Multiband Digital Filter Design for WCDMA Systems

Transcription

1 2011 International Conference on Circuits, System and Simulation IPCSIT vol.7 (2011) (2011) IACSIT Press, Singapore Multiband Digital Filter Design for WCDMA Systems Raweewan Suklam and Chaiyod Pirak The Sirindhorn International Thai-German Graduate School of Engineering (TGGS) King Mongkut s University of Technology North Bangkok 1518 Pibulsongkram Road, Bangsue, Bangkok 10800, Thailand Abstract. This paper introduces structure characteristics, the basic principles of the finite impulse response (FIR) digital filter, and design methods based on MATLAB simulation. FDATool in MATLAB is used to determine filter coefficients and simulate FIR bandpass filters by means of window function methods. There are several types of window function such as Hamming, Hanning and Blackman. We bring all of window functions to compare its results. It can be shown that a Blackman window has the highest performance. The FIR filters are simulated using a system generator for implementation on FPGA. The results prove that the performance of the designed filter reaches the appointed requirement. Keywords: FIR, Digital Filter, Window function. 1. Introduction Digital filters can be categorized in infinite impulse response (IIR) digital filter and finite impulse response (FIR) digital filter. An FIR system has a lot of useful properties, such as only zeros, system stability, fast operating speed, linear phase characteristics and design flexibility, so that FIR has been widely used in digital audio, image processing, data transmission and other areas. FIR filter has a variety of ways to achieve, with the processing of modern electronic technology. In addition field programmable gate array (FPGA) for digital signal processing technology has made a rapid development with high integration, high speed and reliability advantages. In this paper, we present a digital filter design for wideband code division multiple access (WCDMA) interference cancellation system. The concept of interpolation is applied to the implementation of the input and output filters for frequency band selection and spectrum control. The organization of the proposed paper is as follows. In section 2, an expansion the filter design will be given. The simulation results are discussed and concluded in section 3 and 4, respectively. 2. FIR Digital Filter 2.1. The Basic Concept of FIR Filter The basic structure of FIR filters can be considered as a delay line of articulator, tooting-up the outputweighting of each articulator to obtain the output filter. For impulse response h(n) of FIR filter has been limited, the difference equation of N order of the recursive digital filters can be expressed as (1) x( n) 1 z z 1 z 1 h( 0) h( 1) h( 2) hn ( 2) hn ( 1) yn ( ) Figure 1. N-order FIR digital filter block diagram 122

2 where, y(n) is the output signal, x(n-k) is the input sample sequence on the nth times, h(n) is the filter tap coefficient and N is the number of the filter tap. Its basic structure is shown in Fig.1. We can express the output signal in frequency domain by convolution of the input signal x(n) and the impulse response h(n). The output signal is determined as, (2) (3) The coefficient b k in equation (1) equals to the successive value h(n) of unit-sample response. The system function H(z) can be expressed in the following form : (4) H(z) is a polynomial of z -1. This means that all poles are only plotted at the origin of the Z-plane The Method of Window Function The basic design principles of window function are to calculate h d (n) by the anti-fourier transform based on the ideal demanded filter frequency response H d (e jw ). The formula of h d (n) is as follows. (5) Because h d (n) is infinitely long, we have to deal with it by the window function to get to the unit impulse response h(n) which meets the requirement. Its calculation formula is shown in (6), where w(n) is the window function. (6) TABLE I PERFORMANCE COMPARISON OF ALL SORTS OF WINDOW FUNCTIONS Window function Coherent Integration Gain Highest Sidelobe Level (db) Sidelobe Rolloff Ratio Frequency Straddle Loss (db) Equivalent Noise Bandwidth 3-dB Bandwidth Hanning Hamming Blackman There are many types of window functions in engineering including Hanning, Hamming and Blackman. 1. Hanning 1 π (1 cos ), for n = 0 to N - 1 wn ( ) = 2 0, (7) The Hanning window function is accompanied by an improvement in the highest sidelobe level and sidelobe rolloff ratio. 2. Hamming 2π ( *cos ), for n = 0to N -1 wn ( ) = 0, (8) 123

3 The Hamming window functionn provides an even greater improvement to the highest sidelobe level but is accompanied by a poorer sidelobee rolloff ratio. 3. Blackman 2π ( * cos ) + 4π w( n) = 0.08*cos, for n = 0 to N -1 (9) 0, The Blackman window functionn has the lowest coherent integration gain out of the six window functions discussed in this chapter, but it also has the lowest of the sidelobe level responses. The sidelobe rolloff ratio is equal to that of the Hanning window function. This window function provides high rejection of signalss outside of its main lobe. Performance comparison of alll sorts of window functions can be seen in Table 1. During the design process of FIR filters, a suitable window function is chosen in order to meet the requirements. 3. FIR Filter Design The frequency spectrum is divided into bands and channels. Specifically, the frequency band is MHz wide which contains several 5 MHz channels and chip rate of 3.84MHz. A channel is used to refer to the frequency range used by a network operatorr who offers a WCDMA service. In this paper, we design the digital filter at four bands with a cut-off frequency of 62.5 MHz, 67.5 MHz, 72.5 MHz and 77.5 MHz,respectively, as shown in Fig 2. We design a bandpass filter for WCDMA system which a guardbandd equals to MHz and Adjacent Channel Leakage Ratio (ACLR) has to be lower than -50 db Digital Filter Design using FDATool The Filter Design and Analysis Tool (FDATool) is a powerful user interface for designing and analyzing filters quickly. FDATool enables us to design digital FIR or IIR filters by setting filter specifications, by importing filters from a MATLAB workspace, or by adding, moving or deleting poles and zeros. FDATool also provides various window functions, designing functions of filter and realizablee functions of filter. The method of window function is the most commonly used method to design the FIR filter. FDATool has very important function in the design of FIR filters. The performance of digital filter design can be improved, if the proper window function is chosen. In this design, we use the specifications as following : Response type : Bandpass filter Passband attenuation : 3 db Sample Frequency : 200 MHz Window Function : Blackman Order : 200 Cut-offf Frequency : 62.5 MHz, 67.5 MHz, 72.5 MHz and 77.5 MHz The simulation of magnitude response and impulse response of FIR filter using FDATool are shown in Fig 3., Fig 4. and Fig 5, respectively. The order of the digital filter is more or less proportional to the number of operations. This means that by choosing a low order filter, the computation time can be reduced. In this design, we use the orderr of 200 so that it takes 1 μsecond to operate. The simulation results of the magnitude at the first side lobe of FIR filter using Hanning, Hamming and Blackman are -40 db, -50 db and -80 db, respectively. We can see that the filter using Blackman windoww function method can achieve the highest performance comparing with other functions. Figure 2. Frequency band specification 124

4 (a) Figure 3. (a) Magnitude Response, Impulse Response(dB) of Hanning window function (a) Figure 4. (a) Magnitude Response, Impulse Response(dB) of Hamming window function (a) Figure 5. (a) Magnitude Response, Impulse Response(dB) of Blackman window function 3.2. Digital Filter Design with System Generator System Generator is a software tool for modeling and designing FPGA-based DSP systems in Simulink. The tool presents a high level abstract view of a DSP system, yet nevertheless automatically maps the system to a faithful hardware implementation. Simulink provides a powerful high level modeling environment for DSP systems, and consequently is widely used for algorithm development and verification. System Generator maintains an abstraction level very much in keeping with the traditional Simulink blocksets, but at the same time automatically translates designs into hardware implementations that are faithful, synthesizable, and efficient. Figure 6. Filter design platform with FDATool in system generator 125

5 Figure 7. Multibands FIR filter using Hanning window Figure 8. Multibands FIR filter using Hamming window Figure 9. Multibands FIR filter using Blackman window Fig 6 shows the filter design platform with FDATool in system generator. The multiband digital filter was generated using simulink in MATLAB, (that uses the digital filter designed from the FDATool and uses the system generator to comply). Fig 7. to Fig 9., show the magnitude response of FIR multiband filter using different window functions. The simulation results of the magnitude response at the first side lobe of multiband FIR filter using Hanning, Hamming and Blackman are -40 db, -50 db, and -80 db, respectively. We can see that the filter using Blackman window function method can achieve the highest performance comparing with other functions. 4. Conclusion FIR filters are widely used in digital signal processing. In this paper, FIR filter response coefficients are calculated by MATLAB toolbox FDATool. Then we analyzed the performance of the filter. It turns out that a Blackman window function method has the highest performance. It has the magnitude response at the first side lobe under 75 db for every cut-off frequencies. Then the system generator is applied to simulate the digital filter for implementation on FPGA. The simulation results show that the designed FIR filter fully complies with design requirements. 5. References [1] Rulph Chassaing, Digital Signal Processing and Applications with the C6713 and C6416 DSK. New Jersey : John Wiley&Sons, Inc.,2005. [2] Rudolf Tanner and Jason Woodard, WCDMA Requirementsand Practical Design, 2004 [3] Marc Defossez, Connecting Virtex-6 FPGAs to ADCs with Serial LVDS Interfaces and DACs with Parallel LVDS Interfaces, XAPP1071 (v1.0), June 23, [4] M.Lee, B.Keum, Y.Son, J.W.Kim and H.S.Lee, A New Low-Complex Interference Cancellation Scheme for WCDMA Indoor Repeaters, IEEE REGION 8 SIBIRON 2008 [5] Xiaoyan Jiang and Yujun Bao, FIR Filter Design Based on FPGA, International Conference on Computer Application and System Modeling (ICCASM) [6] A.H.A.Razak, M.I.A.Zaharin and N.Z.Haron, Implementing Digital Finite Impulse Response Filter Using FPGA, Asia-Pacific Conference on Applied Electromagnetic Proceedings