High order amplitude shift keying modulation and demodulation method for severe phase noise

Abstract

This invention provides a high-order amplitude-shift keying (APSK) modulation and demodulation method for severe phase noise. In terms of modulation, APSK constellation diagrams exhibit stronger phase noise resistance compared to orthogonal amplitude modulation (QAM). While conventional APSK cannot be Gray-mapped, this invention proposes an APSK constellation diagram where each ring has the same number of constellation points (a power of 2). The phase distribution of constellation points on different rings is identical, and the number of rings is also a power of 2. Adjacent constellation points within the same ring and adjacent constellation points with the same phase differ by only one bit, allowing for Gray-mapping. This constellation diagram can also determine the ring radius through nonlinear optimization, further enhancing its phase noise resistance compared to traditional QAM constellation diagrams. In terms of demodulation, this invention proposes a soft demodulation method, which achieves the same performance as, and does not reduce, maximum likelihood-based soft demodulation, but significantly reduces complexity.

Description

Technical Field

[0001] This invention belongs to the field of modulation and demodulation technology in wireless communication, specifically relating to a high-order amplitude phase shift keying (APSK) modulation and demodulation method for severe phase noise. Background Technology

[0002] With the rapid development of wireless communication, people have increasingly higher requirements for transmission rates and system capacity. The spectrum resources below 6GHz currently used in communication will gradually become insufficient to meet these demands. Millimeter-wave bands, on the other hand, possess a large available bandwidth, which can meet the high-speed transmission requirements of future wireless communication. Furthermore, combining millimeter-wave characteristics with higher-order modulation and demodulation can further improve communication transmission rates. However, the non-ideal characteristics of the millimeter-wave band are more severe than those of commonly used low-frequency bands. These non-ideal characteristics mainly include phase noise, quadrature / in-phase imbalance, and power amplifier nonlinearity. Among these, phase noise has the most significant impact.

[0003] The common phase noise of oscillators in the millimeter-wave band is -100 to -80 dBc / Hz. If the impact of phase noise is mitigated through frequent compensation, it consumes a significant amount of spectrum resources, reducing spectrum utilization and further decreasing the transmission rate. While higher-order modulation and demodulation can increase the transmission rate, it increases demodulation complexity and reduces demodulation accuracy.

[0004] To address the aforementioned problems, this invention proposes a high-order APSK modulation and demodulation method suitable for millimeter-wave systems. Compared to traditional modulation and demodulation methods, this method offers stronger resistance to phase noise and lower demodulation complexity while maintaining similar performance, making it suitable for practical millimeter-wave communication. Summary of the Invention

[0005] Technical Problem: The purpose of this invention is to provide a high-order amplitude-shift phase-keying modulation and demodulation method for systems with severe phase noise, primarily targeting millimeter-wave systems with severe phase noise. In terms of modulation, the proposed APSK constellation diagram exhibits stronger phase noise resistance compared to traditional QAM. In terms of demodulation, the performance of the proposed modulation method is similar to that of traditional soft demodulation based on maximum likelihood demodulation, but with significantly reduced demodulation complexity.

[0006] Technical solution: The high-order amplitude-shift phase-keying modulation and demodulation method for severe phase noise of the present invention includes the following steps:

[0007] Step 1: Amplitude-Shift Keying (APSK) Modulation: Using the Gray-APSK constellation diagram, determine the number of Gray-APSK rings and the distribution of constellation points on each ring, and then determine the radius of the Gray-APSK rings to complete the digital modulation of APSK.

[0008] Step 2: APSK demodulation: A soft demodulation method is used. First, the amplitude and phase of the complex received signal are calculated, and then the log-likelihood ratio of the i-th bit is calculated to complete the soft demodulation.

[0009] The determination of the number of Gray-APSK rings and the distribution of constellation points on each ring is as follows: the order of Gray-APSK is M = 2. m The number of rings is To perform the Gray map, the number of constellation points on each ring must be equal. T is the number of constellation points on the ring, m1 + m2 = m, where m1 and m2 are both non-negative integers; the phase distribution of constellation points on each ring is the same, and the angular distance δθ between adjacent constellation points is:

[0010]

[0011] The phase θ of the p-th constellation point on the ring p for:

[0012]

[0013] 1≤p≤T, where p is an integer;

[0014] Let the radius of the k-th annulus be a. k 1≤k≤N, where k is an integer; the set C of Gray-APSK constellation points is:

[0015]

[0016] The radius of the Gray-APSK annulus is determined by the expression for the theoretical symbol error rate of Gray-APSK:

[0017]

[0018] Where σ n 2 , The variances of Gaussian additive white noise and phase noise are respectively obtained through channel estimation. The Q function is the right-tail function of the standard normal distribution; a0 is 0, a N+1 P(e) is positive infinity. s ) is a nonlinear function, and a set of a is found through nonlinear optimization. kTo minimize this, i.e., to minimize the theoretical symbol error rate of Gray-APSK, the radii of each ring in Gray-APSK are determined. The nonlinear optimization process is carried out using common methods such as gradient descent. Each m bits of the digital signal is Gray-mapped to a constellation point of Gray-APSK, with each constellation point representing a transmitted signal, thus completing the digital modulation of APSK.

[0019] The calculation of the amplitude and phase of the complex received signal, the expression for the complex received signal r, is as follows:

[0020] r=I+Qj (18)

[0021] Where I and Q are the real and imaginary parts of the complex received signal, If the sign is imaginary, then the amplitude r of the complex received signal is... ρ and phase r θ :

[0022]

[0023] The calculation of the log-likelihood ratio of the i-th bit is given by 1 ≤ i ≤ m, where i is an integer. The distribution of the first m1 bits of Gray-APSK depends only on the radius of the ring and is independent of the phase; that is, the i-th bit at any constellation point on the same ring is either 0 or 1, 1 ≤ i ≤ m1. The distribution of the last m2 bits of Gray-APSK depends only on the phase and is independent of the radius of the ring; that is, the phase is any given θ. p The i-th bit of the constellation point is all 0 or 1, m1 < i ≤ m; when i ≤ m1, find the distance r. ρ The radius a of the circle containing the nearest i-th constellation point whose position is all 0s and 1s i0 and a i1 To satisfy:

[0024]

[0025] Where a0 and a1 are the radii of the rings where the i-th bit is all 0 and 1, respectively. and Let be the set of radii of the rings where the i-th bit is all 0 and all 1, respectively. Then the log-likelihood ratio of the i-th bit is:

[0026]

[0027] When m1 < i ≤ m, find the distance r θ The phase θ of the most recent i-th constellation point that is all 0s and 1s i0 and θ i1 To satisfy:

[0028]

[0029] Where θ0 and θ1 are the phases of constellation points where the i-th bit is all 0 and 1 respectively. and Let be the set of phases of constellation points where the i-th bit is all 0 and all 1, then the log-likelihood ratio of the i-th bit is:

[0030]

[0031] The log-likelihood ratio of all bits is obtained; if the log-likelihood ratio is greater than 0, the bit is 1, otherwise it is 0, thus obtaining the bit stream of the received signal and completing soft demodulation.

[0032] Beneficial Effects: The high-order APSK modulation and demodulation method proposed in this invention has the following advantages: In terms of modulation, APSK constellation diagrams have stronger anti-phase noise capabilities compared to QAM (Quadrature Amplitude Modulation), but general APSK cannot be Gray-mapped. Therefore, this invention proposes an APSK constellation diagram where each ring has the same number of constellation points (a power of 2), the phase distribution of constellation points on different rings is the same, and the number of rings is also a power of 2. Adjacent constellation points on the same ring and adjacent constellation points with the same phase differ by only one bit, allowing for Gray-mapping. This constellation diagram can also determine the ring radius through nonlinear optimization, making it more resistant to phase noise than traditional QAM constellation diagrams. In terms of demodulation, this invention proposes a soft demodulation method, which does not reduce performance compared to soft demodulation based on maximum likelihood demodulation, but significantly reduces complexity. Attached Figure Description

[0033] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and, together with their descriptions, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0034] Figure 1 This is a 4x4 Gray-APSK constellation diagram;

[0035] Figure 2 A schematic diagram of the soft demodulation decision region for a 4*4 Gray-APSK constellation. Detailed Implementation

[0036] The high-order APSK modulation and demodulation method of the present invention will be described using a 4*4 Gray-APSK with M=16, m1=2, and m2=2 as an example.

[0037] Step 1: APSK modulation. This invention uses a Gray-APSK (Gray-Amplitude Phase Shift Keying) constellation diagram, the determination of which includes the following process:

[0038] (1) Determine the number of Gray-APSK rings and the distribution of constellation points on each ring. The order of Gray-APSK is M = 2. m The number of rings is In order to perform a Gray map, the number of constellation points on each ring must be equal. (T is the number of constellation points on the ring). Where m1 + m2 = m, and m1 and m2 are non-negative integers. The phase distribution of constellation points on each ring is the same, and the angular distance δθ between adjacent constellation points is:

[0039]

[0040] The phase θ of the p-th (1≤p≤T, p is an integer) constellation point on the ring p for:

[0041]

[0042] Let a be the radius of the k-th (1≤k≤N, k is an integer) ring. k The set C of Gray-APSK constellation points is:

[0043]

[0044] (2) Determine the radius of the Gray-APSK ring. The expression for the theoretical sign error rate of Gray-APSK is:

[0045]

[0046] Where σ n 2 , These are the variances of Gaussian additive white noise and phase noise, respectively, which can be obtained through channel estimation. The Q function is the right-tail function of the standard normal distribution. Note that a0 is 0, and a... N+1 P(e) is positive infinity. s ) is a nonlinear function, and a set of a can be found through nonlinear optimization. k To minimize this, i.e., to minimize the theoretical symbol error rate of Gray-APSK, the radii of each ring in Gray-APSK are determined. The nonlinear optimization process can be performed using general methods such as gradient descent. This completely defines Gray-APSK. Each m bits of the digital signal is Gray-mapped to a constellation point in Gray-APSK, with each constellation point representing a transmitted signal, thus completing the digital modulation of APSK.

[0047] The steps described above are explained in detail below: In the example, M = 16, m1 = 2, and m2 = 2 form a 4x4 Gray-APSK constellation diagram, as shown below. Figure 1 As shown. From Figure 1 The data shows that adjacent constellation points differ by only one bit, indicating a Gray mapping has been performed. Furthermore, the number of constellation points on each ring is the same, four in total, and the phase distribution is also identical. The first two bits depend only on the radius of the ring, while the last two bits depend only on the phase.

[0048] Step 2: APSK Demodulation. This invention employs a software demodulation method. The software demodulation process is as follows:

[0049] (1) Calculate the amplitude and phase of the complex received signal. The expression for the complex received signal r is:

[0050] r=I+Qj (31)

[0051] Where I and Q are the real and imaginary parts of the complex received signal, then the amplitude r of the complex received signal... ρ and phase r θ :

[0052]

[0053]

[0054] (2) Calculate the log-likelihood ratio of the i-th (1≤i≤m, i is an integer) bit. The distribution of the first m1 bits of the Gray-APSK depends only on the radius of the ring and is independent of the phase, that is, the i-th (1≤i≤m1) bit of any constellation point on the same ring is all 0 or 1. The distribution of the last m2 bits of the Gray-APSK depends only on the phase and is independent of the radius of the ring, that is, the phase is any θ p The i-th bit (m1 < i ≤ m) of the constellation point is all 0 or 1. When i ≤ m1, find the distance r. ρ The radius a of the circle containing the nearest i-th constellation point whose position is all 0s and 1s i0 and a i1 To satisfy:

[0055]

[0056] Where a0 and a1 are the radii of the rings where the i-th bit is all 0 and 1, respectively. and Let be the set of radii of the rings where the i-th bit is all 0s and 1s. Then the log-likelihood ratio of the i-th bit is:

[0057]

[0058] When m1 < i ≤ m, find the distance r θ The phase θ of the most recent i-th constellation point that is all 0s and 1s i0 and θi1 To satisfy:

[0059]

[0060] Where θ0 and θ1 are the phases of the constellation points where the i-th bit is all 0 and 1, respectively. and Let be the set of phases of constellation points where the i-th bit is all 0 or 1. Then the log-likelihood ratio of the i-th bit is:

[0061]

[0062] In this way, the log-likelihood ratio of all bits is obtained. If the log-likelihood ratio is greater than 0, the bit is set to 1; otherwise, it is set to 0. This yields the bit stream of the received signal, completing soft demodulation.

[0063] The steps described above will be explained in detail below: Figure 2 The decision region for soft demodulation of the 4*4 Gray-APSK constellation is composed of the radius and phase threshold of the ring where the i-th bit closest to the received signal is all 0 and 1. It is defined by formulas (21), (22), (24), and (25). As shown in the figure, taking the first bit as an example, if... The constellation points with the nearest first bit set to 0 and 1 are located on the second and third rings, and their phases are the same. Therefore, the log-likelihood ratio of the first bit is... Taking the fourth bit as an example, if 0 < r θ If <π, then the phases of the constellation points whose fourth bit is 0 and 1 are π / 4 and 3π / 4 respectively, and their radii are the same. Therefore, the log-likelihood ratio of the fourth bit is...

[0064]

[0065] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A high-order amplitude-shift phase-keying modulation and demodulation method for severe phase noise, characterized in that, The method includes the following steps: Step 1: Amplitude-Shift Phase-Keyed (APSK) Modulation: Using the Gray-APSK constellation diagram, first determine the number of Gray-APSK rings and the distribution of constellation points on each ring, then determine the radius of the Gray-APSK rings to complete the digital modulation of APSK. Step 2: APSK Demodulation: Using a soft demodulation method, first calculate the amplitude and phase of the complex received signal, then calculate the... i The log-likelihood ratio of each bit completes soft demodulation; The determination of the number of Gray-APSK rings and the distribution of constellation points on each ring: the order of Gray-APSK is... The number of rings is , To perform the Gray map, the number of constellation points on each ring must be equal. T is the number of constellation points on the ring, m1 + m2 = m, where m1 and m2 are both non-negative integers; the phase distribution of constellation points on each ring is the same, and the angular distance between adjacent constellation points is... ,for: （1） The aspect of the p-th constellation point on the ring for: （2） p is an integer; Let the radius of the k-th annulus be . , k is an integer; the set C of Gray-APSK constellation points is: （3） The radius of the Gray-APSK annulus is determined by the expression for the theoretical symbol error rate of Gray-APSK: （4） in The variances of Gaussian additive white noise and phase noise are respectively obtained through channel estimation. Q The function is the right-tail function of the standard normal distribution; positive infinity It is a nonlinear function, and a set of methods is found through nonlinear optimization. To minimize this, i.e., to minimize the theoretical symbol error rate of Gray-APSK, the radius of each ring in Gray-APSK is determined; each m bits of the digital signal is Gray-mapped to a constellation point of Gray-APSK, with each constellation point representing a transmitted signal, thus completing the digital modulation of APSK.

2. The high-order amplitude-shift phase-keying modulation and demodulation method for severe phase noise according to claim 1, characterized in that, The calculation of the amplitude and phase of the complex received signal, the expression for the complex received signal r, is as follows: (5) in I and Q To reconstruct the real and imaginary parts of the received signal, , representing the imaginary number sign, then the amplitude r of the complex received signal ρ and phase ; (6) (7)。 3. The high-order amplitude-shift phase-keying modulation and demodulation method for severe phase noise according to claim 2, characterized in that, The calculation of the first i The log-likelihood ratio of bits, 1≤ i ≤ m , i The values ​​are integers; the distribution of the first m1 bits of Gray-APSK depends only on the radius of the ring and is independent of the phase, that is, the distribution of the first m1 bits of the constellation point on any given ring is independent of the phase. i All bits are either 0 or 1, 1 ≤ i ≤ m 1 ; The aftermath of Gray-APSK m 2 The distribution of bits depends only on the phase and is independent of the radius of the annulus; that is, the phase is arbitrarily uniform. The i-th bit of the constellation point is all 0 or 1, m1 ρ The radius of the circle containing the nearest i-th constellation point that is all 0s and 1s. To satisfy:​ （8） （9） in Let be the radii of the ring whose i-th bit is all 0 and 1, respectively. Let be the set of radii of the rings where the i-th bit is all 0 and all 1, respectively. Then the log-likelihood ratio of the i-th bit is: （10 ） When m1 < i When ≤m, find the distance The phase of the most recent i-th constellation point that is all 0s and 1s To satisfy: （ 11 ） （12） in Let i be the phase of the constellation point where the i-th bit is all 0 and all 1 respectively. Let be the set of phases of constellation points where the i-th bit is all 0 and all 1, then the log-likelihood ratio of the i-th bit is: （13） The log-likelihood ratio of all bits is obtained; if the log-likelihood ratio is greater than 0, the bit is 1, otherwise it is 0, thus obtaining the bit stream of the received signal and completing soft demodulation.

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