A digital automatic gain control method for burst signals

Abstract

A digital automatic gain control (DAGC1) method for burst signals includes: determining a reference amplitude of DAGC1; inputting two real sub-signals of the input signal y in parallel into DAGC1; iteratively estimating the larger of the absolute values ​​and sums of the signal samples with the highest energy in each sub-signal as the amplitude estimate of the input signal y to estimate the coarse gain; calculating the numerical bit width of the amplitude estimate first, then calculating the coarse gain estimate to estimate the fine gain; calculating the coarse gain estimate first, then calculating the fine gain estimate to estimate the total gain; and amplifying the input signal based on the total gain estimate. This method can precisely adjust the amplitude of the burst signal, ensuring sufficient signal amplification and fully utilizing the quantization bit width to preserve the numerical accuracy of the signal, while effectively avoiding overflow distortion. It is applicable to PSK, APSK, and QAM burst modulation signals.

Description

Technical Field

[0001] This invention relates to the field of digital communication technology, and specifically to a digital automatic gain control method for burst signals. Background Technology

[0002] In the burst communication receiver of the return link of an MF-TDMA satellite communication system, at least two digital automatic gain controllers (DAGCs) are required to adjust the signal amplitude to meet the requirements of the subsequent signal processing modules. One is DAGC1, located between the matched filter and the timing, frequency, and phase synchronization module (hereinafter referred to as the synchronization module), and the other is DAGC2, located between the synchronization module and the soft demapping module. Figure 1 This paper demonstrates a typical distribution of DAGC in a burst communication receiver. The main reason for setting up DAGC1 is that the digital downconverter and matched filter filter out some unwanted signals in the received signal, resulting in a smaller output signal power and consequently a smaller amplitude. When the quantization bit width of the signal is small, in order to make full use of the quantization bit width and preserve the numerical accuracy of the signal, a digital automatic gain controller (DAGC1) is needed after the matched filter to adjust the signal amplitude. This application will focus on the digital automatic gain control method of DAGC1.

[0003] The traditional control method for DAGC1 is based on power normalization. Its working principle is as follows: First, the average power of the burst signal is estimated; then, a gain estimate is calculated based on the estimated power and the desired power (the gain estimate equals the square root of the ratio of the desired power to the estimated power); finally, the burst signal is amplified based on the gain estimate. The power normalization-based gain control method is an indirect amplitude control method, adjusting the signal amplitude by adjusting the average power of the signal. Research has found that this method cannot achieve precise signal amplitude control, mainly because when the average power of the burst signal is amplified to the desired power, the amplitudes of some relatively high-energy samples in the signal are over-amplified, leading to overflow distortion. Moreover, the lower the signal-to-noise ratio, the greater the probability of this phenomenon. Summary of the Invention

[0004] In view of the shortcomings and defects of the above-mentioned prior art, the present invention provides a digital automatic gain control method for burst signals, which is applicable to three types of burst modulation signals: PSK, APSK and QAM. It can accurately adjust the amplitude of burst signals, not only so that the signal is fully amplified and thus the quantization bit width is fully utilized to preserve the numerical accuracy of the signal, but also effectively avoids overflow distortion.

[0005] To achieve the above objectives, the present invention employs the following techniques:

[0006] A digital automatic gain control method for burst signals, comprising the following steps:

[0007] S100, determine the reference amplitude of DAGC1, and obtain The DAGC1 mentioned above refers to the digital automatic gain controller located between the matched filter and the timing, frequency, and phase synchronization modules in the burst receiver of the MF-TDMA satellite communication system's return link. It is assumed that in the burst receiver, each signal sample is represented by a signed number, and the total quantization bit width of the signal sample is W, in bits, where the highest bit is the sign bit, and the remaining W-1 bits are the value bits. This represents the maximum absolute value of positive numbers in the quantization scheme. This represents the maximum absolute value of a negative number in the quantization scheme;

[0008] S200, convert the two real sub-signals of the input signal y. and Parallel input DAGC1, where, This represents a burst signal frame received by the burst receiver, where y[k] = y I [k]+jy Q [k] is a complex signal sample, y I [k] and y Q [k] represents the real and imaginary parts of y[k], j is the imaginary unit, and L is the number of complex signal samples. This represents the I-channel real sub-signal of y, i.e., the in-phase component of y. This represents the Q-path real sub-signal of y, i.e., the quadrature components of y; during this process, the following two steps are performed simultaneously:

[0009] S210, Sub-signal and The samples are fed into the buffer in parallel;

[0010] S220. Estimate the amplitude of the input signal: For the two real signals of the input signal y and Parallel iterative estimation of the absolute value of the signal sample with the highest energy among the sub-signals. and Pick and The larger value in the range is used as the amplitude estimate of the input signal y. Specifically, the steps include the following:

[0011] S221, convert the two real sub-signals of the input signal y. and Parallel input magnitude estimator, simultaneously performing parallel iterative estimation and Including the following steps:

[0012] S2211. Set an iteration counter k, whose counting range is k = 1, 2, ..., L;

[0013] S2212. Initialize relevant parameters, set k=1.

[0014] S2213, y I and y Q The kth signal sample y I [k] and y Q [k] Parallel input magnitude estimator, and simultaneously compute its absolute value |y I [k]| and |y Q [k]|;

[0015] S2214, Regarding y I and y Q Two signals, simultaneously estimated and That is, to perform the following operations in parallel

[0016]

[0017] S2215. Determine whether the L-fold estimation is complete; if complete, output the estimation result. and If not, update the counter: k←k+1, and repeat S2213~S2215 until L iterations of estimation are completed;

[0018] S222. Estimate the amplitude of the input signal y, and obtain...

[0019] S300, Estimating coarse gain: First calculate the amplitude estimate. The width of the numerical bits

[0020] Then calculate the coarse gain value to obtain the coarse gain estimate.

[0021] S400, Estimate Fine Gain: First calculate have to

[0022] Then calculate the fine gain value for the nonlinear function. Pre-design a set of piecewise linear approximation functions: Among them, a n and b n They are The coefficient of the linear term and the constant term,

[0023]

[0024] It is a bounded closed interval [A] ref / 2,A ref The interval is divided into N disjoint subintervals. It is the length of each subinterval, when At that time, the precise gain estimate

[0025] S500, Estimate the total gain to obtain the estimated total gain value.

[0026] S600, Amplify the input signal based on the total gain estimate, including:

[0027] S610. Set the iteration counter k, whose counting range is k = 1, 2, ..., L;

[0028] S620. Initialize the iteration counter and set k = 1;

[0029] S630, simultaneously output sub-signal y from DAGC1's buffer. I and y Q The kth signal sample y I [k] and y Q [k];

[0030] S640, Based on the total gain estimate At the same time, for y I [k] and y Q [k] is amplified, that is, the following operations are performed in parallel.

[0031]

[0032] Then, the enlarged sample and Parallel output DAGC1;

[0033] S650, Determine y I and y Q Check if all L samples have completed gain control. If so, end the current automatic gain control operation; otherwise, update the counter: k←k+1, and repeat S630~S650 until y is completed. I and y Q Gain control for all L samples.

[0034] The beneficial effects of this invention are as follows:

[0035] The method of this invention can accurately adjust the amplitude of burst signals, which not only fully amplifies the signal and makes full use of the quantization bit width to preserve the numerical accuracy of the signal, but also effectively avoids overflow distortion. It is applicable to three types of burst modulation signals: PSK, APSK and QAM. Attached Figure Description

[0036] Figure 1 This is a typical distribution method for DAGC in burst communication receivers.

[0037] Figure 2 This is a diagram of the open-loop feedforward structure of DAGC1 as described in the embodiments of this application.

[0038] Figure 3 This is a structural diagram of the amplitude estimator of DAGC1 described in the embodiments of this application.

[0039] Figure 4 This is a structural diagram of the gain estimator of DAGC1 described in the embodiments of this application. Detailed Implementation

[0040] To make the purpose, technical solution, and specific implementation method of this application clearer, this application will be further described in detail below.

[0041] This application provides a digital automatic gain control method for burst signals, the design process of which is as follows:

[0042] First, we analyze the processing objects and characteristics of DAGC1. In MF-TDMA satellite communication systems, the digital modulation methods mainly used for return link burst communication are PSK and QAM. Therefore, the processing objects of DAGC1 described in this application are PSK and QAM signals. This application will design a digital automatic gain control method for these two types of burst modulation signals. Furthermore, given that APSK and QAM modulation signals have similar characteristics—both are non-constant envelope complex signals with joint amplitude and phase modulation—the method is also applicable to gain control of APSK burst modulation signals. In the burst communication receiver, the aforementioned complex modulation signals are decomposed into two real sub-signals, I (in-phase component) and Q (quadrature component), and quantized using the same quantization scheme. During signal processing, to ensure I / Q balance, the parameters used for both sub-signals are identical. For example, DAGC1 will use the same gain estimate to adjust the amplitude of both the I and Q sub-signals.

[0043] Next, we define the role and operating process of DAGC1 in the burst communication receiver. Qualitatively speaking, the role of DAGC1 should be to precisely adjust the amplitude of the burst signal, not the power of the burst signal. The connotation of "precise" can be further explained as follows: when the burst signal is amplified by DAGC1, the amplitude of the signal sample with the highest energy (the amplitude of the signal sample refers to the absolute value of the signal sample) is exactly amplified to the desired amplitude. This amplitude control method not only ensures that the signal is fully amplified, thus making full use of the quantization bit width to preserve the numerical accuracy of the signal, but also effectively avoids overflow distortion. Based on the above analysis, the operating process of DAGC1 can be summarized as follows: First, determine the reference amplitude of DAGC1, that is, the desired amplitude of the output signal; second, estimate the amplitude of the input signal; third, calculate the gain estimate based on the estimated amplitude and the reference amplitude (the gain estimate equals the reference amplitude divided by the estimated amplitude); fourth, amplify the input signal according to the gain estimate so that the amplitude of the output signal reaches the desired value. Figure 2 The open-loop feedforward structure diagram of the burst communication receiver DAGC1 is shown.

[0044] Finally, a suitable digital automatic gain control method is designed. Assume that in the burst receiver, each signal sample is represented by a signed number, and the total quantization bit width of the signal sample is W (in bits), where the highest bit is the sign bit, and the remaining W-1 bits are the value bits. This represents the maximum absolute value of positive numbers in the quantization scheme. This represents the maximum absolute value of a negative number in this quantization scheme. This represents a burst signal frame received by the burst receiver, where y[k] = y I [k]+jy Q [k] is a complex signal sample, y I [k] and y Q [k] represents the real and imaginary parts of y[k], j is the imaginary unit, and L is the number of complex signal samples. This represents a sample sequence consisting of the real parts of y[k], which is the I-path real sub-signal of y (the in-phase component of y). Let represent the sample sequence consisting of the imaginary part of y[k], which is the Q-path real sub-signal of y (the orthogonal component of y). In DAGC1, the burst signal y is divided into y[k]. I and y Q Gain control is applied to both sub-signals separately.

[0045] The key issues and methods involved in each step will be discussed in detail below, following the DAGC1 workflow.

[0046] The first step is to determine the reference amplitude A of DGAC1. ref .

[0047] The reference amplitude of DAGC1, also known as the expected amplitude of the output signal, refers to the maximum value that the output signal amplitude can reach without overflow distortion. Because, under normal circumstances, the maximum value of the absolute value of a positive number in a quantization scheme is not equal to the maximum value of the absolute value of a negative number, i.e. To ensure that the output signal of DAGC1 does not overflow or become distorted under any circumstances, this solution adopts... and The smaller value in the range is used as the reference amplitude for DAGC1, i.e.

[0048]

[0049] The second step is to estimate the amplitude of the input signal.

[0050] First, the amplitude of the input signal needs to be clearly defined. Although the input signal y is a complex modulated signal, as mentioned above, in DAGC1, the input signal y will be divided into ym and ym. I and y Q The two real signals are subjected to gain control separately. Therefore, based on the requirements of the method described in the embodiments of this application, the standard definition of complex signal amplitude is not adopted here, but the following definition is adopted: Assume y I and y Q These are the two real sub-signals of the complex signal y. It is y I The absolute value of the signal sample with the highest energy. It is y Q The amplitude A of the complex signal y is defined as the absolute value of the signal sample with the highest energy. and The larger value in, i.e.

[0051]

[0052] Based on the above definition, a two-step amplitude estimation method can be designed: First, for the two real sub-signals of the input signal y... and Parallel iterative estimation of the absolute value of the signal sample with the highest energy among the sub-signals. and The second step is to take... and The larger value in the range is used as the amplitude estimate of the input signal y. Below, we combine... Figure 3 Provide a detailed description:

[0053] 1. Convert the two real signals of the input signal y and Parallel input magnitude estimator, simultaneously performing parallel iterative estimation and The specific steps are as follows:

[0054] 1.1 Set an iterative counter k, whose counting range is k = 1, 2, ..., L.

[0055] 1.2 Initialize relevant parameters, set k=1,

[0056] 1.3, y I and y Q The kth signal sample y I [k] and y Q [k] Parallel input magnitude estimator, and simultaneously compute its absolute value |y I [k]| and |y Q [k]|.

[0057] 1.4. Regarding y I and y Q Two signals, simultaneously estimated and That is, to perform the following operations in parallel

[0058]

[0059] 1.5 Determine if the L-th iteration estimation is complete. If complete, output the estimation result. and If not, update the counter: k←k+1, and repeat steps 1.3 and 1.5 until L iterations of estimation are completed.

[0060] 2. Estimate the amplitude of the input signal y have to

[0061]

[0062] The third step is to calculate the gain estimate based on the estimated amplitude and the reference amplitude.

[0063] From the above analysis of the function and working process of DAGC1, it can be seen that the gain estimate is equal to the reference amplitude divided by the estimated amplitude, that is...

[0064]

[0065] Although the gain estimation method expressed in the above formula is easy to understand, implementing a general-purpose real number divider in hardware circuitry is quite complex and computationally expensive. Therefore, this embodiment breaks down the gain estimation operation based on real number division into three relatively simple steps. For example... Figure 4As shown, gain estimation comprises three parts: coarse gain estimation, fine gain estimation, and total gain estimation. These are described in detail below:

[0066] 1. Estimate coarse gain

[0067] Coarse gain estimation is used to estimate gain. 2 in m Multiplier Right now m = 0, 1, 2, ... The specific method is as follows: First, calculate the amplitude estimate. The width of the numerical bits Then, the coarse gain value is estimated using the following formula.

[0068]

[0069] 2. Estimate the precision gain

[0070] Fine gain estimation is used to estimate gain. Fractional factors in, The specific method is as follows: First, calculate DAGC1 according to the coarse gain estimate. After amplifying the input signal y, the amplitude of the output signal is... have to Then, the precision gain value is estimated using the following formula.

[0071]

[0072] 3. Estimate the total gain

[0073] Total gain equal to coarse gain With precision gain The product of, i.e.

[0074]

[0075] In the above steps, equation (1) still uses real number division, which needs further simplification. Analysis shows that if DAGC1 is based on the coarse gain estimate... If the input signal y is amplified, then the amplitude of the output signal will be... The region located in the bounded closed interval [A] ref / 2,A ref [Inside] And the function It is also a bounded closed interval [A] ref / 2,A refA continuous function on [A], therefore it can be used on a bounded closed interval [A]. ref / 2,A ref [On the function] Piecewise linear approximation is used to transform nonlinear division operations into linear operations mainly consisting of multiplication and addition, thereby significantly reducing the computational complexity in the fine gain estimation process.

[0076] Suppose that the bounded closed interval [A] is... ref / 2,A ref Divide the intervals into N disjoint subintervals I. n n = 1, 2, 3, ..., N, where the length of each subinterval is... Then subinterval I n It can be represented as

[0077]

[0078] Assume that in the nth subinterval I n Above, function The approximate linear function is

[0079]

[0080] Among them, a n and b n They are The coefficient of the linear term and the constant term. Then, in the bounded closed interval [A] ref / 2,A ref On, function It can be approximated by piecewise linearity as follows:

[0081]

[0082] Using equation (2) as an approximation formula for equation (1) allows for convenient and quick estimation of the fine gain value. The error in the approximation calculation is positively correlated with the length of the subinterval; the smaller the subinterval length, the smaller the error in linear approximation, and therefore the smaller the error in approximating the fine gain value using equation (2). In the case of uniform segmentation described above, the larger the number of segments N, the smaller the error in linear approximation. N is a design parameter, and its value should be determined based on the estimation error tolerance under the specific application scenario.

[0083] The fourth step is to amplify the input signal based on the gain estimate.

[0084] As mentioned above, in burst receivers, DAGC1 will use the same gain estimate. For the two sub-signals of the input signal y and Gain control is performed separately. and Representing signal samples y I [k] and y Q The output of [k] after being amplified by DAGC1 is then:

[0085]

[0086] Based on the above description of the design process, this application provides a digital automatic gain control method for burst signals, and the implementation steps of the method can be specifically described as follows:

[0087] Assume that in a burst receiver, each signal sample is represented by a signed number, and the total quantization bit width of the signal sample is W (in bits), where the highest bit is the sign bit, and the remaining W-1 bits are the value bits. This represents the maximum absolute value of positive numbers in the quantization scheme. This represents the maximum absolute value of a negative number in the quantization scheme; This represents a burst signal frame received by the burst receiver, where y[k] = y I [k]+jy Q [k] is a complex signal sample, y I [k] and y Q [k] represents the real and imaginary parts of y[k], j is the imaginary unit, and L is the number of complex signal samples; Let I represent the I-channel real sub-signal of y (the in-phase component of y), with Represents the Q-channel real sub-signal of y (the orthogonal components of y); with A ref Indicates the reference amplitude of DAGC1; and These represent the coarse gain estimate, fine gain estimate, and total gain estimate of DAGC1, respectively; This represents the amplitude estimate of the input signal y; This indicates that DAGC1 is based on the coarse gain estimate. The amplitude estimate of the output signal after amplifying the input signal y; and Representing signal samples y I [k] and y Q [k] is the output after being amplified by DAGC1.

[0088] For nonlinear functions Pre-design a set of piecewise linear approximation functions

[0089]

[0090] Among them, a n and b n They are The coefficient of the linear term and the constant term,

[0091]

[0092] It is a bounded closed interval [A] ref / 2,A ref The interval is divided into N disjoint subintervals. It is the length of each subinterval. When When n = 1, 2, 3, ..., N

[0093] The specific steps of the control method are as follows:

[0094] S100, determine the reference amplitude of DAGC1, and obtain

[0095] S200, convert the two real sub-signals of the input signal y. and Parallel input to DAGC1 is performed, during which the following two steps are executed simultaneously:

[0096] S210, Sub-signal and The samples are fed into the cache in parallel.

[0097] S220. Estimate the amplitude of the input signal. The estimation process is performed in two steps: First, for the two real sub-signals of the input signal y... and Parallel iterative estimation of the absolute value of the signal sample with the highest energy among the sub-signals. and The second step is to take... and The larger value in the range is used as the amplitude estimate of the input signal y. The specific steps are as follows:

[0098] S221, convert the two real sub-signals of the input signal y. and Parallel input magnitude estimator, simultaneously performing parallel iterative estimation and The specific steps are as follows:

[0099] S2211. Set an iteration counter k, whose counting range is k = 1, 2, ..., L.

[0100] S2212. Initialize relevant parameters, set k=1.

[0101] S2213, y I and y Q The kth signal sample y I [k] and y Q[k] Parallel input magnitude estimator, and simultaneously compute its absolute value |y I [k]| and |y Q [k]|.

[0102] S2214, Regarding y I and y Q Two signals, simultaneously estimated and That is, to perform the following operations in parallel

[0103]

[0104] S2215. Determine whether the L-fold estimation is complete. If complete, output the estimation result. and If not, update the counter: k←k+1, and repeat S2213~S2215 until L iterations of estimation are completed.

[0105] S222. Estimate the amplitude of the input signal y, and obtain...

[0106]

[0107] S300, Estimate coarse gain, the specific steps are as follows:

[0108] S310, Calculate the amplitude estimate The width of the numerical bits

[0109] S320. Calculate the coarse gain value, and obtain...

[0110] S400, Estimate the fine gain, the specific steps are as follows:

[0111] S410, Calculation have to

[0112] S420. Calculate the fine gain value, and obtain n = 1, 2, 3, ..., N.

[0113] S500, estimate the total gain, and get

[0114] S600. Amplify the input signal based on the total gain estimate. The specific steps are as follows:

[0115] S610. Set an iteration counter k, whose counting range is k = 1, 2, ..., L.

[0116] S620. Initialize the iteration counter and set k = 1.

[0117] S630, simultaneously output sub-signal y from DAGC1's buffer. I and y Q The kth signal sample y I [k] and y Q [k].

[0118] S640, Based on the total gain estimate At the same time, for y I [k] and y Q [k] is amplified, that is, the following operations are performed in parallel.

[0119]

[0120] Then, the enlarged sample and Parallel output DAGC1.

[0121] S650, Determine y I and y Q Check if all L samples have completed gain control. If so, end the current automatic gain control operation; otherwise, update the counter: k←k+1, and repeat steps 6.3 and 6.5 until y is completed. I and y Q Gain control for all L samples.

Claims

1. A digital automatic gain control method for burst signals, characterized in that, Including the following steps: S100, Determine the reference amplitude of DAGC1, and obtain The DAGC1 mentioned above refers to the digital automatic gain controller located between the matched filter and the timing, frequency, and phase synchronization modules in the burst receiver of the MF-TDMA satellite communication system's return link. It is assumed that in the burst receiver, each signal sample is represented by a signed number, and the total quantization bit width of the signal sample is W, in bits, where the highest bit is the sign bit, and the remaining W-1 bits are the value bits. This represents the maximum absolute value of positive numbers in the quantization scheme. This represents the maximum absolute value of a negative number in the quantization scheme; S200, convert the two real sub-signals of the input signal y... and Parallel input DAGC1, where, with This represents a burst signal frame received by the burst receiver, y[k] = y I [k]+jy Q [k] is a complex signal sample, y I [k] and y Q [k] represents the real and imaginary parts of y[k], j is the imaginary unit, and L is the number of complex signal samples. This represents the I-channel real sub-signal of y, i.e., the in-phase component of y. This represents the Q-path real sub-signal of y, i.e., the quadrature components of y; during this process, the following two steps are performed simultaneously: S210, Sub-signal and The samples are fed into the buffer in parallel; S220. Estimate the amplitude of the input signal: For the two real signals of the input signal y and Parallel iterative estimation of the absolute value of the signal sample with the highest energy among the sub-signals. and Pick and The larger value in the range is used as the amplitude estimate of the input signal y. S300, Estimating coarse gain: First calculate the amplitude estimate. The width of the numerical bit Then calculate the coarse gain value to obtain the coarse gain estimate. S400, Estimate Fine Gain: First calculate have to Then calculate the fine gain value for the nonlinear function. Pre-design a set of piecewise linear approximation functions: Among them, a n and b n They are The coefficient of the linear term and the constant term, It is a bounded closed interval [A] ref / 2,A ref The interval is divided into N disjoint subintervals. It is the length of each subinterval, when At that time, the precise gain estimate S500, Estimate the total gain to obtain the estimated total gain value. S600, Amplify the input signal based on the total gain estimate, including: S610. Set the iteration counter k, whose counting range is k = 1, 2, ..., L; S620. Initialize the iteration counter and set k = 1; S630, simultaneously output sub-signal y from DAGC1's buffer. I and y Q The kth signal sample y I [k] and y Q [k]; S640, Based on the total gain estimate At the same time, for y I [k] and y Q [k] is amplified, that is, the following operations are performed in parallel. Then, the enlarged sample and Parallel output DAGC1; S650, Determine y I and y Q Check if all L samples have completed gain control. If so, end the current automatic gain control operation; otherwise, update the counter: k←k+1, and repeat S630~S650 until y is completed. I and y Q Gain control for all L samples.

2. The digital automatic gain control method for burst signals according to claim 1, characterized in that, S220. Estimate the amplitude of the input signal, specifically including the following steps: S221, convert the two real sub-signals of the input signal y. and Parallel input magnitude estimator, simultaneously performing parallel iterative estimation and Including the following steps: S2211. Set an iteration counter k, whose counting range is k = 1, 2, ..., L; S2212. Initialize relevant parameters, set k=1. S2213, y I and y Q The kth signal sample y I [k] and y Q [k] Parallel input magnitude estimator, and simultaneously compute its absolute value |y I [k]| and |y Q [k]|; S2214, Regarding y I and y Q Two signals, simultaneously estimated and That is, to perform the following operations in parallel S2215. Determine whether the L-fold estimation is complete; if complete, output the estimation result. and If not, update the counter: k←k+1, and repeat S2213~S2215 until L iterations of estimation are completed; S222. Estimate the amplitude of the input signal y, and obtain...

3. The digital automatic gain control method for burst signals according to claim 1 or 2, characterized in that, It is applicable to three types of burst modulation signals: PSK, APSK, and QAM.

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