A large dynamic range line spectrum estimation method based on analog sampling

Abstract

The present invention belongs to the field of radio signal processing technology, and specifically relates to an infinite amplitude line spectrum estimation method based on robust compressed sensing and analog sampling ADC analog sampling when the amplitude of the signal arriving at the front end of the receiver exceeds the dynamic range of the ordinary ADC input. The analog sampling ADC analog sampling mode of the present invention and the proposed line spectrum estimation method utilize the robust compressed sensing theory to realize infinite line spectrum estimation when the amplitude of the signal arriving at the front end of the receiver is higher than the dynamic range of the ordinary ADC input, accurately estimate the amplitude of the signal and its carrier frequency information, and can overcome the problem of weak signal loss caused by direct sampling and quantization using an ordinary ADC. Experiments show that the present invention successfully estimates the amplitude and carrier frequency of multiple source signals when the input signal amplitude is higher than the ADC input dynamic range, thereby achieving reliable weak signal estimation performance at a low quantization level.

Description

Technical Field

[0001] The present invention relates to the technical field of radio signal processing, and in particular to a large dynamic range line spectrum estimation method based on an analog sampling analog-to-digital conversion device. Background Art

[0002] The line spectrum estimation problem is an important problem in the fields of radar / sonar, wireless communications, etc., and is widely used in scenarios such as angle of arrival estimation, azimuth and distance measurement, beamforming, channel estimation, and acoustic signal processing. Specifically, line spectrum estimation refers to the problem of obtaining the parameters of a mixed complex exponential signal (including the number of complex exponential functions and the frequency and amplitude of each complex exponential function) using a finite number of noise-contaminated samples collected by an analog-to-digital converter (ADC). Traditional methods for solving the line spectrum estimation problem include the Prony algorithm, the MUSIC algorithm, and the ESPRIT algorithm. In addition, with the development of compressed sensing theory and technology in recent years, the line spectrum estimation problem can be converted into a sparse signal recovery problem and solved within the framework of compressed sensing.

[0003] In practical applications, the limited range of ADC devices is a bottleneck for achieving high-precision, high-resolution line spectrum estimation, especially in scenarios where complex exponential signals with large amplitude differences exist within a mixed complex exponential signal. Once the amplitude of the signal to be sampled input to the ADC exceeds the ADC's range, the sampled signal output by the ADC becomes severely distorted due to saturation nonlinearity, resulting in a decrease in the estimation accuracy or even failure of the aforementioned line spectrum estimation method. To prevent ADC saturation, the signal to be sampled often passes through an automatic gain control (AGC) module before being sampled by the ADC. The AGC module proportionally scales the various components of the mixed complex exponential signal. Therefore, when the amplitudes of the different components differ significantly, that is, when both strong and weak signals exist, the weak signal is often scaled down by the same proportion to match the strong signal with the ADC's range. This is then submerged in the ADC's quantization noise, resulting in an inability to effectively detect weak signals. Summary of the Invention

[0004] In response to the deficiencies in the prior art, the present invention provides a large dynamic range line spectrum estimation method based on an analog sampling analog-to-digital converter, which is used to solve the technical problem mentioned in the background art that ordinary ADC devices have limited dynamic range and cannot effectively detect weak signals.

[0005] The above technical objectives of the present invention are achieved through the following technical solutions:

[0006] When the signal amplitude reaching the receiver front end exceeds the input dynamic range of a common ADC, an infinite-amplitude line spectrum estimation method based on robust compressed sensing and analog sampling is proposed. The threshold of the analog sampling ADC in the system is λ, and the number of signal sources to be identified is K. The method includes the following steps:

[0007] S1: The signal that needs to be input into the ADC for sampling is expressed as

[0008]

[0009] Where m represents the sampling index, ΔT represents the sampling time interval, ω k ∈[0,2π) and α k Represent the frequency and complex amplitude of the corresponding signal respectively. In the actual sampling system, due to the limited input dynamic range of ordinary ADC, the input signal beyond this range will be clipped during sampling, resulting in serious information loss; the analog sampling ADC with a threshold of λ folds the input signal into the interval [-λ, λ], so the signal z after the analog sampling ADC sampling m Expressed as

[0010] z m =U λ (y m )+v m

[0011] where v m The mean is 0 and the variance is σ 2 Gaussian white noise, U λ It is a complex modulo operation defined as

[0012]

[0013] in It means taking the fractional part of a, so U λ (a)∈[-λ,λ], that is, U λ (y m )∈[−λ,λ];

[0014] S2: Discretize the continuous frequency parameter space into a finite set of P grid points, and (P □ K); define as well as The sampling result of the analog sampling ADC can be expressed as follows

[0015] z=U λ (y)+v

[0016] =U λ (Aα)+v

[0017] Where α is a vector with sparsity K; for the vector form z, the method of obtaining the sparse vector α from it can be described as the following problem

[0018] min||α||0

[0019] st||zU λ (Aα)||2≤ε

[0020] Where ||·||0 represents the l0 norm, i.e., the number of non-zero values, and ε is the error factor specified according to the actual situation;

[0021] S3: Definition is a first-order difference matrix, and its specific form is as follows

[0022]

[0023] Through the differential matrix, the first-order difference of the analog sampling ADC sampling result z is defined for

[0024]

[0025] S4: Definition Design and determine sampling intervals Sampling the signal input to the analog sampling ADC can ensure that the first-order differential signal output by the analog sampling ADC has the same sparse representation as the first-order differential signal of the ADC input signal. s is an unknown sparse outlier vector; then the above formula It can be further expressed as

[0026]

[0027] in

[0028] S5: According to the above definition, for the vector form of z, from its first-order differential signal The method of obtaining the sparse vector α can be further described as the following problem

[0029]

[0030] Therefore, by using the analog sampling ADC and designing a suitable sampling interval, the original non-convex problem is transformed into a convex problem, and the sparse vector can be obtained by using a robust compressed sensing method. definition The set of non-zero indexes is N={n1,…,n K |n k ∈[1, P]}, then according to the defined discrete frequency grid set, the carrier frequency can be estimated using the set N

[0031] The beneficial effects of the present invention are as follows: the line spectrum estimation method without amplitude limitation of the present invention has strong practicality, and the above steps realize line spectrum estimation when the amplitude of the signal to be sampled exceeds the input dynamic range of the ordinary ADC, and weak signals can be effectively detected. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Illustration of the original signal, the sampling of the analog sampling ADC and the sampling of the ordinary ADC;

[0033] Figure 2 Graph showing the signal when the sampling interval is 0.05 seconds and the analog sampling ADC threshold is λ = 0.5;

[0034] Figure 3 Graph showing the NMSE versus SNR curve of α estimated using the line spectrum estimation method of the present invention, with sampling intervals of ΔT = 0.004s, 0.014s, and 0.024s, respectively;

[0035] Figure 4 The success rate of the line spectrum estimation method of the present invention and the line spectrum estimation of ordinary ADC sampling is a function curve of the number of quantization bits when the energy gap between strong and weak signals reaches 60dB. DETAILED DESCRIPTION

[0036] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0037] Example:

[0038] Reference Figures 1 to 4 The present invention is a method for estimating line spectrum with a large dynamic range based on analog-to-digital converters (ADCs). This method is primarily used to solve the problem of line spectrum estimation when the amplitude of the signal to be sampled exceeds the input dynamic range of a typical ADC using analog-to-digital converters (ADCs) and robust compressed sensing theory. The threshold of the analog-to-digital converter in the system is λ, the number of signal sources to be identified is K, and the signal to be sampled by the ADC is represented by Where m represents the sampling index, ΔT represents the sampling time interval, ω k ∈[0,2π) and α k Represent the frequency and complex amplitude of the corresponding signal respectively. In the actual sampling system, due to the limited input dynamic range of ordinary ADC, the input signal beyond this range will be clipped during sampling, resulting in serious information loss. Using the analog sampling ADC with a threshold of λ to fold the input signal into the interval [-λ, λ], the signal z after the analog sampling ADC sampling m Expressed as

[0039] z m =Uλ (y m )+v m

[0040] where v m The mean is 0 and the variance is σ 2 Gaussian white noise, U λ It is a complex modulo operation defined as

[0041]

[0042] in It means taking the fractional part of a, so U λ (a)∈[-λ,λ], that is, U λ (y m )∈[−λ,λ];

[0043] Based on the robust compressed sensing theory, the continuous frequency parameter space is discretized into a finite set of P grid points, and (P=K), and it is assumed that the frequency to be estimated is located in the defined grid points; by defining as well as The sampling result of the analog sampling ADC can be expressed as follows

[0044] z=U λ (y)+v

[0045] =U λ (Aα)+v

[0046] Where α is a vector with sparsity K; for the vector form z, the method of obtaining the sparse vector α from it can be described as the following problem

[0047] min||α||0

[0048] st||zU λ (Aα)||2≤ε

[0049] Among them, ||·||0 represents the l0 norm, that is, the number of non-zero values, and ε is the error factor specified according to the actual situation; obviously, here due to the modulo operation U λ It is a nonlinear operation, so the constraint of this problem is non-convex. Next, we will use the characteristics of the analog sampling ADC and the input signal characteristics to design its sampling interval and consider converting this non-convex constraint into a convex constraint.

[0050] definition is a first-order difference matrix, and its specific form is as follows

[0051]

[0052] Through the differential matrix, the first-order difference of the analog sampling ADC sampling result z is defined for

[0053]

[0054] definition Design and determine sampling intervals Sampling the signal input to the analog sampling ADC can ensure that the first-order differential signal output by the analog sampling ADC has the same sparse representation as the first-order differential signal of the ADC input signal. s is an unknown sparse outlier vector; then the above formula It can be further expressed as

[0055]

[0056] in Obviously, from the above first-order differential signal The recovered sparse vector α depends on Most of the observations are non-outliers, that is, s is extremely sparse, which means that It is still a sparse representation of α; at the same time, the sparsity of s depends on the sampling rate. Therefore, by designing a suitable sampling interval ΔT, the first-order differential signal of the analog sampling ADC sampling output and the first-order differential signal of the ADC input signal can have the above mathematical relationship;

[0057] Through the above analysis, for the vector form of z, from its first-order differential signal The method of obtaining the sparse vector α can be further described as the following problem

[0058]

[0059] And the l0 norm constraint target is convexly approximated as the l1 norm, then the problem is transformed into

[0060]

[0061] Therefore, by using the analog sampling ADC and designing a suitable sampling interval, the original non-convex problem is transformed into a convex problem, and the sparse vector can be obtained by using a robust compressed sensing method. definition The set of non-zero indexes is N={n1,…,n K |n k ∈[1, P]}, then according to the defined discrete frequency grid set, the carrier frequency can be estimated using the set N

[0062] In the simulation, we first consider the signal y(t) = 4sin(πt / 6) - 2sin(πt / 3) + 2sin(2πt-0.2t), and set the sampling interval ΔT = 0.05s; Figure 1 As shown in the figure, the clipping result of the ordinary ADC sampling the signal beyond its dynamic range will cause serious information loss.

[0063] like Figure 2 As shown, the difference between the first-order differential signal of the analog sampling ADC sampling output and the first-order differential signal of the ADC input signal is a sparse outlier vector;

[0064] like Figure 3 As shown in Figure 2, the simulation considers the mixture of three sinusoidal signals with amplitudes and frequencies of |α1|=10, |α2|=3.1, |α3|=0.5, ω1=0.4π, ω2=1.0π, ω3=1.8π, so ω=1.8π and The initial phase of the signal is randomly generated from (0, 2π]; the signal-to-noise ratio is defined as the ratio of the average power of the signal to the average power of the noise, that is, SNR = E(||z|| 2 ) / E(||v|| 2 ), the analog sampling ADC threshold is λ=1, and the normalized mean square error is defined as α and They represent the real sparse vector and the estimated sparse vector respectively, the number of sampling points M = 400, and the sampling intervals are ΔT = 0.004s, 0.014s, and 0.024s respectively. It can be seen that the invented line spectrum estimation method can achieve reliable estimation performance at low SNR under different sampling intervals.

[0065] like Figure 4 As shown in the figure, this simulation considers a mixture of two strong and weak sinusoidal signals with an energy gap of 60dB, whose amplitudes and frequencies are |α1|=1000, |α2|=1, ω1=0.2π, and ω2=1.8π, respectively. We set the input dynamic range threshold of the analog sampling ADC and the ordinary ADC to 10, the sampling interval to ΔT=0.01s, and the number of sampling points M=400. We see that when the sample is quantized using 11 bits, the analog sampling ADC can achieve a success rate of 1. In contrast, the ordinary ADC requires 15 quantization bits to achieve a good success rate in detecting weak signals. It can be seen that the invented line spectrum estimation method can achieve reliable weak signal estimation performance at a low quantization level in the case of a mixture of strong and weak signals with a high energy gap.

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for estimating line spectrum with a large dynamic range based on an analog-to-digital conversion device using analog sampling, characterized in that: The threshold of the analog sampling ADC in the system is λ, and the number of signal sources that need to be identified is K; S1: Input ADC for sampling. The signal that needs to be input ADC for sampling is expressed as Where m represents the sampling index, ΔT represents the sampling time interval, ω k ∈[0,2π) and α k Represent the frequency and complex amplitude of the corresponding signal respectively. The analog sampling ADC with a threshold of λ folds the input signal into the interval [-λ,λ]. Then the signal z after the analog sampling ADC is sampled m Expressed as z m =U λ (y m )+v m Among them, v m The mean is 0 and the variance is σ 2 Gaussian white noise, U λ Is a complex modulo operation defined as in, It means taking the fractional part of a, so U λ (a)∈[-λ,λ], that is, U λ (y m )∈[-λ,λ]; S2: Discretize the continuous frequency parameter space into a finite set of P grid points, and define as well as The sampling result of the analog sampling ADC is expressed as z=U λ (y)+v =U λ (Aα)+v Among them, α is a vector with sparsity K; for the vector form z, the method of obtaining the sparse vector α from it is described as the following problem min||α||0 s.t.||z-U λ (Aα)||2≤ε Among them, ||·||0 represents the l0 norm, that is, the number of non-zero values, and ε is the error factor specified according to the actual situation; S3: Define D M 1 is a first-order difference matrix, and its specific form is as follows Define the first-order difference of the self-resetting ADC sampling result z through the differential matrix for S4: Definition Design and determine sampling intervals To sample the signal of the input analog sampling ADC, s is an unknown sparse outlier vector; then the above formula Further expressed as in, S5: According to the above definition, for the vector form of z, from its first-order differential signal The method of obtaining the sparse vector α is further described as the following problem min||α||1 Therefore, by using the analog sampling ADC and designing a suitable sampling interval, the original non-convex problem is transformed into a convex problem, and the sparse vector can be obtained by using a robust compressed sensing method. definition The set of non-zero indexes is N={n1,…,n K |n k ∈[1,P]}, then according to the defined discrete frequency grid set, the carrier frequency is estimated using the set N

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