Receiving device and receiving program

Abstract

This disclosure aims to suppress abrupt deterioration of characteristics such as the error rate of received bits, while suppressing an increase in the overall system delay of the receiving device and the amount of computation per demodulated symbol when switching the modulation method from a fixed-envelope modulation signal to a non-fixed-envelope modulation signal in order to compensate for the nonlinear distortion of the modulated signal. [Solution] In this disclosure, the level shifter 3 provided in the receiving device R shifts the constant envelope modulated signal to multiple envelope levels and adjusts the frequency of the level shift to multiple envelope levels. Then, when the receiving device R switches between receiving a constant envelope modulated signal and a non-constant envelope modulated signal, the equalizer 4 provided in the receiving device R can adjust the weight coefficients of the equalization filter to be equal, thereby suppressing abrupt deterioration of characteristics such as the error rate of the received bits.

Description

[Technical Field]

[0001] This disclosure relates to a technique for compensating for nonlinear distortion in modulated signals. [Background technology]

[0002] In amplifiers equipped in transmitting or relaying devices, high power utilization efficiency can be achieved by setting the operating point near the saturation region. However, modulated signals with nonlinear distortion cause radiation outside the transmission band and degrade the error rate of received bits.

[0003] Therefore, techniques for compensating for the nonlinear distortion of modulated signals are disclosed in Non-Patent Documents 1 and 2 and Patent Documents 1 and 2. Non-Patent Document 1 compensates for the nonlinear distortion of modulated signals using an equalizer that utilizes a Volterra series. Non-Patent Document 2 compensates for the nonlinear distortion of modulated signals using an equalizer that approximates the Volterra series with a memory polynomial in order to reduce the amount of computation.

[0004] In Patent Document 1, in order to reduce the amount of computation, an equalizer that approximates the Volterra series with a memory polynomial is used to compensate for the nonlinear distortion of the modulated signal, and the filter coefficients of the equalizer are calculated using a known signal with fewer symbols than the number of taps of the equalizer. In Patent Document 2, nonlinear distortion is compensated by performing error correction on a received signal that does not contain a known signal with the same signal point arrangement as the data section, and then performing the equalization process. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] International Publication No. 2019 / 171655 [Patent Document 2] International Publication No. 2016 / 056395 [Non-patent literature]

[0006] [Non-Patent Document 1] S. Benedetto and E. Biglieri, “Nonlinear Equalization of Digital Satellite Channels,” IEEE Journal on Selected Areas in Communications, vol. 1, No. 1, pp. 57-62, Jan 1983. [Non-Patent Document 2] Yasuyoshi Noda, Shunsuke Uehashi, Shigenori Tani, Katsuyuki Motoyoshi, and Atsushi Okamura, "An Adaptive Equalization Method Applicable to Single-Carrier Broadband Transmission with Nonlinear Distortion," IEICE Technical Report, WBS2018-2, vol.118, No.51, pp.7-12, May 2018. [Overview of the Initiative] [Problems that the invention aims to solve]

[0007] Incidentally, the modulation method may be switched between the pull-in process and the data transmission process. Furthermore, depending on the transmission path conditions, the modulation method may be switched using the ACM (Adaptive Coding and Modulation) method. For example, the modulation method may be switched between a fixed-envelope modulated signal (such as QPSK or 8PSK) and a non-fixed-envelope modulated signal (such as 32APSK or 64QAM).

[0008] However, Non-Patent Documents 1 and 2 and Patent Documents 1 and 2 do not explicitly state that the modulation method is switched between a fixed-envelope modulation signal and a non-fixed-envelope modulation signal. Furthermore, in Non-Patent Documents 1 and 2 and Patent Document 1, even if the modulation method is switched from a fixed-envelope modulation signal to a non-fixed-envelope modulation signal, the characteristics such as the error rate of the received bits deteriorate rapidly. Moreover, in Patent Document 2, even if the modulation method is switched from a fixed-envelope modulation signal to a non-fixed-envelope modulation signal, it is necessary to perform error correction and then equalization processing, which increases the system delay of the entire receiving device and the amount of computation per demodulated symbol.

[0009] Therefore, in order to solve the aforementioned problems, the present disclosure aims to suppress a rapid deterioration of characteristics such as the error rate of received bits while suppressing an increase in the overall system delay of the receiving device and the amount of computation per demodulated symbol when switching the modulation method from a fixed-envelope modulation signal to a non-fixed-envelope modulation signal in order to compensate for the nonlinear distortion of the modulated signal. [Means for solving the problem]

[0010] To solve the aforementioned problem, the level shifter in the receiving device shifts the constant envelope modulated signal to multiple envelope levels and adjusts the frequency of the level shift to multiple envelope levels. Then, when the receiving device switches between receiving a constant envelope modulated signal and a non-constant envelope modulated signal, the equalizer in the receiving device can adjust the weight coefficients of the equalization filter to be equal, thereby suppressing abrupt deterioration of characteristics such as the error rate of the received bits.

[0011] Specifically, the present disclosure relates to a receiving device for wireless or wired communication, which receives a constant envelope modulated signal and a non-constant envelope modulated signal from a transmitting device that transmits a constant envelope modulated signal and a non-constant envelope modulated signal by switching between them, and is characterized by comprising: an equalizer that compensates for the nonlinear distortion of the constant envelope modulated signal and the non-constant envelope modulated signal; a demodulator that demodulates the constant envelope modulated signal and the non-constant envelope modulated signal by switching between them; and a level shifter that, when the receiving device receives the constant envelope modulated signal and the non-constant envelope modulated signal by switching between them, the equalizer adjusts the weight coefficients of the equalization filter to be equal, by level shifting the constant envelope modulated signal to a plurality of envelope levels and adjusting the frequency of occurrence of the level shift to the plurality of envelope levels.

[0012] This configuration makes it possible to suppress the rapid deterioration of characteristics such as the error rate of received bits when switching the modulation method from a fixed-envelope modulation signal to a non-fixed-envelope modulation signal. Furthermore, since it is not always necessary to perform equalization processing after error correction, it is possible to suppress the overall system delay of the receiving device and the increase in the amount of computation per demodulated symbol.

[0013] Furthermore, the present disclosure is a receiving device characterized in that, when the receiving device switches between receiving the fixed envelope modulated signal and the non-fixed envelope modulated signal, the level shifter adjusts the frequency of the level shift to the plurality of envelope levels so as to equalize the expected value of the α-power of the received signal level (where α is a natural number of 2 or greater).

[0014] In this configuration, when the receiving device switches between receiving a fixed-envelope modulated signal and a non-fixed-envelope modulated signal, the level shifter in the receiving device adjusts the expected value of the α-power value of the received signal level (where α is a natural number greater than or equal to 2) to be equal. As a result, the equalizer in the receiving device can adjust the weight coefficients of the equalization filter to be equal, as described above.

[0015] Furthermore, the present disclosure is a receiving device characterized in that, when the receiving device receives the constant envelope modulation signal which the receiving device has determined to have small nonlinear distortion, the equalizer adjusts the weight coefficient of the equalization filter of order 3 or higher to 0, the level shifter level shifts the constant envelope modulation signal to the plurality of envelope levels, and adjusts the frequency of occurrence of the level shift to the plurality of envelope levels.

[0016] With this configuration, when the receiving device receives a constant envelope modulation signal that it has determined to have small nonlinear distortion, the level shifter in the receiving device level shifts the constant envelope modulation signal to multiple envelope levels at a predetermined frequency. As a result, the equalizer in the receiving device can adjust the weight coefficients of the third-order or higher equalization filter to be equal to zero, as described above.

[0017] Furthermore, this disclosure provides a receiving device characterized in that the level shifter level shifts the constant envelope modulated signal and imparts a phase rotation to the constant envelope modulated signal according to the phase difference between the received signal point and the ideal signal point, or according to the amount of phase distortion estimated based on the amplifier's backoff condition and nonlinear distortion characteristics.

[0018] With this configuration, the level shifter in the receiving device can shift the constant envelope modulated signal to multiple envelope levels at a predetermined frequency, and can also impart phase rotation to the constant envelope modulated signal according to the nonlinear phase distortion characteristics of the amplifier.

[0019] Furthermore, this disclosure relates to a receiving program installed on a computer for causing the level shifter in the receiving device described above to level shift the constant envelope modulation signal to the plurality of envelope levels and to adjust the frequency of the level shift to the plurality of envelope levels.

[0020] This configuration makes it possible to provide a program that has the effects described above.

[0021] Furthermore, the inventions disclosed above can be combined as much as possible. [Effects of the Invention]

[0022] Thus, in compensating for the nonlinear distortion of the modulated signal, this disclosure makes it possible to suppress a rapid deterioration of characteristics such as the error rate of the received bits while suppressing an increase in the overall system delay of the receiving device and the amount of computation per demodulated symbol when switching the modulation method from a fixed-envelope modulated signal to a non-fixed-envelope modulated signal. [Brief explanation of the drawing]

[0023] [Figure 1] This diagram shows the configuration of the transmission and reception system disclosed herein. [Figure 2] This diagram shows the procedure for sending and receiving data according to this disclosure. [Figure 3] This figure shows the weight coefficients of a conventional third-order equalization filter. [Figure 4] This figure shows the level shift of the constant envelope modulated signal in the first embodiment. [Figure 5] This figure shows the configuration of the level shifter in this disclosure. [Figure 6] This diagram shows distortion compensation during switching of modulation methods in conventional technology. [Figure 7] This figure shows the distortion compensation during switching of the modulation scheme in the first embodiment. [Figure 8] This figure shows the MER characteristics when switching between the conventional technology and the modulation scheme of the first embodiment. [Figure 9] This diagram shows distortion compensation during switching of modulation methods in conventional technology. [Figure 10] This figure shows the distortion compensation during switching of the modulation scheme in the first embodiment. [Figure 11] This figure shows the MER characteristics when switching between the conventional technology and the modulation scheme of the first embodiment. [Figure 12] This diagram shows distortion compensation during switching of modulation methods in conventional technology. [Figure 13] This figure shows the distortion compensation during switching of the modulation scheme in the first embodiment. [Figure 14] This figure shows the MER characteristics when switching between the conventional technology and the modulation scheme of the first embodiment. [Figure 15] This diagram shows distortion compensation during switching of modulation methods in conventional technology. [Figure 16] This figure shows the distortion compensation during switching of the modulation scheme in the first embodiment. [Figure 17] This figure shows the MER characteristics when switching between the conventional technology and the modulation scheme of the first embodiment. [Figure 18] This figure shows the received signal level of the non-deterministic envelope modulation signal in the second embodiment. [Figure 19] This figure shows the level shift of the constant envelope modulated signal in the second embodiment. [Modes for carrying out the invention]

[0024] Embodiments of the present disclosure will be described with reference to the attached drawings. The embodiments described below are examples of the implementation of the present disclosure, and the present disclosure is not limited to these embodiments.

[0025] (Configuration of the transmission and reception system in this disclosure) Figure 1 shows the configuration of the transmitting and receiving system of this disclosure. Figure 2 shows the procedure for transmitting and receiving processing of this disclosure. The transmitting and receiving system S is applicable to wireless or wired communication and comprises a transmitting device T and a receiving device R. The transmitting device T comprises a modulator 1 and an amplifier 2. The receiving device R comprises a level shifter 3 (provided before and after the equalizer 4, respectively), an equalizer 4, a demodulator 5, and a switch 6. In order to execute step S3 on the level shifter 3, the receiving program for step S3 can be installed on a computer.

[0026] Transmitter T switches between transmitting a fixed-envelope modulated signal and a non-fixed-envelope modulated signal. Modulator 1 switches between generating a fixed-envelope modulated signal and a non-fixed-envelope modulated signal (step S1). Amplifier 2 amplifies the fixed-envelope modulated signal and the non-fixed-envelope modulated signal (step S2).

[0027] The receiving device R receives by switching between a fixed-envelope modulated signal and a non-fixed-envelope modulated signal. The equalizer 4 compensates for the nonlinear distortion of the fixed-envelope modulated signal and the non-fixed-envelope modulated signal (step S3). The demodulator 5 demodulates by switching between a fixed-envelope modulated signal and a non-fixed-envelope modulated signal (step S4). The switch 6 outputs a known signal such as a pilot signal during the pull-in process and the hard judgment value of the demodulator 5 during the data transmission process, as a reference signal described later.

[0028] The equalizer 4 comprises a first-order equalizer filter 41, a weight coefficient calculation unit 42, a cube value calculation unit 43, a third-order equalizer filter 44, a weight coefficient calculation unit 45, an adder 46, and a subtractor 47. The level shifter 3 (provided before and after the equalizer 4, respectively) is a feature of this disclosure and will be described later. As a modification, the equalizer 4 may include a third-order or higher equalizer filter.

[0029] The first equalization filter 41 takes, as an input signal y 1、n a modulated signal and additive noise x n + z n (see the first equation of Equation 1). The cube value calculation unit 43 calculates the cube value |x n + z n | 2 (x n + z n ). The third equalization filter 44 takes, as an input signal y 2、n the cube value |x n + z n | 2 (x n + z n ) (see the second equation of Equation 1).

Equation

[0030] The first equalization filter 41 and the third equalization filter 44 can apply a FIR (Finite Inpulse Response) filter or the like. The modulated signal x n may be sampled at the symbol timing of the aperture point of the eye pattern, or may be oversampled at a sampling frequency P times that symbol timing. The additive noise z n may assume AWGN (Additive White Gaussian Noise) or the like.

[0031] As will be described later, the weight coefficient calculation unit 42 calculates the weight coefficient vector w1 of the first equalization filter 41 (see the first equation of Equation 2, where 0, 1, ···, M1-1 indicate tap numbers). As will be described later, the weight coefficient calculation unit 45 calculates the weight coefficient vector w2 of the third equalization filter 44 (see the second equation of Equation 2, where 0, 1, ···, M2-1 indicate tap numbers).

Equation

[0032] The first-order equalization filter 41 uses a weight coefficient vector w1 and an input signal vector y 1、n The inner product w1 between and T y 1、n The following is calculated (see the first equation of Equation 3 and the first term on the right-hand side of Equation 4). The third-order equalization filter 44 uses the weight coefficient vector w2 and the input signal vector y 2、n The dot product w2 between and T y 2、n Calculate (see the second equation of Equation 3 and the second term on the right side of Equation 4). Adder 46 calculates the inner product w1 T y 1、n And the dot product w2 T y 2、n The added value x between and n ^ Calculate (see formula 4).

number

number

[0033] Demodulator 5 adds up x n ^ Restore hardness judgment value etc x n-m It outputs the reference signal x. Switch 6 outputs the reference signal x n-m During the pull-in process, known signals such as pilot signals x n-m It outputs the hard judgment value of demodulator 5, etc. during the data transmission process. n-m It outputs the following. Subtractor 47 adds x n ^ And, reference signal x n-m The error value e between and n Calculate (see formula 5).

number

[0034] In this disclosure, the first-order equalization filter 41 and the third-order equalization filter 44, when ROF (Roll Off Filter) is not applied, w in one m. 1、m and w 2、mThis is defined as non-zero. Here, when m=0, the reference signal x n-m The value at the same time as the present is adopted, and when m=1, the reference signal x n-m The value from one time step prior to the present is adopted. As an example, the first-order equalization filter 41 and the third-order equalization filter 44, when applying ROF, use multiple values ​​for m, for example, at the central tap of ROF, w 1、m and w 2、m It may be treated as non-zero.

[0035] The weight coefficient calculation unit 42 calculates the error value e n The expected value of the squared value E[|e n | 2 The weight coefficient vector w1 of the first-order equalization filter 41 is set to minimize ] ^ The weight coefficient calculation unit 45 calculates the error value e n The expected value of the squared value E[|e n | 2 The weight coefficient vector w2 of the third-order equalization filter 44 is set to minimize ] ^ Calculate (see the second term on the left side of equation 6).

number

[0036] In this disclosure, the weight coefficient calculation units 42 and 45 calculate the weight coefficient vector w1 in accordance with the MMSE (Minimum Mean Square Error) standard. ^ w2 ^ As such, Wiener solution w1 ^ w2 ^ The following is calculated. As an example, the weight coefficient calculation units 42 and 45 calculate the weight coefficient vector w1 according to the LMS (Least Mean Square) standard or the RLS (Recursive Least Square) standard. ^ w2 ^ The following can also be calculated: In other words, the weight coefficient calculation units 32 and 35 calculate the error value e n The squared value of |e n | 2 To minimize this, the weight coefficient vector w1^ w2 ^ You just need to calculate that.

[0037] Weight coefficient vector w1 of the first-order equalization filter 41 ^ This is expressed as shown in equation 7. The weight coefficient vector w2 of the cubic equalization filter 44. ^ This can be expressed as shown in equation 8. Here, the modulation signal x n The nonlinear distortion is extremely small, and the added noise z n It is assumed that it is an AWGN.

number

number

[0038] In equations 7 and 8, P 11 , P 12 , P 22 r1 and r2 are expressed as shown in equations 10 and 11. Here, P x P is the modulated signal power. z This is the additional noise power (see Equation 9). And E[|x| α ](α≧2) is the modulated signal x n It is the expected value of the alpha power of, and E[|z| 2 ] is additional noise z n This is the expected value of the square of (see formulas 9-11).

number

number

number

[0039] Incidentally, when the receiving device R switches between receiving a fixed-envelope modulated signal and a non-fixed-envelope modulated signal, if the equalizer 4 provided in the receiving device R can adjust the weight coefficient vectors w1 and w2 of the first-order equalizing filter 41 and the third-order equalizing filter 44 (or, as a modified example, the weight coefficient vectors of the third-order or higher equalizing filters) to be equal, then a rapid deterioration of characteristics such as the error rate of the received bits can be suppressed.

[0040] Therefore, the level shifter 3 (located before the equalizer 4) in the receiving device R shifts the constant envelope modulation signal to multiple envelope levels s and adjusts the frequency p of the level shift to multiple envelope levels s (step S3). Specifically, the level shifter 3 (located before the equalizer 4) in the receiving device R performs the level shift of the constant envelope modulation signal in the first and second embodiments. The first and second embodiments will be described below.

[0041] In this way, when switching the modulation method from a fixed-envelope modulation signal to a non-fixed-envelope modulation signal, it is possible to suppress a rapid deterioration of characteristics such as the error rate of the received bits. Furthermore, since it is not always necessary to perform equalization processing after error correction, it is possible to suppress the increase in the overall system delay of the receiving device R and the amount of computation per demodulated symbol.

[0042] (Level shift of the constant envelope modulated signal in the first embodiment) Figure 3 shows the weight coefficients of a conventional third-order equalization filter. The expected value E[|x| of the alpha power of the constant envelope modulation signal x] α ] is expressed as in the first equation of Equation 12. The signal-to-noise ratio CNR is expressed as in the second equation of Equation 12. Modulated signal power P x On long-term scales, it is variable, but on short-term scales (switching between constant-envelope modulated signals and non-constant-envelope modulated signals), it is constant (e.g., 1) (see Equation 3 of Equation 12). Alternatively, the receiving device R may be equipped with a gain adjuster to keep the received signal power constant.

number

[0043] In the constant envelope modulation signal x, the weight coefficient w of the third-order equalization filter 44 2、m ^ is expressed as in Equation 13 based on Equations 8 to 12. In the upper left column of FIG. 3, the weight coefficient w of the third-order equalization filter 44 2、m ^ approaches 0 when the signal-to-noise ratio CNR is low, approaches -0.5 when the signal-to-noise ratio CNR is high, and can take a value smaller than 0 and larger than -0.5 when the signal-to-noise ratio CNR is within the assumed -10 to 30 dB.

Number

[0044] That is, in Equation 8, contrary to the assumption that the non-linearity distortion of the constant envelope modulation signal x is extremely small, the weight coefficient w of the third-order equalization filter 44 2、m ^ can take a non-zero value.

[0045] The expected value E[|x| of the α-power value of the non-constant envelope modulation signal x (in FIG. 3, 16QAM signal, 32APSK signal or 64QAM signal) α is not expressed as in the first equation of Equation 12. The signal-to-noise ratio CNR is expressed as in the second equation of Equation 12. The modulation signal power P x is variable on a long-time scale, but is constant (e.g., 1) on a short-time scale (the switching between the constant envelope modulation signal and the non-constant envelope modulation signal) (see the third equation of Equation 12). Alternatively, the receiving device R may include a gain adjuster and may make the received signal power constant.

[0046] In the non-constant envelope modulation signal x (in FIG. 3, 16QAM signal, 32APSK signal or 64QAM signal), the weight coefficient w of the third-order equalization filter 44 2、m ^ is expressed in a different form from Equation 13 based on Equations 8 to 11. In the upper right column, lower left column and lower right column of FIG. 3, in any case, the weight coefficient w of the third-order equalization filter 44 2、m ^When the signal-to-noise ratio (CNR) is low or high, it approaches 0, and when the CNR is within the expected range of -10 to 30 dB, it can take a value less than 0 and greater than about -0.1, but it will never take a value as small as -0.5.

[0047] In other words, in equation 8, the weight coefficient w of the third-order equalization filter 44 is determined by assuming that the nonlinear distortion of the non-deterministic envelope-modulated signal x is extremely small. 2、m ^ It can be said that it takes a value of almost zero.

[0048] Therefore, in the conventional technology, when the receiving device R switches between receiving a fixed-envelope modulated signal and a non-fixed-envelope modulated signal, the equalizer 4 provided in the receiving device R adjusts the weight coefficient vector w2 of the third-order equalization filter 44 (or, in a modified example, the weight coefficient vector of an equalization filter of the third order or higher) to different values, making it impossible to suppress the rapid deterioration of characteristics such as the error rate of the received bits.

[0049] Figure 4 shows the level shift of the constant envelope modulated signal in the first embodiment. The level shifter 3 (located before the equalizer 4) of the receiving device R shifts the constant envelope modulated signal to multiple envelope levels s and adjusts the frequency p of the level shift to multiple envelope levels s (step S3). In Figure 1, the level shifter 3 (located before the equalizer 4) of the receiving device R is x n '+z n From (what the receiving device R receives), x n +z n The modulated signal and added noise are level-shifted to match the input of equalizer 4.

[0050] Then, when the receiving device R receives a constant envelope modulation signal that it has determined to have small nonlinear distortion, the equalizer 4 provided in the receiving device R can adjust the weight coefficient vector w2 of the third-order equalization filter 44 (or, in a modified example, the weight coefficient vector of an equalization filter of order 3 or higher) to 0.

[0051] Here, the level shifter 3 (provided at the subsequent stage of the equalizer 4) included in the receiving apparatus R level-shifts the reference signal to a plurality of envelope levels s, and adjusts the occurrence frequency p of the level shift to the plurality of envelope levels s (step S3). In FIG. 1, the level shifter 3 (provided at the subsequent stage of the equalizer 4) included in the receiving apparatus R is x n-m ’ (output by the switch 6), from x n-m (input to the equalizer 4), and level-shifts the reference signal.

[0052] That is, the subtractor 47 calculates the error value e n ^ between the added value x n-m and the reference signal x n . When the modulation signal and the added noise are level-shifted from x n ’+z n to x n +z n , the reference signal should also be level-shifted from x n-m ’ to x n-m . Here, the demodulator 5 performs a hard decision on the level-shifted and equalized constant envelope modulation signal to the ideal points of the same symbols as the modulator 1. For example, when the modulator 1 generates a QPSK signal, the demodulator 5 performs a hard decision on the level-shifted and equalized 8APSK signal (see FIG. 4) as a QPSK signal rather than as an 8APSK signal.

[0053] In the constant envelope modulation signal x (in FIG. 4, a QPSK signal), the weight coefficient w 2、m ^ of the third-order equalization filter 44 is adjusted to 0 (see the first equation of Equation 14). Therefore, the expected value E[|x| 4 of the fourth power value of the constant envelope modulation signal x is adjusted as in the second equation of Equation 14. Moreover, the weight coefficient w 1、m ^ of the first-order equalization filter 41 is adjusted as in the third equation of Equation 14.

Equation

[0054] In the left column of Figure 4, in the constant envelope modulated signal x (QPSK signal) before the level shift, one envelope level is s. In the right column of Figure 4, in the constant envelope modulated signal x (QPSK signal) after the level shift, the two envelope levels are s1 and s2, and the frequency of the level shift to the two envelope levels s1 and s2 is p1 and p2 (see Equation 15).

number

[0055] In the right column of Figure 4, the expected value E[|x| of the squared value of the constant envelope modulation signal x is shown. 2 ] is the modulated signal power P x It is expressed as the first equation of Equation 16, and is the expected value E[|x| of the fourth power of the constant envelope modulation signal x]. 4 ] is expressed by the second equation of equation 16, based on the second equation of equation 14.

number

[0056] In the right column of Figure 4, the frequency of level shifts to two envelope levels s1 and s2, p1 and p2, are known, and the two envelope levels s1 and s2 are unknown, and the result can be obtained as shown in Equation 17. As a variation, one of the two envelope levels s1 and s2 is a known, and the frequency of level shifts to the two envelope levels s1 and s2, and the other envelope level s1 and s2 are unknown, and the result can be obtained in the same way as Equation 17. However, if the inner envelope level s1 is a known, then 0 ≤ s1 < √P x It is necessary that the outer envelope level s2 is a known number, and if √(2P) x It is necessary that )≦s2. Also, it is necessary that p1≧p2.

number

[0057] Figure 5 shows the configuration of the level shifter in this disclosure. The level shifter 3 comprises a multiplier 31, a multiplier 32, a random number generator 33, a switch 34, a modulation detector 35, and a switch 36.

[0058] Level shifter 3 (located before equalizer 4) receives the input signal α n 'as modulated signal and added noise x n '+z n Enter ' (see the first term on the right-hand side of equation 1 of equation 18), and output signal α n The modulated signal and the added noise x n +z n It outputs (see the first term on the right-hand side of the second equation in Equation 18). Level shifter 3 (located after equalizer 4) receives the input signal α n ' as reference signal x n-m Enter ' (see the second term on the right-hand side of the first equation in equation 18), and output signal α n As reference signal x n-m Output (see the second term on the right-hand side of equation 2 in equation 18).

number

[0059] The multiplier 31 processes the input signal α n For the envelope level s (see equation 1 of equation 19), multiply by the gain g1 to obtain the level shift signal g1α n The multiplier 32 outputs the first envelope level s1, see equation 2 of equation 19. The multiplier 32 outputs the input signal α n Multiply the envelope level s (see Equation 1 of Equation 19) by the gain g2 to obtain the level shift signal g2α n The output is '(see the third equation of equation 19 for other envelope levels s2). Here, multipliers 31 and 32 should refer to the modulation scheme (modulation order of the constant envelope modulation signal, etc.) using the frame header, etc.

number

[0060] The random number generator 33, using the frame header, etc., refers to the modulation scheme (modulation order of the constant envelope modulation signal, etc.), and then generates the numbers according to the Bernoulli distribution, b n = Generates a random number of 0 or 1 (see the first equation of equation 20). Here, the random number generator 33 is b n The frequency of random numbers where =0 is made equal to the frequency p1 of level shifts to the envelope level s1 (see the second equation of Equation 20). On the other hand, the random number generator 33, b n The frequency of random numbers where =1 is made equal to the frequency of level shifts p2 to other envelope levels s2 (see Equation 3 of Equation 20).

number

[0061] Switch 34 is activated when the output signal of the random number generator 33 is b n When = 0 (frequency p1), the level shift signal h n =g1α n '(one envelope level s1) is output (see the first case in Equation 21). On the other hand, switch 34 is switched when the output signal of random number generator 33 is b n When =1 (occurrence frequency p2), the level shift signal h n =g2α n The output is (another envelope level s2) (see the second case in Equation 21). In this way, the constant envelope modulation signal is level-shifted.

number

[0062] The modulation determination unit 35 uses the frame header, etc., to refer to the modulation method (fixed envelope modulation signal or non-fixed envelope modulation signal) and then controls the switch 36. When the modulation method is a fixed envelope modulation signal, the switch 36 outputs the output signal α n =h n It outputs (see the first case in Equation 22). On the other hand, when the modulation scheme is an undefined envelope modulation signal, switch 36 outputs the output signal α n =α nThe output is left as is (see the second case in Equation 22). In this way, the modulation method is switched between a fixed-envelope modulated signal and a non-fixed-envelope modulated signal.

number

[0063] Here, the modulation determination device 35 determines that the switch 36 outputs the output signal α for the entire period during which the modulation method is a constant envelope modulation signal. n =h n The control may be configured to output the following. On the other hand, the modulation determination device 35 may be controlled to output the output signal α only immediately before the modulation method switches from a fixed envelope modulation signal to a non-fixed envelope modulation signal when the switch 36 is turned on. n =h n You may also control it to output [this].

[0064] Furthermore, in order for the receiving device R to determine that the nonlinear distortion of the constant envelope modulated signal x is small, it may refer to the backoff condition of the transmitted signal level using the frame header, etc. (the smaller the backoff, the smaller the nonlinear distortion is determined to be), or it may refer to the modulation order of the constant envelope modulated signal x (the lower the modulation order, the smaller the nonlinear distortion is determined to be). In addition, the level shifter 3 provided in the receiving device R may level shift the constant envelope modulated signal to three or more envelope levels s, and may adjust the frequency p of the level shift to three or more envelope levels s.

[0065] Thus, when the receiving device R receives a constant envelope modulation signal that it has determined to have small nonlinear distortion, the level shifter 3 of the receiving device R shifts the constant envelope modulation signal to multiple envelope levels at a predetermined frequency. As a result, the equalizer 4 of the receiving device R can adjust the weight coefficients of the third-order or higher equalization filter to be equal to zero, as described above.

[0066] In Figure 5, the multipliers 31 and 32 of the level shifter 3 level-shift the constant envelope modulated signal x and also apply a phase rotation to the constant envelope modulated signal x according to the phase difference between the received signal point and the ideal signal point. Alternatively, the multipliers 31 and 32 of the level shifter 3 level-shift the constant envelope modulated signal x and also apply a phase rotation to the constant envelope modulated signal x according to the amount of phase distortion estimated based on the back-off condition and nonlinear distortion characteristics of the amplifier 2.

[0067] In the former case, the multipliers 31 and 32 of the level shifter 3 apply phase rotations θ1 and θ2 to the constant envelope modulated signal x according to the phase difference between, for example, the received signal point after level shifting in the upper middle column of Figures 10 and 16 and the ideal signal point after level shifting in the upper left column of Figures 10 and 16. In the latter case, the multipliers 31 and 32 of the level shifter 3 apply phase rotations θ1 and θ2 to the constant envelope modulated signal x according to the amount of phase distortion estimated based on, for example, the back-off condition of amplifier 2 and the nonlinear distortion characteristics of amplifier 2. In either the former or latter case, the phase rotations θ1 and θ2 applied to the constant envelope modulated signal x may be calculated by an automatic algorithm or stored as fixed values ​​in a table.

[0068] Thus, the level shifter 3 provided by the receiving device R can level-shift the constant envelope modulated signal to multiple envelope levels at a predetermined frequency, and can also impart phase rotation to the constant envelope modulated signal according to the nonlinear phase distortion characteristics of the amplifier 2.

[0069] Figures 6 and 7 show the distortion compensation during the switching between the modulation methods of the prior art and the first embodiment, respectively. Figure 8 shows the MER (Modulation Error Ratio) characteristics during the switching between the modulation methods of the prior art and the first embodiment. In Figures 6-8, there is no nonlinear distortion, CNR = 20 dB, and the modulation method switches from a QPSK signal to a 32APSK signal. The upper left, upper middle, and upper right columns of Figures 6 and 7 show constellations of the QPSK signal in an ideal, noisy environment and after distortion compensation, respectively. The lower left, lower middle, and lower right columns of Figures 6 and 7 show constellations of the 32APSK signal in an ideal, noisy environment and after distortion compensation, respectively.

[0070] In conventional techniques (see Figures 6 and 8), in the distortion-compensated QPSK signal, the signal points are compressed in the amplitude direction, so the signal point deviation characteristic MER from the ideal point appears to improve, but the weight coefficient vector w2 of the third-order equalization filter 44 is over-tuned to the QPSK signal only. After switching the modulation scheme, in the distortion-compensated 32APSK signal, the weight coefficient vector w2 of the third-order equalization filter 44 is over-tuned to the QPSK signal only, so the signal points are compressed in both the amplitude and phase directions, and the signal point deviation characteristic MER from the ideal point deteriorates rapidly.

[0071] In the first embodiment (see Figures 7 and 8), in the distortion-compensated QPSK signal, the signal points are not compressed in the amplitude direction, so the signal point deviation characteristic MER from the ideal point is sufficient, and the weight coefficient vector w2 of the third-order equalization filter 44 is not over-tuned to the original QPSK signal. After switching the modulation scheme, in the distortion-compensated 32APSK signal, the weight coefficient vector w2 of the third-order equalization filter 44 is not over-tuned to the original QPSK signal, so the signal points are not compressed in either the amplitude or phase direction, and the signal point deviation characteristic MER from the ideal point does not change.

[0072] Figures 9 and 10 show the distortion compensation during the switching between the modulation methods of the prior art and the first embodiment, respectively. Figure 11 shows the MER characteristics during the switching between the modulation methods of the prior art and the first embodiment. In Figures 9-11, there is some nonlinear distortion, CNR = 20 dB, and the modulation method switches from a QPSK signal to a 32APSK signal. The upper left, upper middle, and upper right columns of Figures 9 and 10 show the ideal constellations of the QPSK signal after distortion addition and distortion compensation, respectively. The lower left, lower middle, and lower right columns of Figures 9 and 10 show the ideal constellations of the 32APSK signal after distortion addition and distortion compensation, respectively.

[0073] In conventional techniques (see Figures 9 and 11), in the distortion-compensated QPSK signal, the signal points are compressed in the amplitude direction, so the signal point deviation characteristic MER from the ideal point appears to improve, but the weight coefficient vector w2 of the third-order equalization filter 44 is over-tuned to the QPSK signal only. After switching the modulation scheme, in the distortion-compensated 32APSK signal, the weight coefficient vector w2 of the third-order equalization filter 44 is over-tuned to the QPSK signal only, so the signal points are compressed in both the amplitude and phase directions, and the signal point deviation characteristic MER from the ideal point deteriorates rapidly.

[0074] In the first embodiment (see Figures 10 and 11), in the distortion-compensated QPSK signal, the signal points are not compressed in the amplitude direction, so the signal point deviation characteristic MER from the ideal point is sufficient, and the weight coefficient vector w2 of the third-order equalization filter 44 is not over-tuned to the original QPSK signal. After switching the modulation method, in the distortion-compensated 32APSK signal, the weight coefficient vector w2 of the third-order equalization filter 44 is not over-tuned to the original QPSK signal, so the signal points are not compressed in either the amplitude or phase direction, and the signal point deviation characteristic MER from the ideal point does not change. However, in Figures 9 to 11, unlike Figures 6 to 8, there is some nonlinear distortion, so the signal point deviation characteristic MER from the ideal point changes slightly before and after switching the modulation method.

[0075] Figures 12 and 13 show the distortion compensation during the switching between the modulation schemes of the prior art and the first embodiment, respectively. Figure 14 shows the MER characteristics during the switching between the modulation schemes of the prior art and the first embodiment. In Figures 12-14, there is no nonlinear distortion, CNR = 25 dB, and the modulation scheme switches from a QPSK signal to a 64QAM signal. The upper left, upper middle, and upper right columns of Figures 12 and 13 show constellations of the QPSK signal in an ideal, noisy environment and after distortion compensation, respectively. The lower left, lower middle, and lower right columns of Figures 12 and 13 show constellations of the 64QAM signal in an ideal, noisy environment and after distortion compensation, respectively.

[0076] In conventional techniques (see Figures 12 and 14), in the distortion-compensated QPSK signal, the signal points are compressed in the amplitude direction, so the signal point deviation characteristic MER from the ideal point appears to improve, but the weight coefficient vector w2 of the third-order equalization filter 44 is over-tuned to the QPSK signal only. After switching the modulation scheme, in the distortion-compensated 64QAM signal, the weight coefficient vector w2 of the third-order equalization filter 44 is over-tuned to the QPSK signal only, so the signal points are compressed in both the amplitude and phase directions, and the signal point deviation characteristic MER from the ideal point deteriorates rapidly.

[0077] In the first embodiment (see Figures 13 and 14), in the distortion-compensated QPSK signal, the signal points are not compressed in the amplitude direction, so the signal point deviation characteristic MER from the ideal point is sufficient, and the weight coefficient vector w2 of the third-order equalization filter 44 is not over-tuned to the original QPSK signal. After switching the modulation scheme, in the distortion-compensated 64QAM signal, the weight coefficient vector w2 of the third-order equalization filter 44 is not over-tuned to the original QPSK signal, so the signal points are not compressed in either the amplitude or phase direction, and the signal point deviation characteristic MER from the ideal point does not change.

[0078] Figures 15 and 16 show the distortion compensation during the switching between the modulation schemes of the prior art and the first embodiment, respectively. Figure 17 shows the MER characteristics during the switching between the modulation schemes of the prior art and the first embodiment. In Figures 15-17, there is some nonlinear distortion, CNR = 25 dB, and the modulation scheme switches from a QPSK signal to a 64QAM signal. The upper left, upper middle, and upper right columns of Figures 15 and 16 show the ideal constellations of the QPSK signal after distortion addition and distortion compensation, respectively. The lower left, lower middle, and lower right columns of Figures 15 and 16 show the ideal constellations of the 64QAM signal after distortion addition and distortion compensation, respectively.

[0079] In conventional techniques (see Figures 15 and 17), in the distortion-compensated QPSK signal, the signal points are compressed in the amplitude direction, so the signal point deviation characteristic MER from the ideal point appears to improve, but the weight coefficient vector w2 of the third-order equalization filter 44 is over-tuned to the QPSK signal only. After switching the modulation scheme, in the distortion-compensated 64QAM signal, the weight coefficient vector w2 of the third-order equalization filter 44 is over-tuned to the QPSK signal only, so the signal points are compressed in both the amplitude and phase directions, and the signal point deviation characteristic MER from the ideal point deteriorates rapidly.

[0080] In the first embodiment (see Figures 16 and 17), in the distortion-compensated QPSK signal, the signal points are not compressed in the amplitude direction, so the signal point deviation characteristic MER from the ideal point is sufficient, and the weight coefficient vector w2 of the third-order equalization filter 44 is not over-tuned to the original QPSK signal. After switching the modulation scheme, in the distortion-compensated 64QAM signal, the weight coefficient vector w2 of the third-order equalization filter 44 is not over-tuned to the original QPSK signal, so the signal points are not compressed in either the amplitude or phase direction, and the signal point deviation characteristic MER from the ideal point does not change. However, in Figures 15 to 17, unlike Figures 12 to 14, there is some nonlinear distortion, so the signal point deviation characteristic MER from the ideal point changes slightly before and after switching the modulation scheme.

[0081] (Level shift of the constant envelope modulated signal in the second embodiment) Figure 18 shows the received signal level of the non-constant envelope modulation signal in the second embodiment. Figure 19 shows the level shift of the constant envelope modulation signal in the second embodiment. The level shifter 3 (located before the equalizer 4) of the receiving device R shifts the constant envelope modulation signal to multiple envelope levels s, regardless of the presence or absence of nonlinear distortion, and adjusts the frequency p of the level shift to multiple envelope levels s (step S3). In Figure 1, the level shifter 3 (located before the equalizer 4) of the receiving device R is x n '+z n From (what the receiving device R receives), x n +z n The modulated signal and added noise are level-shifted to match the input of equalizer 4.

[0082] Then, when the receiving device R switches between receiving a fixed-envelope modulated signal and a non-fixed-envelope modulated signal, the level shifter 3 provided in the receiving device R can adjust the expected value of the α-power value of the received signal level (where α is a natural number greater than or equal to 2, depending on the order of the equalization filter) to be equal.

[0083] Here, the level shifter 3 (located after the equalizer 4) of the receiving device R shifts the reference signal to multiple envelope levels s and adjusts the frequency p of the level shifts to multiple envelope levels s (step S3). In Figure 1, the level shifter 3 (located after the equalizer 4) of the receiving device R is x n-m ' (What switch 6 outputs) from x n-m The reference signal is level-shifted to (what equalizer 4 inputs).

[0084] In other words, subtractor 47 adds x n ^ And, reference signal x n-m The error value e between and n When calculating, the modulated signal and the added noise are x n '+z n 'from x n +z n If the level shift is to x, then the reference signal will also be x n-m 'from x n-mThe level should be shifted to this. Here, demodulator 5 performs a hard judgment on the level-shifted and equalized constant envelope modulated signal to the ideal symbol point, similar to modulator 1. For example, when modulator 1 generates a QPSK signal, demodulator 5 performs a hard judgment on the level-shifted and equalized 8APSK signal (see Figure 19) not as an 8APSK signal, but strictly as a QPSK signal.

[0085] When there is no nonlinear distortion, the weight coefficient w of the third-order equalization filter 44 2、m ^ This is expressed by equations 8-11. Here, in the case of a fixed envelope modulated signal and a non-fixed envelope modulated signal, of the terms in equations 8-11, the modulated signal power P x Since they are equally tuned (see Equation 1 of Equation 23), the signal-to-noise ratio (CNR) is also automatically equal (see Equation 2 of Equation 23).

number

[0086] Therefore, in both fixed-envelope modulated signals and non-fixed-envelope modulated signals, the expected value E[|x| of the modulated signal x to the power of 4 is obtained from each term in equations 8 to 11. 4 If ] are equally adjusted, and the expected value E[|x| of the modulated signal x to the power of 6 is equal to E[|x| 6 If ] are equally adjusted, (the weight coefficients w of the first-order equalization filter 41) 1、m ^ (Of course) the weight coefficients w of the 3rd order equalization filter 44 2、m ^ These should also be adjusted equally (see Equation 24).

number

[0087] When there is nonlinear distortion, the weight coefficient vector w2 of the third-order equalization filter 44 becomes more complex than equations 8-11. However, in the case of fixed-envelope modulated signals and non-fixed-envelope modulated signals, the modulated signal power P is the modulated power P among the terms in the weight coefficient equations. xSince they are equally tuned (see Equation 1 of Equation 23), the signal-to-noise ratio (CNR) is also automatically equal (see Equation 2 of Equation 23).

[0088] Therefore, in both fixed-envelope modulated signals and non-fixed-envelope modulated signals, the expected value E[|x| of the modulated signal x to the power of 4 is obtained from each term in the formula for the weight coefficient. 4 If ] are equally adjusted, and the expected value E[|x| of the modulated signal x to the power of 6 is equal to E[|x| 6 If ] are equally adjusted, then it can be assumed that the weight coefficient vector w2 of the cubic equalization filter 44 (as well as the weight coefficient vector w1 of the first-order equalization filter 41) will also be equally adjusted (see Equation 24).

[0089] Although not illustrated, it can be demonstrated in practice that even in the presence of nonlinear distortion, if equation 24 holds, the signal point deviation characteristic MER from the ideal point does not change before and after switching the modulation scheme. Therefore, even in the presence of nonlinear distortion, if equation 24 holds, it can be empirically seen that the weight coefficient vector w2 of the third-order equalizer filter 44 (as well as the weight coefficient vector w1 of the first-order equalizer filter 41) remains equal before and after switching the modulation scheme.

[0090] In the left or right column of Figure 18, the three envelope levels for the non-deterministic envelope modulation signal x (16QAM signal or 32APSK signal) are s1, s2, and s3, and the frequencies of mapping to the three envelope levels s1, s2, and s3 are p1, p2, and p3.

[0091] In the left or right column of Figure 18, the expected value E[|x| of the fourth power of the non-deterministic envelope modulation signal x (16QAM signal or 32APSK signal) is shown. 4 E[|x|] is expressed by the first equation of equation 25 and is the expected value of the sixth power of the non-deterministic envelope modulation signal x (16QAM signal or 32APSK signal). 6 ] is expressed by the second equation of equation 25. Here, γ k This is the first envelope level s1 relative to the kth envelope level s kThis is the ratio. As the first step, the calculation of Equation 25 is performed on the non-deterministic envelope modulation signal x (16QAM signal or 32APSK signal).

number

[0092] In the left column of Figure 19, in the constant envelope modulated signal x (QPSK signal) before the level shift, one envelope level is s. In the right column of Figure 19, in the constant envelope modulated signal x (QPSK signal) after the level shift, the two envelope levels are s1 and s2, and the frequency of the level shift to the two envelope levels s1 and s2 is p1 and p2 (see Equation 15).

[0093] In the right column of Figure 19, the expected value E[|x|] of the fourth power of the constant envelope modulation signal x (QPSK signal) after level shifting is shown. 4 E[|x|] is expressed by the first equation of equation 25 and is the expected value of the sixth power of the constant envelope modulation signal x (QPSK signal) after level shifting. 6 This is expressed by the second equation of Equation 25, where γ2 is the ratio of the second envelope level s2 to the first envelope level s1. In the second step, s1, s2, p1, and p2 are calculated based on Equations 24 and 25 for the level-shifted constant envelope modulated signal x (QPSK signal).

[0094] Furthermore, the receiving device R can apply the second embodiment regardless of whether the nonlinear distortion of the constant envelope modulated signal x is small or large, in contrast to the first embodiment, which can only be applied when the nonlinear distortion of the constant envelope modulated signal x is small. In addition, the level shifter 3 provided in the receiving device R may level shift the constant envelope modulated signal to three or more envelope levels s, and the frequency p of the level shift to three or more envelope levels s may be adjusted.

[0095] Thus, when the receiving device R switches between receiving a fixed-envelope modulated signal and a non-fixed-envelope modulated signal, the level shifter 3 of the receiving device R adjusts the expected value of the α-power of the received signal level (where α is a natural number greater than or equal to 2, depending on the order of the equalization filter) to be equal. As a result, the equalizer 4 of the receiving device R can adjust the weight coefficients of the equalization filter to be equal, as described above.

[0096] In Figure 5, the multipliers 31 and 32 of the level shifter 3 level-shift the constant envelope modulated signal x and also apply a phase rotation to the constant envelope modulated signal x according to the phase difference between the received signal point and the ideal signal point. Alternatively, the multipliers 31 and 32 of the level shifter 3 level-shift the constant envelope modulated signal x and also apply a phase rotation to the constant envelope modulated signal x according to the amount of phase distortion estimated based on the back-off condition and nonlinear distortion characteristics of the amplifier 2.

[0097] In the former case, the multipliers 31 and 32 of the level shifter 3 apply phase rotations θ1 and θ2 to the constant envelope modulated signal x according to the phase difference between, for example, the received signal point after level shifting in the upper middle column of Figures 10 and 16 and the ideal signal point after level shifting in the upper left column of Figures 10 and 16. In the latter case, the multipliers 31 and 32 of the level shifter 3 apply phase rotations θ1 and θ2 to the constant envelope modulated signal x according to the amount of phase distortion estimated based on, for example, the back-off condition of amplifier 2 and the nonlinear distortion characteristics of amplifier 2. In either the former or latter case, the phase rotations θ1 and θ2 applied to the constant envelope modulated signal x may be calculated by an automatic algorithm or stored as fixed values ​​in a table.

[0098] Thus, the level shifter 3 provided by the receiving device R can level-shift the constant envelope modulated signal to multiple envelope levels at a predetermined frequency, and can also impart phase rotation to the constant envelope modulated signal according to the nonlinear phase distortion characteristics of the amplifier 2. [Industrial applicability]

[0099] The receiving device and receiving program of this disclosure, when compensating for nonlinear distortion of the modulated signal, can suppress a rapid deterioration of characteristics such as the error rate of the received bits while suppressing an increase in the overall system delay of the receiving device and the amount of computation per demodulated symbol when switching the modulation method from a fixed-envelope modulated signal to a non-fixed-envelope modulated signal. [Explanation of symbols]

[0100] S: Transmit / Receive System T: Transmitter R: Receiver 1: Modulator 2: Amplifier 3: Level Shifter 4: Equalizer 5: Demodulator 6: Switch 31: Multiplier 32: Multiplier 33: Random number generator 34: Switch 35: Modulation Detector 36: Switch 41:1st-order equalization filter 42: Weight coefficient calculation unit 43: Calculation unit for the cubed value 44:3rd order equalization filter 45: Weight coefficient calculation unit 46: Adder 47: Subtractor

Claims

1. A transmitting device that switches between transmitting a fixed-envelope modulated signal and a non-fixed-envelope modulated signal, and a receiving device that switches between receiving the fixed-envelope modulated signal and the non-fixed-envelope modulated signal, An equalizer that compensates for the nonlinear distortion of the fixed envelope modulated signal and the non-fixed envelope modulated signal, A demodulator that switches between the fixed envelope modulated signal and the non-fixed envelope modulated signal for demodulation, When the receiving device switches between receiving the fixed envelope modulated signal and the non-fixed envelope modulated signal, the equalizer adjusts the weight coefficients of the equalization filter to be equal by level-shifting the fixed envelope modulated signal to multiple envelope levels, and the level shifter adjusts the frequency of the level shifts to the multiple envelope levels. A receiving device applicable to wireless or wired communications, characterized by comprising the following:

2. When the receiving device switches between receiving the fixed envelope modulated signal and the non-fixed envelope modulated signal, the level shifter adjusts the fixed envelope modulated signal to the multiple envelope levels and adjusts the frequency of the level shifts to the multiple envelope levels so that the expected value of the α-power of the received signal level (where α is a natural number greater than or equal to 2) is equal. The receiving device according to claim 1, characterized in that

3. When the receiving device receives the constant envelope modulated signal which it has determined to have low nonlinear distortion, the level shifter levels the constant envelope modulated signal to the multiple envelope levels and adjusts the frequency of the level shifts to the multiple envelope levels so that the equalizer adjusts the weight coefficients of the third-order or higher equalization filter to zero. A receiving device according to claim 1 or 2, characterized in that

4. The level shifter shifts the constant envelope modulated signal and applies a phase rotation to the constant envelope modulated signal according to the phase difference between the received signal point and the ideal signal point, or according to the amount of phase distortion estimated based on the amplifier's backoff condition and nonlinear distortion characteristics. The receiving device according to claim 1, characterized in that

5. A receiving program installed on a computer to cause the level shifter in the receiving device according to claim 1 to level shift the constant envelope modulation signal to the plurality of envelope levels and to adjust the frequency of the level shift to the plurality of envelope levels.

Images