Simple algorithm for peak windowing and its application in GSM, EDGE and WCDMA systems . anen, . O. Va. an J. Vankka and K. Halonen Abstract: In conventional GSM base station solutions, transmitted carriers are combined after power amplifiers. A GSM signal is a constant envelope signal which means that a power efficient nonlinear power amplifier can be used. However, in third generation systems the signal is no longer a constant envelope signal, which means that linearity requirements for the PA are increased. Also, in the case of multicarrier GSM or EDGE transmission the peak to average power of the signal becomes high if the carriers are combined in the digital domain. High linearity requirements lead to low power efficiency and therefore to high power consumption. In order to achieve good efficiency in the PA the PAR must be reduced, i.e. the signal must be clipped. In the paper the effect of a peak windowing clipping algorithm is studied in the cases of WCDMA, GSM and EDGE transmission. Also, an efficient way to implement the peak windowing algorithm is presented.
1
Introduction
In conventional GSM base station solutions, transmitted carriers are combined in the analogue domain after the power amplifiers by a lossy RF combiner. An alternative method is to combine the carriers in the digital domain [1, 2] that provides a number of benefits over the conventional solution. It saves a large number of analogue components, and there is no need for cavity or hybrid combiners. The GSM signal is a constant envelope signal, which means that a power efficient nonlinear power amplifier (PA) can be used. However, in third generation (3G) systems the signal is no longer a constant envelope signal, which means that linearity requirements for the PA are increased. In a wideband code division multiple access (WCDMA) system the downlink signals is a sum of signals intended for different users. The composite signal is Gaussian distributed that leads to a high peak-to-average-ratio (PAR) [3]. Theoretically, the situation is even worse if the carriers are combined in the digital domain before the amplifier. The same problem arises also in the case of GSM and EDGE transmission if the carriers are combined in the digital domain. The high PAR sets strict requirements for the linearity of the power amplifier. High linearity requirements lead to low power efficiency and therefore to high power consumption. Despite this drawback, for the reasons mentioned earlier, it might be beneficial to combine the carriers in the digital intermediate frequency (IF) domain. In order to achieve a good efficiency in the PA the PAR must be reduced, i.e. the signal must be clipped. Advanced clipping methods, especially for orthogonal frequency division multiplexing (OFDM), are presented in [4–6]. In the cases of WCDMA, GSM and EDGE clipping, the peak windowing method presented in [4] and [5] can be applied r IEE, 2005 IEE Proceedings online no. 20059014 doi:10.1049/ip-com:20059014 Paper first received 3rd March 2003 and in revised form 7th September 2004 The authors are with the Electronic Circuit Design Laboratory, Helsinki University of Technology, Otakaari 5A, FIN-02150, Espoo, Finland E-mail:
[email protected].fi IEE Proc.-Commun., Vol. 152, No. 3, June 2005
easily. It is advantageous to place the clipping operation after the carrier combining at IF, because the carrier combining is the major reason for the high PAR. Otherwise a complex feedback structure is needed if the carriers are clipped independently before the combining operation. In this paper, an efficient way to implement the peak windowing algorithm is presented. Also the effect of this method is studied in the cases of WCDMA, GSM and EDGE multicarrier transmission. In the cases of WCDMA the single carrier transmission, where the high PAR is a problem, is also considered. 2
2.1
Signal model
WCDMA
In a WCDMA system the base station spreads and sums the baseband signals intended for different users. The signal intended for user k (in I or Q branch) can be written as dtðkÞ ðtÞ ¼ bðkÞ ðtÞcðkÞ ðtÞ
ð1Þ
where bðkÞ ðtÞ is the data waveform and cðkÞ ðtÞ is the spreading waveform. The data waveform can be written as bðkÞ ðtÞ ¼
1 X
bðkÞ n qT ðt nT Þ
ð2Þ
n¼1 ðkÞ
where the data bits bn 2 f1; 1g are equally likely, T is the bit duration and qT(t) is the rectangular pulse of duration T. Correspondingly the spreading waveform can be expressed as cðkÞ ðtÞ ¼
1 X
cðkÞ n qTc ðt nTc Þ
ð3Þ
n¼1 ðkÞ
where cn 2 f1; 1g are equally likely, Tc is the chip duration and qTc ðtÞ is the rectangular pulse of duration Tc. The spreading waveform is different for each user and it is known as the channelisation code. Equation (1) shows that a baseband signal has only two different levels {1, 1}. After the spreading operation the signals intended for different users are weighted and added 357
together according to d¼
K X
bk d ðkÞ
ð4Þ
k¼1
Assuming that all K signals are added with the same weighting factor bk ¼ 1, the real part (and the imaginary part) of the composite signal can be modelled as a random variable with a discrete binomial probability distribution function (PDF). Another way to model the PDF of the composite signal is to use the central limit theorem. Because the composite signal is a sum of K independent identically distributed random variables, it can be modelled as a truncated Gaussian random variable with a zero mean, variance of s2. Even if the weighting factors bk are assumed to be unequal, the real and imaginary components of the signal d can be assumed to be Gaussian distributed with a zero mean and some variance s2. The complex signal d is scrambled by multiplying it with a pseudo-random scrambling code. After this, the I- and Qbranches are filtered (0.22 root raised cosine) and upconverted to the IF according to xðnÞ ¼ IðnÞ cos ðonÞ QðnÞ sin ðonÞ
ð5Þ
where o is the angular frequency of the carrier. It can be shown that after these operations the signal still remains Gaussian distributed [7]. As a Gaussian distributed signal the downlink signal has a very high crest factor. When the different carriers are combined to form a multicarrier signal the central limit theorem can be applied again. Theoretically this results to a Gaussian distributed signal with an extremely high crest factor. If all the carriers are assumed to be statistically independent, the power of the composite signal is doubled when the number of carriers is doubled. In the worst case, all the carriers have their maximum simultaneously, which means that when the number of carriers is doubled, the maximum of the composite signal is doubled and the peak power is multiplied by four. In this case the PAR is doubled and the crest factor is increased about 3 dB. According to simulations the crest factor of a single carrier WCDMA signal is around 14 dB depending on the number of the active code channels. The crest factor of the multicarrier signal is about the same order of magnitude as in the single carrier case. It is very unlikely that all the carriers reach their maximum values simultaneously and therefore the worst case crest factor increment is not obtained in practice. All the test signals used are generated as specified in [8]. The oversampling ratio of 16 is used and in the multicarrier case the separation between carriers is 5 MHz.
2.2
Table 1: Simulated crest factors for signals with different number of carriers Number of carriers
CF GSM, dB
CF EDGE, dB
1
3.010
2
6.020
8.969
4
9.012
11.102
8
11.397
12.956
16
14.258
15.747
32
17.395
18.649
3
6.176
Windowing algorithm
Conventional clipping causes sharp corners in a clipped signal. This leads to out of band radiation and reduces the adjacent channel leakage power ratio (ACLR), the ratio of the transmitted power to the power measured in the adjacent channel. It is possible to increase the ACLR by smoothing the sharp corners. This is done by multiplying the signal to be clipped with a window function [4, 5]. The difference between the conventional clipping and windowing is presented in Fig. 1. Conventional clipping can be expressed as a multiplication xclip ðnÞ ¼ cðnÞ x ðnÞ
ð6Þ
GSM/EDGE
In the GSM system Gaussian minimum shift keying (GMSK) modulation is used. This means that a single carrier GSM signal has a constant envelope. The crest factor of the real single carrier GSM IF signal is approximately equal to the crest factor of the sinusodial signal, 3.01 dB. In the EGDE system, 3p/8 rotated 8-phase shift keying (PSK) is used. This triples the data rate compared to the GSM but the filtered signal (linearised Gaussian filter) has no more constant envelope. Simulations have shown that the crest factor of a single carrier EGDE signal is about 6.18 dB. In both cases, GSM and EDGE, a single carrier IF signal is generated using the burst format specified in [9]. The length of the test signal is 7 data bursts that corresponds to 358
260000 samples at IF frequency. The oversampling ratio of 240 is used at the IF. This corresponds to 65 MHz sampling frequency in the digital modulator because the symbol rate is 270.833 k symbols in GSM/EDGE. Multicarrier signal is generated by combining several single carrier signals at IF using a channel spacing of 600 kHz. All combined signals are generated by using independent random data and the initial phase of the carrier is chosen randomly. Again, the theoretical crest factor increment is as high as 3 dB but in reality, it is very unlikely that all the carriers have their maxima simultaneously, and the crest factor does not increase as much as predicted. Simulated crest factors for composite signals with different number of carriers are presented in Table 1. The results show that the crest factor does not increase as much as in the worst possible case but anyway, for a large number of carriers, it becomes very high in both cases, GSM and EDGE.
clipped clipping threshold
windowed
Fig. 1
Clipped signal and windowed signal IEE Proc.-Commun., Vol. 152, No. 3, June 2005
where
cðnÞ ¼
1; A jxðnÞj;
jxðnÞ jxðnÞ
A 4A
c (n) − +
ð7Þ
− + y
1
where A is the maximum allowed amplitude for the clipped signal. The idea of this method is to replace the function c(n) with the function 1 X ak wðn kÞ ð8Þ bðnÞ ¼ 1
+ w w/2 +1w w/2 +2 w w w/2 +3 w −1
max(y,0)
Z −1
Z −1 w0
Z −1 w1
k¼1
where w(n) is the window function and ak is a weighting coefficient. To achieve the desired clipping level the function b(n) must satisfy the inequality 1 X ak wðn kÞ cðnÞ ð9Þ 1
Z −1 w2
1
Fig. 2
Z −1
w w/2 −1 w w/2 −1 −
Z −1
Z −1
ww −2 ww −1
b (n)
FIR filter structure with feedback
1.0 0.5
k¼1
for all n. To minimise the error vector magnitude (EVM), which measures the difference between the ideal and the transmitted waveform in the time domain, inequality (9) must be as near equality as possible. The difference between c(n) and b(n) depends on the window length W defined as a number of samples w(n) that are not equal to zero, and weighting coefficients ak. The spectral properties of the clipped signal depend on the window length W and choosing W is a trade-off between the EVM and ACLR. After W is chosen, weighting coefficients ak must be optimised. If it is assumed that the clipping probability and the window length are so small that windows do not overlap in time domain, i.e. the distance between the nonzero samples of 1c(n) is larger than the window length W, the easiest way to form the function b(n) is to find the term 1 X ak wðn kÞ ð10Þ k¼1
in (8) by convolving the function 1c(n) with the window wðnÞ, when b(n) becomes 1 X bðnÞ ¼ 1 ½1 cðkÞwðn kÞ ð11Þ k¼1
The convolution can be implemented as a finite impulse response (FIR) filter structure. The ideal convolution is not physically realisable, since it is non-causal and of infinite duration. In order to create a realisable filter, the impulse response, i.e. the window, must be truncated and shifted to make the system causal. If the window function is symmetric then the FIR filter has the symmetric impulse response wðkÞ ¼ wðW 1 kÞ: In a real system windows unfortunately overlap and as a result of convolution the signal is clipped much more than needed. In the worst case the sign of function b(n) may become negative, which is fatal for the system (this can be seen in Fig. 3). Hence another way to form the function b(n) must be found. A simple solution to the problem mentioned above is to combine the conventional FIR structure with a feedback structure that scales down the incoming value if necessary. The proposed structure is presented in Fig. 2. In Fig. 2, ‘I m’ denotes floor operation. The impulse response of the filter (coefficients wn) is equal to the window function w. The previous values are used for calculating a correction term that can be subtracted from input while the output still satisfies (9). If the correction term is larger than the input value, signal y (Fig. 2) becomes negative after the subtraction, which leads to an unwanted clipping result. This is prevented by adding a block that replaces negative values IEE Proc.-Commun., Vol. 152, No. 3, June 2005
0 −0.5
c (n) convolved feedback
−1.0 −1.5 −2.0 −2.5
Fig. 3 Function b(n) formed by convolution (11) and by present algorithm
with zeroes. Function b(n) formed by convolution and by the present algorithm is shown in Fig. 3. 4
Results
4.1
WCDMA
Simulation results for some common known windows are presented in Table 2. All windows have equal length. The results show that the Hamming window has the best relationship between EVM and ACLR. The spectrum as a result of windowing is presented in Fig. 4. Table 2: Simulation results for different windows Window type
EVM, %
PCDE, dB
ACLR, dB
4.415
47.604
36.119
Hamming
10.459
40.013
58.580
Hanning
10.431
40.074
57.432
Kaiser
11.547
38.740
41.438
Gauss
10.800
39.478
48.451
No window
Three different test signals are used: a single carrier signal with 32 active codes, a single carrier signal with 16 active codes and a multicarrier signal with four carriers. The crest factors of the unclipped signals are 15.418, 15.414 and 13.745 dB, respectively. Simulations are performed for two cases and the results are presented in Table 3. At first, the signal must fulfil the EVM, peak code domain error (PCDE) and ACLR requirements specified in [8]. The PCDE is closely related to the EVM and it measures the difference between the ideal and the transmitted data in 359
0
0
−10 −20
−20
clipped
dB
−40
relative power, dB
−30 Kaiser
−50
Gauss
−60 −70
measurement filter
measurement filter
bandwidth 30 kHz
bandwidth 100 kHz
−40
unclipped clipped Hanning Blackman
−60 −80
spectrum mask
Hamming
−80
−100 Hanning
−90
−120 0.4
0.5
0.6
0.7
0.8
0.9
0
1000
frequency (normalised)
Table 3: Crest factor reduction of WCDMA signal as a result of peak windowing Signal
DCF, dB EVM, %
PCDE, dB ACLR, dB
32 codes
7.35
17.5
33.4
56.1
32 codes with margin
3.65
3.0
49.9
72.0
16 codes
6.17
9.7
33.0
61.5
16 codes with margin
4.09
2.8
50.0
72.8
Multicarrier
5.57
17.5
34.7
51.1
Multicarrier with margin 3.03
3.0
50.5
65.0
the code domain. These requirements are set for the whole modulator, and therefore cannot be applied in the real situation, so in the second case there is some margin left for the following transmitter stages. The EVM is kept below 3%, PCDE below 49 dB and ACLR must be at least 65 dB. The clipping ratio and the window length used are chosen to maximise the crest factor reduction (DCF) with the constraints mentioned above. Choosing the window length is a problematic issue. Results show that in most cases the EVM or PCDE is the limiting parameter and there is some margin for ACLR. In theory, reducing the window length decreases the EVM, PCDE and ACLR, which leads to a situation where the clipping ratio could be decreased. Simulations showed that in this case the crest factor increased so no advantages was gained. As the results show, the crest factor can be reduced significantly by using the peak windowing algorithm. In [10], the peak windowing is compared to some other clipping methods and it has the best performance.
4.2
GSM
The clipped signal must fulfil the system specifications outlined in [11]. In the case of GSM the signal quality is measured by phase error and the spectrum of the signal must fit in the spectrum mask. At first different window types are compared. The spectrum of the unclipped signal, the spectrum of the clipped signal and the spectra of the windowed signals are presented in Fig. 5. Results for the Hanning and Blackman windows are presented. Other common window functions i.e. Kaiser, Hamming and Gaussian are investigated also, and the Hanning and 360
5000
Fig. 5 Spectrum of GSM signal when different clipping methods are used
Frequency spectrum as a result of windowing
Blackman windows are found to be better than the other windows. The test signal consists of 16 carriers and the crest factor of the unclipped signal is 14.258 dB. In every case, the signal is clipped so that the crest factor becomes 10 dB. Figure 5 shows 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 window seems to give better spectral properties than the Hanning window. The effect of the used window length is presented in Fig. 6 and in Table 4. The crest factor of the test signal is clipped to 12 dB. In this example, the window length of 240 corresponds to the length of one symbol (an oversampling ratio of 240 is used). It is obvious that a long window gives better spectral properties than a short window, but the interesting result is that the long window gives better phase error performance than the short window. This is surprising because when the window length increases the difference between the transmitted and the ideal waveform increases and therefore, intuitively, the phase error should increase. The achieved crest factor reduction (DCF), in the case of 8, 16 and 32 carriers is presented in Table 5. The used window length is 601 and the clipping level is set so that the spectrum is the limiting element. The results show that the crest factor of the multicarrier GSM signal can be reduced significantly while the distortion is still kept to a tolerable level. The phase error specifications are 51 for rms and 201
0 −20 relative power, dB
Fig. 4
2000 3000 4000 frequency from carrier, kHz
measurement filter
measurement filter
bandwidth 30 kHz
bandwidth 100 kHz
−40
101 201 401 601
−60 −80
spectrum mask
−100 −120
Fig. 6
0
1000
2000 3000 4000 frequency from carrier, kHz
5000
Spectrum of GSM signal as function of window length IEE Proc.-Commun., Vol. 152, No. 3, June 2005
Table 4: Phase error of GSM signal as a function of window length rms
Peak
101
0.957
5.049
201
1.033
5.567
401
0.667
3.308
601
0.157
0.818
−20 relative power, dB
Window length
0 measurement filter
measurement filter
bandwidth 30 kHz
bandwidth 100 kHz
−40
101 201 401 601
−60 −80
spectrum mask
−100
Table 5: Crest factor reduction in the case of a multicarrier GSM signal Number of carriers
CF, dB
DCF, dB
rms
−120
0
1000
Peak
Fig. 8 length
8
9.131
2.266
0.199
0.866
16
10.207
4.051
0.230
1.212
32
10.658
6.737
0.360
2.805
2000 3000 4000 frequency from carrier, kHz
5000
Spectrum of clipped EDGE signal as function of window
Table 6: EVM of clipped EDGE signal as a function of window length
for peak error [11]. In practice, implementing the windowing algorithm presented with a window length of 601 might lead to high area and power consumption in the circuit implementation.
4.3
rms EVM, %
Peak EVM, %
101
2.763
11.526
201
3.683
15.156
401
5.690
21.920
601
6.944
24.783
EDGE
Again different window types are compared. The spectrum of the unclipped signal, the spectrum of the clipped signal and the spectra of the windowed signals are presented in Fig. 7. Two different windows, Hanning and Blackman are used. The test signal consists of 16 carriers and the crest factor of the unclipped signal is 15.747 dB. In every case, the signal is clipped so that the crest factor becomes 12 dB. Figure 7 shows that, as previous, the conventional clipping causes very high out of band radiation and therefore it is not applicable in the case of EDGE transmission. A Blackman window seems to given better spectral properties than a Hanning window. The effect of the used window length is presented in Fig. 8 and in Table 6. The crest factor of the test signal is clipped one decibel. The longer window
0 −20 relative power, dB
Window length
measurement filter
measurement filter
bandwidth 30 kHz
bandwidth 100 kHz
−40 unclipped clipped Hanning Blackman
−60 −80
spectrum mask
−100 −120
0
1000
2000 3000 4000 frequency from carrier, kHz
5000
Fig. 7 Spectrum of EDGE signal when different clipping methods are used IEE Proc.-Commun., Vol. 152, No. 3, June 2005
gives better spectral behaviour but the EVM becomes high. A window long enough to meet the spectral specifications causes EVM, which is very near or above the EVM specifications, 7% for rms and 24% for peak value [11]. In a real digital modulator an EVM this high cannot be tolerated because some margin must be left for the following 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 a one decibel reduction in the crest factor leads to an intolerable error. Generally, the EDGE signal seems to be very sensitive for clipping errors and so 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 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 we down-convert 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 while the phase error remains low the EVM can be high. For the signal with 0.19 degrees rms and 0.88 degrees peak phase error, the corresponding EVM values are 5.4% and 19.6% respectively. 5
Conclusions
In this paper, a straightforward manner to implement the peak windowing algorithm is presented. The algorithm is used in the base station to reduce the crest factor of the 361
downlink signal in order to enhance the power efficiency of the PA. When we are moving towards software radios, where the same hardware is used to generate different modulation formats it would be beneficial to have a single clipping algorithm that can handle all the different signals. Simulation results are given for the cases of WCDMA, GSM and EDGE transmission. It is shown that in the cases of WCDMA and GSM, the crest factor can be reduced significantly by using the peak windowing. In the case of EDGE, no such advantage is gained.
6
References
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3 Ozluturk, F.M., and Lomp, G.: ‘Effect of limiting the downlink power in CDMA systems with or without forward power control’. Military Communications Conf., November 1995, Vol. 3, pp. 952–956 4 Pauli, M., and Kuchenbecker, H.-P.: ‘Minimization of the intermodulation distortion of a nonlinearly amplified OFDM signal’, Wirel. Pers. Commun., 1996, 4, pp. 90–101 5 Van Nee, R., and De Wild, A.: ‘Reducing the peak-to-average power ratio of OFDM’. Vehicular Technology Conf., May 1998, Vol. 3, pp. 2072–2076 6 Chow, J., Bingham, J., and Flowers, M.: ‘Mitigating clipping noise in multi-carrier systems’. IEEE Int. Conf. on Communications, June 1997, Vol. 2, pp. 715–719 7 V.aa. n.anen, O.: ‘Clipping in wideband CDMA base station transmitter’. Master’s Thesis, Helsinki University of Technology, 2001 8 3GPP Technical Specification Group Acess Network: ‘Base station conformance testing’. TS 25.141 V3.2.0, 2000 9 European Telecommunication Standards Institute ‘Digital cellular telecommunications system (Phase 2+); Modulation’ (GSM 05.04) V8.1.0, 1999 10 V.aa. n.anen, O., Vankka, J., and Halonen, K.: ‘Effect of clipping in wideband CDMA system and simple algorithm for peak windowing’. World Wireless Congress, San Franciso, USA, May 2002, pp. 614–619 11 European Telecommunications Standards Institute ‘Digital cellular telecommunication system (Phase 2+): Radio transmission and reception’, (GSM 05.05) V8.3.0, 1999
IEE Proc.-Commun., Vol. 152, No. 3, June 2005
