Comparison of zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA for use in Software Radio zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA e-mail: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA phone: +49 721 608 37 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA GMSK and linear approximated GMSK A. Wiesler, R. Machauer, F. Jondral Institut fur Nachrichtentechnik, Universitat Karlsruhe D-76128 Karlsruhe, Germany wiesler@inssl.etec.uni-karlsruhe.de fax: f49 721 608 60 71 48 dulation index zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA In 1 a common Software Radio 1 1 system impulse response assumes this linear channel Abstract- GMSK modulated signal is zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA structure for second generation mobile systems model. The consequence of the usage of this estima- has been introduced. This SWRADIO combi- tes for the nonlinear GMSK is described in Section 111. g(r - zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA nes different standards of mobile communica- Some simulation results are discussed in Section IV. tion systems like GSM, DECT, IS-54 and PDC. 11. LINEAR APPROXIMATION OF GMSK All baseband functions like channel coding, mo- with the NRZ-stream zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA dulation and equalisation are implemented in a impulse zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA GMSK is a special kind of a 2-level FSK with mo- h = general, parametrized way, so that all of them 0.5 [4]. The complex envelope of a can be used for the selected standards. This structure has several advantages like a redu- ced size of the hardware platform, fast perfor- 1 mance by changing the air interface for a system nT)dT (1) handover and the possibility of global roaming. -03 The linear approximated GMSK is used in the dn E {-1,l) and the frequency SWRADIO because this enables a common I/Q- g(t). For MSK a rectangular frequency impulse modulator for all second generation systems. In this paper it is proved, that with a usual recei- is used, which causes hard phase changes and thus a ver (Viterbi equalizer with least square channel broad spectrum. To reduce the bandwidth for GMSK estimate) there is no performance loss by using the following frequency impulse the approximated GMSK instead of the original GMSK. is used. h ~ ~ ~ ~ ~ ( t ) ist the known Gaussian impulse with I. INTRODUCTION the time bandwidth product BT. The reduction of bandwidth is achieved with the trade of a controlled in- Third generation systems like the European UMTS tersymbol interference (ISI). For the GSM-system the will perform a very flexible communication technology factor BT = 0.3 was chosen, that results in a IS1 over [2]. As the new standards can not replace established about 2 symbols but a small bandwidth. With DECT systems like GSM at once, a seamless change to the a BT = 0.5 is used, which causes minor ISI, because third generation is aimed. That means future hand- the frequency impulse is shorter and so this GMSK is helds must be able to perform different communication more a kind of MSK. technologies and also seamless system handover. This The theoretical infinite long Gaussian impulse can only be realized with a transmitter structure which is cut to the length LT, with L 2 3. Thus at h ~ ~ ~ ~ ~ ( t ) is totally software programmable, a so called Software time t = nT the phase response is determined to Radio [3]. In [l] a solution for different second generation systems t (GSM, DECT, IS-54, PDC) is introduced to show that (3) a common software structure is possible for different The nth NRZ-bit dn causes a phase change of zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA -03 standards. These are all TDMA systems so the main difference between them lies in the modulation. The Fig. 1 shows the phase response for MSK and GMSK. European systems use nonlinear GMSK, the American With q(t) the GMSK signal s(t) can be described as and Japanese systems use a/4-DQPSK. For a common, ] follows parametrized modulator structure a linear approxima- [ 03 tion of the GMSK is necessary, which is reviewed in - s ( t ) = exp j27rh dnQ(t nT) (4) Section 11. In the SWRADIO a common MLSE equa- n = O lizer using the Viterbi algorithm is implemented. This nq(t) or algorithm is based on a discrete channel model which assumes a linear modulation. Also the estimate of the -.lrq(t), which is added to the changes of the previous 0-7803-4281-X/97/$10.00 01998 IEEE 557
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA nonlinear part snl(t). In Fig.2 the two first impulses zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA That means zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 2 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 3 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA s(t) consists of a linear part slin(t) 0 , 2 5 U G M S K , , t/T and a CO and C 1 for GMSK are displayed. impulses zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA of zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 0 0 4 1 r N, = P1 CK: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA with Since CO has 99% of the signal energy, the following n L-1 linear approximation of sft) is obvious: = 4 - (6) A K , ~ dn-1. Q K , ~ 01) ZnCo(t - M srin(t) = (14) nT) s(t) n = O 1=1 with the symbols from (10). That means the symbols zn which are determinated from the accumulated bit This representation can be used for all CPM-signals. stream di are only formed by one impulse CO. So this For example, the complex envelope of a MSK-signal (here is L = 1) can be written as follows approximated GMSK has the advantage, that it can be realized with a usual I/&-Modulator for PSK or &AM 01) and is therefore easy to integrate into a Software Radio = nT) (8) S M S K (t) COMSK (t - exp structure. n = O Now the question whether the approximation of the with { sin(r;/2T) O<t 5 2T = (9) COMSK 0 6 - otherwise This is the well known representation of MSK as 0- 0 0 - QPSK modulation. The symbols -06- E {-I, 1, - j , j ) . (10) ; b 1 -il BT = BT = 0 . 3 0.5 Fig. 3. Complex envelope of the approximated GMSK are alternately real and imaginary. For GMSK with L = 4 the exact superposition (5) GMSK causes it performance loss will be discussed. is made by eight impulses. So the following represen- First the approximation of the GMSK causes a change tation o f the complex envelope of an exact GMSK- of the eye diagram, the scatter diagram, and the power modulated signal s(t) can be used: density spectrum. In Fig.3 the sca.tter diagram of the approximated GMSK with different values for BT is shown. The approximation causes fluctuations of the complex envelope din(t). For BT = 0.5 the fluctua- tions are very small. As it was mentioned before the GMSK with BT = 0.5 is very similar to the linear MSK and therefore the linear approximation does not change the signal remarkably. So the main emphasis of the dis- cussion lies on the GMSK which is used in the GSM system. The eye diagram of the linear approximated 558
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