A Modified Transposed Farrow Solution to Multipurpose Multirate Filtering in Software Defined Radio
(SDR)
Wenzhen Li, Masayuki Tomisawa OK1 Techno Centre (Singapore) Pte Ltd, 20 Science Park Road #02-06/10, Teletech Park, Singapore Science Park 11, Singapore 117674, Fax: -t(065) 6779-2382, E-mail:
[email protected]
Abstract- How to implement multi-purpose filtering with high flexibility and low cost is one of the biggest challenges for SDR receiver design. Rlecently proposed transposed Farrow structure is the most, competitive candidate for this purpose. However the existing transposed Farrow structure faces the problem of timing control in the output sample, which seriously limits its potential applications. In this paper, an efficient modified transposed Farrow structure is implemented. Its efficiency is verified by comparing it with the method existing in the literature. The analysis and simulation results clearly show that the proposed solution removes the obstacle in the implementation of transposed Farrow structure, which may lead to its potential extensive applications in SDR systems. Index Terms- Transposed Farrow structure, SRC, SDR, multi-purpose filtering
I. Introduction Software-defined radios require a programmable and dynamically reconfigurable hardware to implement the physical layer processing of multiple communication systems. These standards generally employ different data rates and thus using different master clocks. Hence sample rate conversion (SRC) should be introduced to the signal processing of digital communication transceivers. Moreover, in the SDR receiver, the digital front end (DFE) portion interface analogldigital conversion and baseband processing. Thus it bears the required flexibility and parameterizability of a SDR system which can be adaptive to various air interfaces. How to implement a low cost and high efficient DFE is a big challenge. Much efforts have been reported on integrating the multiple filtering functions like channel selection filtering, matched filtering, SRC and timing adjustment into a multipurpose digital filtering structure [l] [2]. There are many SRC solutions proposed in the literature [3]-[8],including multistage FIR filter, CIC filter, and polyphase filter. Generally CIC filters have narrow usable passband, serious finite word length effect, and the problem of filter gain[8]. With respect to multistage FIR filters, it is difficult to choose a generic multistage architecture adaptive to all system standards, in addition, the extra control structure
0-7803-8523-3/04/$20.00 02004 IEEE.
is another problem[S]. Regarding the polyphase FIR filter, it is resource-consuming to use it for a general purpose SRC, i.e., if a rational or arbitrary factor SRC is needed, namely in a time-varying system, only a certain set of samples of FIR filter is involved in the computations for each output, but all sets of coefficients should be stored and employed. Hence, in a SDR system with rate conversion factor L / M , if L and M are large, the necessary memory size might be infeasible [5][8][ 101. The polynomial filter based Farrow structure with an unique tunable parameter is an efficient solution to arbitrate SRC by trading off the complexity and filtering performance [5][4]. It keeps the effort low for calculating the coefficients of the filter, but it can only achieve good performance in the case of rate increase. Tim and Gerhard in [5]proposed a transposed Farrow structure with much better anti-aliasing capability than the Farrow structure. This feature entitles it as one of the best solutions to sample rate decrease [5]. It possesses strong potential for the SDR applications where multi-purpose filtering all need an efficient low cost scheme. Although some modified transposed Farrow structure and its implementation are investigated in the literature [10][9],there is not yet an efficient scheme proposed to implement the multi-purpose filtering, which seriously limits the potential applications of the transposed Farrow structure. Trying to solve this problem, a scheme is proposed in [7] for a simplified SRC system with integer conversion rate, but it introduces a timing error into the system, which may be fatal for the multipurpose application in a timing phase sensitive SDR system. In this paper, based on the mathematical model of the transposed Farrow structure, a generic implementation of the modified transposed Farrow structure is proposed, which is applicable for both rational and non-rational SRC based on an flexible timing control scheme. Its efficiency is verified by comparing it with the method existing in the literature. This paper is organized as follows, in Section 11, a solution to a programmable and dynamically reconfigurable
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common hardware is presented. This solution involves the well-known Farrow structure and the attractive transposed Farrow structure to provide a multipurpose filtering. In Section 111, the mathematic model of modified transposed Farrow structure is revisited and the existing timing control method is reviewed. In section IV, a generic modified transposed Farrow structure solution is proposed. Section IV includes the simulation results and the conclusions are drawn in the last section. 11. System model For simplicity, an indoor wireless communication SDR system is considered in this paper, which provides a programmable and dynamically reconfigurable common hardware to implement the physical layer processing of Bluetooth and WLAN. Of course, the considered system can be easily extended to other SDR systems. The common hardware is extracted from the transceivers and shown in Fig.1. Here we define the digital front end (DFE), which includes multi-purpose functions, e.g., digital down conversion, channelization, matched filtering, and sample rate conversion in the receiver branch; digital upconversion, pulse shaping and sample rate conversion in the transmit branch. Evidently the DFE interfaces the analog/digital (A/D converter in the receiver branch, and D/A converter in the transmit branch) on one side, and the baseband processing on the other side. In general, the combination of filtering with decimation or interpolation enables very efficient implementations like polyphase filters. However, as mentioned before, this is not so efficient when a nonrational or arbitrary factor sampling rate conversion is needed. A way out to this problem is to calculate the necessary coefficients at the required time. This can be implemented by a Farrow structure or Transposed Farrow structure. Therefore a generic solution involving the Farrow structure and transposed Farrow structure is adopted to implement the multi-tasks of filtering, SRC and timing adjustment, as shown in Fig.1. Here the transposed Farrow structure is used to implement multi-purpose filtering, including matched filter and channel selection. At the same time, the decimation task and timing adjustment are also intermeshed due to its excellent anti-aliasing properties. In this paper, the transposed Farrow structure for the SDR receiver is our main concern. 111. Transposed Farrow Structure A straightforward solution to SRC is to reconstruct the original analog signal from the discrete-time signal with sample period TI and resample the reconstructed signal with the new clock period T2. Actually, the
azb SRC and
binary
Genem
matched filter and SRC (Transposed
pulse
(Farrow structure)
demod
sturcture)
pi+ recovery
Fig. 1. The diagram of a simplified baseband system model
multirate signal processing technique, we need not perform reconstruction and resampling explicitly, just utilize the appropriate linear filtering operating at the chosen sampling rate. Assuming the multirate filter being h ( t ) ,the analog output can be represented as, y,(t)
=
/
m
m
z(kTl)h(t- kT1)
z,(t)h(t - 7 ) d = ~
-CO
k=-m
(1) The interpolated output sequence y(m) is then obtained by sampling y,(t) at t , = mT2. The mth interpolated output sample can be expressed as m
y(m) = ya(mT2)
z(kTi)h(mT2- kTi) (2) k=-m
Assuming that h(t) is a symmetric FIR filter with the response length of N A , i.e., h ( t ) = h(-t) in the interval range of -NA/2 < t < NA/2; Thus h(t)can be composed from N piecewise polynomials, N-1
hj(t - jA)
h(t) =
(3)
j=O
2
here each piece hj(t - j A ) with - 1 as the base has equal degree Q and covers equal length A,
hj(t)=
ci(j)
(2 - l ) z
0 M ? l : 0 if ov(m) = 1, index = index mod M
overflow: ow(m) = index > M?1 : 0 if o v ( m ) = 1, index = index mod M
Init: index = 0, uo = 1.0, Update: index = (1 - Uk)M L ; uk = 1 - i n d e x mod M M overflow: ow(m) = index > M?1 : 0 if ov(m) = 1, index = ino!ez mod M
Init: index = 0, uo = M Update: index = (1 - U k ) M L ; u~= 1 - i n d e x mod M
+
e, +
M
overflow: o v ( m ) = index > M?1 : 0 if ov(m) = 1, index = index mod M
fluences the timing of the filtered sig:nal. The proposed two solutions are equivalent in BER performance, which is shown in Fig.3. Evidently the proposed solutions can achieve the performance closed to theoretic one. Similarly, the two ex.tension schemes from the literature shown in the second column of Table 1 have the same performance, which is shown in Fig.4. Comparing Fig.4 with the previous BER curves, it is observed that these inter-sample position generation methods derived from the literature either does not work or results in significant performance degradation due to constant timing phase error. This is the biggest reason that limits the extensive application of Transposed Farrow structure for the flourishing software defined radio sy,,c’tems.
VI. Conclusions A new generic timing control solution for the modified transposed Farrow structure and its DSP and ASIC friendly implementations are proposed in this paper. Through analysis and simulation, the feasibility of the proposed solution is verified. It is clearly shown that the proposed solution clears the obstruct in the road to the extensive application of Transposed Farrow structure in SDR, systems.
[3] Tim Hentschel, Gerhard Fettweis, “Sample rate conversion for software radio”, IEEE Communication Magazine, Aug. 2000, pp142-150. [4] C.W.Farrow, “A Countinuously Variable Digital Delay Element”, Proc. IEEE International Symposium on Circuits and Systems (ISCAS’88), pp2642-2645, Espoo, Finland, June 1988. [ 51 Tim Hentschel, Gerhard Fettweis, “Continuous-time digital filters for sample rate conversion in reconfigurable radio terminals”, Proc. of European Wireless 2000, Sep.12-14, Dresden, German, pp55-59. [6] Tim Hentschel, Matthias Henker, Gerhard Fettweis, “The digital front end of software radio terminals”, IEEE Personal Communications, August 1999, pp6-12. [7] Tim Hentschel, “Sample rate conversion in software configurable radios”, Artech House, 2002. [8] Ronald E. Crochiere, Lawrence R. Rabiner, “Multirate Digital Signal Processing”, Acounstics Research Department, Bell Laboratories, Murrey Hill, New York. [9] Djordje Babic, Jussi Vesma, Tapio Saramaki, and Markku Renfors, “Implementation of the Tranposed Farrow Structure’’, Proc. of IEEE International Symposium on Circuits and Systems, 2002, ISCAS 2002, 26-29 May 2002, ): ppIV-5 -1V-8 vo1.4. [lo] Matthias Henker, Gerhard Fettweis, “Combined filter for sample rate conversion, matched filtering, and symbol synchronization in software radio terminals”, Proc. of European Wireless 2000, Sep.12-14, Dresden, German, pp61-66.
References [l] Wolfgang Konig, Gerd Wolfle, Christian Fischer, Tim Hentschel, , “Front end architecture for a software defined radio base station”, Software radio technologies and services, Springer, 2001. [2] Fredric J . Harris, Michael Rice, “Multirate digital filters for sysmbol timing synchronization in software defined radios”, IEEE Journal on Selected Areas in Communications, Vo1.19, No.12, December 2002, pp2346-2357.
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