**FORWARD LINK FILTER**

Pavlovic, Boris (2/2 Knox Street, NOBLE PARK, Victoria 3174, AU)

*;*

**H03H17/06***; (IPC1-7): H03H17/00; G06F17/00*

**H04L25/03**US6209013B1 | ||||

US5838744A | ||||

US5778029A |

1. | A software defined forward link finite impulse response (FIR) filter for performing filtering on the forward link of a code division multiple access (CDMA) system, said FIR filter having a number of taps and being characterised in that: said forward link FIR filter performs both baseband filtering and phase equalisation filtering ; and said forward link FIR filter has a number of taps which is a multiple of twelve which is at least twenty four and less than a theoretical number of taps required to combine a FIR filter for performing baseband filtering and a FIR filter for performing phase equalisation filtering. |

2. | A filter as claimed in claim 1, wherein said number of taps is a multiple of twelve. |

3. | A filter as claimed in claim 1, wherein said forward link FIR filter has fortyeight taps or less. |

4. | A filter as claimed in claim 1, wherein said forward link FIR filter has twentyfour taps. |

5. | A filter as claimed in claim 4, wherein the coefficients of the taps are approximately as follows: k hd (k) 00.00362693778292 1 +0.00802090990285 2 +0.01006559752104 30. 01571528593967 40.03132727806071 5 +0.01481661445718 6 +0. 05458001925757 7 +0. 00132458035184 80. 04936295831208 9 +0.04004271558163 10 +0.13273006685876 11 +0.00811170487654 120.17554005340532 130.04996561130871 14 +0.32857796026358 15 +0.50285441818962 16 +0.30564953412358 17 +0.04828772968724 180.01726252649559 19 +0.01056919626843 200.00660408946221 210.03500169168975 220.01938548819596 23 +0.00442585877230. |

6. | A method of designing a software defined forward link finite impulse response (FIR) filter for performing baseband and phase equalisation filtering in a code division multiple access (CDMA) system including: selecting a number of taps (n) of a desired forward link FIR filter ; determining a complex frequency response of a desired equivalent filter (H) to a FIR baseband filter (H1) and a FIR phase equalisation filter (Hz) ; and calculating a set of n coefficients for a designed forward link FIR filter (Hd) which minimises error between the complex frequency response of the designed FIR filter (Hd) and the complex frequency response the desired FIR filter (H). |

7. | A method as claimed in claim 6, wherein determining a complex frequency response of a desired equivalent filter involves: determining the impulse response of a FIR baseband filter (H1) which satisfies the baseband filtering requirements of a CDMA system ; sampling the determined impulse response of said FIR baseband filter (H1) at a sampling rate which is related to the selected number of taps (n) to thereby obtain a set of nlr coefficients of a resampled FIR baseband filter each coefficient corresponding to a respective one of the taps ; scaling the coefficients of the resampled FIR baseband filter to produce unity gain in the baseband ; determining the complex frequency response of the scaled and resampled FIR baseband filter ; determining the complex frequency response of a FIR phase equalisation filter which satisfies the phase equalisation filtering requirements of said CDMA system ; determining a complex frequency response of said scaled and resampled FIR baseband filter (Hir) combined with said FIR baseband filter (H2) to thereby determine a complex frequency response of a desired equivalent FIR filter (Hd). |

8. | A method as claimed in claim 7, wherein the transfer function of the designed filter is in the general form :<BR> B(z) = b1 + b2z1 + ... + bnb+1Znb<BR> Hd(z) = A(z) a1 + a2z1 +... + ana+1Zna Where: nb = n1 na = 0. |

9. | A method as claimed in claim 8, wherein the error is minimised using the equation where: A (@k) and B (@k) are the Fourier transforms of the polynomials A and B respectively ; Mk is frequency in radians at point k ; nf is the number of frequency points at which Hd (j) is defined ; Hd (wok) is the complex frequency response of the desired filter for frequency Mk ; and wt (k) is a weighting function which is defined in the same number of points as H (wok). |

10. | A method as claimed in claim 9, wherein the number of taps (n) is twentyfour. |

11. | A filter produced in accordance with the method of any one of claims 6 to 10. |

12. | A method of filtering a forward link of a code division multiple access system involving using the filter of claim 1. |

13. | A method of filtering a forward link of a code division multiple access system involving using the filter of claim 11. |

Background to the Invention Standards, such as the interim standard 95 (IS- 95) administered by the US Telecommunications Industry Association, prescribe performance requirements for baseband filtering and phase equalisation filtering.

Baseband filtering is used to shape the transmission wave to meet with bandwidth constraints while minimising intersymbol interference. Phase equalisation is used to simplify the design of the mobile station receive filter.

In particular, the hardware implementation of a finite impulse response (FIR) filter of the IS-95 specification calls for a minimum of 48 taps for the baseband filter in addition to a filter for phase equalisation.

It is also known, to implement filters in software, where, for example, program representative of the filtering function and including a set of coefficients for a FIR filter is stored in memory and run by a processor such as a digital signal processor to provide the necessary filtering functions. When a 48-tap FIR filter is implemented in software, the number of computations required to implement such a filter becomes very important. Implementing both a baseband filter and a phase equalisation filter in software represents a significant computational burden. Accordingly, it would

be advantageous to provide an alternative FIR filter for use on the forward transmission link which reduces computational requirements while still satisfying the filter requirements of the CDMA system.

Summary of the Invention In a first aspect, the invention provides a forward link finite impulse response (FIR) for performing filtering on the forward link of a code division multiple access (CDMA) system, said FIR filter having a number of taps and being characterised in that: said forward link FIR performs both baseband filtering and phase equalisation filtering ; and said forward link FIR filter has a number of taps which is a multiple of two which is at least twenty-four and less than a theoretical number of taps required to combine a FIR filter for performing baseband filtering and a FIR filter for performing phase equalisation filtering.

Preferably, said forward link FIR has forty-eight taps or less.

Preferably, said forward link FIR has twenty-four taps.

In accordance with a second aspect of the invention there is provided a method of designing a forward link finite impulse response (FIR) filter for performing baseband and phase equalisation filter in a code division multiple access (CDMA) system including: selecting a number of taps (n) of a desired forward link FIR filter ; determining a complex frequency response of a desired equivalent filter (H) to a FIR baseband filter (H1) and a FIR phase equalisation filter (Hz) ; and calculating a set of n coefficients for a designed forward link FIR filter (Hd) which minimises error

between the complex frequency response of the designed FIR filter (Hd) and the complex frequency response the desired FIR filter (H).

Preferably, determining a complex frequency response of a desired equivalent filter involves : determining the impulse response of a FIR baseband filter (H1) which satisfies the baseband filtering requirements of a CDMA system ; sampling the determined impulse response of said FIR baseband filter (FIl) at a sampling rate which is related to the selected number of taps (n) to thereby obtain a set of nlr coefficients of a resampled FIR baseband filter each coefficient corresponding to a respective one of the taps ; scaling the coefficients of the resampled FIR baseband filter to produce unity gain in the baseband ; determining the complex frequency response of the scaled and resampled FIR baseband filter ; determining the complex frequency response of a FIR phase equalisation filter which satisfies the phase equalisation filtering requirements of said CDMA system ; determining a complex frequency response of said scaled and resampled FIR baseband filter (Hlr) combined with said FIR baseband filter (H2) to thereby determine a complex frequency response of a desired equivalent FIR filter (Hd).

Preferably, the transfer function of the designed filter is in the format: Where: nb = n-1 na = 0 Preferably the error is minimised using the equation :

where: A (wok) and B (k) are the Fourier transforms of the polynomials A and B respectively ; wk is frequency in radians at point k ; nf is the number of frequency points at which Hd (jim) is defined ; Hd (k) is the complex frequency response of the desired filter for frequency tdk ; and wt (k) is a weighting function which is defined in the same number of points as H (wok).

Preferably, the number of taps (n) is twenty- four.

In a further aspect the invention provides a filter produced in accordance with the above method.

Brief Description of the Drawings A preferred embodiment of the invention will now be described in relation to the accompanying drawings in which: Figure 1 is a basic model of a data transmission system of the prior art ; Figure 2 shows the position of a baseband filter on the forward link of an IS-95 system ; Figure 3 shows the limits for the frequency response of the baseband filter ; Figure 4 shows how the baseband filter and the phase equalisation filter may be cascaded ; Figure 5 shows the impulse response of a baseband FIR filter as defined in the IS-95 specification ; Figure 6 illustrates resampling of the impulse

response of the filter of Figure 5 ; Figure 7a and 7b show the frequency and phase responses of the resampled filter of Figure 6 ; Figure 8 shows the phase characteristics of the phase equalisation filter ; Figure 9 shows the amplitude characteristics of the designed and desired filter ; Figure 10 illustrates the phase response of the designed filter and desired filter ; Figures lla and llb show the frequency response of the designed and desired filter in the pass band and stop band respectively ; and Figure 12 shows the phase error between the designed and desired filters.

Description of the Preferred Embodiment A key issue in designing a baseband waveform is the efficient use of the available bandwidth and the minimisation of inter symbol interference (ISI). It is important that the transmission signal D (t) be"shaped"in the form of Nyquist pulses to reduce the required bandwidth for transmission of the signal and remove or minimise ISI.

The position of the baseband filter 1 in the IS- 95 code division multiple access (CDMA) system is shown in Figure 2.

The IS-95 system uses a pair of baseband wave- shaping filters designed to meet a bandwidth constraint while minimizing ISI. Each filter is specified by the IS- 95 standard to have a frequency response H (f) that satisfies the limits shown in Figure 3. The figure illustrates that the normalized frequency response of the filter shall be contained within Si in the pass band, Os f<fp, and shall be less than or equal to-82 in the stop band, f>fs. In the IS-95 system 61=1. 5dB, 82=40dB,

Fp=590kHz and Fs=740kHz.

In addition to the frequency domain limits specified in Figure 3, the baseband filter 1 must also satisfy the following time domain constraint. If h (t) is the impulse response of the filter then the following relation must be satisfied: Mean Squared Error = E [ah (kTs-T)-ho (k) t < 003 k=0 where the constants a and T are used to minimize the mean squared error. The constant Tg is equal to 203.451... ns, which equals one quarter of the psuedo-noise (PN) chip. The values of the coefficients ho (k), for k<48 are given in Table 1. Thus, it will be appreciated that the IS-95 standard specifies a 48 tap finite impulse response (FIR) filter.

Table 1. Coefficients h (k) of filter prototype k k h (k) 0 47-0.025288315 1 46-0.034167931 2 45-0.035752323 3 44-0.016733702 4 43 0.021602514 5 42 0.064938487 6 41 0.091002137 7 40 0.081894974 8 39 0.037071157 9 38-0. 021998074 10 37-0.060716277 11 36-0.051178658 12 35 0.007874526 13 34 0.084368728 14 33 0. 126869306 15 32 0.094528345 16 31-0.012839661 17 30-0.143477028 18 29-0. 211829088 19 28-0. 140513128 20 27 0.094601918 21 26 0.441387140 22 25 0. 785875640 23 24 1.0

The IS-95 standard also requires the base station to provide phase equalisation for the transmit signal path designed to provide the equivalent baseband transfer function. where K is an arbitrary gain, j=V-l, a=1.36, wo=273. 15X105, and w is the radian frequency phase. This phase equalisation filter thus simplifies the design of the mobile station receive filter.

It will be appreciated that while the IS-95 specification is not prescriptive of the-exact manner in which the phase equalisation filter is implemented, it would usually be implemented as a FIR filter. Thus, the hardware implementation of the FIR filter as per to the IS-95 specification calls for a minimum of 48 taps for the baseband filter 1 in addition to filter 3 for phase equalisation. When either of these filters is implemented in software, it will be appreciated that the computational intensity will be directly proportional to the total number of taps of the baseband and phase equalisation filters. Thus, it is difficult to achieve the required function within the limited time available or alternatively will place a computational burden on the system which will affect the processing time available for

other processes. Hence, it would be desirable to provide an improved filter in terms of computational intensity.

The preferred embodiment of the invention provides a method by which a single 24-tap, software implemented FIR filter replaces the baseband and phase equalisation filters on the forward transmission link while satisfying the filter requirements of the IS-95 specification.

Functionally the baseband FIR filter 1 and phase equalization filter 3 have a complex frequency response Hi (j) and H2 (j) respectively, and can be cascaded such that they occur adjacent to each other as shown in Fig. 4 Hl) is a frequency characteristic of the 48- tap FIR filter prototype, the coefficients of which are defined in the IS-95 specification and reproduced in table 1. The 48 taps relates to the input signal being sampled with a rate of four times the IS-95 chip rate (or 4 times 1.2288MHz).

The frequency characteristic H2 (j) is defined in the IS-95 specification and set out in equation 2.

The forward link FIR filter described in the preferred embodiment of the invention replaces the two cascaded filters. It has 24 taps and relates to the input signal being sampled at the rate of two times the IS 95 chip rate (or 2 times 1. 2288MHz).

It is to be noted that in theory if two FIR filters are combined the number of taps required for the combined FIR filter will equal the sum of the number of taps required for each filter minus one. Thus, the design of the FIR filter of the preferred embodiment of the present invention represent a significant reduction of the

number of taps. For example, if the phase equalisation filter were implemented as a 48-tap filter, 95 taps would be required to implement a theoretical combined filter.

The steps for designing the new filter are summarized briefly below and then described in further detail.

1. Determine the impulse response of the filter Ho on the basis of the 48 coefficients ho (k) for the FIR filter H1 and the sampling rate, fs=4*1. 2288MHz.

2. Re-sample the impulse response of H1 with the new sampling rate, fs=2*1. 2288MHz. The new 24 samples are now coefficients for the 24-tap FIR filter Hlr (re-sampled).

3. Scale the 24 coefficients for the FIR filter Hlr to produce unity gain in pass band.

4. Determine the complex frequency response Hlr (j) from the coefficients of the FIR filter Hlr.

5. Determine the complex frequency response of H2 (jw) as defined in the IS-95 specification (note step 5 can be performed asymmetrically with steps 1 to 4) 6. Determine the coefficients of the FIR filter Hd by an iterative scheme while minimizing the error between the complex frequency response of the filer H (j) and complex frequency response of the FIR filter Hd (j).

The final result is a newly designed FIR filter (Hd) with characteristics that closely approximate the overall characteristics of the baseband and phase equalization filers cascaded together.

The starting point is the 48 coefficients of the FIR baseband filter HI defined in the IS-95 specification.

This filter uses a sampling rate (fus) of 4 times the PN chip rate (fs=4*1. 2288MHz), so the coefficients 5 of the FIR baseband filter represent the values of an impulse response hl (t) for t=nTs, n=1, 2,..., 48 (TS=l/fs). The values of the impulse response in between these sampled points are interpolated in accordance with known techniques. The impulse response of the FIR baseband filter H1 is shown in Figure 5. The MATLAB function"interpIO"with cubic interpolation can be used for calculating the values of impulse response between samples.

The impulse response of Figure 5 is re-sampled with half the original sampling points to reduce the number of taps for the new filter. This approach satisfies the time domain constraint given by equation (1) for an IS-95 baseband filter as the error between the impulse response of the 24-tap FIR baseband filter and the 48-tap FIR baseband filter are both minimized. Figure 6 shows the position of new samples that represent the values of the coefficient for the re-sampled 24-tap FIR baseband filter Hlr.

The coefficients of the FIR filter Hlr are then scaled to produce an amplitude characteristic with unity gain in the pass band.

The complex frequency response of the FIR filter Hlr is calculated using the MATLAB function"freqz ()".

The amplitude and phase characteristics are shown in Figure 7.

The complex frequency response of the phase equalization filter H2 is calculated from the equation (2) as already defined in the IS-95 specification. This is an "all pass"filter with an amplitude characteristic equal to one for all frequencies. Its phase characteristic is shown in Figure 8.

The complex frequency response H (j) of the equivalent filter represents the cascaded connection of the resampled baseband filter Hlr and the phase equalization filter H2 is calculated as follows.

H(j#) = H1r(j#)H2(j#) This filter can be referred to as the"desired filter".

The complex frequency response of the desired filter H calculated from equation 3 is used in the iterative procedure for designing the FIR filter which satisfies the amplitude and phase characteristics of the equivalent filter H (jw) with minimal error.

Equation 4 defines the transfer function of the filter Hd (z) whose complex frequency response is given by equation 3. This filter can be referred to as the "designed filter".

Where: nb = n-1 na = 0 The algorithm for searching for the coefficients of filter bk and ak is based on the following equation: A (@k) and B (@k) are the Fourier transforms of the polynomials A and B respectively Uk is frequency in radians at point k, nf is the number of frequency points at which

Hd (j) is defined, Hd (k) is the complex frequency response of the desired filter for frequency Wk, wt (k) is a weighting function which is defined in the same number of points as H (@k). It changes the"significance"of error in different frequency bands.

The method is implemented using the MATLAB function"invfreqz ()". Polynomial A will be equal to unity because the filter Hd (z) is of a FIR type.

It will be appreciated that an appropriate iterative regime can be carried out to calculate optimal coefficients. In the example given herein, the amplitude and phase characteristics were"trimmed"by manually adjusting the weighting function we. Comparison of the amplitude and phase characteristics of designed and desired 24-tap FIR filter are shown in Figure 9 and Figure 10. Figures 9 and 10 demonstrate that the characteristics of the designed filter approximate the amplitude and phase characteristics of the desired filter H (jw) very closely.

Comparison of the amplitude in the pass and stop bands are shown in Figures lla and llb respectively.

Thus, the designed filter satisfies the frequency limits defined for the baseband filter in the IS-95 specification. The phase error is shown in Figure 12.

A better result could be achieved if the number of taps for the designed FIR filter is increased, but increasing the number of taps causes an increase in the number of computation cycles for the implementation of the FIR filter on a DSP processor and thus, leads to a sub- optimal implementation. This 24-tap FIR filter has been successfully tested on a prototype of a CDMA base station and it satisfies all test measurements specified in IS-95 specifications. The 24 coefficients are given in Table 2.

Table 2. Set of 24 coefficients for designed FIR filter. k hd (k) 0-0.00362693778292 1 +0.00802090990285 2 +0.01006559752104 3-0.01571528593967 4-0.03132727806071 5 +0.01481661445718 6 +0.05458001925757 7 +0.00132458035184 8-0.04936295831208 9 +0.04004271558163 10 +0.13273006685876 11 +0.00811170487654 12-0.17554005340532 13-0.04996561130871 14 +0.32857796026358 15 +0.50285441818962 16 +0. 30564953412358 17 +0.04828772968724 18-0.01726252649559 19 +0. 01056919626843 20-0.00660408946221 21-0. 03500169168975 22-0.01938548819596 23 +0. 00442585877230

It will thus be appreciated that a forward link finite impulse response filter of the preferred embodiment has 24 taps. However, it will be appreciated that computational improvement can be provided, provided that the number of taps is less than the theoretical number of taps required to combine a FIR filter performing baseband filtering and a FIR filter for performing phase equalisation filtering. In order to satisfy the sampling

rate of IS-95, the number of taps will need to be a multiple of 2 and will need to have at least twenty-four taps in order to provide a filter of sufficient quality to meet the IS-95 specifications.

Once the filter has been designed, a software program for carrying out the filtering functions can be programmed by a person skilled in the art to thereby implement the filter in software and the program can be run on a suitable processor, such as a digital signal processor to carry out filtering.

A MATLAB program that produces a set of coefficients for the desired 24-tap FIR filter is set out below. This program uses as its input the 48 coefficients for the baseband filter and the complex frequency response of the phase equalisation filter both of which are provided in the IS-95 specification.

% This program first calculates the coefficients of H1 filter from the coefficients % of prototype filter. First, the program calculates the impulse response of the % prototype filter.

% The program uses cubic interpolation to calculate impulse response between % samples (sampling frequency for filter prototype is 4*1.2288MHz). After that the % program is sampling impulse response with a new sampling frequency 2*1. 2288Mhz to % calculate the coefficients of the'resampled'FIR filter.

% These coefficients are scaled to produce the amplitude frequency response of % the filter with gain equal to 1 in pass band.

% The number of taps of prototype filter is 48.

% The Mean Squared Error between the resampled filter and prototype filter % (in mean of error between the coefficients of filters) is calculated also.

% % The complex frequency response of desired filter is given by the following % relation : % H (jw) =Hl (jw) *H2 (jw) Hl (jw) -complex frequency response of prototype filter with resampled impulse response % H2 (jw) -complex frequency response of phase equalisation filter % % The complex frequency response of the designed FIR filter Hd (jw) approximates % the complex frequency response of desired H (jw). Designed FIR filter has 24 taps.

% , % Program plots the amplitude and phase characteristics of complex frequency % response for Hl (jw), H2 (jw), H (jw) and Hd (jw) and phase error between desired and % designed filter.

% Program also creates file cresult. txt which contains coefficients of designed FIR filter.

% __________________________________ Coefficients of filter prototype ap= [-0.025288315 - 0. 034167931 - 0. 035752323 - 0. 016733702 0.021602514 0.064938487 0.091002137 0.081894974 0.037071157 - 0. 021998074 - 0. 060716277 - 0. 051178658 0.007874526 0.084368728 0.126869306 0.094528345 - 0. 012839661 - 0. 143477028 - 0. 211829088 - 0. 140513128 0.094601918 0.441387140 0.785875640 1.0 1.0 0.785875640

0.441387140 0.094601918 - 0. 140513128 - 0. 211829088 - 0. 143477028 - 0. 012839661 0.094528345 0.126869306 0.084368728 0.007874526 - 0. 051178658 - 0. 060716277 - 0. 021998074 0. 037071157 0.081894974 0.091002137 0.064938487 0.021602514 - 0. 016733702 - 0. 035752323 - 0. 034167931 - 0. 025288315] ; nap=length (ap); mns=nap-1 ; ns=(0: 1 : mns); % % Interpolation of impulse response for prototype filter % % Parameter di determines the precision of interpolation di=0.005 ; i=O : di: mns; % Sampling frequency for filter prototype is Fsp=4*1. 2288MHz % Fsp=4*1.2288e6 ; Tsp=1/Fsp ; tsp=ns*Tsp; ti=i*Tsp; <BR> <BR> impri=interpl (tsp, ap, ti, '*cubic') ;<BR> impri=impri' ; % sampling of impulse response with new sampling frequency Fs=2*1. 2288MHz % Number of taps of new FIR filter is 24.

% Fs=2*1.2288e6 ; nar=24; ar (l : nar) =0 ; ar=ar ; ar (nar/2 :-1 : 1) =impri ((length (i)-1)/2-(1/di) : -2/di: l/ (2*di)) ; ar (nar/2+l : nar) =ar (nar/2 :-1 : 1) ; tsr=ti (1/(2*di) : 2/di : length (i) ); % % Calculating the frequency response of new FIR filter with resampled % coefficients % % Parameters for filter Wp=590000 ; Ws=740000; % Number of points for calculating frequency response nop=2048; Wpl=450000; wpld=fix (Wpl/ (Fs/2) *nop); % Hr complex frequency response or resampled filter [Hr, F] =freqz (ar, l, nop, Fs); HrdB=20*1oglO (abs (Hr) ) ;

It will be appreciated that sub-optimal implementations of the forward link FIR filter fall within the scope of the present invention. For example a sampling rate of 3 times 1.2288 megahertz could be used.

These and other modifications will be apparent to persons skilled in the art and should be considered as falling within the scope of the invention described herein.