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1、IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 8, AUGUST 20021979 Out-of-Band Emissions of Digital Transmissions Using Kahn EER Technique Dietmar Rudolph AbstractThe Kahn envelope elimination and restoration (EER) technique allows for linear RF power amplification by combining no
2、nlinear, but efficient, RF and AF power amplifiers (PAs). In order to use the EER technique for digital signals, a coordinate transform from the original Cartesian in-phase and quadrature mode into a polar mode has to take place, yielding an envelope (or amplitude) and a PM RF signal. This coordinat
3、e transform is extremely nonlinear and thereby broadens the spectra of the original signals. In the final PA stage, both signals are recombined. However, since this recombination process is imperfect, out-of-band (OOB) emissions come up, also known as adjacent channel power or spectral regrowth. In
4、this paper, the impact of the broadening of the amplitude and phase signals on OOB emissions is investigated with respect to imperfect restoration due to signal delays and limited bandwidth of the amplitude path. It is shown that the amount of OOB emissions can significantly be reduced if the modula
5、tion scheme shows a “hole” at the origin in its vector diagram. Index TermsACPR, amplifier, band-limited communications, delay effects, EER, Kahn technique, PM, spectral regrowth, transmitter. I. INTRODUCTION D IGITAL cellular transmission systems, as well as digital broadcasting systems, widelyuse
6、modulation formats that do not have a constant envelope, e.g.,DQPSK, OQPSK, and additionally with zero crossings in their vector diagram, e.g., QPSK, eight phase shift keying (8PSK), amplitude phase shift keying (APSK), orthogonal frequency division multiplex (OFDM), CDMA. If the amplitude of the di
7、gitally modulated signal is not constant, the transmitter power amplifier (PA) has to operate in linear mode. Linear operation mode can either be established by a linear amplifier, which suffers from low efficiency 2, or by a transmitter that linearizes a high-effi- ciency PA, e.g., by using the env
8、elope elimination and restora- tion (EER) technique proposed by Kahn in 1952 111. In an EER transmitter, basically, the RF signal is split into a PM and an AM signal. The PM signal is directly amplified by a PA that runs in a saturated or even switching mode. In order to re- store the amplitude, the
9、 supply voltage of the PA is modulated by the AM signal. Thereby, although the PA itself is operated in a nonlinear high-efficiency mode, the total transmitter shows linear behavior while maintaining the high efficiency. The ben- efits of the EER technique with respect to the transmitters ef- ficien
10、cy are without any question. The EER technique, how- ever,introducesacoordinatetransformofthedigitalsignalfrom Manuscript received August 15, 2001. The author is with T-Systems Nova GmbH, Berkom, D-10589 Berlin, Germany (e-mail: dietmar.rudolpht-systems.de). Publisher Item Identifier 10.1109/TMTT.20
11、02.801349. Cartesian to polar form, and the PA stage of an EER transmitter afterwards produces the inverse coordinate transform back. In this way, linear distortions within the “polar” branches of the transmitteraretransformedbackintononlineardistortionsinthe RF signal, even if the transmitter itsel
12、f had no additional hard- warenonlinearities.Thecoordinatetransformationprocessisan additional extreme nonlinearity within the transmission chain. Therefore, the EER technique also has its drawbacks, which are the out-of-band (OOB) emissions. For the case of an analog two-tone signal, Raab 6 has ana
13、lyzed the intermodulation distortion (IMD) spectra. In this paper, however, the investigation is limited to the effects produced by the additional EER nonlinearities. As a signal, a band-limited complex Gaussian noise is used. This signal is very similar to an OFDM modulation. With respect to its ve
14、ctor diagram, it has a maximum of zero crossings, and might be in so far together with its high Crest factor the worst case of all digital modulations for EER transmitters. Based on numerical simulations, this paper first examines the broadening of the internal phase and amplitude spectra with respe
15、ct to the modulation scheme. The influence of unequal time delay in the amplitude and phase branch on OOB emissions and the required bandwidth of both branches are then discussed. It turns out that a “hole” in the vector diagram of the modulation scheme significantly reduces the OOB emissions. As a
16、result, the amount of unwanted emissions depends on the type of digital modulation used. A modulation scheme that already has such a “hole,” like digital offset modulations, is better suited for EER techniques than others. Also, the bigger the “hole,” the better. II. CARTESIAN-TO-POLARCONVERSION The
17、 structure of a transmitter using EER is shown in Fig. 1. It is subdivided into two building blocks, i.e., the digital mod- ulator and AM transmitter. In the digital modulator, the signal is split into a phase signal (RF-P) and an amplitude (A) signal, which serve as the input signals of the AM tran
18、smitter. The dig- ital signal (“Digital Signal”) at the input of the modulator shall already describe the transmit symbols, and all coding shall have been done in stages prior to the digital modulator, not shown in Fig. 1. In the first step, the digital modulator forms in-phase and quadrature (I & Q
19、) symbols, consisting of I & Q baseband symbols, and shapes them properly. The spectra of these digital signals are band limited to half the channel bandwidth and have shoulder distances of approximately 70 dB. When modulated, they fit exactly into the channel bandwidth. These Cartesian I & Q signal
20、s are then converted into polar RF-P & A signals. This process introduces the nonlinearity that is typical for EER 0018-9480/02$17.00 2002 IEEE 1980IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 8, AUGUST 2002 Fig. 1.Structure of an EER transmitter. techniques. The AM transmitter
21、 has a conventional structure. The RF path is a chain of RF driver and RF power output stage, both operating in classes C, D, E, or F, respectively, with high efficiency. The PA receives its supply voltage via an amplitude modulator, which operates in class S, switched mode. A partial drive modulati
22、on to overcome amplitude-to-phase (A/Phi) con- versions in the PA, suggested by Raab 8, is also possible, but is not shown in Fig. 1. In this paper, the modulation process in the PA is idealized and, thus, does not suffer from A/Phi con- versions. In the EER application, the I & Q symbols are only i
23、nternal Cartesian signals, which have to be converted to polar signals. According to Fig. 1, the conversion to polar signals is done all digitally in the following way. Generating asignal explicitly is avoided because the phase angle is not limited, and an overflow could happen. Alternatively, two s
24、ignals andare used, which are confined to1. Thecomponent is multiplied byand the component is multiplied by, andis the RF carrier frequency. When using “Cartesian” I & Q signals, the complex dig- ital-modulated signalbecomes (1) The EER technique has to furnish the same digitally modu- lated signala
25、t the transmitters output. Amplitudeand phasesignals, used for exciting the AM transmitter, are “polar” signals, and we get (2) (internal signal) (3) (4) Since the coordinate transform Cartesian to polar is highly nonlinear, theandsignals, as well as theand signals, have a much broader spectra than
26、theand signals. According to Fig. 1, the PM RF signal (i.e., RF-P signal) becomes - (5) Fig. 2.Example of vector diagram of I & Q noise signal. Thus, the RF-P signal - is a purely PM signal. The PA stage of the AM transmitter operates in principle as a multiplier. This is indicated by a letter “X” i
27、n the PA block, and gives the output signal - (6) (7) (8) For convenience, the amplification is set to one, and the time functionsare equal again, thus, the spectra are the same. The TX internal broad-band spectra are compensated and no longer appear in the output signalof the TX. That is the ideal
28、case. III. SPECTRA OFSIGNALS IN ANEER TRANSMITTER The characteristic spectral features of the polar A and RF-P signals can most clearly be shown with band-limited Gaussian-noise-like signals, which have a Rayleigh amplitude distribution function. AllspectrainthispaperarecalculatedwithMATLAB.Forcon-
29、venience, the axes in the figures are normalized with respect to the bandwidth of the noise, and the amplitudes are also normal- ized to one. The zero approaches of the A signal correspond to respective approaches to the origin in the vector diagram of the I & Q signals (Fig. 2). These cause rapid c
30、hanges in the phase angle and, in turn, corresponding frequency deviations, leading to the peaks shown in Fig. 3. However, wedges or cusps of the A signal and rapid phase changes or even phase jumps of thesignal produce broad spectraofeitherthesesignals, andalsoof theRF-P signal.Also, the broader th
31、e spectra are, the worse the compensation in the PAstage becomesand themore OOB emission comesup. Thus, a straightforward idea to avoid all those problems is to “punch a hole” into the vector diagram, provided that the modulation scheme does not have it as before, as in the case of OFDM. Fig.4showss
32、pectraoftheI&QsignalsandtheAsignal.The curvelabeled “without VectorHole”shows theactual spectrum. The curve labeled “with Vector Hole” indicates a method as to RUDOLPH: OOB EMISSIONS OF DIGITAL TRANSMISSIONS USING KAHN EER TECHNIQUE1981 Fig. 3.Phase and frequency deviations of the I & Q noise signal
33、. Fig. 4.Spectra of the I & Q and A signals. how to overcome the problem for noise-like signals, and will be discussed below. In Fig. 5, the spectra of the modulated digital and RF-P sig- nals are shown. The actual spectrum is again labeled “without Vector Hole.” IV. SOFTCLIPPING OF THEA SIGNAL For
34、noise-like signals, the A signal will be clipped, usually at its top in order to reduce the Crest factor of the modulated signal. This is a well-known practice to yield higher output sig- nals of a transmitter. In this approach, the clipping will be done at the lower end of the A signal, in order to
35、 prevent zero cross- ings. First, a clipping threshold is defined, which, here, for con- venience, is 10% of the maximum of the A signal. The amount of the A signal beneath this threshold defines a clipping signal. This clipping signal is shaped Gaussian in order to fit spectrally into the signal ba
36、ndwidth. Afterwards, it is then added vecto- rially to the I & Q signal and, thus, “punches a hole” into the vectordiagram(Fig.6).Thiskindof“softclipping”avoidsspec- tral splatter. Fig.7showstheAsignalandclippingthresholdtogetherwith the soft clipping signal. The time positions of the latter signal
37、correspond to the frequency peaks in Fig. 3. Fig. 5.Spectra of the RF-P and the modulated digital RF signal. Fig. 6.Example of vector diagram of complex noise with a “hole.” Fig. 5 shows the improvement in the spectrum of the RF-P signal by “punching or drilling a hole” into the vector diagram. The
38、improvement in the A signal is similar. All spectral com- ponents now attenuated within these signals are no doubt more easily compensated in the PA stage of the transmitter. It is beyond the scope of this investigation as to how big the hole might become regarding the increase of the bit error rate
39、 of the digital transmission. However, it is evident that modulation schemes that already provide a “vector hole” will better fit to an EER transmitter. Also. it is known from AM transmitters that they do have difficulties with attaining a real zero in their envelope signal. A method to mitigate thi
40、s problem is a partial drive modulation 8, which is unfortunately not applicable to all types of AM transmitters. The greater the “hole” in the vector diagram of a given mod- ulation scheme, the steeper the slope in the spectra of the A and RF-P signals will become. Fig. 8 shows simulation results,
41、de- pending on the radius of the hole in percent of the maximum vector diagram radius, which is normalized to one. Without a hole, the slopes for the RF-P signal are only3.5 dB and for the A signal are only9.5 dB within a frequency range equal to the RF bandwidth. Note that all figures given are nor
42、malized to the RF bandwidth. A modulation scheme with a hole in the vector diagram greatly improves the slopes of both signals. 1982IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 8, AUGUST 2002 Fig. 7.A signal, clipping threshold, and soft clipping signal. Fig. 8.Slopes of A and
43、RF-P signals as a function of the radius of the hole in the vector diagram. V. DELAY ANDBANDWIDTHWITHIN ANEER TRANSMITTER After analyzing the spectra of the A and RF-P paths sepa- rately, the impact of nonideal signal restoration on the OOB emissions will be discussed here. Signal delay and bandwidt
44、h limitations of the two signals will be considered. A. Influence of the Delay on the OOB Emissions In this section, the bandwidths are taken sufficiently broad, and all effects to the OOB emissions will come from delay mis- match only. First, the case without a “vector hole” is regarded. The A sign
45、al has been delayed byi.e., in a pro- gressive order.is the clock frequency used in the simulation, and is about ten times the RF bandwidth, thus, . Fig. 9 shows that this clock frequency is too coarse for delay fine tuning and, in a practical case, upsampling has to take place. To extrapolate to sm
46、aller delays, the progressive order has to be taken into consideration. Therefore,approximately5dBmoreshoulderdistanceisgained if the delay is halved again, and so forth. Something very important can be seen from this figure, as noted below. If the delay is unequal to zero, the spectrum of the digit
47、al signal becomes similar to the spectrum of corresponding Fig. 9.Spectra of the modulated digital RF signal for various delays (without a vector hole). Fig. 10.Spectra of the modulated digital RF signal for various delays (with a 10% vector hole). the RF-P signal, and the slope of the OOB is identi
48、cal to the slope of the RF-P signal (see Fig. 5). For smaller delays,theshoulderbecomeshigherand,forbigdelays,in this example, the spectrum of the digital signal is more or less identical to the spectrum of theRF-P signal. This should be kept in mind when aligning an EER transmitter for minimum OOB
49、because, for big delays, there is hardly any difference between the RF-P spectrum and the spectrum of the digitally modulated signal. The same interrelation holds also for signals with a “vector hole” (Fig. 10), even though steeper slopes result. “Punching a hole” into the vector diagram only gives an improvement in the slope of the OOB emissions, but gives no improvement to the shoulder distance. Each doubling of the delay reduces the shoulder distance inthespectrumofthemodulateddigitalRFsignalapprox- imately by the same amount in decibels. Therefore, delay matching