequency response, i.e., it equals the receiver pulse shaping filter&#39;s frequency response, G(ω) equals the frequency response of the propagation channel through which the communication signal was received, G*(ω) equals the conjugate of that frequency response, I or  equals the total transmit power of the transmitter transmitting the communication signal (e.g., a network base station transmitter in a given cell or other coverage area), Φ(ω) equals the PSD of inter-cell interference plus noise at the receiver  12 , and k is an arbitrary real constant.
 
   To cast Eq. (1) in terms of the conceptual optimal receiver filtering structure depicted in  FIG. 2 , one can rewrite the composite filter H(ω) as the product of the whitening and channel compensation filters: 
   
     
       
         
           
             
               
                 
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   The form shown in Eq. (2) can be manipulated to provide more than one SISO embodiment of the invention, and can be simplified based on the assumption that P(ω) is known a priori by the receiver  12 . That assumption is consistent with the practice of configuring receiver filtering to impart the conjugate response of the transmit pulse shaping filter. Such filter response information can be embodied in a fixed filter structure at the receiver  12 , or can be based on filter response information stored at receiver  12  for use in a digital filtering algorithm. 
   A further assumption with respect to Eq. (2) is the existence of a pilot channel (e.g. common pilot or CPICH in W-CDMA) and a means for estimating channel delays and net channel coefficients at the receiver  12 . In other words, from Eq. (2), the frequency responses for the transmit and receiver pulse shaping filters, P(ω) and P*(ω) are known a priori at receiver  12 , and the frequency responses for the net propagation channel and its conjugate, G(ω) and G*(ω), can be calculated directly from the pilot channel estimates. That leaves as unknowns the total transmit power I or  and the PSD of the inter-cell interference plus noise, Φ(ω). 
   With the substitution 
             γ   =       I   or       Φ   ⁡     (   ω   )           ,         
the whitening filter representation is
 
                     W   ⁡     (   ω   )       =     1         γ   ⁢              G   ⁡     (   ω   )       ⁢     P   ⁡     (   ω   )              2       +   1           ,           (   3   )               
where γ may be viewed as a frequency domain scaling factor for the whitening filter expression. Thus, whitening filter determination reduces to the determination of the γ as the ratio of I or  to Φ(ω).
 
     FIG. 4  illustrates exemplary processing logic for determining the whitening filter, W(ω), or the time-domain embodiment of it, w(t), based on the scaling factory γ. Exemplary processing begins with estimating I or  and Φ(ω) (Step  100 ). From there, processing continues with the calculation of γ based on a ratio of the estimates for I or  and Φ(ω) (Step  102 ). With the scaling factor γ thus determined, and with the transmit filter&#39;s frequency response known (or calculated), and with estimation of the medium channel&#39;s frequency response, the whitening filter can be determined according to Eq. (3) (Step  104 ). 
   The above exemplary processing can be applied in the context of specific receiver structures. For example,  FIG. 5  illustrates an exemplary chip-equalization embodiment of receiver  12 . In this embodiment, receiver  12  comprises a receiver front-end  40 , a searcher  42 , a delay estimator  44 , a channel estimator  46 , pilot channel correlators  48 , a medium channel estimator  50 , a ratio estimator  52  to estimate the ratio of I or /Φ(ω), a chip equalizer  54 , and a traffic correlator  56 . 
   The chip-equalization filter implemented by chip equalizer  54  can be derived by rewriting Eq. (2) as 
                   H   ⁡     (   ω   )       =           P   *     ⁡     (   ω   )       ⁢       H   ′     ⁡     (   ω   )         =           P   *     ⁡     (   ω   )       ⁡     [         kG   *     ⁡     (   ω   )             I   or     ⁢              P   ⁡     (   ω   )       ⁢     G   ⁡     (   ω   )              2       +     Φ   ⁡     (   ω   )           ]       .               (   4   )               
Recognizing that P*(ω) represents the receive pulse shaping filter in the received signal processing path of receiver  12 , a primary task for this embodiment lies in the determination of H′(ω). By modeling the other-cell interference plus noise term as a white Gaussian noise process with one-sided spectral density of N 0 , H′(ω) can be rewritten as
 
                       H   ′     ⁡     (   ω   )       =         kG   *     ⁡     (   ω   )           γ   ⁢              P   ⁡     (   ω   )       ⁢     G   ⁡     (   ω   )              2       +   1         ,           (   5   )               
where γ is now a real scale factor, and is equal to
 
               I   or       N   0       .         
The magnitude of the scale factor k does not affect the optimality of the final chip equalizer and is therefore assigned an arbitrary value (e.g., 1). Thus, the main estimation task for the chip equalizer embodiment is to compute G(ω) and γ.
 
   Considering the computation of G(ω) first, and per the above pilot channel assumptions, the receiver  12  estimates the channel delays and the net channel coefficients, which include the transmit/receive signal processing effects, as well as the medium (propagation) channel effects. Given L channel delays in a multipath propagation channel, the medium channel coefficients can be obtained from the net channel coefficients via 
                       c   ⁡     (     τ   0     )       =         E   CPICH       ⁢       ∑     j   =   0       L   -   1       ⁢           ⁢       g   j     ⁢       R   p     ⁡     (       τ   0     -     τ   j       )               ,     
     ⁢       c   ⁡     (     τ   1     )       =         E   CPICH       ⁢       ∑     j   =   0       L   -   1       ⁢           ⁢       g   j     ⁢       R   p     ⁡     (       τ   1     -     τ   j       )               ,   and     ⁢     
     ⁢   ⋮   ⁢     
     ⁢         c   ⁡     (     τ     L   -   1       )       =         E   CPICH       ⁢       ∑     j   =   0       L   -   1       ⁢           ⁢       g   j     ⁢       R   p     ⁡     (       τ     L   -   1       -     τ   j       )               ,             (   6   )               
where τ i  is the ith channel delay indicated by the delay searcher, E CPICH  equals an energy measurement of a common pilot channel (CPICH), g j  equals the jth medium coefficient, c(τ k ) is the net channel coefficient at delay τ k  and R p (τ) represents the pulse shape correlation function given as
 
             ∫   ∞   ∞     ⁢       p   ⁡     (     t   +   τ     )       ⁢       p   *     ⁡     (   τ   )       ⁢           ⁢       ⅆ   τ     .             
Eq. (6) can be rewritten in vector-matrix notation by absorbing the constant factor of E CPICH  into the medium channel coefficient as
   R   p   {tilde over (g)}=c.   (7) 
Eq. (7) can be solved by direct matrix inversion or by application of an iterative technique, such as Gauss-Seidel. The solution yields medium channel coefficients at the path delays. A fast Fourier transform (FFT) can then be applied to the time domain medium coefficients to obtain the frequency response G(ω) of the medium channel. Thus, one or more FFT circuits can be included as part of receiver  12 .
 
   In considering the calculation of the scaling factor γ, receiver  12  can be configured to use a pilot channel-based estimation technique that is based on a parametric model of the received communication signal&#39;s impairment correlations. An exemplary parametric model is disclosed in the co-pending patent application, which is assigned Ser. No. 10/800,167, and which was filed on Mar. 12, 2004. That application is incorporated in its entirety herein by reference. 
   While the above-identified application includes additional background and explanatory details, an exemplary parametric model of communication signal impairment correlations includes one or more impairment terms, each scaled by a model fitting parameter. The model fitting parameters are then updated on a recurring basis as part of an ongoing fitting process wherein the model is fitted to impairment correlation estimates. In more detail, an exemplary parametric model can be expressed as
 
 {tilde over (R)}=αR   I   +βR   N ,  (8)
 
where R I  represents an interference correlation term (matrix) scaled by the first model fitting parameter α and R N  represents a noise correlation term (matrix) scaled by the second model fitting parameter β. The model fitting parameters are adapted during a fitting process—e.g., during a Least Squares (LS) fitting process, wherein the model fitting parameters are adapted to minimize the model error.
 
   It can be shown that α=1/(E c /I or ) CPICH , where (E c /I or ) CPICH  represents the fraction of the base station energy given to the common pilot channel, and β=N 0 . Thus, given an estimate of the pilot channel power and the values α and β, the parameter γ can be determined from 
                   γ   =       E   ⁢     {         g   ~     H     ⁢     g   ~       }     ⁢   α     β       ,           (   9   )               
where E{*} represents statistical expectation, and {tilde over (g)} represents a scaled medium coefficient estimate. A statistical approximation can be used to solve the estimation problem for γ. An exemplary method is given as
   E{{tilde over (g)}   H   {tilde over (g)}}≡I   CPICH ( n )=λ I   CPICH ( n− 1)+(1−λ) {tilde over (g)}   H   {tilde over (g)}.   (10) 
In the above expression, I CPICH (n) is the pilot channel power at time index n (some multiple of the pilot symbol rate) and λ is a value between 0 and 1.
 
   With the above in mind, then, the receiver embodiment illustrated in  FIG. 5  may be configured such that is operative to carry out whitening filter generation in accordance with the present invention based on a number of exemplary processing steps. Those steps include these items:
         estimate channel delays by using searcher  42  and delay estimator  44 ;   estimate net channel coefficients via channel estimator  46 ;   estimate the scaled version of medium coefficients using equations (6) and (7) as implemented in medium channel estimator  50 ;   estimate α and β using parametric modeling of received signal impairment correlations in receiver circuit  30 , an embodiment of which may be implemented as part of chip equalizer  54 ;   compute medium coefficients as g=α{tilde over (g)} in chip equalizer  54 ;   compute FFT of g to get G(ω), which may be done in chip equalizer  54 ;   compute γ from Eqs. (9) and (10), which may be done in chip equalizer  54 ; and   compute chip equalizer filter from Eq. (5), which may be done in chip equalizer  54 .
 
Note that chip equalizer may include one or more processing circuits configured to carry out the above whitening/composite filter calculations. Further, note that the final filter obtained from the last step can be implemented in either the time or frequency domain, and received communication signal filtering as described herein can be carried out in either the time domain, or the frequency domain.
       

   In any case, the single traffic correlator  56  operates on the filtered (whitened and channel equalized) signal output by chip equalizer  54 . More particularly, traffic correlator  56  computes estimates of the transmitted symbols contained in the received communication signal, r′, which is input to the chip equalizer  54  from the receiver front-end  40 . As such, receiver front-end  40  can include low-noise amplifiers, filters, analog-to-digital-converters, and other circuits as needed or desired to produce a digital samples representing the received communication signal. 
   The present invention also can be implemented in an “over-whitening plus RAKE” embodiment, wherein an over-whitening filter provides a filtered version of the received communication signal for subsequent processing by a RAKE receiver. The over-whitening filter suppresses colored noise from the received communication signal before RAKE processing, thus improving the performance of RAKE combining. 
   In support of this RAKE-based embodiment of the present invention, Eq. (2) can be rewritten as 
                   H   ⁡     (   ω   )       =           P   *     ⁡     (   ω   )       ⁢       W   ^     ⁡     (   ω   )       ⁢       G   *     ⁡     (   ω   )         =           P   *     ⁡     (   ω   )       ⁡     [     k         I   or     ⁢              P   ⁡     (   ω   )       ⁢     G   ⁡     (   ω   )              2       +     Φ   ⁡     (   ω   )           ]       ⁢         G   *     ⁡     (   ω   )       .                 (   11   )               
Again, P*(ω) represents the receive pulse shape filter, and G*(ω) represents channel compensation as implemented in the RAKE receiver circuit. Thus, as with the chip equalization embodiment of  FIG. 5 , the primary effort for this embodiment lies in the determination of Ŵ(ω). As before, by modeling the inter-cell interference plus noise term as a white Gaussian noise process with one-sided spectral density of N 0 , the whitening filter Ŵ(ω) can be rewritten as
 
   
     
       
         
           
             
               
                 
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   The scale factor {circumflex over (k)} in the numerator does not affect the optimality of the final result, so it can be assigned a convenient value, such as “1.” The same methods for computing G(ω) and γ described above can be used here, and may be implemented in an exemplary RAKE-based embodiment of receiver  12 , such as illustrated in  FIG. 6 . 
   As shown in  FIG. 6 , receiver  12  comprises a receiver front-end circuit  60 , a searcher  62 , a delay estimator  64 , a channel estimator  66 , pilot channel correlators  68 , a medium channel estimator  70 , a ratio estimator  72  to estimate 
               I   or       N   0       ,         
an over-whitening filter  74 , and a RAKE receiver circuit  76 , including a plurality of traffic correlators (“fingers”)  78 , and a RAKE combining circuit  80 . Note that the over-whitening filter  74  can be configured to include some or all of the functionality of the earlier-depicted receiver circuit  30 , and thus is adapted to carry out whitening filter determination.
 
   That determination can be carried out according to an overall processing method similar to that described for the chip equalization embodiment. Specifically, an exemplary receiver processing method in the RAKE-based embodiment comprises these steps:
         estimate channel delays by using searcher  62  and delay estimator  64 ;   estimate net channel coefficients via channel estimator  66 ;   estimate the scaled version of medium coefficients using equations (6) and (7) as implemented in medium channel estimator  70 ;   estimate α and β using parametric modeling of received signal impairment correlations in receiver circuit  30 , an embodiment of which may be implemented as part of over-whitening filter  74 ;   compute medium coefficients as g=α{tilde over (g)} in over-whitening filter  74 ;   compute FFT of g to get G(ω), which may be done in over-whitening filter  74 ;   compute γ from Eqs. (9) and (10), which may be done in over-whitening filter  74 ; and   compute over-whitening filter from Eq. (12)—note that the final filter can be implemented in either the time or frequency domain; and   RAKE combine over-whitened communication signal to compute estimates of the transmitted symbols within the received communication signal—i.e., despread the over-whitened signal in each of one or more fingers  78  according to multipath delays, and combine the finger outputs to form a RAKE-combined signal for subsequent demodulation processing.       

   While the above RAKE-based embodiment, and the earlier described chip-equalization embodiment, represent exemplary SISO embodiments of the present invention, the present invention can be readily extended to Single-Input-Multiple-Output (SIMO) embodiments.  FIG. 7  illustrates an exemplary SIMO embodiment, wherein receiver  12  of device  10  includes M receive antennas ( 16 - 1  through  16 -M), and the kth antenna receives s k (t). The antennas  16  are coupled to one or more receiver processing circuits  82 , which may be configured to implement an embodiment of the earlier illustrated receiver circuit  30  for whitening filter determination. 
   In operation, each antenna  16 - k  receives signal s k (t), which is obtained by passing the data signal s(t) through propagation channel k. The impulse response of the propagation channel from the base station (BTS) transmitter to the kth receive antenna at receiver  12  is denoted by g k (t) with Fourier transform G k (ω). Therefore, the noise-free signal at the kth antenna is given by
 
 s   k ( t )= s ( t )* g   k ( t ),  (13)
 
where * denotes convolution. Considering Eq. (13), the total received signal at the kth antenna can be expressed as
 
 r   k ( t )= s   k ( t )+ v   k ( t ).  (14)
 
Here, v k (t) is a noise that models inter-cell interference and thermal noise at the kth antenna.
 
   It can be shown that a decision statistic for detecting data symbols has the form 
                     Y   ⁡     (   t   )       =       ∑     k   =   1     M     ⁢     ∫       h   ⁡     (       t   -     t   ′       ,   k     )       ⁢       y   k     ⁡     (     t   ′     )       ⁢     ⅆ     t   ′               ,           (   15   )               
where y k (t) is the signal at the kth antenna after despreading the received signal r k (t), and where h(t,k) is the impulse response of the linear filter with frequency response
 
   
     
       
         
           
             
               
                 
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                     ω 
                     ) 
                   
                 
                 = 
                 
                   
                     
                       
                         
                           kP 
                           * 
                         
                         ⁡ 
                         
                           ( 
                           ω 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           G 
                           k 
                           * 
                         
                         ⁡ 
                         
                           ( 
                           ω 
                           ) 
                         
                       
                     
                     
                       
                         
                           I 
                           or 
                         
                         ⁢ 
                         
                           
                              
                             
                               P 
                               ⁡ 
                               
                                 ( 
                                 ω 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             M 
                           
                           ⁢ 
                           
                             
                                
                               
                                 
                                   G 
                                   k 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   ω 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                       + 
                       
                         Φ 
                         ⁡ 
                         
                           ( 
                           ω 
                           ) 
                         
                       
                     
                   
                   . 
                 
               
             
             
               
                 ( 
                 16 
                 ) 
               
             
           
         
       
     
   
   Noting that Eq. (15) essentially describes a receiver with M parallel sub-channels, it is advantageous to rewrite (16) in the form
 
 H (ω, k )= P *(ω) G*   k (ω) Ŵ (ω),  (17)
 
where
 
   
     
       
         
           
             
               
                 
                   
                     W 
                     ^ 
                   
                   ⁡ 
                   
                     ( 
                     ω 
                     ) 
                   
                 
                 = 
                 
                   
                     k 
                     
                       
                         
                           I 
                           or 
                         
                         ⁢ 
                         
                           
                              
                             
                               P 
                               ⁡ 
                               
                                 ( 
                                 ω 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             M 
                           
                           ⁢ 
                           
                             
                                
                               
                                 
                                   G 
                                   k 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   ω 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                       + 
                       
                         Φ 
                         ⁡ 
                         
                           ( 
                           ω 
                           ) 
                         
                       
                     
                   
                   . 
                 
               
             
             
               
                 ( 
                 18 
                 ) 
               
             
           
         
       
     
   
   One can observe that the over-whitening filter in the above SIMO embodiment is common across antennas  16 , and the receiver structure illustrated in  FIG. 8  represents an exemplary capitalization on that commonality. In  FIG. 8 , receiver  12  is implemented as a beamformer comprising a RAKE receiver circuit  84 - k  for each antenna  16 - k , each circuit  84 - k  including a pulse shaping filter P*(ω) and a channel compensation filter G k *(ω), a RAKE combining circuit  86  for additively combining the antenna streams (the RAKE outputs), and an over-whitening filter circuit  88  for over-whitening the RAKE combined signal output from combiner circuit  86  by applying the over-whitening filter Ŵ(ω). 
   It should be noted that the RAKE receiver circuits  84  can include, or can be associated with, one or more FFT circuits for converting the received communication signal to a frequency domain for processing, or the above filters can be transformed into the time domain for application to the time-domain received communication. Likewise, the over-whitening filter implemented by circuit  88  can be determined based on the exemplary frequency domain processing described herein, but applied to the received communication signal in either the time or frequency domain. 
   Further, because of the linear nature of the described processing, over-whitening could be performed in advance of each RAKE receiver circuit  84 - 1 —i.e., the filtering order could be swapped. While swapping the order might require replication of the over-whitening filter in each RAKE processing path, such an arrangement may be advantageous in some design implementations. For example, if the over-whitening-plus-RAKE embodiment of  FIG. 6  is implemented in modular integrated-circuit form, e.g., for ASIC/FPGA implementation, that basic module could be replicated as many times as needed for a given SIMO receiver implementation. 
   For the illustrated SIMO embodiment, the other-cell interference plus noise PSD term again can be modeled as a white Gaussian noise process with one-sided spectral density of N 0 . Using this model, Eq. (18) can be rewritten in the form 
                     W   ^     ⁡     (   ω   )       =         k   ^         γ   ⁢            P   ⁡     (   ω   )            2     ⁢       ∑     k   =   1     M     ⁢              G   k     ⁡     (   ω   )            2         +   1       .             (   19   )               
As with the SISO embodiments, the scale factor in the numerator does not affect the optimality of the final result, so it can be assigned a value of 1, for example. Again, then, the primary computational task for whitening filter determination lies with calculation of the scaling factor γ (and with the computation of G k (ω) on which γ depends).
 
   An exemplary processing method for whitening filter determination in the SIMO embodiment is similar to the SISO method(s) described earlier. Such processing includes these steps:
         For each antenna  16 - k:  
           Estimate channel delays;   Estimate net channel coefficients;   Estimate scaled version of medium coefficients using Eqs. (6) and (7);   Estimate α k  and β k  using parametric modeling (or using direct estimation);   Compute medium coefficients as g k =α{tilde over (g)} k ;   Compute FFT of g k  to get G k (ω);   Rake combine traffic data;   Compute γ k  from equations (9) and (10);   
           Compute final estimate of γ as the arithmetic mean of the γ k , or by selecting one of the γ k ;   Compute the over-whitening filter from Eq. (19)—note that the final filter can be implemented in either the time or frequency domain; and   Filter the combined signal with over-whitening filter to compute estimates of transmitted symbols contained in the received communication signal.       

   Thus, the receiver processing steps for the exemplary SIMO embodiment are similar to the processing steps for the exemplary SISO embodiments (RAKE, chip equalizer), with the exception that some of the processing is done on a per-antenna basis for SIMO. Regardless, those skilled in the art should appreciate that the present invention provides an advantageous basis for whitening filter computation based on a frequency domain representation of the whitening filter that reduces essentially to one unknown, namely, a scaling factor that depends on an estimate of the ratio of total transmitter power, I or , to the PSD of other-cell interference plus noise, Φ(ω). 
   While that ratio can be estimated using the model fitting parameters from a parametric model of received signal impairment correlations as described herein, it also can be directly estimated from a direct estimate of total transmit power, and from a direct estimate of the inter-cell interference plus noise. The direct estimate of total transmit power can be based on a value received from the base station, or estimated from the pilot power, or based on some configured value. The direct estimate of inter-cell interference plus noise can be based on signal measurements, such as where each base station is configured to transmit an individualized signal, much like a training sequence burst, or other identifying data pattern, from which the device  10  can generate inter-cell interference measurements based on receiving such signals from each of one or more neighboring base station transmitters. 
   However, regardless of whether the ratio used for calculation of the scaling factor γ is indirectly estimated based on parametric modeling, the present invention provides many advantages with respect to its method of whitening filter determination. For example, the chip equalizer embodiment of  FIG. 5 , and the RAKE receiver embodiment of  FIG. 6  can be generally considered as “RAKE plus filter” implementations that can be cleanly realized in modular chip set-type integrated circuit structures, or embodied as synthesizable library modules for use in chip design software. For example, a basic chipset would include a RAKE receiver circuit, and a higher-performance embodiment would add the over-whitening filter function. Since the over-whitening filter function can be implemented in hardware or software, or some combination thereof, the present invention provides system designers with significant design flexibility. 
   It should be understood, then, that the present invention broadly provides a method and apparatus for whitening filter determination in the context of received communication signal processing. While the present invention can be implemented in conjunction with RAKE receiver structures and chip equalization receiver structures, it is not limited to those embodiments, nor is it limited to SISO or SIMO systems, as it has broad applicability across a range of receiver types and system arrangements. Thus, the present invention is not limited by the foregoing discussion, nor by the accompanying figures, but rather is limited only by the following claims and their reasonable legal equivalents.