Method for integrated sensing and communication waveforms based on superimposed symbols

Abstract

An integrated design method for integrated sensing and communication (ISAC) based on superimposed symbols, which enables the linear superposition of communication signals and sensing signals within the same time-frequency resource block in the symbol domain using a power allocation method by generating and transmitting integrated waveforms of superimposed pilots and data, realizing the increase of environmental sensing without loss of communication performance; comprising: transmitting communication perception in the form of superimposed symbols integrated signals, joint design of environmental parameter extraction and communication data detection based on received signals. Compared with the RIS-assisted communication system without sensing function, various embodiments of the present disclosure can obtain accurate environmental sensing accuracy without additional hardware equipment, and at the same time, it can achieve close to the original communication system's spectral efficiency.

Description

METHOD FOR INTEGRATED SENSING AND COMMUNICATION WAVEFORMS BASED ON SUPERIMPOSED SYMBOLSCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to Chinese Patent Application No. CN202311089194.2, filed August 28, 2023, and to Chinese Patent Application No. CN202311151350.3, filed September 7, 2023, which are both hereby incorporated by reference in their entireties.FIELD OF INVENTION

[0002] The present disclosure relates to the field of wireless communication technology, particularly to a method for integrated communication and sensing design based on superimposed symbols.BACKGROUND

[0003] To support emerging applications that require both low-latency sensing and high- rate communication, the next generation of wireless networks proposes integrated communication and sensing technology to simultaneously realize wireless sensing and communication using the same wireless signals and hardware infrastructure. In communication systems, the millimeter-wave band with large bandwidth has been proven to achieve high-rate communication to meet the needs of real-time massive data transmission. Meanwhile, millimeter-wave radar has been extensively used in existing sensing systems to provide precise sensing information. Due to the excellent performance of millimeter-wave bands in both communication and sensing systems, the application of millimeter-wave signals in integrated communication and sensing systems is considered to have great potential and has been a research hotspot in both academia and industry in recent years.

[0004] However, millimeter-wave signals can lead to significant propagation losses, often blocking the line-of-sight (LoS) path between the receiver and the transmitter, which hinders the reliable connection service of the integrated communication and sensing system. A reconfigurable intelligent surface (RIS) can create a virtual LoS path betweenthe base station and the user by digitally controlling the phase shift of the reflective elements, making it an effective solution for stable connections in integrated communication and sensing systems at millimeter-wave frequencies. Specifically, RIS is a fully passive two-dimensional array consisting of many sub -wavelength controllable elements that can flexibly alter the physical properties of incident electromagnetic waves by adjusting the phase. Moreover, RIS is generally manufactured using inexpensive hardware components without RF links, significantly reducing hardware costs and energy consumption. Extensive research has demonstrated the significant improvement in communication and sensing performance provided by RIS-assisted integrated communication and sensing systems.

[0005] In the design of RIS-assisted integrated communication and sensing systems at millimeter-wave frequencies, a practical and efficient approach is to combine existing communication modulation methods, protocol architectures, and hardware infrastructure with sensing signal processing technologies to simultaneously achieve communication and sensing functions. This approach allows for environmental sensing during data transmission, avoiding the additional hardware costs of deploying a separate sensing network. In existing technologies, the realization of sensing functions often involves allocating some additional time or frequency resources, enabling the sensing pilot to utilize these independent resources for sensing functions. As a result, some methods have been developed to study the trade-off between the performance of communication signals and sensing pilots in time and frequency resources. However, there are some limitations: the sensing pilot consumes additional time or frequency resources, which can reduce the spectral efficiency of the original communication system. Furthermore, simultaneously achieving communication and sensing functions in RIS-assisted systems requires significant computational resources, depending on channel state information, which may be difficult to obtain accurately and timely in high-speed mobile scenarios such as vehicular networks, thus compromising the accuracy of communication and sensing.

[0006] Based on the above issues, to improve the performance of RIS-assisted communication and sensing and to enhance the spectral efficiency of integrated communication and sensing systems, the present disclosure proposes a design method for integrated communication and sensing waveforms based on superimposed symbols to simultaneously achieve communication and environmental sensing functions.SUMMARY

[0007] The present disclosure addresses the problem of poor accuracy and low spectral efficiency in RIS-assisted integrated communication and sensing systems, where communication signals and sensing signals occupy independent time or frequency resources. By transmitting an integrated communication and sensing waveform based on superimposed communication symbols and pilot symbols, communication and sensing signals are linearly superimposed in the symbol domain using power allocation coefficients. Additionally, a new signal processing method at the receiver based on the received symbols is proposed, increasing the accuracy of the sensing function without significantly compromising communication performance.

[0008] The present disclosure solves the technical problem with a specific technical solution: a design method for integrated communication and sensing waveforms based on superimposed symbols that can be applied in RIS-assisted millimeter-wave integrated communication and sensing scenarios.

[0009] The method provided by the present disclosure processes the symbols received at the receiving end, realizing joint communication data detection and environmental sensing parameter extraction, while simultaneously achieving high-speed communication rates and high-precision sensing functions. In practical applications, the integrated communication and sensing waveform based on superimposed symbols generated by the present disclosure can support various modulation methods and parameter settings in existing wireless communication systems to achieve an efficient uplink communication and sensing link.

[0010] The present disclosure proposes a method for simultaneously realizing communication and sensing functions on the uplink communication link from a user to a base station assisted by RIS. The method includes the following steps: at the signal transmission end, communication signals and pilot signals within the same timefrequency resource block are linearly superimposed in the symbol domain using a power allocation coefficient and transmitted to the RIS; at the signal reception end, the signals reflected by the RIS are received, and the received signals over multiple time slots are stacked to obtain the reception matrix; the extraction of environmental angle parameters is converted into the estimation of angle grid values and sparse vectors. The received signal is substituted into a preset millimeter-wave channel model, the reception matrix isvectorized, and an initial estimate of the sparse vector is obtained using the least squares estimation with Tikhonov regularization. The initial estimate of the equivalent channel between the base station and the user is derived from the estimated sparse vector.

[0011] Based on the initial estimate of the equivalent channel, the initial estimate of the communication data is obtained using the linear minimum mean square error method, followed by demodulation and re-modulation. The initial estimate of the communication data after re-modulation is iteratively computed under the expectation-maximization framework to obtain the final estimates of the sparse vector, angle grid, and communication data. Finally, the communication data, angle parameters in the environmental channel, and user coordinates are recovered. Further, the transmitting end generates and transmits the superimposed symbols:where xd tand xp tare the communication symbols and pilot symbols generated in the t-th time slot, respectively, and is the power coefficient assigned to the communication symbols, satisfying 0 < ^ < 1.

[0012] Further, the received signal is stacked over multiple time slots to construct a reception matrix. Specifically, in the t-th time slot, the base station receives the symbols:where Hr sis the channel from the s-th RIS to the base station (BS), 0s tis the phase of the s-th RIS at the t-th time slot, hb sis the channel from the user equipment (UE) to the s-th RIS, and ntis the noise at the t-th time slot. The reception matrix is constructed by stacking the BS received symbols of the time slots as:where 0 = [0S;1, 0s T], X = diag(x1, ... , xT'), and N = [n1(... , nT].

[0013] Further, the RIS consists of controllable reflective units that construct a virtual line-of-sight (LoS) path between the base station and the user, with the number of RIS units S > 1. The millimeter- wave channel modeling between the base station and the s-th RIS is given by:where ai srepresents the complex gain consisting of path loss for the 1-th path. The array responses can be expressed as aM(u)an(j bNs(u, v) =angles of arrival(AoAs) and effective azimuth angles of departure (AoDs) as

[0014] Further, the extraction of environmental angle parameters is transformed into the estimation of angle grid values (jd, (p) and sparse vectors m, specifically by representing the millimeter-wave angle domain uB2B sbUB2B,SI and vB2B siand converting the millimeter-wave channel into:is the dictionary matrix of the array response with respect to the angular domain grid points WR2B,S5WR2B,S,and §R2B S '’s a sParse matrix, and the positions of the non-zero elements in the matrix correspond to the positions of the elements selected from the grid points.

[0015] Further, the angle domain grid points WR2B,S>wR2B,s,equivalent arrival / departure angles for the Lspaths in Hr s, where the first path corresponds to the LoS path, and the effective arrival / departure angles corresponding to the LoS path can be determined by the relative positions of the BS and the RIS. Hence, the first elements wR2B,s,wR2B,s,ar|d SB2B Sequivalent arrival / departure angles corresponding to the LoS path, and the rest of the elements are quantized for the angle domain uniformly in equal parts of Gr— 1, G2— 1 and G3— 1, respectively.

[0016] Further, the initial estimate of the sparse vector a> is obtained using the least squares estimation with a Tikhonov regularization term, specifically as:where Xpis the pilot matrix and Q denotes the data uncertainty, where

[0017] Further, the initial estimate of the communication data is specifically:where Nois the noise variance, Pois the user transmit power, is the equivalentchannel initial estimate obtained by affine transformation between the base station and the user.

[0018] Further, the re-modulated communication data initial estimate is iteratively computed under the expectation maximization (EM) framework to obtain the final estimates of the sparse vector, angle grid, and communication data, specifically as follows. First, the system sets the prior distribution of the sparse vectorwherethe corresponding variance of a>g. It can be observed that when yj1tends to zero, a>galso tends to zero, so the estimate of a> can be translated into the estimate of y. Next the EM iterative update is used to calculate the parameter dataset / = [Xd, y, v, / 3] and the parameter set as v = whereP is modeled to handle the uncertainty of unknownnoise variance in practice. Next, the system obtains the maximum posterior estimation of and takes the angle values corresponding to the L-largest elements ofas the estimated grid, where Lsis the number of paths in the channel between the base station and the s-th RIS.

[0019] The system then set the elements inbelow a preset threshold to zero and obtains a more accurateusing the least square error (LSE) method. The equivalent channel estimation between the base station and the user is recovered by affine transformation. Then, the system subtracts the received part corresponding to the sensing pilot from the reception matrix Y using the EM step to obtain the communication dataestimate. Iterations are performed followed by j <- j + 1 until j = jmaxor a difference betweenless than 6X.

[0020] Further, to promote the sparse structure ofthe prior is modeled to satisfy a Gamma distribution:where setting ayby-> 0 to meet spikes at zero.

[0021] Through the above steps, the efficiency and accuracy of the integrated communication and sensing in the RIS-assisted system can be effectively enhanced to realize the communication efficiency and sensing accuracy enhancement of the communication and sensing integrated waveform based on superimposed symbols.

[0022] The present disclosure provides a new waveform design scheme in the RIS- assisted communication and sensing integrated system. By superimposing the communication signals and sensing pilots in the symbol domain through power allocation, this method can add sensing functions on top of the existing communication functions. Moreover, the present disclosure employs efficient signal processing methods to achieve high-precision sensing while maintaining a transmission rate close to that of the original communication system. The existing communication protocols and hardware require minimal modification, allowing the sensing function to be added to the original communication system flexibly and at a low cost.

[0023] The present disclosure comprehensively considers both communication and sensing performance, linearly superimposing communication symbols and pilot symbols in the same symbol domain according to the power allocation coefficient. This not only enables the estimation of environmental parameters but also ensures that communication capabilities are not compromised, truly realizing the integration of communication and sensing functions.

[0024] By using the designed efficient signal processing methods, the interference between communication signals and sensing signals is nearly eliminated, ensuring the efficiency and accuracy of both communication and sensing functions.

[0025] The recovered communication signals can be re-used to improve sensing accuracy, while the improvement in sensing accuracy also benefits the communicationrate. This achieves the effect of mutual enhancement between communication and sensing functions.

[0026] The design of the integrated waveform for transmission enables the simultaneous realization of efficient communication and sensing functions. It also fully utilizes the existing communication systems, adding high-precision sensing capabilities.BRIEF DESCRIPTION OF THE DRAWINGS

[0027] FIG. l is a system block diagram illustrating an example RIS-assisted integrated sensing and communication (ISAC) system, according to some embodiments.

[0028] FIG. 2 is simulation diagram illustrating an example of a convergence effect under different signal-to-noise ratios and power allocation coefficients according to some embodiments.

[0029] FIG. 3 is a simulation diagram illustrating an example of the performance under different signal-to-noise ratios with respect to normalized mean square error (NMSE), according to some embodiments.

[0030] FIG. 4 is a simulation diagram illustrating an example of the performance under different signal-to-noise ratios with respect to bit error rate (BER), according to some embodiments.

[0031] FIG. 5 is a simulation diagram illustrating an example for compensating for the reduction in spectral efficiency by adding sensing functionality, according to some embodiments.

[0032] FIG. 6 is a diagram illustrating an example of the NMSE performance with sensing functionality, according to some embodiments.

[0033] FIG. 7 is a schematic diagram illustrating a required transmission symbol length to achieve satisfactory sensing performance at SNR = 30 dB, according to some embodiments.

[0034] FIG. 8 is a performance gain diagram illustrating an effective throughput, according to some embodiments.DETAILED DESCRIPTION

[0035] Fig. 1 schematically depicts an example transceiver design of an RIS-assisted integrated sensing and communication (ISAC) system.

[0036] ISAC systems modeling: The present disclosure investigates the uplink from S RISs (S > 1) assisted single-antenna user equipment (UE) to a base station (BS). The direct link path from the BS to the UE is assumed to be blocked by an obstacle because of the easy occlusion characteristics of millimeter-wave (mmWave) signals. The BS consists of an M-antenna uniform linear array placed along the Y-axis, and the first RIS consists of a uniform rectangular array in the Y-o-Z plane with Ns= Ns yX Ns z. The BS detects both the UE's communication signal and senses the environmental parameters between the BS and the RIS through the uplink signal of the user reflected from the RIS.

[0037] In the t-th time slot, the transmitting end generates and transmits the superimposed symbols xt= ^,xd t+ ^ / l — ^xp twhere xd tand xp tare the communication symbols and pilot symbols generated in the t-th time slot, respectively, and is the power coefficient assigned to the communication symbols, satisfying 0 < ^ < 1.

[0038] The BS receives the UE’s uplink signal reflected by the RIS as:where Hr sis the channel from the s-th RIS to the BS, 6s tis the phase shift of the s-th RIS at the t-th time slot, hb sis the channel from the UE to the s-th RIS, and ntis the noise at the t-th time slot. The receive matrix is constructed by stacking the BS receive symbols for T time slots:where 0 = [0S;1, ... , 0S;T], X = diag(x1;... , xT'), and A = [n^ ... , nT].

[0039] Angular domain sparse modeling of the mmWave channel: In the mmWave band, the radio channel follows a geometric channel model. Specifically, the mmWave channel between the BS and the s-th RIS is modeled as:where Lsrepresents the number of paths between the BS and the s-th RIS, and at srepresents the complex gain consisting of path loss for the 1-th path. The array responses = angles of arrival(AoAs) and azimuth angles of departure (AoDs) U£2B ’SI=-v A ^sin(?9^B> si)>uR2B •si=is the AoA at the s-th RIS for the 1-th path, and $R2Bsiand VR2B,SIarethe elevation and azimuth AoDs from the BS towards the s-th RIS, respectively. dBSand dRISare the BS antenna spacing and the s-th RIS element spacing, respectively, and A denotes the carrier wavelength.

[0040] By representing uB2B shuB2B siand VR2B,SI on the mmWave angular domain by selecting elements within the grid points wR2B s, wR2B s, and gB2B s, one can transform the mmWave channel into:is the dictionary matrix of the array response with respect to the angular domain grid points wR2B s, wR2B s, and gR2B s-is a sparse matrix, and the positions of the non-zero elements in the matrix correspond to the positions of the elements selected from the grid points.

[0041] Specifically, the angle domain grid points wR2B s, wR2B s, and gB2B sare the equivalent arrival / departure angles for the Lspaths in Hr s, where the first path corresponds to the LoS path, and the effective arrival / departure angles corresponding to the LoS path can be determined by the relative positions of the BS and the RIS. Hence, the first elements of wR2B s, wR2B s, and gB2B sare the equivalent arrival / departure angles corresponding to the LoS path, and the rest of the elements are quantized for the angle domain uniformly in equal parts of Gr— 1, G2— 1 and G3— 1, respectively.

[0042] RIS consists of controllable reflection units, constructing a virtual LoS path between the base station and the user, where the number of RIS units S > 1.

[0043] Referring to Fig. 1, the specific steps of the present disclosure are shown as follows.

[0044] STEP1 : In the t-th time slot, the transmitter generates and transmits the superimposed symbols xt=where xd tand xp tare the communication symbols and the pilot symbols, respectively, and is the power coefficient assigned to the communication symbols, satisfying 0 < ^ < 1.

[0045] STEP2: In the t-th time slot, the receive symbol at the BS is:where Hr sis the channel from the s-th RIS to the BS; 6s tis the phase of the s-th RIS at the t-th time slot; hb sis the channel from the UE to the s-th RIS, and ntis the noise at the t-th time slot. The receive matrix is constructed by stacking the BS received symbols of the time slots aswhere 0 = [0S;1, ... , 0s T], X = diag(x1;... , xT'), and N = [n^ ... , nT]. Then substituting into the millimeter wave angular domain sparse channel model of Hr s, and vectorize the receive matrix, one obtains: s | v-1\MNST y = / H— [5R2B,sdiag( / ii, / S)0sX) ® 4R2B,S] • vec((ls) + n = ZR2B(X, v)a) + n s=i N where M is the number of the antenna of the base station, Nsis the number of elements of the s-th RIS, AR2B s( w$2B s) dictionary matrices of thearray response with respect to the angular domain grid points wR2B s, wR2B s, and gR2B s- Q.sis a sparse matrix, and a>s= vec((ls).

[0046] STEP3: The initial estimate of the sparse vectoris obtained by using the least square estimate (LSE) with a Tikhonov regularization (TR) term based on the information of the second-order moments of the pilot symbols and communication symbols, and the initial estimate of the equivalent channel between the BS and the UE is furtherobtained, and the estimate of the communication data A® is further obtained by using the linear minimum mean square error (LMMSE).

[0047] STEP4: Using the initial estimates X^ from STEP 3, the following steps are iteratively computed under the expectation maximization (EM) framework until convergence, for the j-th iteration:

[0048] (1) Recovering the superimposed symbol estimate X^-1^ based on the communication symbol estimatefrom the previous iteration and obtaining the grid estimate^ <jo^) and sparse vector estimate 0)^ by the off-grid SBL method. Specifically, the mmWave channel between the BS and the s-th RIS is:where at sis the 1-th path gain; the array response is aM(u) andand

[0049] Furthermore, according to the mmWave sparse channel model, we can obtain:are the dictionary matrices of the array response with respect to the angular domain grid pointsrespectively.

[0050] Furthermore, angular domain grid points wR2B s, wR2B s, and gB2Bare utilized to estimate effective AoAs and AoDs of Lspaths corresponding to Hr s. Among them, the first path corresponds to the LoS path, and the effective arrival / departure angle corresponding to the LoS path can be determined by the relative positions of the base station and the RIS, so set the first elements of wR2B s, wR2B s, and gB2B sare theequivalent arrival / departure angle corresponding to the LoS path. The remaining elements are quantized uniformly in equal parts of Gr— 1, G2— 1 and G3— 1 respectively, for the angle domain.

[0051] Furthermore, the SBL for sparse vectors in the EM framework is obtained based on the following a priori distribution:the corresponding variance of a>g. It can be observed that when yj1tends to zero, a>galso tends to zero, so the estimate of a> can be translated into the estimate of y.

[0052] Furthermore, in order to promote the sparsity structure, the prior modeled to satisfy the Gamma distribution:where setting ayby-> 0 to meet spikes at zero.

[0053] Furthermore, in the EM procedure, we give the complete information set as{y0> <»}, and the parameter set as v = [w^2B^R2B,S< £R2B,S]where / 3 is modeled to handle the uncertainty of unknown noise variance in practice.

[0054] Furthermore, to compute the parametric set, the EM framework is divided into a expectation step and a maximization step during each iteration.

[0055] Furthermore, in the j -th iteration of expectation step, we evaluate the loglikelihood function T(x|x<’7-1')) as the cost function:where the channel posterior density can be expressed as:The closed-form expressions are given as: diag(yO-i)))-1and

[0056] Furthermore, in the j -th iteration, the maximization step can be divided into two separate steps. For the first maximization step, the estimate of y in the j-th iteration is calculated as:respectively.

[0057] For the second maximization step, the estimates of / 3, v, and Xdin the j-th iteration are calculated as:is the closed-form derivative of:with respect to v2,is a dynamically chosen step-size sequence.

[0058] The maximum a posteriori estimate yields a> = gM. The angles corresponding to the L elements of the vector with the largest values are combined to form an estimation grid (i9, <p).

[0059] (2) Setting most of the estimates w® obtained in step (1) to zero and then use theLSE method to obtain a more accurate estimate of the equivalent channelbetween the base station and the user.

[0060] (3) Based on the estimated valueobtained in step (2), the estimated value of the communication data is solved by subtracting the received portion corresponding to the sensing pilots from the received matrix, and is demodulated and then modulated to obtain the processed Xd\ Specifically for the second maximization step, the estimates of Xdin the j-th iteration are calculated as:-'4R2B,S] -

[0061] Iterations are performed (3. l)-(3.5) followed by j <~ j + 1, until j = jmaxor the difference between -C1')) is lessthan 6X. As a result, the communication data, the angular parameters in the environmental channel and the user coordinates are finally recovered.

[0062] The functions and effects of the present disclosure are further illustrated and demonstrated by the following simulation experiments:

[0063] Example Simulation setup: Let the number of RIS be S = 2; the number of RIS configuration elements be = N2= 12 x 12; the locations of the BS, RIS and UE be qB= [0,0,0], qR1= [—30,28,21], qR2= [—20,30,20] and Pu = [10,20,5], in meters (m), respectively. Set the number of BS antennas M = 16, the number of paths between the BS and RIS Ls= 3, the number of transmission symbols T = 256, and the remaining parameters are set as follows: Q = 1, j_max = 100, 6X= 10-3and Gr= G2= G3= 8 respectively.

[0064] In the simulation, we compared the performance of the superimposed symbol scheme of the present disclosure with that of the existing technology such as pure pilot scheme and blind estimation for communication and ISAC, respectively, with respect to the metrics of sensing accuracy (NMSE), communication bit error rate (BER), and spectral efficiency (SE). The NMSE is specified as:where Hr sand 0Sare the estimated values of Hr sand (ps, respectively.

[0065] Example simulation results: Fig. 2 illustrates the convergence behaviors of the proposed algorithm under various SNR regimes and It demonstrates that the proposed method ensures the monotonical descent of NMSE, which is shown to converge within only a few iterations. As can be also observed, the performance of channel estimation becomes progressively better as the SNR increases, and the power proportion factor % also significantly affects the performance. This is to be expected because the communication and sensing performance are subject to the power allocation for data and pilot, respectively.

[0066] Fig. 3 and 4 show the superior performance of our proposed method on BER, and NMSE versus different SNR regimes. For comparison purposes, we use three on-grid based methods and two off-grid based methods, all of which update a>swithout iterative procedures. We first compare the three on-grid based methods with off-grid SBL and off- grid OMP in Fig. 3, which shows that the severe model mismatch by on-grid methods heavily degrades ISAC performance. Furthermore, it can be observed that even using off- grid based methods, i.e., off-grid SBL and off-grid OMP, provides little improvement in terms of NMSE and BER since the symbols used for sensing contain unknown data. Specifically, the BER of these unknown data is nearly 10-1, which in turn, reduces sensing capabilities. This highlights the benefits of updating data symbols via an iterative manner as in proposed method, especially in the high SNR range. In addition, the performance of the proposed method with pure pilot is included as a lower bound for the proposed superimposed symbol scheme in Fig. 4. The NMSE of proposed method is very close to this lower bound, indicating that the benefits of the proposed algorithm are comparable to removing most of the interference between sensing pilots and data, especially at high SNR.

[0067] Results in Fig. 5 underline the valuable role of the proposed superimposed symbol scheme in compensating for the SE degradation caused by having sensing capabilities, where we consider two cases, i.e., with and without sensing functions denoted by “W / Sensing Function” and “W / O Sensing Function”, respectively. It can be observed that the addition of sensing function lowers the SE, as more sensing pilots consume spectrumresources. Surprisingly, the proposed superimposed symbol scheme provides comparable SE to that of conventional communication without sensing function in the high or moderate SNR regime, achieving 96% SE at 20 dB. This is expected since our proposed superimposed symbol scheme can obtain accurate channel angle information which can nearly eliminate the mutual interference between pilots and data. Moreover, we also evaluate the typical blind estimation with very few pilots, which is shown as the solution closest to the upper bound through perfect CSI. However, once the blind estimation method is implemented to have the sensing function, SE will be severely degraded due to the demand for extensive pilots to eliminate the quadrant ambiguity in the channel angle extraction procedure. In addition, compared with the double-RIS setup, the single-RIS scenario still experiences a decrease in SE, even though it removes the interference between double RISs. This is because the other RIS is turned OFF, resulting in a decrease in channel gain.

[0068] Fig. 6 illustrates the NMSE performance among the abovementioned methods with the sensing function. The numerical results show again that the proposed superimposed symbols can significantly outperform other benchmarks. This trend is almost in agreement with the SE performance. The reason for this behavior is that the method with high SE can yield more data symbols, which in turn improves the channel sensing performance.

[0069] Fig. 7 exhibits how many symbols are needed to achieve satisfactory sensing performance at SNR=30 dB. It shows that the NMSE is a decreasing function of for all methods and eventually reaches stable accuracy. Regarding the cases of superimposed symbol schemes, abrupt transitions around 7\=112, 160 and 192 can be observed in the fast fading regime, wherethreshold values increase with This can be explained by the fact that more symbols are needed to reduce NMSE while more power is allocated to data.

[0070] Fig. 8 illustrates the performance gain in effective throughput by our proposed superimposed symbol scheme. It shows that the superiority of the superimposed symbol scheme covers the entire T range. This effect is explained by the fact that sensing pilots are inserted into each transmission block along with data symbols, resulting in little dedicated consumption of time-frequency resources for communications. Particularly, the effective throughput by the superimposed symbol scheme is 200% larger than that ofpilot-based sensing scheme and 133% larger than blind-based sensing scheme at T = 256.

[0071] The above results show that the present disclosure has significantly improved in sensing accuracy, BER and spectral efficiency compared with the existing integrated method of communication and sensing using separate pilots as well as blind estimation, and is close to the spectral efficiency of conventional communication without sensing function.

[0072] The above embodiments are used to explain and illustrate the present disclosure, not to limit it, and any modifications and changes made to the present disclosure within the spirit of the present disclosure and the scope of protection of the claims fall within the scope of protection of the present disclosure.

Claims

CLAIMSWHAT IS CLAIMED IS:

1. A method for integrated communication and sensing design based on superimposed symbols, comprising:SI : at a signal transmission end, a communication signal and a pilot signal within a same time-frequency resource block are linearly superimposed in a symbol domain using a power allocation coefficient and transmitted to a reconfigurable intelligent surface (RIS);S2: at a signal reception end, signals reflected by the RIS are received, and the received signals over multiple time slots are stacked to obtain a reception matrix;S3: an extraction of environmental angle parameters is converted into an estimation of angle grid values and sparse vectors, wherein a received signal is substituted into a preset millimeter-wave channel model, the reception matrix is vectorized, an initial estimate of the sparse vector is obtained using a least squares estimation with Tikhonov regularization, and an initial estimate of an equivalent channel between a base station and a user is derived from the estimated sparse vector;S4: based on the initial estimate of the equivalent channel, an initial estimate of communication data is obtained using a linear minimum mean square error method, followed by demodulation and re-modulation;S5: the initial estimate of the communication data after re-modulation is iteratively computed under an expectation-maximization framework to obtain final estimates of the sparse vector, an angle grid, and the communication data.S6: finally, recovering the communication data, angle parameters in an environmental channel, and user coordinates.

2. The method of claim 1, wherein the transmission end generates and transmits the superimposed symbols xt= y / fycd,t + -^ / l — ^xp t, wherein xd tand xp tare the communication symbols and pilot symbols generated in the t-th time slot, respectively, and is the power allocation coefficient assigned to the communication symbols, satisfying 0 < ^ < 1.

3. The method of claim 1, further comprising:in a t-th time slot, the base station receives a symbol yt=where Hr sis the channel between the s-th RIS and the base station, 6s tis a phase of a s-th RIS in the t-th time slot, hb sis a channel between the user and the s-th RIS, and ntis a noise in the t- th time slot, and a stacked base station received symbols over T time slots constitute the reception matrixdiag(x1, ... , xT) and N = [n1(... , nT].

4. The method of claim 1, wherein the RIS consists of controllable reflection units constructing a virtual line of sight (LoS) path between the base station and the user, where a number of RIS units S > 1; a millimeter- wave modeling between the base station (BS) and a s-th RIS is expressed as Hr s= aliSaM«B,sZ)b^(«R2B,si< v°2BiSl), wherein Lsrepresentsthe number of paths between the BS and the s-th RIS, and at srepresents a complex gain consisting of a path loss for an 1-th path, array responses can be expressed as aM(u) =effective angles of arrival (AoAs) and azimuth angles of departure (AoDs) as uB2B st=where $B2B slisthe AoA at a s-th RIS for the 1-th path, dB2B, / ar|darethe elevation and azimuth AoDs from the BS towards the s-th RIS, respectively, and dBSand dRISsare a BS antenna spacing and a s-th RIS element spacing, respectively, and A denotes a carrier wavelength.

5. The method of claim 4, wherein an extraction of environmental angle parameters is transformed into an estimation of angle grid values (Y), <p) and sparse vectors m, specifically by representing a millimeter- wave angle domain uR2B shUB2B,SIand VR2B,SI and converting the millimeter-wave channel into Hr sM / R2B,S< £R2B,S) , whereinisadictionary matrix of an array response with respect to angular domain grid pointsa sparse matrix, and positions of non-zero elements in the sparse matrix correspond to positions of elements selected from the grid points.

6. The method of claim 5, wherein the angle domain grid points points wB2B s, WB2B S, and gB2fi sareeffective arrival / departure angles for Lspaths in Hr s, where a first path corresponds to the LoS path, and the effective arrival / departure angles corresponding to the LoS path can be determined by the relative positions of the BS and the RIS, and remaining elements are quantized for the angular domain uniformly in equal parts of Gr— 1, G2— 1 and G3— 1, respectively.

7. The method of claim 5, wherein the initial estimate of the sparse vector is obtained using the least squares estimation with a Tikhonov regularization term8. The method of claim 7, wherein the initial estimate of the communication data is X^ = wherein Nois a noise variance, PQis auser transmit power, and is the equivalent channel estimate obtained by an affinetransformation between the base station and the user.9 The method of claim 7, wherein a remodulated communication data initial estimate is iteratively computed under an expectation maximization (EM) framework to obtain final estimates of the sparse vector, angle grid, and communication data by:S901 : first, setting a prior distribution of the sparse vectorp(m,y) = CJV’(m|O,diag(y-1)), wherein y = [y1(... ,y2G1G2G3], *9 G {1> ... ,2G1G2G3], y"1is a corresponding variance of a>g, and when y^1tends to zero, a>galso tends to zero, and an estimate of m can be translated into an estimate of y;S902: using an EM iterative update to calculate a parameter dataset / = [Xd, y, v, / 3] and a parameter set v = where / 3 is modeled to handle an uncertainty ofunknown noise variance in practice;S903: obtaining a maximum posterior estimation of afl') and taking angle values corresponding to L-largest elements of afl') as the estimated grid, wherein Lsis a number of paths in the channel between the base station and the s-th RIS;S904: setting the elements of w® below a preset threshold to zero and obtaining a more accurate using a least squares estimate (LSE) method, wherein the equivalent channel estimation between the base station and the user is recovered by an affine transformation;S905: subtracting a received part corresponding to a sensing pilot from the reception matrix Y using the EM framework to obtain the communication data estimate, and iterating over S901-S905 followed by j <- j + 1 until j = jmaxor a difference betweenthan 6X.

10. The method of claim 9, wherein the prior distribution, to promote a sparse structure of f A . 2(7 G G a is modeled to satisfy a Gamma distribution p(y) =2 3^(Yg! 1 +ay> by), wherein ayand bYare specific parameters and setting aYbY-> 0 to meet spikes at zero.11 A method comprising: linearly superimposing a plurality of pilot symbols and a plurality of data symbols within a plurality of time frequency resource blocks using a power proportion factor to create a plurality of superimposed signals; transmitting the plurality of superimposed signals to a reconfigurable intelligent surface (RIS reflecting the plurality of superimposed signals using the RIS over a plurality of time slots wherein the plurality of signals are stacked inside a reception matrix; calculating a coarse sparse vector estimation of the plurality of pilot symbols; calculating a coarse estimation of the plurality of data symbols; iteratively refining the coarse sparse vector estimation and the coarse estimation of the plurality of data symbols; recovering a refined channel angle estimation, a refined estimation of the plurality of data symbols, and user coordinates as a result of the refining.12 The method of claim 11, wherein: the plurality of superimposed signals are characterized by xt= ^,xd t+xd trepresents a data symbol, xp trepresents a pilot symbol, and represents the power proportion factor.

13. The method of claim 11, wherein: a superimposed symbol of the plurality of superimposed symbols reflected by the RIS is characterizedHr srepresents a channel between the RIS and a base station,6s trepresents a phase of the RIS, hr srepresents a channel between the RIS and a user, and ntrepresents a noise in a t-th time slot.

14. The method of claim 11, wherein: the reception matrix is represented by Y = Zs=i ^r,sdiag( / tfc s)0sX + N,0Srepresents a vector of RIS phase shifts,X represents a diagonal vector of the plurality of superimposed symbols reflected by the RIS, andN represents a noise vector.

15. The method of claim 11, wherein the RIS comprises a plurality of controllable reflectors that construct a virtual line of sight (LoS) path between a base station and a user.

16. The method of claim 15, further comprising: modeling a channel between a reflector of the plurality of controllable reflectors and the base station.

17. The method of claim 16, wherein: the modeling is characterized by Hr svR2B,si),aMcomprises a plurality of array responses, uR2B,sZ comprises a sine transformation of an effective angle of arrival (AoA), uR2B,si comprises a cosine transformation of an effective elevation angle of departure(AoD) and a sine transformation of an effective azimuth AoD, andvR2B,si comprises a sine transformation of the effective elevation AoD.

18. The method of claim 17, further comprising: applying a basis expansion model by discretizing an angle domain using a set of grids on the effective AO A, the effective elevation AoD, and the effective elevation AoD.

19. The method of claim 17, further comprising: converting the modeled channel to a function of angular domain grid points.

20. The method of claim 19, wherein: the function is characterized bys),wR2B,s,wR2B,s,and gR2B sarethe angular domain grid points, and flsis a sparse matrix corresponding to positions of elements selected from the angular domain grid points.

21. The method of claim 11, wherein the calculating the course sparse vector comprises: performing Tikhonov regularization.

22. The method of claim 11, wherein: the calculating the coarse sparse vector estimation is characterized byXp 0represents a matrix of pilot symbols,Q represents a data uncertainty, andY represents a channel response matrix.

23. The method of claim 11, wherein the calculating the coarse estimation of the plurality of data symbols comprises: calculating a using linear minimum mean squared error.

24. The method of claim 11, wherein: the calculating the coarse estimation of the plurality of data symbols is characterized byNorepresents a noise variance,Porepresents a user transmission power, and represents a coarse effective channel estimation.

25. The method of claim 11, wherein the iteratively refining comprises: performing an expectation maximization algorithm.

26. The method of claim 11, wherein the refining further comprises remodulating the coarse estimation of the plurality of data symbols.

27. The method of claim 11, wherein the refining comprises: setting an a priori distribution of the coarse sparse vector estimation; estimating a log likelihood function with respect to a hyperparameter vector, the coarse estimation of the plurality of data symbols, a plurality of predefined angle grids, and an uncertainty parameter; performing a first maximization step with respect to the hyperparameter vector, performing a second maximization step to update the coarse estimation of the plurality of data symbols, a plurality of predefined angle grids, and an uncertainty parameter; and converging on an a posteriori probability estimate of the coarse sparse vector estimation.

28. The method of claim 27, wherein the priori distribution is modeled to satisfy an independent gamma distribution.

29. The method of claim 28, wherein the gamma distribution is characterized by

Images