A statistical calculation-based method and apparatus for calculating ADC quantization noise power.

Abstract

This invention provides a statistical calculation-based method and apparatus for calculating ADC quantization noise power, comprising: Step 1, obtaining the probability density function of the ADC input signal; Step 2, calculating the probability density function of the ADC output signal using the probability density function of the input signal; Step 3, representing the probability density function using frequency characteristics to obtain the characteristic function of the output signal; Step 4, adjusting the ADC input, and obtaining the probability density function and characteristic function of the quantization noise based on the probability density function and characteristic function of the output signal; Step 5, establishing quantization theorem conditions, determining whether the quantization theorem conditions are satisfied, and if satisfied, then the quantization noise power is q. 2 / 12, otherwise, the variance of the quantization noise is calculated based on the probability density function and characteristic function of the quantization noise, and the power of the quantization noise can be obtained. This invention realizes the calculation of quantization noise under non-full power and non-sinusoidal signal input conditions, thereby assisting in the design of radar and communication receiver acquisition circuits.

Description

Technical Field

[0001] This invention relates to the field of data acquisition circuit design, and in particular to a method and apparatus for calculating ADC quantization noise power based on statistical calculation. Background Technology

[0002] The traditional method for calculating the quantization noise power of the acquisition circuit is to estimate it using the commonly used formula ENOB = 6.02N + 1.761. However, this formula has two drawbacks. First, it only calculates the quantization noise power under full-power input conditions. Second, the calculation results are inaccurate under low-power and low-signal input conditions; for example, in satellite communication, the expected signal power is much lower than the noise signal power. Summary of the Invention

[0003] To address the problems existing in the prior art, a statistical calculation-based method and apparatus for calculating ADC quantization noise power is provided. This method can quickly calculate the quantization noise introduced after passing through the ADC for any target signal with arbitrary input power and input signal waveform.

[0004] The technical solution adopted in this invention is as follows: A method for calculating ADC quantization noise power based on statistical calculation, comprising:

[0005] Step 1: Calculate the probability density function of the input signal based on the ADC input signal;

[0006] Step 2: Calculate the probability density function of the ADC output signal using the probability density function of the input signal;

[0007] Step 3: Based on the frequency domain characteristics of the probability density function, obtain the characteristic function of the output signal;

[0008] Step 4: Adjust the input of the ADC, and obtain the probability density function and characteristic function of the quantization noise based on the probability density function and characteristic function of the output signal;

[0009] Step 5: Establish the quantization theorem conditions and determine whether the quantization theorem conditions are satisfied. If satisfied, the quantization noise power is q. 2 / 12, where q is the unit quantization level; otherwise, the variance of the quantization noise is calculated based on the probability density function and characteristic function of the quantization noise, and the power of the quantization noise can be obtained.

[0010] Furthermore, in step 2, the probability density of the output signal is calculated as follows:

[0011]

[0012] Where x represents the input signal, f x (x) is its probability density function; x′ represents the output signal, fx′ (x) is its probability density function; q represents the unit quantization level, ε represents the quantization noise, and m represents the period of the periodic impulse sequence in the time domain.

[0013] Further, in step 3, the probability density function of the output signal is Fourier-transformed to obtain the characteristic function of the output signal:

[0014]

[0015] where, Φ x′ (u) is the characteristic function of the output signal x′; -∞ < u < +∞, and l is also the period of the periodic impulse sequence in the frequency domain, corresponding to m in the probability density function formula.

[0016] Further, the specific process of step 4 is: set the input as x = mq + ε. At this time, the probability density function of the input x is the same as the probability density function f ε (x) of the quantization noise ε, and thus the probability density function and characteristic function of the quantization noise are obtained, which are respectively:

[0017]

[0018]

[0019] Further, in step 5, the quantization theorem condition is specifically: the characteristic function of the input random variable x satisfies The necessary and sufficient condition for this is that the probability density function of the quantization noise ε satisfies:

[0020] Further, in step 5, the specific method for calculating the variance of the quantization noise according to the probability density function of the quantization noise is:

[0021] D[ε] = E[ε 2 - E 2 [ε]

[0022] where,

[0023] Further, in step 5, the specific method for calculating the variance of the quantization noise according to the characteristic function of the quantization noise is:

[0024]

[0025] Further, it further includes step 6, combining the receiver sensitivity inequality, determining the resolution of the ADC, solving the power requirement of the input signal, and thus determining the channel amplification factor.

[0026] Further, the receiver sensitivity inequality is:

[0027]

[0028] Among them, SNR o Here, H0 represents the receiver sensitivity, and H0 represents the sensitivity threshold. This invention also proposes an apparatus comprising a memory and a processor, wherein the memory stores a computer program that can be loaded and executed by the processor to correspond to the aforementioned statistical calculation-based ADC quantization noise power calculation method.

[0029] Compared with the prior art, the beneficial effects of adopting the above technical solution are as follows: In the design of the acquisition circuit of communication or radar receivers, the method proposed in this invention can effectively solve the two technical problems of difficulty in quantization noise calculation under non-full power and non-sinusoidal signal input conditions, thereby assisting in the design of radar and communication receiver acquisition circuits. Attached Figure Description

[0030] Figure 1 This invention presents a method for calculating ADC quantization noise power.

[0031] Figure 2 This is a schematic diagram of the quantizer signal in one embodiment of the present invention. Detailed Implementation

[0032] The embodiments of this application are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar modules or modules having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application. Rather, the embodiments of this application include all variations, modifications, and equivalents falling within the spirit and scope of the appended claims.

[0033] Example 1

[0034] like Figure 2 As shown, the relationship between the input signal x and the output signal x′ of the ADC (Analog-to-Digital Converter) in the receiver is nonlinear, making direct analysis difficult, as the quantizer is included within the ADC. However, statistical analysis reveals that the input and output of the quantizer are linear, greatly simplifying the analysis. Furthermore, the input signal x and the output signal x′ are essentially two random variables or random processes, allowing analysis of the quantization output and its quantization noise based on the signal probability density function. Therefore, this embodiment proposes a statistical calculation method for calculating ADC quantization noise power, such as... Figure 1 As shown, it includes:

[0035] Step 1: Calculate the probability density function of the input signal based on the ADC input signal;

[0036] Step 2: Calculate the probability density function of the ADC output signal using the probability density function of the input signal;

[0037] Step 3: Use frequency characteristics to represent the probability density function to obtain the characteristic function of the output signal;

[0038] Step 4: Adjust the input of the ADC, and obtain the probability density function and characteristic function of the quantization noise based on the probability density function and characteristic function of the output signal;

[0039] Step 5: Establish the quantization theorem conditions and determine whether the quantization theorem conditions are satisfied. If satisfied, the quantization noise power is q. 2 / 12, if not, then calculate the variance of the quantization noise based on the probability density function and characteristic function of the quantization noise, and the power of the quantization noise can be obtained.

[0040] Specifically, for an input signal x, its probability density function is f x Let f(x) represent the probability density function of the output signal x′. x′ (x) represents the input x, which is a continuous signal, so its probability density function f x (x) is a continuous curve whose integral equals 1. The output signal x′ is discrete, but its probability density function f is still defined using continuous variables. x′ (x), therefore, f x′ (x) represents discrete spectral lines, each of which is a Dirac δ(x) function, not a probability corresponding to the abscissa value. The input-output relationship of the above probability density function can be viewed as an alternative sampling method, called region sampling. Based on the above description, expressing the unit quantization level as q, we can obtain the probability density function f. x′ (x):

[0041]

[0042] In this context, when the receiver system is determined, the number of bits in its internal ADC is fixed, q is a fixed value, q = 1 / (2^bits); at the same time, the input signal x used to calculate the quantization noise of the ADC can be considered as a known quantity, which is a sinusoidal input signal or a Gaussian input signal; m is the period of the periodic impulse sequence in the time domain.

[0043] Just as the time-domain characteristics of a signal can be represented by the frequency-domain characteristics of its Fourier transform, the probability density function characteristics of the input and output signals can also be represented by the corresponding frequency-domain characteristics of the probability density function, i.e., the characteristic function of the random variable. Taking the Fourier transform of the probability density function of the output signal yields the characteristic function of the output signal x′:

[0044]

[0045] Among them, -∞ < u < +∞; the characteristic function and the probability density function are one-to-one, and l is the period of the periodic impulse sequence in the frequency domain, corresponding to m in the probability density function formula.

[0046] Adjust the input to x = mq + ε. At this time, the probability density function f ε (x) of the quantization noise ε is the same as that of the input x. From this, the probability density function and the characteristic function of the quantization noise can be obtained:

[0047]

[0048]

[0049] After obtaining the probability density function and the characteristic function of the quantization noise, the calculation of the quantization noise power can be carried out:

[0050] First, a quantization theorem condition needs to be established:

[0051] The characteristic function of the input random variable x satisfies: The necessary and sufficient condition for n ≠ 0 is that the probability density function of the quantization noise ε satisfies:

[0052] Under the condition of satisfying this quantization theorem, an artificial noise noise that is independent of the input and uniformly distributed can be used to calculate the actual quantization noise. At this time, this noise is called pseudo-quantization noise. The probability density function of this noise is:

[0053]

[0054] In this case, the power of the quantization noise is q 2 / 12. If the probability density function of the input signal can be controlled so that it satisfies the "narrowband" condition, that is, the quantization theorem condition, then the quantization noise can also be directly obtained.

[0055] When the quantization theorem condition is not satisfied, the quantization noise power needs to be calculated. Essentially, it is to calculate the quantization noise variance. In this embodiment, two calculation methods are proposed. One is to calculate through the probability density function, and the other is to calculate through the characteristic function.

[0056] The specific method of calculating through the probability density function is:

[0057] For the probability density function of the quantization noise ε:

[0058]

[0059] Given the given premise (formula (6) is equivalent to formula (3), only the simplified expression is different), we also need to know the probability density function f of the input signal x. x (x), at this point, the variance of the quantization power is:

[0060] D[ε]=E[ε 2 ]-E 2 [ε] (7)

[0061] in,

[0062] The specific method for calculating using the characteristic function is as follows:

[0063] At this point, the quantization noise ε characteristic function is obtained according to formula (4). Then, according to the theorem of solving the variance from the characteristic function, it is clear that when the mean is assumed to be 0, the quantization noise variance is expressed as:

[0064]

[0065] For a quantizer output signal: x′=x+ε, it can be seen that the useful signal output by the ADC is actually the input x, and the ADC output noise is the quantization noise ε. That is to say, the power of the ADC output x′ may be increased relative to the power of the input x, and the increased part is due to the introduction of quantization noise.

[0066] If the receiver sensitivity is only the SNR (Short-Range Frequency), then only the power of the input x and the quantization noise ε needs to be calculated, and the power of x′ does not need to be calculated. The input signal x, since its probability density function is known, can be calculated directly according to the definition. The calculation of the quantization noise power can be divided into two cases: one where the quantization theorem conditions are satisfied, in which case the quantization noise power is q. 2 / 12, another option is to use the probability density function formula or the characteristic function formula for calculation.

[0067] Finally, the ADC resolution (i.e., unit quantization level q) or the ADC input signal power can be calculated using the receiver sensitivity inequality. The receiver sensitivity inequality is:

[0068]

[0069] Where H0 is the sensitivity threshold.

[0070] Specifically, the inequality gives In this case, the input signal power is E[x] 2 The receiver sensitivity requirement is H0, and the quantization noise power E[ε] can then be calculated. 2Then, the unit quantization level q, i.e. the resolution of the ADC, is obtained by solving formula (8).

[0071] When the ADC resolution is known, i.e., the number of bits in the ADC is known, the unit quantization level q can be calculated; based on q, E[ε] can be solved. 2 Then, based on the inequality, the required ADC input signal power is calculated to meet the sensitivity requirements, thereby calculating the amplification factor of the channel module for the antenna received signal. The unit quantization level is thus calculated. Therefore, the calculation method of this invention can realize the calculation of quantization noise under non-full power and non-sinusoidal signal input conditions, assisting in the design of radar and communication receiver acquisition circuits.

[0072] It should be noted that, in the description of the embodiments of the present invention, unless otherwise explicitly specified and limited, the terms "set" and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in the present invention based on the specific circumstances. The accompanying drawings in the embodiments are used to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0073] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A method for calculating ADC quantization noise power based on statistical computation, characterized in that, include: Step 1: Calculate the probability density function of the input signal based on the ADC input signal; Step 2: Calculate the probability density function of the ADC output signal using the probability density function of the input signal; Step 3: Based on the frequency domain characteristics of the probability density function, obtain the characteristic function of the output signal; Step 4: Adjust the input of the ADC, and obtain the probability density function and characteristic function of the quantization noise based on the probability density function and characteristic function of the output signal; Step 5: Establish the quantization theorem conditions and determine whether they are satisfied. If satisfied, the quantization noise power is: ,in, If the quantization level is not specified, then the variance of the quantization noise can be calculated based on the probability density function and characteristic function of the quantization noise to obtain the power of the quantization noise. In step 5, the specific method for calculating the variance of the quantization noise based on the probability density function of the quantization noise is as follows: in, , , Indicates quantization noise. Indicates the input signal. Indicates quantization noise. Indicates the unit quantization level. Represents the probability density function; In step 5, the specific method for calculating the variance of the quantization noise based on the characteristic function of the quantization noise is as follows: ； in, It is the characteristic function.

2. The ADC quantization noise power calculation method based on statistical calculation according to claim 1, characterized in that, In step 2, the probability density of the output signal is calculated as follows: in, Indicates the input signal. Its probability density function; Indicates the output signal. Its probability density function; Indicates the unit quantization level. This represents quantization noise, where m is the period of the periodic impulse sequence in the time domain.

3. The ADC quantization noise power calculation method based on statistical calculation according to claim 2, characterized in that, In step 3, the probability density function of the output signal is subjected to a Fourier transform to obtain the characteristic function of the output signal: in, For output signal The characteristic function; -∞ <u<+∞, The period of a periodic impulse sequence in the frequency domain corresponds to m in the probability density function formula.

4. The ADC quantization noise power calculation method based on statistical calculation according to claim 3, characterized in that, The specific process of step 4 is as follows: Set the input to... At this point, input probability density function and quantization noise probability density function Similarly, the probability density function and characteristic function of the quantization noise are obtained as follows: 。 5. The ADC quantization noise power calculation method based on statistical calculation according to claim 4, characterized in that, In step 5, the quantization theorem condition is specifically: input random variable The characteristic function satisfies The necessary and sufficient condition is quantization noise. The probability density function satisfies: .

6. The ADC quantization noise power calculation method based on statistical calculation according to claim 1, characterized in that, It also includes step 6, which combines the receiver sensitivity inequality to determine the ADC resolution, solve for the power requirement of the input signal, and thus determine the channel amplification factor.

7. The ADC quantization noise power calculation method based on statistical calculation according to claim 6, characterized in that, The receiver sensitivity inequality is: in, For receiver sensitivity, This is the sensitivity threshold.

8. An apparatus, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program that can be loaded by the processor and executed according to any one of claims 1 to 7, corresponding to the ADC quantization noise power calculation method based on statistical calculation.

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