Calculation method of optimal quantization bit number in ISAC system
Through quantitative noise modeling and detection probability analysis, an inhomogeneous quantization strategy is adopted in the ISAC system to calculate the optimal quantized bit number, solving the contradiction between communication overhead and perception accuracy of quantitative research in the ISAC system, and achieving efficient resource coordination and perception performance improvement.
Patent Information
- Application Number
- CN202510745780.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-05
- Publication Date
- 2025-08-12
AI Technical Summary
In the existing ISAC systems, quantitative research has not fully tapped the optimization potential of multi-bit non-uniform quantization between communication overhead and perceptual performance, resulting in the loss of perceived signal information and the decrease in the probability of object detection, especially in low signal-to-noise ratio scenarios, it is difficult to meet the efficient perception needs of resource-constrained devices.
Through quantitative noise modeling and detection probability analysis, an explicit mapping relationship between quantized bit count and perceived performance is established, and a non-uniform quantization strategy is adopted to optimize the quantization interval, and the optimal detector is calculated in combination with NP criterion to achieve accurate calculation of quantized bit count.
On the premise of ensuring the probability of target detection, the occupancy rate of communication resources for perceived data backhaul is reduced, and an efficient resource coordination solution for the ISAC system in a dynamic network environment is provided, which is suitable for scenarios such as vehicle collaborative perception and industrial environment monitoring.
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Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of communication perception integration, and particularly relates to a method for approximating the optimal number of quantization bits in an ISAC system. Background Art
[0002] In next-generation wireless networks, sensing technology plays a key role in intelligent transportation, smart manufacturing, smart cities, and public safety. Integrated Sensing and Communication (ISAC) is considered a core technology for achieving ubiquitous sensing. Its goal is to simultaneously implement sensing and communication functions on shared wireless resources and hardware. This is because sensing and communication share similarities in hardware architecture, channel characteristics, and signal processing processes, resulting in significant advantages such as reduced hardware costs, improved spectrum utilization, and energy efficiency. In ISAC systems, sensing modes must be deployed to adapt to diverse scenarios. Monostatic sensing uses co-located transmit and receive antennas, but must overcome strong self-interference caused by transmit signal leakage and relies on complex hardware isolation or digital interference cancellation techniques. Bistatic sensing avoids self-interference by separating transmit and receive nodes, but faces challenges such as high-precision synchronization between the transmit and receive ends, dynamic clutter suppression, and node switching during mobile target tracking. Existing research often improves sensing accuracy through multi-receiver data fusion. However, such approaches often assume that the original sensing data can be transmitted losslessly to the central node, ignoring the overhead bottleneck of sensing data transmission. Towards the 6G vision of intelligent connectivity of all things, the receiving end of the perception signal may be a resource-constrained device such as a mobile phone or an in-vehicle terminal, whose computing power, storage space and power consumption are strictly constrained. In addition, different perception use cases have significantly different requirements for data volume: for example, high-precision environmental modeling requires a large amount of perception measurement data, while real-time target detection only requires key feature information. In order to reduce the air interface transmission bandwidth, the receiving end needs to efficiently compress the perception data (such as the channel state information matrix). At the same time, the ISAC system needs to support dynamic resource allocation and flexibly allocate resources between communication and perception tasks, such as improving the quantization accuracy of perception data to improve perception performance when the communication load is low. Therefore, the impact of quantization strategies on perception performance (such as target detection probability and parameter estimation error) urgently needs to be systematically studied.
[0003] Current quantization research in the field of ISAC is still in its early stages. Existing literature mainly focuses on the mechanism by which 1-bit quantization degrades perception performance, and most of the analysis is based on radar waveforms (such as linear frequency modulation signals). However, this type of research has the following limitations: mobile communication systems are dominated by OFDM signals, and their perception signal characteristics are essentially different from radar waveforms, making it difficult to directly migrate existing quantization models. Although 1-bit quantization can maximize the reduction of transmission overhead, its extremely coarse quantization will introduce severe nonlinear distortion, resulting in loss of perception signal information, especially in low signal-to-noise ratio scenarios, which significantly reduces the probability of target detection. Multi-bit non-uniform quantization can achieve a better trade-off between communication overhead and perception performance by optimizing the quantization interval, but its potential has not yet been fully explored. Therefore, to address this problem, the present invention provides a method for calculating the optimal number of quantization bits in the ISAC system. This method provides key technical support for high-energy-efficiency, low-overhead intelligent perception in 6G networks, and is particularly suitable for typical scenarios that are sensitive to real-time and resource efficiency, such as vehicle collaborative perception and industrial environment monitoring. Summary of the Invention
[0004] The core purpose of this invention is to address the contradiction between communication overhead and perception accuracy faced by ISAC systems in perceptual data transmission, and propose a method for calculating the optimal number of quantization bits in ISAC systems. This method establishes an explicit mapping relationship between the number of quantization bits and perception performance through quantization noise modeling and detection probability analysis. This method minimizes the communication resource utilization required for perceptual data return while ensuring key perceptual indicators such as target detection probability, providing a theoretical basis and implementation framework for efficient resource collaboration in ISAC systems in dynamic network environments. Specifically, it includes the following steps:
[0005] S1: UE receives the OFDM signal sent by the base station;
[0006] S2: Calculate the channel estimation matrix, i.e., the perception information matrix;
[0007] S3: Quantize the perception information matrix to obtain a quantization result, and the UE sends the quantized data to the perception information processing center;
[0008] S4: For the non-uniform quantizer, when the input is a signal with Gaussian signal distribution, calculate the characteristic function and probability density function of the output result of the non-uniform quantizer when Δ→0;
[0009] S5: Consider the quantization process as superimposing quantization noise on the input signal and determine the approximate expression of the quantized data;
[0010] S6: After converting the quantized data into the delay-Doppler domain, determine the detection model and the optimal detector.
[0011] S7: Under the assumptions of H1 and H0, calculate the detection probability based on the approximate distribution of the detection statistic;
[0012] S8: Calculate the optimal number of quantization bits.
[0013] As a further optimization, step S1 specifically includes:
[0014] The signal received by the UE is:
[0015]
[0016] Among them, τ and f D is the time delay and Doppler frequency of the path from the transmitter to the receiver through the target, is the OFDM frame signal, is the complex attenuation factor of the corresponding perceived target channel, Δf is the subcarrier spacing, T c represents the OFDM symbol period, f D It represents the Doppler shift. represents clutter plus noise, The mean is 0 and the variance is Complex Gaussian white noise;
[0017] As a further optimization, step S2 specifically includes:
[0018] The perception information matrix is calculated as follows:
[0019]
[0020] in Since the modulation system is normalized to unit power, E{|(F Tx ) l,s | 2}=1,
[0021] As a further optimization, step S3 specifically includes:
[0022] Perception Information Matrix Perform quantization processing to obtain quantized results for:
[0023]
[0024] in Represents uniform quantization of a real number.
[0025] As a further optimization, step S4 specifically includes:
[0026] According to the properties of the uniform quantizer, when the input is a mean μ and a variance σ 2When the signal x is Gaussian, the output is also Gaussian with mean μ and variance σ. 2 +Δ 2 / 12. Non-uniform quantization is achieved by combining uniform quantization with compression and expansion. The encoder first compresses the signal, then uniformly quantizes and encodes it, while the decoder performs uniform quantization and decoding followed by an expansion to restore the original signal. A logarithmic function can approximate the desired compression and expansion characteristics. For example, the μ-law, the international compression standard for speech signals, uses logarithmic compression and expansion, with the following compression and expansion function:
[0027]
[0028] Usually, non-uniform quantization with continuous compression characteristics can be approximated as piecewise uniform quantization. The input range of the quantizer is [-V, V]. [-V, V] is divided into several segments, each of which contains a uniform quantizer with several quantization levels. For example, the compression characteristics of A-law and μ-law can be approximated as 13-fold A-law and 15-fold μ-law. Then we can turn non-uniform quantization into the superposition of multiple uniform quantizations. Based on the properties of uniform quantization, the average power of quantization noise introduced by non-uniform quantization is approximately
[0029]
[0030] Here our non-uniform quantization uses μ-law quantization. According to the analysis, we can get:
[0031]
[0032] where Δ U =V / 2 b-1 , We can regard non-uniform quantization as the linear superposition of multiple uniform quantization segments. When the input is Gaussian distribution, the output after the uniform quantizer is also approximately Gaussian distribution. The linear superposition result of Gaussian distribution is still Gaussian distribution, so we can assume that the output q of the non-uniform quantizer obeys the mean μ and the variance σ 2 +D q Gaussian distribution of .
[0033] Then the probability density function of the non-uniform quantizer output y is obtained:
[0034]
[0035] As a further optimization, step S5 specifically includes:
[0036] A common way to quantize a complex number is to quantize the real and imaginary parts separately through two identical quantizers. Therefore, two identical quantizers are used to quantize the perceptual information matrix The real and imaginary parts of the perception information matrix The real and imaginary parts of are independent Gaussian distributions, in The quantization noise caused by the quantization of the real and imaginary parts is introduced Satisfying zero mean and variance is 2D q Complex Gaussian distribution. Where D q =βΔ 2 / 12, The quantized output Approximately:
[0037]
[0038] in
[0039] As a further optimization, step S6 specifically includes:
[0040] Calculate the quantized output The data converted to the delay-Doppler domain for:
[0041]
[0042] in k is the delay index, k = 1, 2, ..., L, m is the Doppler index, m = 1, 2, ..., S. The target detection task is to determine whether there is a target in the delay-Doppler domain unit (k, m). The detection problem is described as follows:
[0043]
[0044] in, According to the NP criterion, the optimal detector is:
[0045]
[0046] The detection amount α is the detection threshold determined by the false alarm probability P FA =P(T(Y)>α|H0) is determined.
[0047] As a further optimization, step S7 specifically includes:
[0048] The approximate distribution of the test statistic T is calculated as:
[0049]
[0050] in
[0051] The detection threshold under quantization approximation is: α = σall Q -1 (P FA )
[0052] Then the target detection probability is:
[0053]
[0054] Among them A max Perception information matrix The amplitude range of the real and imaginary parts, b is the number of quantization bits.
[0055] As a further optimization, step S8 specifically includes:
[0056] Assume that the target detection probability P that needs to be met in the current scene D ≥P1, so we can get the optimal number of quantization bits as:
[0057]
[0058] The present invention has the following beneficial effects: By combining statistical modeling of quantization noise with analysis of detection probability, an explicit mathematical relationship between the number of quantization bits and target detection probability is established in the ISAC system. This overcomes the limitations of traditional research that relies solely on empirical bit selection and provides a theoretical basis for system-level resource allocation. By adjusting the detection probability threshold, a flexible trade-off between communication overhead and perception accuracy is achieved, providing a unified optimization framework for diverse ISAC application scenarios such as intelligent transportation and industrial monitoring. BRIEF DESCRIPTION OF THE DRAWINGS
[0059] Figure 1 Flowchart of a method for calculating the number of quantization bits required in the ISAC system of the present invention;
[0060] Figure 2 ] is the probability density curve of the non-uniform quantizer output under different bit numbers in the present invention.
[0061] Figure 3 This is the ISAC system model diagram in the present invention;
[0062] Figure 4 This is a curve showing how the detection probability changes with the perceived SNR under different quantization bits in the present invention. DETAILED DESCRIPTION
[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.
[0064] For the convenience of description, we first make the following definitions: * Re{·} represents the real part of a complex number, and Im{·} represents the imaginary part of a complex number.
[0065] The present invention is based on a synaesthesia integrated system; the system includes a base station, a UE, a sensing node, and an environmental scatterer. The base station uses OFDM signals to sense the signal with a delay τ and a Doppler shift f D The user receives the sensing signal reflected by the target. The receiver has N r antennas, and the transmitting end has a single antenna. Each OFDM frame signal at the transmitting end is Each row of the matrix corresponds to the data on a subcarrier, and each column corresponds to the data on an OFDM symbol. We assume that the modulation system is normalized to unit power. The signal we receive is:
[0066]
[0067] in is the complex attenuation factor of the corresponding perceived target channel, Δf is the subcarrier spacing, T c represents the OFDM symbol period, f D It represents the Doppler shift. represents clutter plus noise. Since there are many factors that affect noise, and these factors are independent and randomly distributed, according to the central limit theorem, we can assume that the noise is Gaussian. In addition, we assume that the clutter background is spatially uniform, that is, the scatterers have the same statistical distribution. Since the clutter received by each receiver is the result of a large number of contributions from different clutter scatterers, it is also asymptotically Gaussian. Therefore, we assume The mean is 0 and the variance is Complex Gaussian white noise. We assume that the receiver can perfectly decode and reconstruct the transmitted signal, and its transmitted signal F Tx Negatively impact perception, F Tx Remove and get the perception information matrix:
[0068]
[0069] in Since the modulation system is normalized to unit power, E{|(F Tx ) l,s | 2}=1,
[0070] If the sensing information matrix is not quantized, the sensing data processing center receives the channel response After that, it is transformed into the delay-Doppler domain for target detection. Perform a two-dimensional discrete Fourier transform to obtain the perception information matrix in the delay-Doppler domain, which is expressed as follows:
[0071]
[0072] Since the two-dimensional discrete Fourier transform is a linear transformation, Still obeys the complex Gaussian distribution, the mean remains unchanged, and the variance is σ 2 We consider a specific target detection task, where we find the target in the n-1th target detection task and detect its existence in the nth target detection task. The detection task is to determine whether the target exists in the delay-Doppler domain unit (k, m).
[0073] The detection problem is described as follows:
[0074]
[0075] Assume k = LΔfτ, m = Sf d T c ,but According to the above formula, the corresponding probability density functions under the two assumptions can be written as
[0076]
[0077] The log-likelihood ratio is:
[0078]
[0079] Using the NP criterion, the optimal detector is:
[0080]
[0081] The detection amount, α is the detection threshold determined by the false alarm probability P FA =P(T(Y)>α|H0) is determined,
[0082] In order to enable the receiving end to process the received signal in a more efficient and economical way, it is usually necessary to convert the received perception information matrix The data is transmitted to a unified perception data processing center through a communication loop for signal processing. In order to reduce spectrum overhead, the data needs to be quantized before transmission at the receiving end. In specific implementation, such as Figure 1 As shown, the present invention uses the following steps to calculate the perception data Quantified target detection probability of the ISAC system.
[0083] Step 1: UE receives a signal from the base station;
[0084] The signal received by the UE is:
[0085]
[0086] Among them, τ and f D is the time delay and Doppler frequency of the path from the transmitter to the receiver through the target, is the OFDM frame signal, is the complex attenuation factor of the corresponding perceived target channel, Δf is the subcarrier spacing, T c represents the OFDM symbol period, f D It represents the Doppler shift. represents clutter plus noise, The mean is 0 and the variance is Complex Gaussian white noise;
[0087] Step 2: Calculate the perception information matrix, quantize the perception information matrix, and obtain a quantized result.
[0088] In this step, the perception information matrix is calculated as follows:
[0089]
[0090] in Since the modulation system is normalized to unit power, E{|(F Tx ) l,s | 2}=1,
[0091] Perception Information Matrix Perform quantization processing to obtain quantized results for:
[0092]
[0093] in It means that a real number is uniformly quantized as follows:
[0094]
[0095] where b = 2 q is the number of quantization levels, and q is the number of quantization bits. bis the quantizer threshold. Step 3: When the quantizer input follows a Gaussian distribution with significant "small signal properties," meaning that low-amplitude values are much more likely to occur than high-amplitude values, uniform quantization requires increasing the number of quantization bits to cover a wide dynamic range. However, the low probability of high-amplitude samples in practice leads to redundant allocation of quantization resources, while the dominant low-amplitude region suffers from precision loss due to the fixed quantization interval. Therefore, we use non-uniform quantization, providing more quantization levels in the small-signal range and fewer quantization levels in the large-signal range. This allows for more efficient use of quantization bits and reduces quantization error. Therefore, we now analyze the approximation of the output of non-uniform quantization.
[0096] Typically, non-uniform quantization is achieved by combining uniform quantization with compression and expansion. The encoder first compresses the signal, then uniformly quantizes and encodes it. The decoder then applies a compression and expansion to restore the original signal. A logarithmic function can approximate the desired compression and expansion characteristics. For example, the existing international compression standards for speech signals, A-law and μ-law, use logarithmic compression and expansion. Their compression and expansion functions are:
[0097] μ-law:
[0098]
[0099] Law A:
[0100]
[0101] Typically, non-uniform quantization, whose compression characteristics are continuous, can be approximated as piecewise uniform quantization. The quantizer input range is [-V, V], and [-V, V] is divided into several segments, each containing a uniform quantizer with several quantization levels. For example, the compression characteristics of the A-law and μ-law can be approximated as a 13-fold A-law and a 15-fold μ-law. Therefore, non-uniform quantization can be transformed into the superposition of multiple uniform quantizations. Based on the above analysis of uniform quantization, the average power of the quantization noise introduced by non-uniform quantization is approximately:
[0102]
[0103] K is the number of uniformly quantized segments; P k is the probability that the input signal is in segment k; Δ k is the quantization step size of segment k. For the probability that the input signal is in segment k, we can make the following approximation:
[0104]
[0105] where x k,i is the i-th quantized value in the k-th segment, schematic diagram of non-uniform quantization compression Figure 1 As shown, we can get Δ k ≈Δ / G′(xk,i ), where Δ = 1 / 2 b-1 So formula (3) is approximately:
[0106]
[0107] Using μ-law quantization, the compression and expansion function is:
[0108]
[0109] You can get:
[0110]
[0111] Assuming that the input range V of the quantizer is large enough, the overload noise is ignored, and the data after signal normalization is almost distributed in [-V, V]. Then C1 in the above formula is approximately:
[0112]
[0113] Similarly, C2 is approximately:
[0114]
[0115] Where F(x) = ∫f(x)dx, and C3 is approximately:
[0116]
[0117] Then (18) is approximately:
[0118]
[0119] So we get:
[0120]
[0121] Because V is large enough, then:
[0122]
[0123] where Δ U =V / 2 b-1 , We can regard non-uniform quantization as the linear superposition of multiple uniform quantization segments. When the input is Gaussian distribution, the output after the uniform quantizer is also approximately Gaussian distribution. The linear superposition result of Gaussian distribution is still Gaussian distribution, so we can assume that the output q of the non-uniform quantizer obeys the mean μ and the variance σ 2 +D q Gaussian distribution of .
[0124] Step 4: Determine the quantized output Approximate probability density function.
[0125] A common way to quantize a complex number is to quantize the real and imaginary parts separately through two identical quantizers. Therefore, two identical quantizers are used to quantize the perceptual information matrix The real and imaginary parts of the perception information matrix The real and imaginary parts of are independent Gaussian distributions, in The quantization noise caused by the quantization of the real and imaginary parts is introduced Satisfying zero mean and variance is 2D q Complex Gaussian distribution. Where D q =βΔ 2 / 12, The quantized output Approximately:
[0126]
[0127] in
[0128] Step 5: Convert the quantized perception information matrix to the delay-Doppler domain and determine the detection model.
[0129] Calculate the quantized output The data converted to the delay-Doppler domain for:
[0130]
[0131] in k is the delay index, k = 1, 2, ..., L, and m is the Doppler index, m = 1, 2, ..., S. We consider a specific target detection task, where we discover the target in the n-1th target detection task and detect its existence in the nth target detection task. The detection task is to determine whether the target exists in the delay-Doppler domain unit (k, m).
[0132]
[0133] in, Assume k = LΔfτ, m = Sf d T c ,but According to the NP criterion, the optimal detector is:
[0134]
[0135] The detection amount α is the detection threshold determined by the false alarm probability P FA=P(T(Y)>α|H0) is determined.
[0136] Step 6: Determine the approximate distribution of the detection statistic, obtain the detection threshold under the quantitative approximation, and calculate the approximate target detection probability based on the detection threshold under the quantitative approximation.
[0137] The approximate distribution of the test statistic T is:
[0138]
[0139] in
[0140] The detection threshold under quantization approximation is: α = σ all Q -1 (P FA )
[0141] Then the approximate target detection probability is:
[0142]
[0143] Among them A max Perception information matrix The amplitude range of the real and imaginary parts, assuming that the target detection probability P that needs to be met in the current scene D ≥P1, so we can get the optimal number of quantization bits as:
[0144]
[0145] In the simulation, it is assumed that the transmitter has a single antenna and the receiver has multiple antennas. The specific scenario is as follows: Figure 2 Assume that the carrier frequency is 5 GHz, the subcarrier spacing is 30 kHz, the number of subcarriers is 128, the number of OFDM symbols is 500, the complex attenuation factor of the channel is 1, and the signal transmission power is 1. The sensing delay of the signal from the transmitter to the sensing target to the receiver is 8.3×10 -6 s, the Doppler frequency shift of the perceived target is 1.8×10 3 Hz. The perceptual signal-to-interference-and-noise ratio (SINR) is defined as 6 dB, and the non-uniform quantization coefficient μ is defined as 63.
[0146] Figure 3 The PDF curves of the non-uniform quantizer output under different quantization bit numbers are plotted. The PDF curves of the Gaussian distribution data after μ-law non-uniform quantization and then dequantization are compared with the Gaussian approximate PDF curves of the non-uniform quantizer output derived by us. It can be seen that as the number of quantization bits increases, the probability density distribution of the non-uniform quantizer output approaches the Gaussian approximate distribution. Therefore, we conclude that the assumption of the PDF of the non-uniform quantization output is a valid assumption.
[0147] Figure 4 A graph plots the relationship between detection probability and perceived SNR for different numbers of quantization bits. The graph uses the unquantized detection probability of the optimal detector to measure the detection performance of the quantized ISAC system. The solid line represents the detection probability obtained using quantization approximation, while the dashed line represents the quantized detection probability obtained through 10,000 Monte Carlo simulations. As can be seen from the figure, as the number of quantization bits increases, the quantization interval gradually decreases, and the corresponding curve obtained by Gaussian approximation of the quantized output gradually approaches the curve obtained by direct analysis of the quantized output. When the number of quantization bits is greater than 3, the approximated result is almost identical to the result of direct analysis. Therefore, when the quantization bit number is large enough, the quantized approximate detection probability is almost the same as the true detection probability.
[0148] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation plans of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the scope of protection of the present invention.
Claims
1. A method for calculating the optimal number of quantization bits in an ISAC system, characterized in that: The following steps are involved: S1: The UE receives the OFDM signal sent by the base station and calculates the channel estimation matrix, i.e., the perception information matrix; S2: Perform non-uniform quantization on the perception information matrix to obtain a quantization result. The UE sends the quantized data to the perception information processing center. S3: For the non-uniform quantizer, when the input is a signal with a Gaussian signal distribution, the probability density function of the output result of the non-uniform quantizer when Δ→0 is calculated, and the probability density function of the quantized perceptual information is determined; S4: After converting the quantized data into the delay-Doppler domain, the detection model and the optimal detector are determined; S5: Under the assumptions of H1 and H0, calculate the detection probability based on the approximate distribution of the detection statistic; S6: Calculate the optimal number of quantization bits according to the detection probability.
2. The method for approximating the optimal number of quantization bits in an ISAC system according to claim 1, wherein The calculation process of obtaining the perception information matrix in step S2 includes: Step 1: The signal received by the UE is: Among them, τ and f D is the time delay and Doppler frequency of the path from the transmitter to the receiver through the target, is the OFDM frame signal, is the complex attenuation factor of the corresponding perceived target channel, Δf is the subcarrier spacing, T c represents the OFDM symbol period, f D represents the Doppler shift; represents clutter plus noise, The mean is 0 and the variance is Complex Gaussian white noise; Step 2: The perception information matrix is calculated as follows: in Since the modulation system is normalized to unit power, E{|(F Tx ) l,s | 2 }=1, 3. The method for approximating the optimal number of quantization bits in an ISAC system according to claim 1, wherein In step S3, the probability density function of the quantized perceptual information is determined. The calculation process includes: Step 1: Perception Information Matrix Perform quantization processing to obtain quantized results for: in Indicates uniform quantization of a real number; Step 2: According to the properties of the uniform quantizer, when the input is a mean of η and a variance of σ 2 When the signal x is Gaussian, the output is also Gaussian with mean η and variance σ 2 +Δ 2 / 12; non-uniform quantization is achieved by uniform quantization plus compression and expansion. The encoder first compresses the signal and then uniformly quantizes it, while the decoder performs uniform quantization decoding and then adds an expander to restore the original signal. The logarithmic function can approximately achieve the required compression and expansion characteristics. For example, the existing international compression standard for speech signals, the μ-law, uses logarithmic compression and expansion. The compression and expansion function is: Usually, non-uniform quantization with continuous compression characteristics can be approximated as piecewise uniform quantization. The input range of the quantizer is [-V, V]. [-V, V] is divided into several segments, each of which contains a uniform quantizer with several quantization levels. For example, the compression characteristics of A-law and μ-law can be approximated as 13-fold A-law and 15-fold μ-law. Then, non-uniform quantization can be transformed into the superposition of multiple uniform quantizations. Based on the properties of uniform quantization, the average power of quantization noise introduced by non-uniform quantization is approximately Here our non-uniform quantization uses μ-law quantization. According to the analysis, we can get: where Δ U =V / 2 b-1 , We can regard non-uniform quantization as the linear superposition of multiple uniform quantization segments, so we can assume that the output q of the non-uniform quantizer obeys the mean μ and the variance σ 2 +D q Gaussian distribution; Then the probability density function of the non-uniform quantizer output y is obtained: Step 3: A common way to quantize a complex number is to quantize the real and imaginary parts separately through two identical quantizers; therefore, two identical quantizers are used to quantize the perceptual information matrix The real and imaginary parts of the quantization noise introduced by the quantization of the real and imaginary parts Satisfying zero mean and variance is 2D q Complex Gaussian distribution. Where D q =βΔ 2 / 12, Where V is the perception information matrix The amplitude range of the real and imaginary parts is the quantized output Approximately: in 4. The method for approximating the optimal number of quantization bits in an ISAC system according to claim 1, wherein Step S6, calculation of the number of quantization bits, the calculation process includes: Step 1: Calculate the quantized output The data converted to the delay-Doppler domain for: in k is the delay index, k = 1, 2, ..., L, m is the Doppler index, m = 1, 2, ..., S; the target detection task is to determine whether there is a target in the delay-Doppler domain unit (k, m). The detection problem is described as follows: H0: H1: in, According to the NP criterion, the optimal detector is: The detection amount α is the detection threshold determined by the false alarm probability P FA =P(T(Y)>α|H0)determine; Step 2: Calculate the approximate distribution of the test statistic T as: in The detection threshold under quantization approximation is: α = σ all Q -1 (P FA ) Then the target detection probability is: Among them A max Perception information matrix The amplitude range of the real and imaginary parts, assuming that the target detection probability P that needs to be met in the current scene D ≥P1, so we can get the optimal number of quantization bits as: