A low-complexity method for blind amplitude estimation of QPSK burst signals

Abstract

A low-complexity QPSK burst signal amplitude blind estimation method is applicable to QPSK burst signals, BPSK burst signals and π / 2‑BPSK burst signals. The estimation method comprises the following steps: determining the number of QPSK symbols used for amplitude estimation, that is, determining the value of L; sequentially inputting the QPSK symbol sequence #imgabs0# that has completed timing synchronization, frequency synchronization and phase synchronization into an amplitude estimator, and iteratively calculating the intermediate parameter p1[L]; calculating the intermediate parameter p2: #imgabs1# calculating the amplitude estimation value #imgabs2# the operator |·| represents the modulus of a complex number. When calculating p1[L], the kth QPSK symbol y[k] is input into the amplitude estimator, and sequentially executing: performing an absolute transformation on the symbol y[k] to obtain y′[k]=|y I [k]|+j|y Q [k]|; calculate the intermediate parameter p1[k], and get p1[k]=p1[k‑1]+y′[k]. This method only needs to perform logical judgment and complex addition operations for each input symbol, which greatly reduces the computational complexity. The asymptotic convergence speed of the normalized mean square error of the estimation result is also significantly faster than that of the NDA‑MLE method.

Description

Technical Field

[0001] The invention relates to the field of communication technology, in particular to a signal amplitude estimation method, and in particular to a low-complexity QPSK burst signal amplitude blind estimation method. Background Art

[0002] In the DVB-RCS2 standard, waveforms 5 to 7 and 15 to 17 are all QPSK burst modulation waveforms that contain both preamble symbol sequences and postamble symbol sequences. Since the number of preamble symbols and postamble symbols in these waveforms is too small, it is difficult to achieve a good estimation effect when using the data-aided maximum likelihood estimation (DA-MLE) method to estimate the amplitude of the above six waveforms.

[0003] In view of this, the applicant has previously proposed a blind amplitude estimation method for QPSK burst signals (hereinafter referred to as NDA-MLE method), with application number 2022114919957. The NDA-MLE method can obtain better estimation results than the data-assisted method when estimating the amplitude of the above six waveforms, but it also has the following two significant problems:

[0004] 1) Since the fourth power of a complex number needs to be calculated for each input symbol, and the fourth root of a real number needs to be calculated in the last step of the algorithm, the computational complexity of the NDA-MLE method is too high;

[0005] 2) As the symbolic signal-to-noise ratio increases, the asymptotic convergence rate of the normalized mean square error of the estimation result of the NDA-MLE method is too slow. Summary of the invention

[0006] Mainly in view of the shortcomings and defects of the above-mentioned related prior art, the present invention provides a low-complexity QPSK burst signal amplitude blind estimation method, which only needs to perform logical judgment and complex addition operations for each input symbol, greatly reducing the computational complexity, and the asymptotic convergence speed of the normalized mean square error of the estimation result is also significantly faster than that of the NDA-MLE method. The method is also applicable to the amplitude estimation of BPSK burst signals and π / 2-BPSK burst signals.

[0007] In order to achieve the above object, the present invention adopts the following technologies:

[0008] A low-complexity blind estimation method for the amplitude of QPSK burst signals is proposed. represents the QPSK symbol sequence used for amplitude estimation, y[k] is the QPSK symbol after timing synchronization, frequency synchronization and phase synchronization, L represents the number of symbols, y[k] = y I [k]+jy Q [k],y I [k] and yQ [k] are the real and imaginary parts of the symbol y[k], respectively. The absolute transformation of the symbol y[k] is defined as y′[k] = |y I [k]|+j|y Q [k]|, where |·| means finding the absolute value of a real number;

[0009] The method comprises the steps of:

[0010] S100, determining a value of the number L of QPSK symbols used for amplitude estimation;

[0011] S200, completing the symbol sequence of timing synchronization, frequency synchronization and phase synchronization The amplitude estimator is input serially in sequence, and the intermediate parameter p1[L] is calculated iteratively at the same time;

[0012] S300, calculate the intermediate parameter p2:

[0013] S400, calculate the amplitude estimate Here, the operator |·| acts on a complex number, which means finding the modulus of the complex number;

[0014] The iterative calculation of the intermediate parameter p1[L] in S200 includes:

[0015] S210, set an iteration counter k, whose counting range is k=1, 2, ..., L;

[0016] S220, initializing parameters, setting the initial value of the iteration counter k to 1, and setting the initial value of the intermediate parameter p1 to 0, that is, setting k = 1, p1[0] = 0;

[0017] S230, input the kth symbol y[k] that has completed timing synchronization, frequency synchronization and phase synchronization into the amplitude estimator, and perform the following two steps of calculation in sequence:

[0018] S231, perform an absolute transformation on the symbol y[k], and obtain y′[k]=|y I [k]|+j|y Q [k]|;

[0019] S232, calculate the intermediate parameter p1[k], and obtain p1[k]=p1[k-1]+y′[k];

[0020] S240, determine whether the L-iterative calculation is completed; if completed, output the calculation result p1[L] of the intermediate parameter; if not completed, update the counter: k←k+1, and repeat S230 and S240 until the L-iterative calculation is completed.

[0021] The beneficial effects of the present invention are:

[0022] Compared with the NDA-MLE method, in the method of the present application, only logical judgment and complex addition operations need to be performed for each input symbol, and the entire algorithm contains at most one complex multiplication and complex modulus operation, and the computational complexity is greatly reduced; and, as the symbol signal-to-noise ratio increases, the asymptotic convergence speed of the normalized mean square error of the estimation result of the method of the present application is also significantly faster than that of the NDA-MLE method. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is an estimated performance evaluation of the method described in the present invention. DETAILED DESCRIPTION

[0024] The embodiment of the present application provides a low-complexity method for blindly estimating the amplitude of a QPSK burst signal. The method is also applicable to the amplitude estimation of a BPSK burst signal and a π / 2-BPSK burst signal.

[0025] The following only takes the QPSK burst signal as an example to illustrate the design process of the present application method:

[0026] At the output of the matched filter of the receiver, the signal is sampled at the symbol rate R to obtain a symbol sequence with the following representation

[0027]

[0028] Where L represents the number of symbols, A is the real amplitude of the symbol sequence,

[0029]

[0030] is the QPSK modulation symbol, j is the imaginary unit, T = 1 / R is the symbol period, τ is the timing deviation of the symbol, represents the phase deviation caused by the frequency offset Δf and the phase noise θ[k], g(t) represents the impulse response of the generalized equivalent baseband transmission channel. For the ideal Nyquist baseband transmission channel,

[0031]

[0032] w[k]=w I [k]+jw Q [k] is complex Gaussian white noise with mean 0 and variance σ 2 The complex Gaussian distribution CN(0,σ 2 ), its actual part I [k] and the imaginary part w Q [k] are independent and have the same Gaussian distribution N(0,σ 2 / 2).

[0033] Because the input symbol has been synchronized with the timing, frequency and phase, the residual timing deviation, frequency deviation and phase deviation can be considered to be close to zero, which can be expressed as

[0034] y[k]≈Aa[k]+w[k] k=1,2,…,L (4)

[0035] From the definition of constellations in formula (2), it is easy to know that:

[0036]

[0037] Let y[k] = y I [k]+jy Q [k], expand a[k] and w[k] in complex expression and substitute them into formula (4), we get

[0038]

[0039] Among them, y I [k]≈Aa I [k]+w I [k] and y Q [k]≈Aa Q [k]+w Q [k] are the real and imaginary parts of y[k], which are independent of each other and each obeys the following Gaussian distribution:

[0040]

[0041] The absolute transformation of y[k] is defined as taking the absolute value of the real and imaginary parts of y[k]. I ′[k]+jy′ Q [k] represents the result of the absolute transformation of y[k],

[0042]

[0043] In formula (8), the operator |·| acts on a real number, indicating that the absolute value of the real number is to be found.

[0044] Next, the real part y of y′[k] I Taking ′[k] as an example, its mathematical characteristics are analyzed.

[0045] First, according to a I [k] and y I The range of values ​​of [k], solving y in four cases I The value of ′[k] is

[0046]

[0047] Taking the mean of both sides of (9), we get

[0048]

[0049] Where E{·} represents the mean of the random variable (also known as the mathematical expectation). From formula (5), we can see that therefore, Substituting into (10) we get

[0050]

[0051] (11) implies a y I Important mathematical characteristics of ′[k]: when When I The mean of ′[k] is a linear function of the amplitude A of y[k].

[0052] Based on this important mathematical feature, a simple and effective amplitude estimation method can be designed. The design process will be described in detail below.

[0053] For y I The sample space of [k] defines the following two opposing events:

[0054]

[0055] From (11), we can get

[0056]

[0057] Similarly, for y Q In the sample space of [k], the following two opposing events can be defined:

[0058]

[0059] From (11), we can get

[0060]

[0061] Combining equation (13) and equation (15), we get

[0062]

[0063] Modulo the left and right sides of (16), we get

[0064]

[0065] Formula (17) shows that when y I [k]∈C I ∩y Q [k]∈C QWhen , the mean value of y′[k] is the amplitude A of y[k]. For the case of a limited number of input symbols as described in equation (4), the following approximate estimate can be obtained according to equation (17):

[0066]

[0067] Taking the mean of both sides of equation (18), we get

[0068]

[0069] From formula (19), we can see that when y I [k]∈C I ∩y Q [k]∈C Q When , (18) is an unbiased estimate of the amplitude A.

[0070] The derivation of the above estimation method is based on y I [k]∈C I ∩y Q [k]∈C Q In practical problems, the value of the input symbol y[k] cannot completely meet the above ideal conditions.

[0071] Next, we will demonstrate the applicability and applicable conditions of the estimation method described in equation (18) in the actual amplitude estimation problem. For the sample space of y[k], define the following two opposing events:

[0072]

[0073] And P(C) and Represents event C and event According to the definition of (20), we can decompose (18) to get

[0074]

[0075] Among them, |C| represents the cardinality of set C (that is, the number of elements in set C), Representing a collection In formula (21), represents the proportion of symbols in event C among all L symbols, Indicates an event The proportion of the symbols in to all L symbols, and and Respectively represent the event C and event The symbol in the form of the estimate of the amplitude A is as follows:

[0076]

[0077]

[0078] By using the method of formula (19), we can know that is an unbiased estimate of the amplitude A, is a biased estimate of the amplitude A. From the law of large numbers, we know that

[0079]

[0080] Therefore, when L is large, it can be approximately considered that

[0081]

[0082] Substituting (25) into (21), we get

[0083]

[0084] Because of y I [k] and y Q [k] are independent of each other, so we have

[0085]

[0086] in,

[0087]

[0088] In formula (28), is the linear value (true value) of the symbol signal-to-noise ratio, and the random variable It obeys the standard normal distribution, that is The same can be said

[0089]

[0090] in, Substituting equations (28) and (29) into equation (27), we obtain

[0091]

[0092] Combining equation (30) and equation (26), we can draw the following conclusions:

[0093] 1) Symbol signal-to-noise ratio The higher the probability P(C) of event C, the greater the probability P(C) of event C. Probability The smaller it is;

[0094] 2) Events Probability The smaller the value, the biased estimation component in (26) The smaller the proportion, the smaller the final estimation result. The smaller the negative impact;

[0095] 3) As the symbol signal-to-noise ratio increases, equation (18) is an asymptotically unbiased estimate of the amplitude A. Therefore, for practical amplitude estimation problems, when the signal-to-noise ratio is high, the estimation method of equation (18) is still applicable.

[0096] Regarding the specific signal-to-noise ratio conditions for applying the amplitude estimation method of formula (18), the following empirical data based on computer simulation are provided for reference: When the symbol signal-to-noise ratio E s When N0>4.5dB, the estimation performance of the method in (18) is better than that of the NDA-MLE method (see Figure 1 ). Under this condition, P(C)>82.23%,

[0097] by represents the QPSK symbol sequence used for amplitude estimation, y[k] is the QPSK symbol after timing synchronization, frequency synchronization and phase synchronization, L represents the number of symbols, y[k] = y I [k]+jy Q [k],y I [k] and y Q [k] are the real and imaginary parts of the symbol y[k], respectively. The absolute transformation of the symbol y[k] is defined as y′[k] = |y I [k]|+j|y Q [k]|, where |·| represents the absolute value of a real number. The steps of the estimation method in this example can be described as follows:

[0098] S100, determining a value of the number L of QPSK symbols used for amplitude estimation;

[0099] S200, completing the symbol sequence of timing synchronization, frequency synchronization and phase synchronization The amplitude estimator is input serially one by one, and the intermediate parameter p1[L] is calculated iteratively at the same time:

[0100] S210, set an iteration counter k, whose counting range is k=1, 2, ..., L;

[0101] S220, initializing parameters, setting the initial value of the iteration counter k to 1, and setting the initial value of the intermediate parameter p1 to 0, that is, setting k = 1, p1[0] = 0;

[0102] S230, input the kth symbol y[k] that has completed timing synchronization, frequency synchronization and phase synchronization into the amplitude estimator, and perform the following two steps of calculation in sequence:

[0103] S231, perform an absolute transformation on the symbol y[k], and obtain y′[k]=|y I [k]|+j|y Q [k]|;

[0104] S232, calculate the intermediate parameter p1[k], and obtain p1[k]=p1[k-1]+y′[k];

[0105] S240, determine whether the L-iterative calculation is completed; if completed, output the calculation result p1[L] of the intermediate parameter; if not completed, update the counter: k←k+1, and repeat S230 and S240 until the L-iterative calculation is completed;

[0106] S300, calculate the intermediate parameter p2:

[0107] S400, calculate the amplitude estimate Here, the operator |·| acts on a complex number, indicating the modulus of the complex number.

[0108] The estimation performance of the method described in this example is evaluated in two aspects:

[0109] 1) First, the estimation method of this example and the NDA-MLE method are applied to the amplitude estimation of the DVB-RCS2 standard No. 5 waveform (both estimation methods use 536 symbols), and then the NDA-MLE method is applied to the amplitude estimation of the DVB-RCS2 standard No. 5 waveform (both estimation methods use 536 symbols). s N0) condition, which method has the smaller normalized mean square error of the estimation result? Figure 1 As shown, when E s When N0>4.5dB, the estimation performance of the method described in this example is consistently better than the estimation performance of the NDA-MLE method.

[0110] 2) Compare the normalized mean square error of the estimation result of the method described in this example with the Cramer-Rao lower bound (CRLB) of the amplitude estimation error. Figure 1 It can be seen that when E s When N0>4.5dB, the normalized mean square error of the estimation result of the method described in this example is at the same order of magnitude as the Cramer-Rao lower bound (CRLB) of the amplitude estimation error, and the difference between the two decreases rapidly as the symbol signal-to-noise ratio increases. s When N0>7dB, the normalized mean square error of the estimation result of the method described in this example has completely approached the Cramer-Rao lower bound.

[0111] The above estimation method is also applicable to the blind amplitude estimation of BPSK burst signal and π / 2-BPSK burst signal.

Claims

1. A low-complexity blind estimation method for the amplitude of QPSK burst signals. represents a QPSK symbol sequence for amplitude estimation, y[k] is a QPSK symbol that has undergone timing synchronization, frequency synchronization, and phase synchronization, and L represents the number of symbols, which is characterized by: y[k]=y I [k]+jy Q [k],y I [k] and y Q [k] are the real and imaginary parts of the symbol y[k], respectively. The absolute transformation of the symbol y[k] is defined as y′[k] = |y I [k]|+j|y Q [k]|, where |·| means finding the absolute value of a real number; y[k] has undergone timing synchronization, frequency synchronization, and phase synchronization. It is assumed that the residual timing deviation, frequency deviation, and phase deviation are approximately zero, which can be expressed approximately as follows: y[k]≈Aa[k]+w[k]k=1,2,…,L where A is the real amplitude of the symbol y[k], w[k] is a complex Gaussian white noise with mean zero, is the QPSK modulation symbol; For y I The sample space of [k] defines the following two opposing events: For y Q The sample space of [k] defines the following two opposing events: When I [k]∈C I ∩y Q [k]∈C Q When , the mean value of y′[k] is the amplitude A of y[k]. For the case where the number of input symbols is limited, the approximate estimate of the amplitude A is as follows: The method comprises the steps of: S100, determining a value of the number L of QPSK symbols used for amplitude estimation; S200, completing the symbol sequence of timing synchronization, frequency synchronization and phase synchronization The amplitude estimator is input serially in sequence, and the intermediate parameter p1[L] is calculated iteratively at the same time; S300, calculate the intermediate parameter p2: S400, calculate the amplitude estimate Here, the operator |·| acts on a complex number, which means finding the modulus of the complex number; The iterative calculation of the intermediate parameter p1[L] in S200 includes: S210, set an iteration counter k, whose counting range is k=1, 2, ..., L; S220, initializing parameters, setting the initial value of the iteration counter k to 1, and setting the initial value of the intermediate parameter p1 to 0, that is, setting k = 1, p1[0] = 0; S230, input the kth symbol y[k] that has completed timing synchronization, frequency synchronization and phase synchronization into the amplitude estimator, and perform the following two steps of calculation in sequence: S231, perform an absolute transformation on the symbol y[k], and obtain y′[k]=|y I [k]|+j|y Q [k]|; S232, calculate the intermediate parameter p1[k], and obtain p1[k]=p1[k-1]+y′[k]; S240, determine whether the L-iterative calculation is completed; if completed, output the calculation result p1[L] of the intermediate parameter; if not completed, update the counter: k←k+1, and repeat S230 and S240 until the L-iterative calculation is completed.

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