Orthogonal time-frequency air conditioning-based flux-inductance integrated waveform design method

Abstract

The invention belongs to the technical field of mobile communication, and particularly relates to an orthogonal time-frequency air conditioning-based integrated waveform design method, which comprises the following steps of: constructing a receiving and transmitting filter bank with a frequency spectrum shaping characteristic on a time domain level, converting an item with a complex analytic expression in a traditional architecture into a scaling factor capable of being linearly processed, and carrying out linear processing on the scaling factor; architectural simplification of a sensing signal processing flow is realized; on a delay Doppler domain level, aiming at an inter-Doppler interference mechanism caused by static environment clutter coupling and a fractional Doppler effect, a pilot frequency sequence matrix with a strong self-correlation main lobe and a weak cross-correlation side lobe is innovatively constructed, and accurate separation of aliasing echoes is realized by using a sharp delay-Doppler resolution characteristic of the pilot frequency sequence matrix. According to the scheme, through the cross-domain cooperation mechanism, on the premise of maintaining the communication sensing dual-mode performance, double breakthrough of signal processing architecture simplification and pilot frequency overhead optimization is achieved, and an innovative design framework is provided for a communication sensing integrated system in a mobile scene.

Description

Technical Field

[0001] The present invention belongs to the technical field of mobile communications, and specifically relates to a communication and sensing integrated waveform design method based on orthogonal time-frequency and space modulation. Background Art

[0002] With the rapid growth of diverse application requirements, future wireless networks will not only improve the performance of communication services but also further expand the support capabilities for more application services. For example, emerging applications such as autonomous driving and extended reality have put forward higher requirements for the network, including highly reliable wireless connections, high-speed data transmission, and high-precision sensing capabilities. To address these challenges, sensing technologies represented by radar have shown great development potential, promoting the continuous development of integrated sensing and communication (ISAC).

[0003] To achieve high-precision sensing in a communication network, the reasonable design of the ISAC waveform becomes the key. The integrated waveform using multiplexing technology is one of the current mainstream solutions, mainly including four mechanisms: time-division multiplexing, frequency-division multiplexing, space-division multiplexing, and code-division multiplexing. By orthogonally allocating time-frequency-space-code domain resources to transmit the ISAC waveform, the dual functions can be realized while reducing interference between each other. However, this multiplexing technology fails to fully share the communication and sensing functions within the same resource domain. Usually, achieving both functions simultaneously often requires some compromise between communication performance and sensing accuracy. In addition, under the multiplexing mechanism, the receiving end needs to effectively separate the multiplexed waveform, and the separation quality directly affects the recovery of communication information and the extraction of sensing information, so it has an important impact on the overall system performance.

[0004] To further improve resource utilization and integration efficiency, integrated design based on a sharing mechanism has attracted wide attention. There are mainly three ways to achieve this goal: one is based on communication signals, with communication as the center for radar target detection, that is, directly using communication signals as integrated signals; the second is based on radar signals, with perception as the center, modulating communication information onto signal parameters (including waveforms, beams, and code patterns, etc.), so that it has both communication and perception functions; the third is to get rid of the dependence on existing waveforms, comprehensively consider various indicators and multi-domain characteristics, and design an integrated waveform suitable for integrated sensing and communication (ISAC). Considering compatibility with existing communication networks, the integrated waveform based on orthogonal frequency division multiplexing (OFDM) has become the research focus. As a common multi-carrier waveform in digital communication, OFDM has the advantages of large throughput, high spectral efficiency, strong anti-multipath effect, and flexible sub-carrier modulation. However, since the OFDM waveform does not have the key characteristics required for sensing, its performance in sensing is significantly limited. In addition, in high-speed mobile scenarios, OFDM signals are difficult to effectively eliminate inter-carrier interference (ICI) and inter-symbol interference (ISI) introduced by the channel, resulting in a sharp decline in performance.

[0005] In recent years, some research has proposed a new modulation method based on orthogonal time-frequency-space modulation (OTFS). By transmitting signals in the time-delay - Doppler (time-delay Doppler DD) domain, the time-varying channel is converted into a quasi-static channel, thereby compensating for the dispersion effect of the channel and enhancing the anti-interference ability, effectively solving the ICI and ISI problems in the time-varying channel. Although orthogonal time-frequency-space modulation (OTFS) shows great application potential in the field of integrated sensing and communication (ISAC), most research assumes the use of an ideal bi-orthogonal pulse shaping filter during application to reduce interference in the time-delay Doppler DD domain. Although this assumption helps to simplify algorithm design, this filter violates the Heisenberg uncertainty principle and actually cannot exist. Therefore, the present invention proposes a realizable transmit-receive filter design to solve this key problem in the application of orthogonal time-frequency-space modulation (OTFS). Summary of the Invention

[0006] The object of the present invention is to provide a method for designing an integrated sensing and communication waveform based on orthogonal time-frequency-space modulation, which has the advantages of simple implementation, low overhead, and adaptability to complex mobile environments, showing broad prospects in future integrated sensing and communication (ISAC) applications.

[0007] The technical solutions adopted by the present invention are specifically as follows:

[0008] A method for designing an integrated sensing and communication waveform based on orthogonal time-frequency-space modulation, comprising the following steps:

[0009] Step 1: Signal modeling stage:

[0010] Under the orthogonal time-frequency space modulation OTFS processing framework, the echo signal in the time-delay Doppler domain under a time-varying channel is derived, and the influence of transceiver filters on the echo signal is analyzed;

[0011] Step 2: Transceiver filter design:

[0012] Based on the received signal, a mathematical model of the optimal receiving filter is constructed, slack variables are introduced to simplify the problem-solving process, and the ADMM framework is used to iteratively update each variable to obtain the optimal receiving filter;

[0013] Step 3: Time-delay Doppler domain pattern design:

[0014] Considering the extension of the inter-carrier Doppler interference IDI and the characteristics of the received signal, the influence of the channel along the time-delay axis is the same, while the influence of the filter on the Doppler axis is different; Therefore, the pilot is expanded along the time-delay axis, and multiple different pilot sequences are arranged on the Doppler axis; Through the orthogonal characteristics of the pilot sequence, the inter-carrier Doppler interference IDI can be effectively reduced, thus simplifying the design of the estimation algorithm; In addition, in order to design a pilot sequence with excellent autocorrelation characteristics and flexibly use the DFT definition to achieve the association between correlation and weighted integral sidelobe ratio, the optimal pilot sequence is obtained;

[0015] Step 4: Integrated sensing and communication ISAC waveform output and solution:

[0016] Through the designed pilot sequence, time-delay Doppler pattern, and pulse shaping filter, the integrated sensing and communication ISAC signal to be transmitted is directly generated through the process of orthogonal time-frequency space modulation OTFS. At the receiving end, the received time-delay Doppler DD domain echo signal can be simplified through the designed receiving filter.

[0017] In the said Step 1, the echo signal in the time-delay Doppler domain under a time-varying channel is derived using the orthogonal time-frequency space modulation OTFS processing framework;

[0018] The base station generates a time-frequency domain signal through the processing process of orthogonal time-frequency space modulation OTFS:

[0019]

[0020] where x i [k, l] is the time-delay Doppler DD domain data of the i-th user, and N and M respectively represent the number of time slots and sub-carriers; Through the Heisenberg transform, the generated time-domain signal is:

[0021]

[0022] where g tx (t) is the pulse shaping filter; Using the beamforming matrix F, the transmitted multi-dimensional signal is:

[0023]

[0024] where \(s(t)=[s_1(t),s_2(t),\cdots,s I (t)] T is the signal transmitted to \(I\) users; in a time-varying channel, the received echo is:

[0025]

[0026] where is additive white Gaussian noise, is the time-delay Doppler (DD) domain channel, expressed as:

[0027]

[0028] where are the reflection coefficient, round-trip delay, and Doppler, respectively; and are the integer parts of the normalized delay and Doppler, is the fractional part of the normalized Doppler; using the Wiener transform and SFFT, the received echo in the DD domain is derived as:

[0029]

[0030] where is the number of symbols extended by the inter-carrier Doppler interference (IDI), \(G tx (f)\) and \(G rx (f)\) are the spectra of the transmit and receive filters; it can be seen that the transceiver filters do not change the positioning performance of the DD domain pulses, but only add additional amplitude and phase shifts.

[0031] In step 2, the transmit filter is fixed as a rectangular filter. To simplify the DD domain echo and combine the \(\Delta m\) terms, \(G\) needs to be made to vary with a period of \(\Delta f\); for this purpose, \(G\) is discretized and written in matrix form:

[0032] G = F 2NM g

[0033] where \(g = \text{diag}(g tx )\Pi 2Nl \Lambda (k+q,2Nl) g rx \), \(\Pi\) is a \(2NM\times2NM\) cyclic shift matrix, \(g tx = 1 2NM \), is a variable, \(\Lambda (k+q,2Nl) is a diagonal matrix, denoted as:

[0034]

[0035] To make G show periodic changes and minimize the errors of corresponding elements in different periods, that is, it is modeled as:

[0036]

[0037] To solve the above problem, first introduce slack variables and transform the above problem into:

[0038]

[0039] To simplify the problem, adopt the ADMM framework and construct the augmented Lagrangian function as:

[0040]

[0041] Through the idea of alternating optimization, obtain the update formulas of each variable in the (d + 1)-th iteration:

[0042]

[0043]

[0044] where

[0045]

[0046] where and Through the above update formulas, iteratively update each variable until convergence to obtain the receiving filter g rx .

[0047] In step 3, according to the designed transceiver filters, simplify the time-delay Doppler (DD) domain received signal to:

[0048]

[0049] where:

[0050]

[0051] The number of conforming quantities affected by the inter-path Doppler interference (IDI) is approximately the same. Considering the influence of the maximum time delay and Doppler, design the time-delay Doppler (DD) domain pattern; two pure pilot sequences of length D' are placed along the time-delay axis for parameter estimation of the user-side NLoS and the sensing receiver, and data × pilot blocks of a certain length are respectively located on the upper and lower sides of the pure pilot sequences, with widths of 2k max +1, k max +N q and 2(k max +N q); The data of these data × pilot blocks are the same along the time delay axis to ensure the correlation performance of the pilot sequence, and different along the Doppler axis to improve communication efficiency; On both sides of the pure pilot sequence, there are (l max -1) × (2k max +3(k max +N q +1)) guard intervals to prevent interference of pure data under different channel time delays; And in other remaining positions, it can be used to transmit data; The pattern designed by the present invention allows the sensing receiver to perform sensing only with the pilot part. Therefore, there is no need to reserve a guard interval at the data position, significantly improving communication efficiency;

[0052] To ensure the sensing accuracy, it is required that the pilot sequence has strong autocorrelation and low cross-correlation; In addition, in the designed pattern, since only the correlation characteristics under partial time delays are concerned, the weighted integrated sidelobe ratio (WISL) is used as the optimization target, that is, to design the optimal pilot sequence to minimize WISL:

[0053]

[0054] Among them

[0055]

[0056] Among them, P rr (k t ) is the non-periodic autocorrelation coefficient, and P rj (k t ) is the non-periodic cross-correlation coefficient, and are the weights at time delay k t , and φ r (d) is the phase of the sequence element p r (d); Using the idea of coordinate descent, the pilot sequence elements are iteratively solved; Taking the d-th element p r (d) of the r-th sequence as an example, P rr (k t ) and P rj (k t ) can be rewritten as

[0057]

[0058] Among them and

[0059]

[0060] Among them, R A (·) and R B(·) is the indicator function of A = {1, 2,..., N} and B = {-1, -2,...,-N + 1}, that is, if k t ∈A, R A (k t ) = 1, otherwise 0; let and where z represents r or j, it can be found that:

[0061]

[0062] Therefore, through DFT, directly calculate WISL, let and vector represent the sum of squares of each column of U z , then the optimal p r (d) satisfies where Iteratively optimize all elements of all pilot sequences until WISL converges, then pilot sequences with strong autocorrelation characteristics and low cross-correlation characteristics can be obtained.

[0063] In step 4, through the designed pilot sequence and delay-Doppler DD pattern, using a rectangular pulse as the pulse shaping filter, directly output the integrated communication and sensing ISAC signal. At the receiving end, use the designed receiving filter to simplify the representation form of the echo in the delay-Doppler DD domain, so as to use a simple and easy-to-implement estimation algorithm to sense the positions and speeds of each user, and identify clutter according to the zero-Doppler characteristic of clutter, so that it can be directly removed in subsequent sensing tasks.

[0064] The technical effects achieved by the present invention are:

[0065] The present invention proposes a practical integrated communication and sensing ISAC waveform design method applicable to clutter environments, multi-users (targets), and multipath scenarios. Considering the Doppler interferences (IDI) caused by channel fractional Doppler, the proposed method includes two parts: transceiver filter design and delay-Doppler domain pattern design; transceiver filter design mainly models the echo signal and performs time-frequency domain conversion, and under the rectangular pulse shaping filter, solves the optimal receiving filter by the alternating direction method of multipliers (ADMM); delay-Doppler domain pattern design focuses on analyzing the influence of the Doppler interferences (IDI) of the signal, and reasonably configures the positions of data, pilots, and guard intervals to ensure the balance between communication efficiency and sensing accuracy. In addition, the excellent autocorrelation characteristics of the pilot sequence are the key to achieving high-precision sensing. Through the discrete Fourier transform (DFT), the optimal pilot sequence can be quickly obtained. Description of the Drawings

[0066] Figure 1It is a schematic diagram of the communication and sensing integrated system of the present invention;

[0067] Figure 2 It is a schematic diagram of the orthogonal time-frequency and space modulation OTFS signal processing adopted by the present invention;

[0068] Figure 3 It is a symbol number performance graph for verifying the influence of the inter-carrier Doppler interference IDI of the present invention;

[0069] Figure 4 It is a schematic diagram of the delay-Doppler DD domain pattern designed by the present invention;

[0070] Figure 5 It is a schematic diagram of the spectrum convolution result of the transceiver filter designed by the present invention;

[0071] Figure 6 It is a normalized integrated sidelobe performance graph of the pilot designed by the present invention under different sequence lengths;

[0072] Figure 7 It is an autocorrelation and cross-correlation performance graph of the pilot designed by the present invention under different time delays. Specific embodiments

[0073] In order to make the purpose and advantages of the present invention clearer, the present invention will be specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific implementation manners of the present invention, and does not strictly limit the specific protection scope claimed by the present invention.

[0074] As Figures 1-7 shown, a communication and sensing integrated waveform design method based on orthogonal time-frequency and space modulation,

[0075] The present invention is applicable to complex mobile scenarios with multipath and multi-user clutter, such as Figure 1 shown. The base station equipped with root antennas transmits orthogonal time-frequency and space modulation OTFS-communication and sensing integrated ISAC signals to communicate with multiple single-antenna users and sense their positions. Due to the presence of buildings and trees in the environment, the transmitted signals reach the users through the direct path (LoS) and the non-direct path (NLoS) simultaneously. At this time, the sensing receiver located at the base station can receive the echo from the LoS, as well as the static clutter reflected by the buildings and trees. In this scenario, the waveform designed by the present invention can simplify the traditional estimation algorithm and achieve high-precision sensing.

[0076] The communication and sensing integrated ISAC waveform design process includes the following steps:

[0077] Step 1: Signal modeling stage:

[0078] Under the orthogonal time-frequency space modulation OTFS processing framework, the echo signal in the time-delay Doppler domain under a time-varying channel is derived, and the influence of transceiver filters on the echo signal is analyzed;

[0079] Step 2: Transceiver filter design:

[0080] According to the received signal, a mathematical model of the optimal receiving filter is constructed, slack variables are introduced to simplify the problem-solving process, and the ADMM framework is used to iteratively update each variable to obtain the optimal receiving filter;

[0081] Step 3: Time-delay Doppler domain pattern design:

[0082] Considering the spread of the inter-carrier Doppler interference IDI and the characteristics of the received signal, the influence of the channel along the time-delay axis is the same, while the influence of the filter on the Doppler axis is different; Therefore, the pilot is expanded along the time-delay axis, and multiple different pilot sequences are arranged on the Doppler axis; Through the orthogonality of the pilot sequences, the inter-carrier Doppler interference IDI can be effectively reduced, thus simplifying the design of the estimation algorithm; In addition, in order to design a pilot sequence with excellent autocorrelation characteristics and flexibly use the DFT definition to achieve the association between the correlation and the weighted integral sidelobe ratio, the optimal pilot sequence is obtained;

[0083] Step 4: Integrated sensing and communication ISAC waveform output and solution:

[0084] Through the designed pilot sequence, time-delay Doppler pattern, and pulse shaping filter, the integrated sensing and communication ISAC signal to be transmitted is directly generated through the process of orthogonal time-frequency space modulation OTFS. At the receiving end, the received time-delay Doppler DD domain echo signal can be simplified through the designed receiving filter.

[0085] In the present invention, considering the inter-carrier Doppler interference IDI caused by fractional Doppler of the channel, the proposed method includes two parts: transceiver filter and time-delay Doppler domain pattern design; The transceiver filter design mainly models the echo signal and performs time-frequency domain conversion, and under the rectangular pulse shaping filter, the optimal receiving filter is solved by the alternating direction method of multipliers (ADMM); The time-delay Doppler domain pattern design focuses on analyzing the influence of the inter-carrier Doppler interference IDI of the signal, and reasonably configuring the positions of data, pilots, and guard intervals to ensure the balance between communication efficiency and sensing accuracy. In addition, the excellent autocorrelation characteristics of the pilot sequence are the key to achieving high-precision sensing. Through the discrete Fourier transform (DFT), the optimal pilot sequence can be quickly obtained.

[0086] In step 1, the echo signal in the time-delay Doppler domain under a time-varying channel is derived using the orthogonal time-frequency space modulation OTFS processing framework;

[0087] In Figure 1In the scenario where the base station processes Orthogonal Time Frequency Space Modulation (OTFS) Figure 2 ), a time-frequency domain signal is generated:

[0088]

[0089] where x i [k, l] is the delay-Doppler (DD) domain data of the i-th user, and N and M represent the number of time slots and subcarriers respectively; through the Heisenberg transform, the generated time-domain signal is:

[0090]

[0091] where g tx (t) is the pulse shaping filter; using the beamforming matrix F, the transmitted multi-dimensional signal is:

[0092]

[0093] where s(t) = [s1(t), s2(t),..., s I (t)] T is the signal transmitted to I users; in a time-varying channel, the received echo is:

[0094]

[0095] where is the additive white Gaussian noise, is the delay-Doppler (DD) domain channel, expressed as:

[0096]

[0097] where are the reflection coefficient, round-trip delay, and Doppler respectively; and are the integer parts of the normalized delay and Doppler, is the fractional part of the normalized Doppler; using the Wiener transform and SFFT, the delay-Doppler (DD) domain received echo is derived as:

[0098]

[0099] where is the number of symbols extended by the Inter-Doppler Interference (IDI), G tx (f) and G rx (f) are the spectra of the transmit and receive filters; it can be seen that the transceiver filters do not change the localization performance of the delay-Doppler (DD) domain pulses, but only add additional amplitude and phase shifts.

[0100] In step 2, the fixed transmit filter is a rectangular filter. To simplify the time-delay Doppler (DD) domain echo and combine the Δm terms, G needs to vary with a period of Δf. For this purpose, G is discretized and written in matrix form as follows:

[0101] G = F 2NM g

[0102] where g = diag(g tx )Π 2Nl Λ (k+q,2Nl) g rx , Π is a 2NM×2NM cyclic shift matrix, g tx = 1 2NM , is a variable, and Λ (k+q,2Nl) is a diagonal matrix, denoted as:

[0103]

[0104] To make G show periodic variation and minimize the error of each element corresponding to different periods, it is modeled as:

[0105]

[0106] To solve the above problem, first introduce slack variables and transform the above problem into:

[0107]

[0108] To simplify the problem, use the ADMM framework to construct the augmented Lagrangian function as:

[0109]

[0110] Through the idea of alternating optimization, the update formulas for each variable in the (d + 1)-th iteration are obtained:

[0111]

[0112] where

[0113]

[0114] where and Through the above update formulas, each variable is iteratively updated until convergence to obtain the receive filter g rx .

[0115] In step 3, according to the designed transceiver filters, the time-delay Doppler (DD) domain received signal is simplified to:

[0116]

[0117] Wherein:

[0118]

[0119] According to Figure 3 the results, it can be obtained that the number of conformances affected by the inter-path Doppler interference IDI is approximately the same. Considering the influence of the maximum delay and Doppler, the designed delay-Doppler DD domain pattern is as shown in Figure 4 ; two pure pilot sequences with a length of D' are placed along the delay axis for parameter estimation of the NLoS at the user side and the sensing receiver, and data×pilot blocks with a certain length are respectively arranged on the upper and lower sides of the pure pilot sequences. The widths from top to bottom are 2k max +1, k max +N q and 2(k max +N q ); the data of these data×pilot blocks are the same along the delay axis to ensure the correlation performance of the pilot sequence, and different along the Doppler axis to improve the communication efficiency; on both sides of the pure pilot sequence, there are (l max -1)×(2k max +3(k max +N q +1)) guard intervals to prevent interference of pure data under different channel delays; and in other remaining positions, it can be used to transmit data; the pattern designed by the present invention allows the sensing receiver to perform sensing only with the pilot part. Therefore, there is no need to reserve a guard interval at the data position, significantly improving the communication efficiency;

[0120] To ensure the sensing accuracy, it is required that the pilot sequence has strong autocorrelation and low cross-correlation; in addition, in the designed pattern, since only the correlation characteristics at some delays are concerned, the weighted integrated sidelobe ratio (WISL) is used as the optimization objective, that is, to design the optimal pilot sequence to minimize the WISL:

[0121]

[0122] Wherein

[0123]

[0124] where P rr (k t ) is the non-periodic autocorrelation coefficient, P rj (k t ) is the non-periodic cross-correlation coefficient, and are the weights at the delay k t , and φ r (d) is the sequence element p r(d) Phase; Adopting the idea of coordinate descent, iteratively solve the pilot sequence elements; Taking the d-th element p of the r-th sequence as an example, P r (d) is taken as an example, P rr (k t ) and P rj (k t ) can be rewritten as

[0125]

[0126] where and

[0127]

[0128] where R A (·) and R B (·) are the indicator functions of A = {1, 2,..., N} and B = {-1, -2,...,-N + 1}, that is, if k t ∈A, R A (k t ) = 1, otherwise it is 0; Let and where z represents r or j, it can be found that:

[0129]

[0130] Therefore, through DFT, directly calculate WISL, let and the vector represents the sum of the squares of each column of U z , then the optimal p r (d) satisfies where Iteratively optimize all elements of all pilot sequences until WISL converges, then pilot sequences with strong autocorrelation characteristics and low cross-correlation characteristics can be obtained.

[0131] In step 4, through the designed pilot sequence and time-delay Doppler DD pattern, using a rectangular pulse as the pulse shaping filter, directly output the integrated communication and sensing ISAC signal. At the receiving end, use the designed receiving filter to simplify the representation form of the echo in the time-delay Doppler DD domain, so as to sense the positions and speeds of each user by using a simple and easy-to-implement estimation algorithm, and identify the clutter according to the zero Doppler characteristic of the clutter, so that it can be directly removed in the subsequent sensing tasks.

[0132] In the present invention, the algorithm process:

[0133] The algorithm for designing the synesthesia-integrated ISAC waveform first executes the signal modeling step in Step 1; then sequentially executes the steps in Step 2 and Step 3. Finally, the algorithm outputs the synesthesia-integrated ISAC transmitted signal and the received time-delay Doppler DD-domain echo according to Step 4. The steps of the algorithm are summarized in Table 1.

[0134]

[0135] Table 1 Synesthesia-integrated ISAC waveform design method based on orthogonal time-frequency space modulation OTFS.

[0136] In practical applications of the present invention, for example:

[0137] For a synesthesia-integrated ISAC system, the center frequency is set to 3 GHz, the bandwidth is 7.68 MHz, the subcarrier spacing is 15 KHz, there are 128 time slots, the maximum normalized time delay and Doppler are set to 4 and 3, and according to Figure 3 the result, the number of symbols affected by the inter-carrier Doppler interference IDI is set to 5. The present invention obtains the performance of the designed filter and the designed pilot through computer simulation.

[0138] Figure 5 Shows the result of the frequency convolution G of the designed receiver filter and the transmitter filter. It can be seen that the receiver filter designed by the proposed algorithm ensures the periodicity of G, making G approximately the same at any Doppler, thus being independent of the summation of Δm. While ensuring the pulse resolution in the time-delay Doppler DD domain, it simplifies the design of the subsequent sensing algorithm of the receiver.

[0139] Figure 6 Shows the normalized integrated sidelobe levels of the designed pilots at different lengths. Among them, Multi-CAN is the code that can reach the Welch bound, We-CAN is the weighted code of Multi-CAN of interest, W-Pro is the code designed according to WISL, and I-Pro is the code designed according to ISL. It can be seen that when L = 64 for the designed I-Pro pilot, the performance is close to that of Multi-CAN, and the performance difference between W-Pro and We-CAN is less than 1 dB, indicating that the proposed method can approach the Welch bound and is better than random codes. And by changing the discrete phase L, it can be observed that when L becomes smaller, the performance of the code will slightly decrease, and the performance difference is less than 0.5 dB, indicating that the proposed method is not sensitive to L and has universality.

[0140] Figure 7The auto-correlation and cross-correlation levels of the above several codes are given. It can be seen that in the region of interest, the auto-correlation and cross-correlation performances of W-Pro and We-CAN are more superior, although the normalized integrated sidelobe levels of W-Pro and We-CAN are higher than those of I-Pro and Multi-CAN. Since the designed delay-Doppler (DD) pattern guarantees the delay range of the code, when the code length is limited, the proposed code design method is still effective.

[0141] The above simulation results verify the effectiveness of the waveform and code design methods proposed in the present invention, as well as the feasibility of short codes under the designed delay-Doppler (DD) pattern, thereby further improving the communication efficiency on the premise of ensuring the sensing accuracy. This indicates that the proposed scheme has broad prospects in future integrated sensing and communication (ISAC) applications.

[0142] It should be noted that in the present invention, OTFS is the English abbreviation of Orthogonal Time Frequency Space modulation in Chinese, ISAC is the English abbreviation of integrated sensing and communication, IDI is the English abbreviation of Inter-Doppler Interference, and DD is the English abbreviation of delay-Doppler.

[0143] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. The structures, devices, and operation methods not specifically described and explained in the present invention are implemented according to the conventional means in the art without special description and limitation.

Claims

1. A synaesthesia integrated waveform design method based on orthogonal time-frequency-space modulation, characterized by: The following steps are involved: Step 1: Signal modeling phase: In the framework of orthogonal time-frequency modulation (OTFS), the delay-Doppler domain echo signal in the time-varying channel is derived, and the influence of the transceiver filter on the echo signal is analyzed. Step 2: Transceiver filter design: According to the received signal, a mathematical model of the optimal receiving filter is constructed, slack variables are introduced to simplify the problem-solving process, and each variable is iteratively updated using the ADMM framework to obtain the optimal receiving filter; Step 3: Delay-Doppler domain pattern design: The pilot is spread out along the delay axis, and multiple different pilot sequences are arranged on the Doppler axis. The DFT definition is used to achieve the association between the correlation and the weighted integrated sidelobe ratio, so as to obtain the optimal pilot sequence; Step 4: Synaesthesia integrated ISAC waveform output and solution: Through the designed pilot sequence, delay Doppler pattern, pulse shaping filter and the process of orthogonal time-frequency space modulation (OTFS), the transmitted synaesthesia integrated ISAC signal is directly generated. At the receiving end, the received delay Doppler DD domain echo signal can be simplified through the designed receiving filter.

2. The synaesthesia integrated waveform design method based on orthogonal time-frequency-space modulation according to claim 1 is characterized in that: In the step 1, the delay Doppler domain echo signal under the time-varying channel is derived using the orthogonal time-frequency space modulation (OTFS) processing framework; The base station generates time-frequency domain signals through the orthogonal time-frequency space modulation OTFS processing flow: where x i [k, l] is the delay-Doppler DD domain data of the i-th user, N and M represent the number of time slots and subcarriers respectively; through the Heisenberg transform, the generated time domain signal is: where g tx (t) is a pulse-shaped filter; using the beamforming matrix F, the transmitted multidimensional signal is: where s(t)=[s1(t),s2(t),...,s I (t)] T is the signal transmitted to I users; under the time-varying channel, the received echo is: in is additive white Gaussian noise, is the delay-Doppler DD domain channel, expressed as: in are reflection coefficient, round-trip delay and Doppler respectively; and is the integer part of the normalized delay and Doppler, is the normalized Doppler fractional part; using Vinagre change and SFFT, the echo received in the delay Doppler DD domain is deduced as: in is the number of symbols spread by inter-Doppler interference IDI, G tx (f) and G rx (f) is the spectrum of the transmit and receive filters; it can be seen that the transceiver filters do not change the positioning performance of the delay Doppler DD domain pulse, but only add additional amplitude and phase shift.

3. The synaesthesia integrated waveform design method based on orthogonal time-frequency-space modulation according to claim 2 is characterized in that: In step 2, the fixed transmit filter is a rectangular filter. In order to simplify the delay Doppler DD domain echo and merge the Δm term, it is necessary to make G change with a period of Δf. For this purpose, G is discretized and written in the form of a matrix: G=F 2NM g Where g = diag (g tx )Π 2Nl Λ (k+q,2Nl) g rx , Π is a 2NM×2NM cyclic shift matrix, g tx =1 2NM , is a variable, Λ (k+q,2Nl) Is a diagonal matrix, denoted as: In order to make G present periodic changes, the errors of the corresponding elements in different periods are minimized, that is, the model is: s.t.G p =D p g rx p=(lN+k)(2N q +1)+q l=0,...,l max ,k=0,...,N-1,q=-N q ,...,N q To solve the above problem, we first introduce slack variables and convert the above problem into: G p =D p g rx p=(lN+k)(2N q +1)+q l=0,...,l max ,k=0,...,N-1,q=-N q ,...,N q To simplify the problem, the ADMM framework is used to construct the augmented Lagrangian function: Through the idea of ​​alternating optimization, the update formula of each variable in the d+1th iteration is obtained: in in and Through the above update formula, each variable is iteratively updated until convergence, and the receiving filter g is obtained rx .

4. The synaesthesia integrated waveform design method based on orthogonal time-frequency-space modulation according to claim 3 is characterized in that: In step 3, according to the designed transceiver filter, the delay Doppler DD domain received signal is simplified to: in: The number of coincidences affected by the Doppler inter-interference IDI of each path is approximately the same. Considering the influence of the maximum delay and Doppler, the delay-Doppler DD domain pattern is designed; two pure pilot sequences of length D' are placed along the delay axis for parameter estimation of the NLoS and perception receiver on the user side, and there are data × pilot blocks of a certain length on the upper and lower sides of the pure pilot sequence, and the width from top to bottom is 2k max +1, k max +N q and 2(k max +N q ); these data × pilot block data are the same along the delay axis to ensure the correlation performance of the pilot sequence, and different along the Doppler axis to improve communication efficiency; on both sides of the pure pilot sequence, there are (l max -1)×(2k max +3(k max +N q +1)) to prevent interference of pure data under different channel delays; the remaining positions can be used to transmit data; In the designed pattern, the weighted integrated sidelobe ratio (WISL) is used as the optimization target, that is, the optimal pilot sequence is designed to minimize the WISL: in Among them, P rr (k t ) is the non-periodic autocorrelation coefficient, P rj (k t ) is the non-periodic mutual correlation coefficient, and is the delay k t The weight under r (d) is the sequence element p r (d); adopt the coordinate descent idea to iteratively solve the pilot sequence elements; take the dth element pr(d) of the rth sequence as an example, P rr (k t ) and P rj (k t ) can be rewritten as in as well as Where R A (·) and R B (·) is the indicator function of A = {1, 2, ..., N} and B = {-1, -2, ..., -N+1}, that is, if k t ∈A,R A (k t )=1, otherwise 0; and Where z represents r or j, we can find that: Therefore, we can directly calculate WISL by DFT, and vector Indicates U z The sum of squares of each column, then the optimal p r (d) Satisfaction in All elements of all pilot sequences are iteratively optimized until WISL converges, and pilot sequences with strong autocorrelation characteristics and low cross-correlation characteristics can be obtained.

5. The synaesthesia integrated waveform design method based on orthogonal time-frequency-space modulation according to claim 4 is characterized in that: In the step 4, a rectangular pulse is used as a pulse shaping filter through the designed pilot sequence and delay Doppler DD pattern to directly output the ISAC signal of interaesthesia integration. At the receiving end, the designed receiving filter is used to simplify the expression of the echo in the delay Doppler DD domain, so as to perceive the position and speed of each user by using a simple and easy-to-implement estimation algorithm, and identify the clutter according to the zero Doppler characteristics of the clutter, so that it can be directly removed in the subsequent perception task.

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