Reduction of average-to-minimum power ratio in communications signals

Reduction of the average to minimum power ratio in the communication signal

Field of invention

The present invention relates to the reduction of the average to minimum power ratio in the communication signal.

Prior art

Many modern digital radio communication systems transmit information by modifying the amplitude and phase of an electromagnetic wave. The process of converting information into the amplitude and phase of the transmitted signal is generally called modulation. Many different modulation techniques are used in communication systems. When selecting a modulation technology, it is generally affected by the computational complexity required to generate radio channel signals, characteristics, and requirements for spectrum efficiency, power efficiency, and small size in mobile radio applications. After selecting a modulation technique for a specific application, it is often difficult or substantially impossible to change the modulation. For example, in cellular radio applications, all users must replace their current mobile phones with new phones designed to be compatible with new modulation technologies. This is obviously very impractical.

Many existing modulation format designs can be transmitted by radio that processes signals with rectangular coordinates. The two components of the rectangular coordinate system are usually called in-phase and quadrature (I and Q) components. This type of transmitter is often called a quadrature modulator. (With regard to modulation, one thing needs to be clarified. The method used to convert information into the transmitted radio signal is a mathematical description (such as BPSK, FSK, GMSK), and the modulator is the physical device used to perform this operation.) Another method is that the transmitter can process signals with polar coordinates. At this time, the signal is expressed in terms of its amplitude and phase. In this case, it can be said that the transmitter uses a polarity modulator. Polar modulators have several performance advantages over slightly traditional quadrature modulators, including higher signal fidelity and spectral purity It is better, and the dependence of device performance on temperature changes is low.

Although the polar modulator has practical advantages over the quadrature modulator, the amplitude and phase components of the signal usually have a higher bandwidth than the in-phase and quadrature components. Bandwidth expansion means that the amplitude and phase need to be processed digitally, because the rate at which the amplitude and phase must be processed is related to its bandwidth.

The rate of amplitude and phase change is closely related to the modulation technique. In particular, modulation formats that result in extremely small amplitude values (relative to average amplitude values) generally have extremely large phase component bandwidths. In fact, if the signal amplitude becomes zero, the signal phase will immediately change up to 180 degrees. In this case, the bandwidth of the phase component is essentially infinite, so the signal is not suitable for transmission by a polarity modulator.

Many commonly used modulation techniques do cause extremely small relative signal amplitudes. To be more precise, that is, the average-to-minimum signal magnitude ratio (AMR) is very large. An important practical example of modulation technology with large AMR is the technology adopted by the UMTS 3GPP uplink (mobile to base station).

Previous work in this area can be divided into two types: one that deals extensively with peak power reduction, and the other deals specifically with "hole-blowing". Blowhole refers to the process of removing low-power events in a communication signal with a time-varying envelope. The reason for this name is that when using this technique, a "hole" will appear in the vector graph of the modified signal.

A lot of work has been done to deal with peak power reduction, among which the goal is to reduce the signal power locally. In contrast, the work done to deal with blowholes (trying to increase the signal power locally) appears to be quite small, and the work done previously The method is known to cause suboptimal performance.

US patent 5,805,640 (the '640 patent), titled: "Method and apparatus for conditioning modulated signal for digital communications" (Method and apparatus for conditioning modulated signal for digital communications), and US patent 5,696,794 (the '794 patent), titled : "Method and apparatus for conditioning digitally modulated signals using channel symbol adjustment" (Method and apparatus for conditioning digitally modulated signals using channel symbol adjustment), both patents explain the removal of low-amplitude (low-power) events of communication signals way of doing. In fact, these two patents also mention the creation of "holes" in the signal distribution. The motivation for these holes is that some power amplifiers, especially LINC power amplifiers, are difficult to perform when the signal amplitude dynamic range is large.

Simply put, the '794 patent states that in order to maintain a partial minimum power, the amplitude and phase of the transmitted symbol must be modified. Since the symbol is modified before the pulse is shaped, the modified signal has the same spectral characteristics as the original signal. The method used in the '640 patent is to add a pulse with a fixed amplitude and phase between the original digital signal before the pulse is shaped. Therefore, the first patent data is processed at the symbol rate (T=1), and the second patent data is processed at twice the symbol rate (T=2). For the sake of simplicity, these two methods will be referred to as the symbol rate method and the T/2 method, respectively. The methods of calculating the amplitude and phase of the corrected pulse are almost identical in the two patents.

Since the correction amplitude and phase calculation methods used in the two patents are only rough estimates, the performance is not ideal. In particular, after using either of these two methods to process the signal, although the probability of low-power events is reduced , But obviously still higher than ideal.

The specific method used by the T/2 method is to add a pulse with a specified amplitude and phase to a signal with a half-symbol timing (ie, t=k*T+T/2) before the pulse is shaped. The amplitude and phase of the additional pulse are designed to maintain the signal amplitude so as not to fall below some ideal critical values. This method does not allow the pulse to be configured at any timing. Therefore, the effectiveness is reduced and the error vector magnitude (EVM) is impaired.

The method of calculating the amplitude and phase of the additional pulse used in the T/2 approach is very restrictive because:

1) The test of signal encapsulation is limited to the minimum value of half-symbol timing (t=i*T+T/2).

2) The phase correction is not based on signal encapsulation, but only based on two symbols adjacent to the low-amplitude event.

These two limitations can cause errors in correcting pulse amplitude and phase. Specifically, the true minimum value of the signal does not appear at T/2, but at a slightly different time, so errors will be introduced into the amplitude of the correction pulse. The validity of this hypothesis and the specific signal modulation are closely related to the pulse shape. For example, this is a reasonable assumption for a UMTS uplink signal with one DPDCH, but it is not a reasonable assumption for a UMTS uplink signal with two DPDCHs active. The magnitude of this amplitude error can be quite large. For example, in some cases, the amplitude of T/2 is very close to the ideal minimum amplitude, but the true minimum is almost zero. At this time, the calculated correction amplitude will be much smaller than the ideal amplitude, resulting in low amplitude events that cannot be removed.

The signal envelope of T/2 will be larger than the ideal minimum, but within this symbol The signal amplitude in the interval will be lower than the critical value, so low-amplitude events will be lost entirely.

In any event, the resulting correction amplitude is usually very different from what is needed.

The method used to calculate the correction pulse essentially assumes that the phase of the T/2 pulse-shaped waveform is very close to the phase of the straight line between adjacent symbols. This is an estimate for any situation (but it is generally a reasonable estimate), but it will cause some errors in the phase. However, this estimate is valid only when the origin is not between the straight line described earlier and the real signal envelope. When this assumption is violated, the correction phase will be shifted by approximately 180 degrees from the appropriate value. This usually leaves uncorrected low-amplitude events.

The T/2 method adds pulses at half-symbol timing, while the symbol rate method adds pulses to the two symbols adjacent to the low-amplitude event. That is, if the signal has a low amplitude event of t=kT+T/2, the symbols k and (k+1) will be modified. These two methods calculate the phase of the additional pulse in the same way, and test the low-amplitude event in the same way, that is, test the signal envelope of the half-symbol timing. Therefore, this method also applies the same source of amplitude error and phase error mentioned above.

The T/2 method repeats the calibration procedure in an iterative manner. In other words, this method will be applied repeatedly, "until no symbol interval minimum value is less than the minimum threshold value."

Compared with the aforementioned method, US Patent 5,727,026, "Method and apparatus for peak suppression using complex scaling values" (Method and apparatus for peak suppression using complex scaling values), raises a significantly different problem, that is, reducing the peak value of the communication signal. Average power ratio (Peak-to- Average power Ratio; PAR). Large PAR, if not most, is also a problem with many traditional power amplifiers (PA). Large PAR signals need to be highly linearly amplified, which affects the power efficiency of the PA. Add the pulse to the original pulse-shaped waveform to complete the reduction, and the pulse has the appropriate amplitude and phase, so the peak power can be reduced. The pulse can be designed to have any desired spectral characteristics so that the distortion can be kept within the frequency band (to optimize ACPR), or to leak out of the band slightly (to optimize EVM). The timing of adding pulses is related to the timing of peak power, and is not limited to a fixed timing instant.

Specifically, this peak reduction method can add low frequency and wide pulses to the original (high PAR) signal. The signal of the added pulse and the peak amplitude is 180 degrees out of phase, and the amplitude of the additional pulse is the difference between the ideal peak and the actual peak. Since pulses are added to the signal (a linear operation), the spectral characteristics of the additional pulses are on the signal spectrum, which can completely determine the effect of the peak reduction technology. Probability can be said to be a peak that occurs at a certain time that does not correspond to the sampling instant. This method emphasizes the ability to control the amount of signal splatter and/or signal distortion.

In addition, U.S. Patent 6,175,551 also describes a method of reducing PAR, especially for OFDM and multi-code CDMA signals, in which "the time offset and scaling reference function are subtracted from the sampling signal interval or symbol, so that each subtracted reference function can be Reduce peak power". In a preferred embodiment, the reference function is a window-type sinc function, or other functions "approximately the same as the bandwidth of the transmitted signal."

Other related patents include U.S. Patents 5,287,387, 5,727,026, 5,930,299, 5,621,762, 5,381,449, 6,104,761, 6,147,984, 6,128,351, 6,128,350, 6,125,103, 6,097,252, 5,838,724, 5,835,536, 5,835,816, 5,838,724, 5,381,449, 5,384,547, 5,349,300,410.

Therefore, a program is needed (believed to be absent in the prior art), which can greatly reduce the AMR of the communication signal without significantly degrading the signal quality. This program is even best to actually implement the polarity modulator for signals with extremely high AMR.

Summary of the invention

The present invention, generally speaking, can modify the pulse amplitude modulation signal to reduce the ratio of average power to minimum power. The modification of the signal makes the quality of the signal maintain an ideal state. The signal quality is described in terms of Power Spectral Density (PSD) and Error Vector Magnitude (EVM).

The present invention will be better understood with reference to the following description together with the accompanying drawings. In the schema:

Figure 1 is a general block diagram of PAM signal generation;

Figure 2a is a block diagram of the PAM generator modified for ARM reduction;

Figure 2b is a detailed block diagram of the device of Figure 2a;

Figure 3 shows the impulse response of the square root raised cosine pulse shaping filter with 22% excess bandwidth;

Figure 4 shows the IQ plot (vector graph) of a part of the QPSK signal, which has square root raised cosine pulse shaping;

Figure 5 shows the power section of a pulse-shaped QPSK signal as a function of time;

Figure 6 is a histogram showing the time position of the minimum signal amplitude, including only the minimum value greater than 12dB below the average power;

Figure 7 shows the phase of the QPSK signal as a function of time;

Figure 8 shows the instantaneous frequency expressed as a multiple of the signal symbol rate of Figure 7;

Figure 9a shows the use of mathematical models to detect the occurrence of low-amplitude events;

Figure 9b is a geometric illustration of a local linear model of complex signal encapsulation;

Figure 9c shows the calculation of t_min according to the local linear model;

Figure 10 shows the comparison of the original signal power and the signal power after adding a single complex weighted pulse (designed to keep the minimum power above the average power -12 dB);

Figure 11 is the IQ plot of the QPSK signal, which has been modified to keep the instantaneous power greater than -12dB relative to the RMS power;

Figure 12 shows the instantaneous frequency of the modified signal, expressed in multiples of the symbol rate;

Figure 13 shows that the minimum power of the modified signal is a function of the added correction pulse time error (the amplitude and phase of the correction pulse remain fixed);

Figure 14 shows the estimated PSD of the traditional QPSK signal and the same signal after applying the precise hole blowing method;

Figure 15a is the IQ plot of the modified signal after modulation, showing that some distortion has occurred in the signal (the measured RMSEVM is 6.3%);

Figure 15b shows the result of nonlinear filtering, which uses the same square root raised cosine pulse as the pulse shaping filter;

Figure 15c shows the result of non-linear filtering, which uses the Hanning window of the correction pulse, where the time duration is equal to 1/2 of the symbol duration;

Figure 16a is a block diagram showing the symbol rate blow hole;

Figure 16b is a detailed block diagram showing the symbol rate blow hole;

Figure 16c is a block diagram showing the iterative symbol rate blow hole;

Figure 16d is a block diagram showing the iterative sample rate blow hole;

Figure 16e is a block diagram showing the symbol rate blow hole of one or more consecutive iterations, followed by the sample rate blow hole of one or more iterations;

Figure 17a is a block diagram of a part of a radio transmitter in which a non-linear filtering in the polar domain is performed;

Figure 17b is a detailed block diagram of the device of Figure 17;

Figure 18 is a waveform diagram showing the amplitude component of the polar coordinate signal and the difference in the phase component of the polar coordinate signal;

Figure 19 is the impulse response diagram of DZ3 pulse;

Figure 20 is a waveform diagram showing the results of nonlinear filtering of amplitude components (showing the original amplitude components before nonlinear filtering in the polar field, the amplitude components after nonlinear filtering in the polar field, the critical value, and the pulse added to the amplitude component);

Figure 21 shows an example of adding pulse suitable for nonlinear filtering of phase components;

Figure 22 is a waveform diagram showing the results of nonlinear filtering of phase difference components;

Figure 23 shows another nonlinear filtering method for phase components in the polar coordinate system;

Figure 24 is a block diagram of a part of a radio transmitter, in which nonlinear filtering is performed in the orthogonal domain first, and then in the polar domain; and

Figure 25 is PSD, showing the result of the non-linear filtering of Figure 34;

Figure 26 shows the IQ plot of the UMTS signal distribution, which has a main Live data channel and 7/15 beta ratio;

Figure 27 shows the IQ plot of the UMTS signal distribution, which has two active data channels and a Beta ratio of 7/15;

Figure 28a shows the way to find the timing of low amplitude events;

Figure 28b uses accurate algorithms and uses real-time estimates to compare the probability density functions of low-amplitude events;

Figure 29 is an IQ plot, showing the straight line comparison method of vector quantization;

Figure 30 shows the CORDIC type algorithm of vector quantization;

Figure 31 shows a known method of calculating the phase of the corrected pulse;

Figure 32 shows the Cumulative Distribution Function (CDF) obtained by the method of the present invention and the known method, where the signal is π/4 QPSK with rising cosine pulse shaping, and the excessive bandwidth is 22% (the ideal minimum power is 9 dB below RMS);

Figure 33 shows an example where the known symbol rate method works quite well (shows the original signal envelope, shows the modified envelope, and indicates the sample used to calculate the corrected amplitude);

Figure 34 shows an example where the known symbol rate method does not work well;

Figure 35 shows an example of the known poor operation of the T/2 method; and

Figure 36 shows the cumulative distribution function (CDF) obtained using the method of the present invention and two known methods, where the signal is a 3GPP uplink with an active DPDCH, and the amplitude ratio is 7/15 (the ideal minimum power is below 9 RMS dB).

Detailed description of preferred embodiments

The polarity modulator can be regarded as a combination of a phase modulator and an amplitude modulator. The requirements of the phase modulator and amplitude modulator are directly related to the signal phase and vibration The composition is related. The amplitude and phase bandwidth are related to the average to minimum amplitude ratio (AMR) of the signal. As will be explained below, a large AMR signal will suddenly change in phase, that is, the signal phase component has obvious high frequency content. In addition, certain transistor technologies also limit the AMR that can be achieved by actual amplitude modulators. If the required amplitude dynamic range exceeds the range that the transistor circuit can generate, this limitation will result in distortion of the transmitted signal. Therefore, if the polarity modulator is used to transmit the signal, it is very necessary to reduce the signal AMR. U.S. Patent Application Serial Number<u style="single">　　　</u>(Dkt.<u style="single">　　　</u>), title: "Multi-mode communications transmitter" (Multi-mode communications transmitter), illustrates an example of a polar modulator. The application was filed on the same day as this case, and it is hereby incorporated by reference.

The nonlinear digital signal processing technology described in this article can modify the amplitude and phase of the communication signal to reduce the performance of the polarity modulator. Specifically, the amplitude of the modified signal can be restricted to fall within the range of a fixed ideal value. This limitation causes the AMR to be lower than the original signal, thus reducing the amplitude and phase bandwidth. The price of this bandwidth reduction is lower signal quality. However, the signal quality degradation is usually small, resulting in the final signal quality being more than adequate.

Signal quality requirements can generally be divided into in-band and out-of-band requirements. The specification of signal quality in the processing frequency band usually ensures that the intended receiver can capture the message sent by the transmitter, regardless of whether the message is voice, video or data. Specifications for processing out-of-band signal quality generally ensure that the transmitter does not excessively interfere with receivers other than the intended receiver.

The quality measurement system in the traditional frequency band is the RMS error vector amplitude (EVM). The mathematically related measurement is rho, which is the distance between the transmitted signal and its ideal version Normalize the cross-correlation factor. EVM and rho are related to the ease with which a predetermined receiver can retrieve information from the transmitted signal. As EVM increases above zero, or rho drops below one, the transmitted signal will gradually be distorted relative to the ideal signal. This distortion increases the possibility of errors when the receiver is retrieving the message.

The traditional out-of-band quality measurement is the power spectral density (PSD) of the transmitted signal, or some measurement derived therefrom, such as ACLR, ACP, etc. The specific impact related to PSD is the degree to which the transmitted signal interferes with other radio channels. In a wireless communication network, interference with other radio channels will reduce the overall capacity of the network (for example, it will reduce the number of simultaneous users).

It goes without saying that any method of reducing the average to minimum amplitude ratio (AMR) must generate the least interference as possible (minimum degradation of out-of-band signal quality), while maintaining signal quality (ie EVM or rho) in-band measurement At a satisfactory level. These considerations are the motivation of the present invention, which is to reduce the AMR while preserving the quality of the out-of-band signal, which is particularly important for the operator of the wireless communication network.

Generally speaking, AMR reduction can be performed by analyzing the transmission signal and adding carefully formed pulses to the signal with a time interval (in which the signal amplitude is less than a part of the critical value). The details of the exemplary embodiments, including signal analysis and pulse formation, are described as follows. First, the types of signals that can use the present invention are described.

<u style="single">Pulse-Amplitude Modulation (PAM)</u>

Many modem communication systems use a mechanism called pulse amplitude modulation (PAM) to transmit digital messages. PAM signal is only frequency-upconverted (frequency-upconverted) of the amplitude calibration, phase offset and time offset version of the signal pulse total. The amplitude calibration and phase shift of the n-th time-shifted version pulse are determined by the n-th component of the digital message. In the field of communication systems, various types of PAM signals include signals generally referred to as PAM, QAM, PSK and many different names. As those skilled in the art of communication theory know, the PAM signal x(t) at time t can be mathematically explained as follows. The description is divided into two parts, namely the frequency-increasing conversion and amplification procedure, and the fundamental frequency modulation procedure, as shown in Figure 1.

The up-conversion and amplification program can be described mathematically as follows:<maths><img file="TW586278B_D0001.tif" /></maths>Where Re{} represents the real part of its complex argument; ω_c=2πf_cThe radio carrier frequency per second and per Hz of radians are respectively defined; j is the square root of the imaginary number of minus one, and g is the amplifier gain. This equation explains the frequency-increasing conversion and the frequency-increasing conversion procedure used to amplify the complex base frequency signal s(t), which is also the so-called I/Q (in-phase/quadrature) representative of the signal. The signal s(t) generated by the fundamental frequency modulation program can be defined mathematically as:<maths><img file="TW586278B_D0002.tif" /></maths>Where p(t) is the pulse at time t, and T is the symbol period (1/T is the symbol rate). For any time instant t when s(t) is ideal, the sum can replace all p(t-nT) as a non-negligible value of n. At the same time, a_nIs the symbol corresponding to the nth component of the digital message. Symbol a_nIt can be a real number or a complex number, and can be obtained from the nth component of the digital message by using a fixed mapping or a time-varying mapping. The fixed mapping example can appear on the QPSK signal, where the nth component of the digital message is an integer d in the set {0,1,2,3}_n, And the mapping can be given as a_n=exp(jπd_n/2). Time-varying mapping will occur on QPSK offset by π/4, which is given by a_n= exp(jπ(n+2d_n/4) modified QPSK mapping; that is, the mapping is not only related to the message value d_nRelated, and related to the time index n.

For the present invention, an important characteristic of the PAM signal is that the PSD shape of the PAM signal (as a function of f) can only be determined by the pulse p(t), and its assumption is that the symbol sequence a_nThe second-order statistical characteristics of is the same as that of white noise. Considering that the signal s(t) is the output of a filter with impulse response p(t), and is subject to a weighted a_nThe driving of the pulse sequence can understand this characteristic. That is, the PSD S of x(t)_x(??) can be displayed equal to:<maths><img file="TW586278B_D0003.tif" /></maths>Where P(??) is the Fourier transform of pulse p(t), σ²_aIs the mean square value of the symbol sequence.

This important observation forms the motivation of the present invention because it proposes that adding additional pulse copies to s(t) does not change the shape of the PSD. That is to say, the non-linear filtering performed in this way causes not only minor changes in the PSD, but also extremely subtle changes in fact. Adding extra copies of the pulse to the signal can be used to increase the amplitude of x(t) to an ideal amplitude, for example when it falls below some critical value. Specifically, in order to form a new signal<img file="TW586278B_D0004.tif" />(t) and<img file="TW586278B_D0005.tif" />(t), s(t) can be modified by adding additional pulses to s(t):<maths><img file="TW586278B_D0006.tif" /></maths>in<maths><img file="TW586278B_D0007.tif" /></maths>And the disturbance instance t_mIt will appear at the point in time when its disturbance signal is needed (for example, whenever the s(t) amplitude falls below a certain critical value). Disturbance sequence b_mrepresent Focus on time t_m(For example, to increase the time t_mThe amplitude calibration and phase shift applied to the pulse of the nearby s(t) amplitude is selected). and<img file="TW586278B_D0008.tif" />The first item in (t) is the same,<img file="TW586278B_D0009.tif" />The second term in (t) can be regarded as the output of the filter with impulse response p(t), and is subject to weighted b_mThe driving of the pulse sequence. Therefore, it can be reasonably expected<img file="TW586278B_D0010.tif" />The PSD of (t) and x(t) will have a very similar shape (as a function of frequency??).

With this theoretical basis, the present invention can be described in detail in a slightly more general form than that used above, as shown in Figure 2a. The present invention uses the signal s(t) as its output. This signal will be sent to the analyzer to determine the appropriate disturbance instance t_m, And at time instant t_mOutput disturbance sequence value b_m. The perturbation sequence will pass through a pulse-shaping filter r(t) with impulse response, and its output will be added to s(t) to produce<img file="TW586278B_D0011.tif" />(t), and then transmitted to any appropriate device, to increase frequency conversion and amplification into the ideal power. As mentioned above, the pulse shaping filter r(t) can be the same as the original pulse p(t), or it can be different from p(t) (for example, to simplify the implementation, it can be a shortened version of p(t) ).

Figure 2b shows a more detailed block diagram showing the main signal path and the correction signal path of the two signal channels (I and Q). Pulse shaping can occur after pulse shaping (sample rate correction) or before pulse shaping (symbol rate correction). In the correction path, the continuous values of I and Q can be used to perform the signal minimum calculation and compare with the ideal minimum. If correction is required based on the comparison result, the required correction amplitude for each channel will be calculated. The pulse (the same as the pulse used for pulse shaping) will be scaled according to the required correction and the channel added to the main path, and will be delayed in order to provide time to perform the correction calculation.

The method and modulation format used to determine the timing, amplitude and phase of the correction pulse Style related. Factors to consider include:

1. The duration of a low-amplitude event related to the symbol period.

2. The time series distribution of low amplitude events.

If the duration of all low-amplitude events is small relative to the symbol (or chip) duration, the low-amplitude events can be corrected by adding a single complex weighted pulse, just like the correction method used for pulse shaping. This approach can be used, for example, M-ary PSK modulation to take effect. The appropriate method of blowing holes in this example can be referred to as the "precise" method of blowing holes. The precise hole blowing method and its actual real-time hardware execution work will be explained below. Other modulation formats can cause low-amplitude events with a relatively long duration. Usually, this is the case for QAM and multi-code CDMA modulation. In such cases, multiple pulses can be added, or multiple iterations of precise hole blowing methods can also be used. The practicality of hole blowing in the polar field has been shown to perform the "final cleanup" of the signal generated using one of the above-mentioned techniques, and even better EVM performance can be achieved. Compared with the (generally) each symbol (chip) in the above-mentioned technical situation, since the amplitude information can be clearly provided in the field of polarity, the hole blowing can be performed on the basis of each sample.

<u style="single">Precise method of blowing holes</u>

Now show the detailed calculation of the precise hole blowing method with an example. This example uses QPSK with square root raised cosine pulse shaping. The pulse shaping filter has 22% excess bandwidth, as shown in Figure 3. A typical I/Q plot of this signal is shown in Figure 4. The signal amplitude can obviously be reduced arbitrarily. The signal power over a short period of time is shown in Figure 5. The average power is normalized to one (0 dB). This figure shows that the AMR of this signal is at least 40 dB. In fact, the AMR of this QPSK signal is effectively infinite, because the signal power can be arbitrarily small. Since it must be decided to insert the school The time of the positive pulse is instantaneous, so the timing of the minimum power is very important. We would expect the minimum power to appear approximately when t=nT/2, where n is an integer and T is the symbol period. It can be confirmed by Fig. 5, which shows that the minimum power appears very close to T/2.

To further confirm this hypothesis, check the distribution of power minimum timing. In order to achieve this goal, a pulse-shaped QPSK waveform with random messages will be generated, and the timing of the appearance of the minimum power will be determined. This example assumes that if the instantaneous signal power is greater than 12 dB below the average signal power, a low-power event will occur.

Figure 6 shows the timing histogram of the minimum amplitude of the QPSK signal. These results are based on 16,384 independent symbols with the same distribution. Note that, as expected, the minimum is indeed tightly clustered around the T/2 symbol timing. This is a very important result, because of its limitation, the search range of the signal minimum must be performed. (Please note that the histogram shown in Figure 6 is only valid for this specific signal type (QPSK). Other signal types, such as high-order QAM, have different distributions, so they must be considered when searching for local power minimums.)

As mentioned earlier, low-power events are related to rapid changes in signal phase. This correspondence is shown in Figure 7, which shows the phase of the QPSK signal corresponding to the power curve of Figure 5. Obviously, the phase changes rapidly near t=T/2, which corresponds to the minimum power. In Figure 8, this characteristic can be seen more clearly, which shows the instantaneous frequency. The sampled data waveform is defined here as:<maths><img file="TW586278B_D0012.tif" /></maths>Among them θ(t) is the signal phase at time instant t, and δ is the sampling period. Figure 8 shows that the instantaneous frequency over this interval is as high as 45 times the symbol rate. From this point of view, UMTS The 3GPP broadband CDMA standard has a chip rate of 3.84 MHz. If the symbol rate of the QPSK signal in our example is 3.84 MHz, the instantaneous frequency will exceed 45×3.84=172.8 MHz. Processing signals at such a high instantaneous frequency is not yet feasible.

Obviously, in order to be able to actually implement the polarity modulator, the signal phase bandwidth must be reduced. The most obvious way is to low-pass filter the phase (or phase difference is the same). However, any substantial filtering of the phase difference will cause substantial non-linear distortion of the signal that is not ideal. Then this distortion will cause the signal energy outside the band to increase significantly, so it is usually not ideal. It should be understood that only when the signal amplitude is very small, will the signal phase change rapidly. Therefore, if the signal amplitude can be kept above these minimum values, the bandwidth of the signal phase will be reduced. After discussing the spectral characteristics of PAM signals, it should be understood that by adding carefully selected pulses without any obvious effect on the signal bandwidth, the signal can be modified.

To avoid low-amplitude events and thus reduce the instantaneous frequency, a complex-weighted version of the pulse-shaping filter can be added to the signal. This complex weighted pulse is called a correction pulse. Select the pulse phase to be consistent with the signal at the point of minimum amplitude. The amplitude of the correction pulse is equal to the difference between the ideal minimum amplitude and the actual minimum amplitude of the signal.

Care must be taken when calculating the correction amplitude and phase in order to obtain the desired effect. More importantly, it must be recognized that the minimum signal amplitude may not correspond to the sampled instance. Since the phase and amplitude change rapidly in the neighborhood of the local power minimum, selecting the correction phase based on the signal value that cannot correspond to the signal minimum will cause a large phase and/or amplitude error. As the minimum amplitude becomes smaller, the possibility of large errors increases. By using very A high sampling rate (that is, a large number of samples per symbol) can reduce the possibility of large errors, but it will greatly increase unnecessary computing load.

The so-called "local linear model" can instead be substituted into the signal in the time neighborhood of the local power minimum, so the minimum amplitude of the model can be solved mathematically. The local linear model can effectively interpolate the signal, so the amplitude can be directly calculated at any instant of time. Calculating the correction pulse in this way will not be limited to the values that appear in the sampled data waveform. In this way, the minimum amplitude and the equally important necessary correction phase can be calculated in a highly accurate manner.

Please note that the complete pulse-shaped signal does not need to exist in order to calculate the corrected amplitude and phase. As long as the complex fundamental frequency signal is calculated at a few important sampling instants, the nonlinear filtering can be operated on pure symbols before the final pulse shaping step. This expedient measure will facilitate immediate execution of the work.

The signal will exist outside the exclusion zone (defined by the ideal minimum of two points very close in time), but will also pass through the exclusion zone between the two points, as shown in Figure 9a. In order to find the true minimum of the signal amplitude and its corresponding phase, it is best to use the following approach. This approach uses a local linear model encapsulated by a complex fundamental frequency signal, as shown in Figure 9b. This model approximates the complex signal envelope with a straight line in the I/Q space near the local power minimum. In many cases, if the ideal minimum power is very small and the signal modulation is not too complicated (such as PSK), then this model is quite accurate. After this model is substituted into the signal, the minimum amplitude of the local linear model can be solved directly.

In order to formulate the model, the complex signal must be known to be no less than two different time instants. These time instants are best to be close to the true minimum of the signal, because the model in this example is more accurate. These time instants don't have to be right It should be the sampling instant that exists in the sampling signal envelope.

s(t1) represents the complex signal at time t1. x1 and y1 represent the real and imaginary parts of s (t1), respectively. Similarly, x2 and y2 represent the real and imaginary parts of s (t2), respectively. These time instantaneous signals can be given as:<maths><img file="TW586278B_D0013.tif" /></maths>Among them, t2&gt;t1 and t2-t1&lt;&lt;T. Then define: x=x2-x1y=y2-y1 As far as the accuracy of the local linear model is concerned, any instantaneous complex signal at time t can be expressed as:<maths><img file="TW586278B_D0014.tif" /></maths>Where c is the slope parameter.

In order to find the minimum amplitude of this linear model, the geometric method according to Figure 9b can be used. The minimum amplitude point corresponds to a point on the local linear model that intersects a second straight line that passes through the origin and is orthogonal to the linear model, as shown in Figure 9b. On the parameter (using parameter g), the equation of this orthogonal line can be explained as: x=-gyy=gx

The intersection point can be found by setting the x-axis and y-axis components of the linear model to be equal to the orthogonal line. In this way, the set of equations can be generated as follows (two equations and two unknowns): x1+cx=-gyy1+cy=gx Rearrange these equations to be given:<maths><img file="TW586278B_D0015.tif" /></maths>Set these two formulas to be equal, and solve g, can be given:<maths><img file="TW586278B_D0016.tif" /></maths>The minimum amplitude of the linear model is then:<maths><img file="TW586278B_D0017.tif" /></maths>

In order to test low-amplitude events and calculate the corrected amplitude, the minimum amplitude calculated from the local linear model must be explicitly calculated. The minimum amplitude can also be used to calculate the amplitude of the correction pulse, so it can be given as:<maths><img file="TW586278B_D0018.tif" /></maths>

The phase of the signal whose correction phase is equal to the minimum amplitude is determined by the local linear model. If the correction is performed in the I/Q domain, there is no need to explicitly calculate the correction phase θ, as long as sin (θ) and cos (θ) are calculated. Referring to Figure 9b, you can see:<maths><img file="TW586278B_D0019.tif" /></maths><maths><img file="TW586278B_D0020.tif" /></maths>Among them, for any quantity c, c/|c-=sign (c). Similarly:<maths><img file="TW586278B_D0021.tif" /></maths>In the rectangular coordinates, the in-phase and quadrature correction factors respectively have the form:<maths><img file="TW586278B_D0022.tif" /></maths>Therefore, it can be seen that cosθ and sinθ are sufficient to calculate the correction factor, so there is no need to determine the signal phase θ separately. The modified signal in the rectangular coordinates can be given as:<maths><img file="TW586278B_D0023.tif" /></maths>Among them, t_min is the approximate time when the local minimum appears, and the pulse is assumed (without impairing generality) that it can be normalized, resulting in p (0)=1.

In some applications, it is better to get an accurate estimate of the time t_min corresponding to the minimum signal power. The "accurate" here is used to indicate an estimate that is not limited by the sample rate, and can have any degree of accuracy. For example, given t_min, the correction pulse can be added to the signal based on the interpolation or highly oversampled prototype pulse p (t). To achieve this, you can use any of the following three programs that utilize local linear models. The first two methods are based on geometric parameters. The third approach is based on directly reduced signal amplitude.

Linear interpolation can usually be used to estimate the signal value at an arbitrary time t (when the signal is only known at two or more separate time indices). In other words, linear interpolation can be used to find s (t) for a given t. However, linear interpolation can also be used to find t for a given s (t). According to the description of Figure 9c, this feature can be used as follows. The linear model is: s(t)=s(t1)+c(x+jy) where<maths><img file="TW586278B_D0024.tif" /></maths>For the real part of the signal,<maths><img file="TW586278B_D0025.tif" /></maths>Solve this formula for t,<maths><img file="TW586278B_D0026.tif" /></maths>

The calculation of t_min is related to the calculation of x_min (the real part of the signal at the local minimum amplitude). As mentioned earlier, the minimum signal amplitude is ρ_m_i_n; The real part of the signal at the minimum amplitude is ρ_m_i_n cosθ. therefore,<maths><img file="TW586278B_D0027.tif" /></maths>In addition, according to the same argument of the imaginary part of the signal,<maths><img file="TW586278B_D0028.tif" /></maths>

The above two formulas are only related to the real or imaginary part of the signal. In the limited precision execution work, if the change of x or y is small, this will become a disadvantage. Therefore, it is actually best to use an equation that relates to both the real and imaginary parts of the signal. This type of calculation can be derived by directly reducing the signal amplitude using standard optimization procedures. Using the linear model, the signal amplitude is: s(t)²=(x₁+cx)²+(y₁+Cy)²Get the derivative with respect to c,<maths><img file="TW586278B_D0029.tif" /></maths>Set the derivative equal to zero, and solve for c,<maths><img file="TW586278B_D0030.tif" /></maths>Therefore, the final formula of t_min is:<maths><img file="TW586278B_D0031.tif" /></maths>

The "precise" hole blowing algorithm can therefore be summarized as follows:

1. Determine the approximate timing t=t1 of potential low-amplitude events in the signal.

2. In the time domain of potential low-amplitude events, for at least two different time instants t1 and t2&gt;t1, where t2-t2&gt;&gt;T, calculate the pulse-shaped signal s(t). In the example of the symbol rate hole, the signal s(t) will be calculated based on the band-limited pulse applied later and some number of symbols near t1 and some number of symbols near t2. In the example of symbol rate (ie, over-sampled) blow holes, pulse shaping will have been performed, so that s(t1) and s(t2) will be selected to correspond to adjacent samples.

3. Use the "local linear model" and ρ described in detail above_m_i_nTime t_m_i_n,Calculate the minimum amplitude ρ_m_i_n。

4. Compare the calculated minimum amplitude with the ideal minimum amplitude.

5. If the calculated minimum amplitude is less than the ideal minimum amplitude, calculate the in-phase and quadrature correction weights C respectively_IWith C_Q, As detailed above.

6. Weight the two copies of the pulse shaping filter with the in-phase and quadrature correction values, respectively.

7. Add the weighted copies of these two pulse shaping filters to the reference as t_m_i_nThe in-phase and quadrature components of the signal.

8. Convert the modified in-phase and quadrature components into amplitude and phase to form the signal processed by the polarity modulator.

The effectiveness of the above-mentioned precise hole blowing method is clearly shown in Figure 10, which compares the instantaneous power of the original QPSK signal and the signal processed by the precise hole blowing method. In this example, the critical value of the ideal minimum power is selected to be 12 dB below the RMS power. Obviously, the accurate method of blowing holes is extremely effective for keeping the signal power above the ideal minimum. The IQ plot of the QPSK signal after the hole is blown is shown in Figure 11. Obviously, all trajectories have been pushed beyond the ideal limit. A "hole" appeared in the IQ plot that had no holes before.

The instantaneous frequency of the modified signal is shown in Figure 12. Compared with Figure 8, it is obvious that the instantaneous frequency has dropped from about 45 times the symbol rate to about 1.5 times the symbol rate. This method obviously has greatly reduced the instantaneous frequency.

Please note that the precise hole blowing method described in this article can be highly tolerant of timing errors, but is rather not tolerant of amplitude and phase errors (or correction factor C_IWith C_QEquivalent error in). Timing errors involve the time when the correction pulse is added to the original signal. The reason for this tolerance for timing errors is that the pulse shaping filter usually has a fairly wide amplitude peak relative to the duration of the low amplitude event. The effect of this timing error is shown in Figure 13, where timing errors up to a quarter symbol period only degrade AMR by 1 dB.

After showing that the precise hole blowing method is effective for removing low-amplitude events, the effects of in-band and out-of-band signal quality are then explained. The PSD of the QPSK signal before and after the hole is hard to distinguish in the frequency domain, as shown in Figure 14. The EVM effect is shown in Figure 15a, which shows the IQ plot of the modified signal after matched filtering and baud-synchronous sampling. Knot The result shows the information that the receiver can get after modulating the signal. Obviously, distortion has appeared in the signal, because not all samples fall exactly on one of the four QPSK distribution points. RMSEVM can be defined as:<maths><img file="TW586278B_D0032.tif" /></maths>Where α_kand<img file="TW586278B_D0033.tif" />_kThey are the ideal and actual PAM symbols. For the specific example shown in Figure 14, the N=16384 symbol is used to calculate the RMS EVM and it is found to be 6.3%. Similarly, the peak EVM can be defined as follows:<maths><img file="TW586278B_D0034.tif" /></maths>In this example, the peak EVM was found to be approximately 38%. If the signal is allowed to have a relatively large amplitude dynamic range, the RMS EVM will be relatively low. However, please remember that increasing the allowable amplitude dynamic range will also increase the bandwidth and peak value of the instantaneous frequency. Therefore, it is possible to exchange between the ideal signal quality (EVM) of the actual polarity modulator and the instantaneous frequency demand.

In order to ensure that the effect of the signal PSD (see Figure 14) is extremely small, the selection of the correct pulse shape should essentially match the signal frequency band that limits the pulse shape. When the pulse oversampling rate is four or more (samples per symbol time), the previous algorithm can be simplified. Specifically, the calculation of t can be eliminated_m_i_n, And the correction pulse of the existing signal sample s (t1) inserted into the alignment time. As shown in Figure 13, the maximum error of the minimum amplitude of 4 times oversampling is 1 dB, and it will be reduced to 0.2 dB for 8 times oversampling.

In fact, consider t_m_i_nThe method of performing hole blowing and eliminating t_m_i_ncomputational The differences between the methods are shown in the examples in Figures 15b and 15c, respectively. In the example of FIG. 15b, the same square root raised cosine pulse as the pulse shaping pulse is used to perform hole blowing. In the example of FIG. 15c, the Hanni window of the correction pulse (where the time duration is equal to 1/2 of the symbol duration) is used to perform hole blowing. In Figure 15c, as can be seen, in order to avoid the hole area, the change of the original signal trajectory is as small as possible. However, in many instances (if not most), t can still be eliminated_m_i_nCalculate (as shown in Figure 15b).

Figure 16a shows the configuration of the symbol rate blow hole. Apply digital information to the main path of pulse shaping and up-conversion. The auxiliary path includes an analyzer block that generates the correction signal. An adder is set in the main path to add the main signal and the correction signal generated by the analyzer.

Referring to FIG. 16b, there is shown a particularly advantageous embodiment of performing symbol rate hole blowing. Provides two signal paths, the main path and the auxiliary path. The output of the main signal path and the auxiliary signal path can be summed to form the final output signal.

The main signal path receives symbols (or chips) and performs pulse shaping of these symbols (or chips), which is mostly traditional. However, the main signal path may include a delay element to achieve synchronization processing between the main signal path and the auxiliary signal path.

In the auxiliary path, the symbol (or chip) can be applied to the correction DSP (which can be implemented by hardware, firmware or software). The calibrated DSP will perform the blow hole according to the above-mentioned precise method, so that it can output the auxiliary stream of the symbol (or chip). These symbols (or chips) will appear at the same rate as the main stream of symbols (or chips), but in comparison, the amplitude will be very small, and in fact it will be zero. The non-primary path signal enters or approaches the hole. The relative timing between the main and auxiliary paths will be offset by T/2, so that symbols with a small value in the auxiliary path will appear in half of the symbol timing of the main signal path.

In an exemplary embodiment, the calibration DSP can calculate the minimum signal value for each consecutive pair of symbols (or chips) by calculating the signal values corresponding to the respective symbols (or chips) and applying a local linear model. When calculating the signal value corresponding to the symbol (or chip), the pulse that is the same as the main signal path will be applied to the symbol (or chip) and some number of previous and subsequent symbols (or chip). After pulse shaping, the pulse is used to calculate the signal value at a specific time, which is different from the usual pulse shaping itself.

After determining the correction sign (or chip) of the auxiliary signal path, the pulse shaping method is the same as that of the main signal path. The pulse shaped output signals of the main and auxiliary paths can then be combined to form the final output signal.

Since the duration of p(t) is finite (L), it is possible to stream between low-amplitude events and input symbols (L^MExample) Evaluate the signal before the correction time. Then it can be alone in {a_i}Decide c_iWith t_i. (Correction symbol c_iVery small, so the effect on message streaming is negligible. ) In this variation of the symbol rate blow hole, calculate the symbol b_mIt can be added to the original message stream, and the entire new stream will be band-limited after passing through the filter.

<u style="single">Iterative method</u>

The above focus is on the symbol rate and sample rate hole blowing technology. Although the term "precision" has been used to refer to these technologies, some errors and inaccuracies cannot be avoided. In other words, the generated signal will still hit the ideal hole. Depending on the needs of the particular system, further processing may be required or best Signal to remove these residual low-amplitude events. One approach is to just specify a hole larger than the actual need to tolerate some error limits. Another approach is to repeat or repeat the blow hole.

In the orthogonal domain, symbol rate hole blowing can be performed one or more times (Figure 16c), and sample rate hole blowing can be performed one or more times (Figure 16d). However, in the second example, the symbol rate at each iteration is doubled. For example, in the first iteration, the correction symbol can be inserted at T/2. In the second iteration, the correction symbols can be inserted at T/4 and 3T/4, and so on. The symbol rate of one or more iterations can be followed by the sample rate of one or more iterations (Figure 16e). (Generally speaking, the sample rate hole cannot be followed by the symbol rate hole.)

Another way is to blow holes in the sample rate in the polar domain.

<u style="single">Polar field blowing hole</u>

The price of the above-mentioned orthogonal field blowing technology to keep ACLR good is the partial degradation of EVM. Other technologies will present different exchange costs. For example, the price of the hole blowing technology in the polar field to keep the EVM good is at the expense of ACLR. Therefore, in specific applications, orthogonal field blowholes, polar field blowholes, or a combination of the two can be applied.

The amplitude and phase components of the polar coordinate system can be correlated with the in-phase and positive components of the rectangular coordinate system as:<maths><img file="TW586278B_D0035.tif" /></maths>

Figure 17a is a block diagram of a part of a radio transmitter in which a non-linear filtering in the polar domain (ie, "blow hole") is performed. The figure shows the amplitude and phase represented by the above equation, and the polarity domain nonlinear filter and polarity modulator such as How relevant.

In Figure 17a, G represents the gain of the polarity modulator. In the calculation, the digital information is first mapped to the in-phase and quadrature components of the rectangular coordinate system. The in-phase and quadrature components are converted into amplitude and phase difference by a rectangular to polarity converter. After knowing the phase difference between the starting point of the phase and the time, the corresponding phase in time can be calculated. The polarity modulator will perform phase calculation in a later stage. Before the phase difference is sent to the polarity modulator, a non-linear filtering in the polarity domain is performed.

Figure 17b shows a more detailed block diagram showing the main signal path and the correction signal path of the two signal channels (ρ and θ). In the correction path, continuous values of ρ can be used to perform signal minimum calculations and compare with the ideal minimum. If correction is required based on the comparison result, the required correction amplitude for each channel will be calculated. The pulse (or the pulse pair in the theta channel example) will be calibrated according to the required correction and the channel added to the main path, and will be delayed in order to provide time to perform the correction calculation.

Figure 18 shows examples of vibration and phase components (phase difference) in polar coordinates. It can be seen from the plot that when the amplitude decreases, a corresponding sharp wave (positive or negative) will appear in the phase difference component.

The sharp wave in the phase difference component indicates that there is a rapid phase change in the signal, because the relationship between the phase and the phase difference is as follows:<maths><img file="TW586278B_D0036.tif" /></maths>

Amplitude drops and rapid phase changes are very undesirable, because peaks will expand the bandwidth of the signal components of each polarity. The goal of non-linear filtering in the polar domain is to reduce the dynamic range of amplitude swings and to reduce instantaneous phase changes. The dynamic range of the amplitude component and the maximum phase change that can be processed by the polarity modulator Modification will be limited by the hardware. Non-linear filtering in the polarity domain can modify the signal before the polarity modulator processes the signal. This pre-processing is to ensure that the signal dynamic range does not exceed the limit of the hardware function performed by the polarity modulator, thus avoiding unwanted signal distortion.

The nonlinear filtering of the polar coordinate system is more complicated than the nonlinear filtering of the rectangular coordinate system. In order to avoid severe signal degradation, the two components (amplitude and phase) in the polar coordinate system must be handled carefully.

The following description will propose an implementation manner of nonlinear filtering in the polar domain in an exemplary embodiment. The nonlinear filtering system in the polar field consists of two parts. The first part is the non-linear filtering of the amplitude component, and the second component is the non-linear filtering of the phase component (phase difference). These two parts will be explained in order as follows.

<u style="single">Non-linear filtering of amplitude components</u>

If the amplitude dynamic range exceeds the function of the polarity modulator, the output signal will be cut. This reduction will cause spectrum regeneration, which will greatly increase the adjacent channel leakage ratio (ALR). One method that can be used to reduce the dynamic range of the amplitude component is to blow holes (or nonlinear filtering).

The purpose of this nonlinear filtering of amplitude components is to remove low-amplitude events of input amplitude ρ (t), thus reducing the dynamic range of amplitude swing. Assuming the critical value of the minimum amplitude is TH_m_a_g; Then by observing the signal ρ (t), the time interval during which the signal falls below the critical value can be obtained. Suppose there are N time intervals when the signal falls below the critical value, and the minimum amplitude of each time interval occurs at t_l_,…_,t_N. Therefore, the nonlinear filtering of the amplitude component can be expressed as:<maths><img file="TW586278B_D0037.tif" /></maths>Where b_nWith p_n(t) represents the insertion amplitude and pulse of the nth time interval. The non-linear filtered signal is composed of the original signal and the inserted pulse. The amplitude of the inserted pulse is given as: b_n=TH_m_a_g-ρ(t_n)

The choice of inserting pulse must be cautious, so as to reduce the signal degradation related to ACLR. The impulse function preferably has a smooth transition between the leading edge and the trailing edge. The appropriate pulse (DZ3) is based on the paper presented by McCune in Davis, California, University of California CIPIC Report #97-3 on June 29, 1997, titled "The Derivative-Zeroed Pulse Function Series" (The Derivative-Zeroed Pulse Function). Family). The impulse response standard of DZ3 pulse is shown in Figure 19.

An example result of nonlinear filtering of amplitude components is shown in Figure 20. It can be seen from the plot that the signal interval where the amplitude drops below the critical value is compensated by the inserted pulse. Therefore, the dynamic range of amplitude swing can be reduced.

<u style="single">Non-linear filtering of phase components</u>

In an exemplary embodiment, the input of the polarity modulator is the phase difference, not the phase. The voltage-controlled oscillator (VCO) in the polarity modulator integrates the phase difference and generates the phase component output by the polarity modulator. The phase difference is directly related to the speed that the VCO must integrate. If the phase difference exceeds the function of the VCO, the output signal phase will delay (or lead) the actual signal phase. Therefore, if the VCO continues to be unable to maintain the actual signal phase, phase jitter will occur. This kind of phase jitter will cause the distribution to rotate, thereby severely degrading the EVM.

The purpose of nonlinear filtering of phase components is to suppress large (positive or negative) phase difference events, so that no phase accumulation error occurs. It is important to know that The VCO output is the accumulation of the input (phase difference). Therefore, any additional processing of the phase difference must ensure that the phase difference does not accumulate. The non-linear filtering of the phase component currently carefully modifies the phase difference, so that the accumulated phase will deviate from the original phase trajectory from time to time. However, after a fixed time interval, it must be merged back to the original phase path.

First, find the position where the absolute value of the phase difference exceeds the VCO integral function, and then the nonlinear filtering of the phase component can be completed. Assume that the absolute value of the phase difference exceeds the function of the VCO in the total number of M events, and the absolute peak value of each event occurs at t_m. Before the phase difference is sent to the polarity modulator, a non-linear filter in the polarity domain will be performed.

<maths><img file="TW586278B_D0038.tif" /></maths>Where p_p_,_m(t) is at time t_mInsert the pulse of the phase difference component, c_mIs the corresponding amplitude, given as:<maths><img file="TW586278B_D0039.tif" /></maths>Where TH_pIt is the critical value of the phase difference. The inserted pulse should conform to the following equation:<maths><img file="TW586278B_D0040.tif" /></maths>

The result of inserting a pulse is basically the same as changing the phase trajectory. However, by inserting pulses that meet the above equation, the modified phase trajectory will eventually merge back to the original phase trajectory. This can be seen from the following equation:<maths><img file="TW586278B_D0041.tif" /></maths>The second item on the right will eventually disappear. Therefore, the modified phase trajectory will eventually merge back to the original phase trajectory.

Figure 21 plots the added pulse p suitable for nonlinear filtering of phase components_p(t) Examples. Likewise, it is very important that the impulse function has a smooth transition between the leading edge and the trailing edge. The pulse system used for the nonlinear filtering of the phase difference path is composed of two pulses. The areas of these two pulses are the same, but the polarity and duration are different. Therefore, the combined pulse integral with respect to time is zero.

An example result of the nonlinear filtering of the phase difference component is shown in Figure 22. It can be seen from the plot that the modified phase trajectory has a smoother trajectory than the original phase trajectory. Modifying the phase trajectory requires less VCO bandwidth than the original phase trajectory.

The non-linear filtering in the polar domain is composed of filtering of amplitude and phase components. If the nonlinear filtering system is done jointly (amplitude and phase), better spectrum roll-off can be achieved. However, each nonlinear filtering operation can also be done independently.

It is also possible to implement direct non-linear filtering of the phase component instead of the non-linear filtering of the phase difference component. Figure 23 shows the phase of the original signal from time t₁To t₂A sharp increase in the paradigm. One way to reduce the phase change is to interpolate between the straight line v(t) and the original phase path. The interpolation method can be expressed as:<img file="TW586278B_D0042.tif" />(t)=W(t)θ(t)+(1-W(t))ν(t) where w(t) is the weighting factor. The weighting factor can be a constant or change with DZ3, Gaussian function, etc. Likewise, it is very important that the weighting function has smooth leading and trailing edges.

The non-linear filtering in the polar domain can be used continuously with the non-linear filtering in the orthogonal domain. This kind of approach involves less computational complexity than iterative orthogonal domain nonlinear filtering.

If only one iteration of the orthogonal domain nonlinear filtering is performed, the same will be There is a low amplitude, high phase change event, but the probability is very low. If not managed properly, these low-probability events can degrade signal quality. In order to eliminate these low-probability events, after a single iteration of the orthogonal domain nonlinear filtering, the above-mentioned polar domain nonlinear filtering method can be used to maintain low EVM and low ACLR. Figure 24 shows a block diagram of this sequential system. Figure 25 shows the PSD of the output signal processed by the quadrature polarity nonlinear filter module. Curve A represents an orthogonal domain nonlinear filter with eight iterations. Curve B represents an iterative nonlinear filter in the orthogonal domain, followed by an iterative nonlinear filter in the polar domain. The spectrum regeneration is lower than -60dB. In addition, a good spectrum roll-off was also achieved.

<u style="single">Reduced computing load for real-time applications</u>

In certain polarity modulators, the hole blowing algorithm must be executed in real time using digital hardware and/or software. There are several challenging problems in the immediate execution of the precise hole blowing method. To some extent, the specific challenges faced are related to the overall architecture selected. There are (at least) two alternative architectures that can be used to perform accurate hole blowing algorithms. In the first architecture, called symbol rate blow hole, the correction pulse is calculated and added to the data stream with appropriate timing, and then pulse shaping is performed. In the second architecture, called the sample rate (or oversampling) blow hole, the complete pulse-shaped signal is calculated, and then weighted pulses are added to the pulse-shaped signal.

Due to its computational complexity, the above-mentioned precise hole blowing algorithm is difficult to implement with digital hardware. In the precise hole blowing algorithm, arithmetic division, square and square root operations are required. These arithmetic operations will greatly increase the complexity of digital hardware and should be avoided as much as possible. Reduce the computational complexity of the execution algorithm Directly reduce hardware complexity. The instant hole blowing algorithm described in this article does not require division, squaring, or square root operations.

Although the real-time hole blowing algorithm can be executed in the form of symbol rate or sample rate, it is generally desirable to perform symbol rate hole blowing. In particular, the symbol rate hole blowing algorithm allows digital hardware to operate at a relatively slow clock speed, and does not require so much memory to perform pulse insertion. Therefore, the following will explain the symbol rate real-time hole blowing algorithm.

Generally speaking, the real-time hole blowing algorithm is very similar to the precise hole blowing algorithm. However, in order to simplify the implementation, the real-time hole blowing algorithm will make certain assumptions and estimates. In the real-time hole blowing algorithm, the assumptions made are about the most likely situation in which the minimum amplitude is based on the structure of the signal distribution. This assumption allows the determination of the pulse insertion position when needed, and the entire signal amplitude does not need to be calculated. In addition, by normalizing the formula<img file="TW586278B_D0043.tif" />As one, you can greatly simplify the arithmetic operations of the precise hole blowing algorithm. This normalization eliminates the need for division, squaring, and square root operations.

By considering the answers to the following questions, you can understand the difference between real-time and precise hole blowing algorithms:

1. What is the potential timing of low-amplitude events?

2. What is the value of the minimum amplitude and how to calculate it in an effective and accurate way?

3. If the signal falls below the specified critical value, what are the in-phase and quadrature correction weights for the minimum amplitude?

The following will use the UMTS signal as an example to illustrate these issues.

<u style="single">1. What is the potential timing of low-amplitude events?</u>

If the timing of the minimum amplitude can be estimated based on the input data bits, there is no need to calculate the entire waveform in order to obtain the minimum amplitude. This shortcut is enough to save a lot of calculations. If the approximate timing of the low-amplitude event is known, the local linear model can be used to calculate the minimum with extremely high accuracy.

As mentioned earlier, the minimum amplitude of a frequency-limited QPSK signal usually appears near the half-symbol instance (nT+T/2). This hypothesis can be confirmed by the histogram in Figure 6. This assumption can also be applied to higher-order pulse-shaped PSK signals whose distribution points are on the same circle. A good example of this type of signal is a UMTS signal with an active data channel. Figure 26 shows an example of UMTS signal distribution with one active data channel. It can be seen from the plot that all the distribution points are on the same circle. If you construct a histogram for this particular signal, you can see that the timing of low-amplitude events is likely to appear on each half-symbol instance. Therefore, it can be assumed for this particular signal that the timing of the low-amplitude event will occur at time nT+T/2, where n is an integer.

The above assumptions will not be true in the more complex signal distribution example. Figure 27 shows an example of UMTS signal distribution with two active data channels. It can be seen from the plot that not all distribution points are on the same circle. The method used to find the minimum amplitude of the signal with a more complex distribution is shown in Figure 28a, and the description is as follows:

1. If the signal changes from distribution point P1 at time nT and ends at point P2 at time (n+1)T, a straight line can be drawn connecting these two points. This line can be represented as the first straight line.

2. The second straight line can be drawn perpendicular to the straight line connecting P1 and P2. Second straight line Including the origin and intersecting the first straight line at point M.

3. The second straight line divides the first straight line into two sections, the lengths of which are respectively proportional to D1 and D2. The timing of the low amplitude event is approximately nT+D1/(D1+D2)T.

4. If the second straight line does not cross the first straight line, no pulse insertion is required.

5. After deciding where the minimum amplitude value is most likely to occur, the local linear model can be used to calculate the local minimum amplitude value.

Using the above algorithm, a comparison table can be established for different signal distributions. If the distribution points are symmetrical to both the x and y axes, the size of the comparison table can be reduced. A special example of the above algorithm will appear where D1 is always equal to D2 to correspond to a UMTS signal with an active data channel. Therefore, the minimum amplitude of an active data channel will always appear near the time nT+T/2. The above algorithm for finding the approximate location of the minimum amplitude can also generalize signals with more complex distributions.

Fig. 28b shows the probability density function according to the sample interval of the minimum amplitude event that needs to be corrected (assuming 15 samples per symbol) based on the precise method described earlier and the real-time estimate just described. Please note the close correspondence between the two functions.

<u style="single">2. What is the value of the minimum amplitude and how to calculate it in an effective and accurate way?</u>

After understanding the possible timing of the minimum amplitude, the local linear model can be used to calculate the minimum amplitude. It must be determined whether the signal amplitude falls below the specified threshold. If the amplitude falls below the specified critical value, the in-phase and quadrature correction weights C of the inserted pulse must be calculated_IWith C_Q。

From the precise hole blowing algorithm, the calculation of the minimum amplitude can use the following equation:<maths><img file="TW586278B_D0044.tif" /></maths>Among them, x1 and y1 are the in-phase and quadrature samples of the signal at time t1, and t1 is the time when the minimum amplitude is most likely to occur.

The above equations involve one division, one square root operation, two square operations, and several other operations: multiplication, addition, and subtraction. By normalizing the denominator of the above equation, the computational complexity can be reduced.

Assuming that the vector (Δx, Δy) can be expressed as: x=ρ_x_ycos(θ_x_y)y=ρ_x_ySin(θ_x_y) Where ρ_x_yAnd θ_x_yIs the amplitude and phase of the vector (Δx, Δy). Then the minimum amplitude of the signal can be expressed as:<maths><img file="TW586278B_D0045.tif" /></maths>

With this normalization, there is no need for division, squaring, or square root operations. In addition, there is no need to know ρ_x_yFor how much. However, sin(θ_x_y) And cos(θ_x_y) Value. Therefore, given the vector (Δx, Δy), it is necessary to effectively obtain (sin(θ_x_y),cos(θ_x_y))The way.

It will be explained that the relatively low hardware complexity is used to estimate sin(θ_x_y) And cos(θ_x_y) In two ways. The first method uses the straight-line comparison method, the second method uses Use the coordinate rotation for digital computer (COordinate Rotation for Digital Computer; CORDIC) algorithm.

First, consider sin(θ_x_y) And cos(θ_x_y) Budget estimates. It can be seen from Fig. 29 that the straight line of the y=Mx function can divide the first quadrant into several subsections. By comparing the points (|Δx-,|Δy-) on the straight line y=Mx, it is possible to determine the subsection into which the point (|Δx-,|Δy-) falls. Any point in a certain subsection can be pre-normalized point (sin(θⁱ_x_y),cos(θⁱ_x_y)), where i represents the section to which the point (|Δx-,|Δy-) belongs.

The details of the algorithm are as follows:

1. First, convert the vector (Δx, Δy) into the first quadrant (|Δx-,|Δy-)).

2. Compare|Δy- with M|Δx-, where M is a positive number.

3. If |Δy- is greater than M|Δx-, then (|Δx-,|Δy-) is located on the left side of the straight line y=Mx.

4. If |Δy- is less than M|Δx-, then (|Δx-,|Δy-) is located on the right side of the straight line y=Mx.

5. According to the comparison of the above different straight lines, the subsection to which the point (|Δx-,|Δy-) belongs can be found. Assuming that the point belongs to section i, the vector (sign(Δx)*sin(θⁱ_x_y),sign(Δy)*cos(θⁱ_x_y)) to estimate the vector (sin(θ_x_y),cos(θ_x_y))。

Pre-calculated (sin(θⁱ_x_y),cos(θⁱ_x_y)) Numerical value. If a straight line of the total number W is used for comparison, there will be (W+1) subsections in the first quadrant. Therefore, all vector planes can be divided into 4*(W+1) subsections.

The second one is used to estimate (sin(θ_x_y),cos(θ_x_y)) The method is CORDIC type algorithm. This method is similar to the straight line comparison method. However, the CORDIC type calculus The vector plane of the method segmentation is more average. The detailed description of the algorithm is presented as follows and as shown in Figure 30:

1. First, convert the vector (Δx, Δy) into the first quadrant (|Δx-,|Δy-).

2. Secondly, according to the angle<img file="TW586278B_D0046.tif" />₀=tan^-¹(1) Rotate the vector clockwise (x-,y-). The vector after the angle rotation is expressed as (x-₀,y-₀)。

3. Assume i=1.

4. Ify-_i_-_lGreater than 0, according to the angle<img file="TW586278B_D0047.tif" />_i=tan^-^l(2^-ⁱ) Clockwise rotation vector (x-_i_-_l,y-_i_-_l). Otherwise, by angle<img file="TW586278B_D0048.tif" />_iRotate the vector counterclockwise. The vector after angle rotation is (x-_i,y-_i)。

5. Suppose i=i+1.

6. Repeat steps 4 and 5 as necessary.

7. Suppose that a total K of vector rotation is performed. This algorithm can divide the first quadrant into 2^︿k subsection. y-₀,y-₁,...,y-_k_-_lThe sign of can be used to determine which vector (x-,y-) belongs to 2^︿k subsection.

8. Then, a table filled with pre-quantized and normalized values can be used to estimate the vector (x-,y-).

9. If the comparison table is a vector (x-,y-) given sin(θⁱ_x_y),cos(θⁱ_x_y)), the vector (sign(x)*sin(θⁱ_x_y),sign(y)*cos(θⁱ_x_y)) Estimate (sin(θ_x_y),cos(θ_x_y))。

In the CORDIC algorithm, vector rotation must be done carefully, so that only arithmetic shift can be used to achieve vector rotation. This can form a very effective structure. By performing multiple CORDIC iterations, the accuracy of the estimates can be improved. If a total of two vector rotations are performed, the divisions generated in the first quadrant will be similar to the straight line comparison method shown in Figure 29.

Can be estimated (Sin(θ_x_y),cos(θ_x_y)) formula<img file="TW586278B_D0049.tif" />The regularization and effective algorithm of, can greatly reduce the computational complexity of the local minimum method. Using these methods, ρ can be estimated at any time_m_i_n. If the minimum amplitude ρ_m_i_nFalling at the critical value ρ_d_e_s_i_r_e_dBelow, the pulse insertion can be performed according to the hole blowing algorithm. This leads to the third problem:

<u style="single">3. If the minimum value of the different signal amplitude falls below the specified critical value, what is the weighting of the in-phase and square correction?</u>

Similar techniques can be applied to calculate sin(θ) and cos(θ), as long as x is replaced by x=ρ_x_ycos(θ_x_y) And replace y with y=ρ_x_ysin(θ_x_y), as shown below:<maths><img file="TW586278B_D0050.tif" /></maths>

After the above simplifications, the in-phase and quadrature correction weight C can be easily calculated using simple subtraction and multiplication_IWith C_Q. C_I=(ρdesired-ρ_m_i_n)cosθC_Q=(ρdesired-ρ_m_i_n)sinθ

<u style="single">Summary of Instant Hole Blowing Algorithm</u>

To facilitate immediate execution of work, novel approaches can be used to estimate the timing of low-amplitude events. At the same time, by normalizing the formula<img file="TW586278B_D0051.tif" />, Which can greatly simplify the local minimum method. Therefore, division and square root operations are not required.

Given the vector (x, y), two methods are recommended to estimate (sin(θ_x_y), cos(θ_x_y)) . The first method is the straight-line comparison method, and the second is the CORDIC-type algorithm. The execution complexity of the above two methods is usually very low, because only arithmetic shift and comparison are required.

Appendix 1

A1.0 O'Dea blow hole method analysis

In this appendix, the detailed analysis of the hole blowing method presented is presented in US Patent Nos. 5,696,794 and 5,805,640. The two patents are very similar, so they will be discussed at the same time. The main difference is that the first patent (5,696,794) will modify the symbols to be transmitted, while the second patent (5,805,640) will add pulses instantaneously at the T/2 symbol timing. For the sake of simplicity, the patent 5,696,794 is referred to as the symbol rate method, and the patent 5,805,640 is referred to as the T/2 method. First presents an overview of the two methods, and then examines the effectiveness of two different signal modulations. The first test signal is π/4QPSK with zero-ISI rising cosine pulse shaping. This is the modulation used in the two patents. The second test signal is a UMTS 3GPP uplink signal with an active DPDCH and a DPDCH/DPCCH amplitude ratio of 7/15. UMTS uses square root rising cosine pulse shaping with 0.22 rolloff characteristics.

<u style="single">A1.1 Overview of O'Dea hole blowing algorithm</u>

The term "half-symbol timing" is defined as the time instant in the exact halfway of the symbol time. In other words, if the PAM signal can be modeled as:<maths><img file="TW586278B_D0052.tif" /></maths>Where T is the symbol period, p(t) is the pulse shape, then the half symbol time corresponds to t=kT+T/2, where k is an integer. In order to make the presentation simpler and clearer, we will assume that the maximum value of p(t) has been normalized to one.

These two methods test the existence of undesirable low-power events by measuring the instantaneous signal amplitude at half symbol time and comparing this value with some ideal minimum amplitude mag_d: Mag_s=s(kT+T/2)<img file="TW586278B_D0053.tif" />mag_d

Both patents use the same method to calculate the phase of the correction pulse. Suppose a low-amplitude event occurs between the symbols k and k+1. First, determine the so-called phase rotation θ_r_o_t, And this is just the change in phase from symbol k to symbol k+1, as shown in Figure 31. Correction phase θ_a_d_jCan be given as:<maths><img file="TW586278B_D0054.tif" /></maths>Where θ_kIs the phase of the kth symbol. A vector with a phase equal to the adjusted phase is orthogonal to the straight line drawn from symbol k to symbol k+1, as shown in Fig. 31. Please note that since the number of possible phase rotations is limited, the number of possible phase adjustments is also limited, so no explicit calculation of the rotation phase is required.

If the symbol rate method (5,696,794) is used, a complex number is added to modify the two symbols adjacent to the low-amplitude event (ie, symbols k and k+1). The amplitude of this complex number is given as: m=0.5(mag_d-mag_s)/p_m_i_dWhere p_m_i_dIs the amplitude of the pulse shaping filter at t=T/2. (However, the basic reason for calculating the correction amplitude in this way is not clear.) Then the complex number is adjusted to: C_a_d_j=mexp(jθ_a_d_j) And the generated modification symbols can be given as:<img file="TW586278B_D0055.tif" />_k=a_k+C_a_d_j<img file="TW586278B_D0056.tif" />_k₊₁=a_k₊₁+C_a_d_j

Please note that both symbols are modified in the same way.

Therefore, by deliberately changing the information symbol {a_k}, the noise component can be added to the signal. This will "confuse" any equalizer in the receiver, because the receiver will expect any signal distortion to be caused by the channel.

If the T/2 method (5,805,640) is used, the complex number will be added to the symbol stream at the appropriate half-symbol time instant before the pulse is shaped. When a low amplitude event is detected at t=kT+T/2, the complex symbol has an amplitude: m=(mag_d-mag_s) and t=kT+T/2 is added equal to θ_a_d_j(Given as above) phase.

This restriction on T/2 insertion timing limits this method to a circular signal distribution.

Another difference between the symbol rate method and the T/2 method is that the symbol rate method is intended to be applied in an iterative manner until the signal amplitude does not fall below a certain critical value. As for the T/2 patent, there is no mention of iterative procedures.

<u style="single">A1.2 The performance of π/4 QPSK</u>

What is to be considered now is the performance of the known hole blowing algorithm related to the disclosed "precise" hole blowing method when the target signal is π/4 QPSK. It is worth noting that if the roll-off is high, for example, α=0.5, then this signal will have a "hole" in its distribution. Choose roll-off 0.22 so that the signal will not have pre-existing holes.

The CDF shown in FIG. 32 is derived from the disclosed method and the two known methods with the above-mentioned p/4 QPSK signal. The ideal minimum power level is set to 9 dB below RMS. These simulation results are based on 16384 with 32 samples/symbols symbol. This figure clearly shows that the precise method is more effective than any known method. In addition, it is also obvious that the execution of the two known methods is similar. It is not surprising that the two methods will be similar. Some explanations of the effectiveness of the known method are shown in Figure 32 in order. As mentioned earlier, it should be noted that there may be sources of error when calculating the amplitude and phase of the correction pulse. Figure 33 shows an example where the previous art symbol rate method works well. The signal encapsulation is not completely pushed beyond the ideal hole, but the method is still performed more or less as expected. In contrast, Figure 34 shows an example of poor performance of the previous art symbol rate method. This example shows that the amplitude and phase of the calibration pulse are both wrong. In this example, the trajectory will pass on the "wrong edge" relative to the origin of the assumption made for calculating the correction pulse. This will push the trajectory in the wrong direction. Moreover, it is obvious from this example that the amplitude of T/2 is not the minimum amplitude. Therefore, even if the phase calculation is correct, the signal cannot be pushed far enough.

Figure 35 shows an example of the poor performance of the prior art T/2 method. (The fragment shown in FIG. 35 is the same as the signal fragment shown in FIG. 34, in which the symbol rate method is not performed well.) Comparing FIGS. 34 and 35, it is obvious that both methods produce almost the same trajectory. Obviously, the symbol rate method will only change the symbols adjacent to the low amplitude event, while the T/2 method will affect more symbols.

<u style="single">A1.3 Effectiveness of 3GPP uplink signal</u>

Now consider the performance of the known method with a more realistic signal (that is, a 3GPP uplink signal with an active DPDCH and an amplitude ratio of 7/15). FIG. 36 shows the CDF obtained by using the disclosed precise method and the known hole blowing method when applied to a signal frame (38400 chip) with 32 samples/chip. Obviously, the accurate correction method is better than the known method, and the two known methods are almost the same.