REDUCING THE PEAK TO AVERAGE RATIO OF MULTICARRIER GSM AND EDGE SIGNALS

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1 REDUCING THE PEAK TO AVERAGE RATIO OF MULTICARRIER GSM AND EDGE SIGNALS Olli Väänänen, Jouko Vankka and Kari Halonen Electronic Circuit Design Laboratory, Helsinki University of Technology, Otakaari 5A, FIN-215 Espoo, Finland Abstract - In conventional base station solutions, the carriers transmitted are combined after the poer amplifiers. An alternative to this is to combine the carriers in the digital domain. The major draback of the digital carrier combining is a strongly varying envelope of the composite signal. The high PAR sets strict requirements for the linearity of the poer amplifier. High linearity requirements for the poer amplifier leads to lo poer efficiency and therefore to high poer consumption. In this paper, the possibility of reducing the PAR by clipping is investigated in to cases, GSM and EDGE. - GSM, EDGE, Multicarrier, Clipping, Peak in- Keyords doing. I. INTRODUCTION The Global System for Mobile communication (GSM) is a idespread second generation system hich uses the.3 Gaussian Minimum Shift Keying (GMSK) modulation. The advantage of this modulation method is the constant envelope signal hich makes it possible to use poer efficient poer amplifiers (PAs). Enhanced Data rates for GSM Evolution (EDGE) is an enhancement to GSM system. The primary objective for the EDGE signal is to triple the on-air data rate hile meeting essentially the same bandidth occupancy as the original.3 GMSK signal. The EDGE system uses 3π/8-shifted 8-Phase Shift Keying (PSK) modulation hich is not a constant envelope modulation. In conventional base station solutions, the carriers transmitted are combined after the poer amplifiers. An alternative to this is to combine the carriers in the digital Intermediate Frequency (IF) domain [1] [2]. This saves a large number of analog components and because there is no analog I/Q modulator, many problems e.g. dc offset can be avoided. The major draback of the digital carrier combining is a strongly varying envelope of the composite signal. When a number of carriers are combined, according to the central limit theorem the envelope of the composite signal becomes normally distributed ith a high peak to average ratio (PAR). Typically the PAR is measured by the Crest Factor (CF) defined as CF = 1log 1 ( max{x(t) 2 } E[x(t) 2 ] ), (1) here x(t) is the composite signal. The high PAR sets strict requirements for the linearity of the poer amplifier. In order to limit the adjacent channel leakage, it is desirable for the poer amplifier to operate in its linear region. High linearity requirements for the poer amplifier leads to lo poer efficiency and, therefore, to high poer consumption (class A amplifier). An alternative to the expense of a ide-dynamic-range poer amplifier is the use of deliberate clipping to distort the signal digitally. Several clipping techniques for other modulation methods hich suffer from high PAR (OFDM, CDMA) is proposed. In this paper, at first the properties of the GSM and EDGE multicarrier signals are discussed and then conventional IF clipping and indoing method [3] [4] is applied in both cases. II. SIGNAL MODEL In both cases, GSM and EDGE, a single carrier IF signal is generated using the burst format specified in [5]. Length of the test signal is 7 data bursts hich corresponds to 26 samples at IF frequency. The oversampling ratio of 24 is used at the IF. This corresponds to 65 MHz sampling frequency in the digital modulator because the symbol rate in the GSM/EDGE is ksym/s. Multicarrier signal is generated by combining several single carrier signals at IF using 6 khz channel spacing. All combined signals are generated using independent random data and the initial phases of the carriers are chosen randomly. The Crest Factor of the real valued single carrier GSM IF signal is approximately equal to the Crest Factor of the sinusoidal signal, 3.1 db. Simulations have shon that the Crest Factor of the corresponding EDGE signal is about 6.18 db. If all the carriers are assumed to be statistically independent, the poer of the composite signal is doubled hen the number of carriers is doubled. In the orst case, all the carriers reach their maximum simultaneously, hich means that hen the number of carriers is doubled, the maximum of the composite signal is doubled and the peak poer is multiplied by four. In this case the PAR is doubled and the Crest Factor is increased about 3 db. In reality, it is very unlikely that all the carriers have their maximum simultaneously, and the Crest Factor does not increase as much as predicted. Simulated Crest Factors for composite signals ith different numbers of carriers are presented in Table I. The results sho that the Crest Factor does not increase as much as in the orst possible case but anyay, for a large number of carriers it becomes very high in both cases, GSM and EDGE. In the future, it is possible to transmit the GSM and EDGE signals simultaneously using the same poer amplifier. The Crest Factor of the signal ith 16 carriers hen the number of EDGE carriers is varied is presented in Table II /2/$ IEEE PIMRC 22

2 TABLE I Simulated Crest Factors for signals ith different number of carriers Number of carriers CF GSM CF EDGE db db db db db db db db db db db db TABLE II Crest Factor of the the signal ith 16 carriers hen the number of EDGE carriers is varied Number of CF EDGE carriers db db db db db III. CLIPPING METHODS The conventional IF clipping can be expressed mathematically as A x > A y = x x A (2) A x < A, here x is the unclipped signal, A is the maximum amplitude alloed and y is the clipped version of signal x. It is obvious that as a nonlinear operation the clipping distorts the signal significantly and generates unanted poer to the adjacent channels. One possible solution to this problem is to smooth the sharp corners caused by clipping. This can be done by multiplying the signal to be clipped ith a indo function [3] [4]. Conventional clipping can be expressed as a multiplication here y(n) = c(n)x(n), (3) { 1, x(n) A c(n) = A, x(n) > A, x(n) and A is the maximum amplitude alloed for the clipped signal. The idea of the indoing method is to replace the function c(n) ith the function b(n) = 1 k= (4) a(k)(n k), (5) here (n) is the indo function and a(k) is a eighting coefficient. A practical algorithm for forming the function b(n), presented in [6], is used in simulations. The algorithm is as follos. To achieve the anted clipping level the function b(n) must satisfy the inequality 1 k= a(k)(n k) c(n), (6) for all n. To minimise the distortion, inequality (6) must be as near to equality as possible. The difference beteen c(n) and b(n) depends on the indo length W defined as a number of samples (n) hich are not equal to zero, and eighting coefficients a(k). The spectral properties of the clipped signal depend on the indo length W and choosing the W is a trade off beteen the distortion in the time domain and the spectral regroth. After the W is chosen, the eighting coefficients a(k) must be optimised. If it is assumed that clipping probability and indo length are so lo that the indos do not overlap in the time domain the easiest ay to form the function b(n) is to find the part a(k)(n k) (7) k= by convolving the function 1 c(n) ith the indo (n), hen b(n) becomes b(n) = 1 k= [1 c(k)](n k). (8) The convolution can be implemented as a Finite Impulse Response (FIR) filter structure. The ideal convolution is not physically realizable, since it is non-causal and of infinite duration. In order to create a realizable filter, the impulse response i.e. the indo must be truncated and shifted to make the system causal. If the indo function is symmetric then the FIR filter has symmetric impulse response (k) = (W 1 k). In a real system indos unfortunately overlap and as a result of convolution the signal is clipped much more than needed. In the orst case the sign of function b(n) may become negative, hich is fatal for the system. Hence another ay to form the function b(n) must be found. A simple solution to the problem mentioned above is to combine the conventional FIR structure ith a feedback structure hich scales don the incoming value if necessary. The proposed structure is presented in Fig. 1. In Fig. 1, denotes floor operation. The impulse response of the filter (coefficients n ) is equal to the indo function. The previous values are used for calculating a correction term hich can be subtracted from input hile the output still satisfies (6). If the correction term is larger than the input value, signal y (Fig. 1) becomes negative after the subtraction, hich leads to an unanted clipping result. This is prevented by adding a block hich replaces the negative values ith zeros. IV. RESULTS The clipped signal must fulfil the system specifications [7]. In the case of GSM the signal quality is measured by phase

3 c(n) 1 y /2 +1 /2 +2 / max(y,) Z -1-1 Z Z -1 Z -1-1 Z Z -1-1 Z Bandidth 3 khz Bandidth 1 khz placements 1 2 Fig. 1. FIR filter structure ith feedback. 1 b(n) /2-1 / unclipped clipped Hanning Blackman error, and in the case of EDGE the signal quality is measured by Error Vector Magnitude (EVM). In both cases the spectrum of the signal must fit in the spectrum mask. Fig. 2. Spectrum of the GSM signal hen different clipping methods are used. A. GSM At first different indo types are compared. The spectrum of the unclipped signal, the spectrum of the clipped signal and the spectrums of the indoed signals are presented in Fig. 2. Results for Hanning and Blackman indos are presented. Also other common indo functions i.e. Kaiser, Hamming and Gaussian are investigated and the Hanning and Blackman indos are found to be better than the other indos. The test signal consists of 16 carriers and the Crest Factor of the unclipped signal is db. In every case, the signal is clipped so that the Crest Factor becomes 1 db. Fig. 2 shos that the conventional clipping causes very high out of band radiation and therefore it is not applicable in the case of GSM transmission. The Blackman indo seems to give better spectral properties than the Hanning indo. The effect of the indo length used is presented in Fig. 3 and in Table III. The Crest Factor of the test signal is clipped to 12 db. In this example, the indo length of 24 corresponds to the length of one symbol (oversampling ratio of 24 is used). It is obvious that a long indo gives better spectral properties than a short indo, but the interesting result is that the long indo gives better phase error performance than a short indo. This is surprising because hen the indo length increases the difference beteen the transmitted and the ideal aveform increases and therefore, intuitively, the phase error should increase. The achieved Crest Factor reduction ( CF), in the case of 8, 16 and 32 carriers is presented in Table IV. The used indo length is 61 and the clipping level is set so that the spectrum is the limiting element. The results sho that the Crest Factor of the multicarrier GSM signal can be reduced significantly hile the distortion is still kept in a tolerable level. The phase error specifications are 5 for rms and 2 for peak error [7]. In practice, implementing the indoing algorithm presented in [6] ith indo length of 61 might be very difficult and lead to a high area and poer consumption in the circuit implementation. Bandidth 3 khz Bandidth 1 khz Fig. 3. Spectrum of the GSM signal as a function of the indo length. TABLE III Phase error of the GSM signal as a function of the indo length. Windo length rms peak B. EDGE Again different indo types are compared. The spectrum of the unclipped signal, the spectrum of the clipped signal and the spectrums of the indoed signals are presented in Fig. 4. To different indos, Hanning and Blackman are used. The test signal consists of 16 carriers and the Crest Factor of the unclipped signal is db. In every case, the signal is clipped

4 TABLE IV Crest Factor reduction in the case of multicarrier GSM signal. number of CF CF rms peak carriers db db db 4.51 db db db Bandidth 3 khz Bandidth 1 khz unclipped clipped Hanning Blackman so that the Crest Factor becomes 12 db. Fig. 4 shos that as earlier, the conventional clipping causes very high out of band radiation and therefore it is not applicable in the case of EDGE transmission. The Blackman indo seems to give better spectral properties than the Hanning indo. The effect of the used indo length is presented in Fig. 5 and in Table V. The Crest Factor of the test signal is clipped one decibel. The longer indo gives a better spectral behaviour but the EVM becomes high. A indo long enough to meet the spectral specifications, causes EVM hich is very near or above the EVM specifications, 7% for rms and 24% for peak value [7]. In a real digital modulator EVM this high cannot be tolerated because some margin must be left for the folloing analogue parts. As a conclusion it can be said that neither of the clipping methods discussed in this paper can be used for EDGE clipping. Even one decibel reduction in the Crest Factor leads to an intolerable error. Generally, EDGE signal seems to be very sensitive for clipping errors hich makes the Crest Factor reduction a very challenging problem. The reason for the poor performance of the EDGE clipping is that the clipping seems to affect more to the amplitude of the signal than the phase of the signal. Because the distortion in the case of EDGE signal is measured by both, amplitude error and phase error, the error metric EVM becomes high. In the case of GSM clipping the error is measured by phase error only and therefore the signal can be clipped significantly. If e donconvert the clipped GSM signal and divide it to the in phase and quadrature branches and calculate the EVM as it is done in the case of EDGE, it can be seen that hile the phase error remains lo the EVM can be high. For the signal ith.19 degrees rms and.88 degrees peak phase error, the corresponding EVM values are 5.4% and 19.6% respectively. TABLE V EVM of the clipped EDGE signal as a function of the indo length. Windo length rms EVM peak EVM % % % % % % % % Fig. 4. Spectrum of the EDGE signal hen different clipping methods are used. Bandidth 3 khz Bandidth 1 khz Fig. 5. Spectrum of the clipped EDGE signal as a function of the indo length. C. GSM/EDGE As it is shon earlier the EDGE clipping is much more complicated than the GSM clipping so it can be assumed that hen the GSM and EDGE carriers are transmitted simultaneously, performance of the EDGE signals restricts the clipping. When a signal ith 15 GSM carriers and one EDGE carrier is clipped by using the indoing method, the Crest Factor is reduced about 1.5 db from db to db. In this case the rms EVM is 3.1 % and the peak EVM is 21.5 %, hich fulfil the specifications but are intolerable high. When the number of the EDGE carriers is varied the results are of the same kind, especially the peak EVM seems to be problematic. V. CONCLUSIONS To different clipping methods, conventional clipping and indoing method, are applied to GSM and EDGE multicar

5 rier signals in order to reduce the Crest Factor. In the case of GSM, the indoing method is shon to be efficient and the Crest Factor is reduced significantly hile the distortion is still kept in a tolerable level. In the case of EDGE, both clipping methods are proved to be inapplicable. REFERENCES [1] J. Vankka, J. Ketola, O. Väänänen, J. Sommarek, M. Kosunen and K. Halonen, A GSM/EDGE/WCDMA Modulator ith On-Chip D/A Converter for Base Station, ISSCC Digest of Technical Papers, February 3-7, 22, San Francisco, USA, pp [2] J. Vankka, J. Pyykönen, J. Sommarek, M. Honkanen, and Kari Halonen, A Multicarrier GMSK Modulator for Base Station, ISSCC Digest of Technical Papers, February 5-7, 21, San Francisco, USA, pp [3] Richard van Nee and Arnout de Wild, Reducing the Peakto-Average Poer Ratio of OFDM, Vehicular Technology Conference, 1998, Page(s): vol.3. [4] M. Pauli and H.-P, Kuchenbecker, Minimization of the Intermodulation Distortion of a Nonlinearly Amplified OFDM Signal, Wireless Personal Communications 4: Page(s) 9-11, [5] Digital cellular telecommunications system (Phase 2+); Modulation (GSM 5.4) V8.1. European telecommunications Standards Institute [6] O. Väänänen, J. Vankka and K. Halonen, Effect of Clipping in Wideband CDMA System and Simple Algorithm for Peak Windoing, World Wireless Congress, May 28-31, 22, San Francisco, USA, pp [7] Digital cellular telecommunications system (Phase 2+); Radio Transmission and reception (GSM 5.5) V8.3. European telecommunications Standards Institute 1999.

A Multicarrier GMSK Modulator

1070 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 19, NO. 6, JUNE 2001 A Multicarrier GMSK Modulator Jouko Vankka, Student Member, IEEE, Mauri Honkanen, and Kari A. I. Halonen Abstract A multicarrier