Joint Beamforming for Backscatter Integrated Sensing and Communication
Zongyao Zhao Tiankuo Wei Zhenyu Liu Xinke Tang Xiao-Ping Zhang Yuhan Dong

[figure]labelformat=default,labelsep=period



 Joint Beamforming for Backscatter Integrated Sensing and Communication
    Zongyao Zhao^1,2, Tiankuo Wei^1,2, Zhenyu Liu^1, Xinke Tang^2, Xiao-Ping Zhang^1, Yuhan Dong^1,2,*

	^1Shenzhen International Graduate School, Tsinghua University, Shenzhen, P. R. China

    ^2Pengcheng Laboratory, Shenzhen, P. R. China

	Email: zhaozong21@mails.tsinghua.edu.cn, 
              wtk23@mails.tsinghua.edu.cn,
              zhenyuliu@sz.tsinghua.edu.cn,

              tangxk@pcl.ac.cn, 
               xiaoping.zhang@sz.tsinghua.edu.cn,
               dongyuhan@sz.tsinghua.edu.cn
    September 9, 2024
===================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================



§ ABSTRACT 
Integrated sensing and communication (ISAC) is a key technology of next generation wireless communication. Backscatter communication (BackCom) plays an important role for internet of things (IoT). Then the integration of ISAC with BackCom technology enables low-power data transmission while enhancing the system sensing ability, which is expected to provide a potentially revolutionary solution for IoT applications. In this paper, we propose a novel backscatter-ISAC (B-ISAC) system and focus on the joint beamforming design for the system. We formulate the communication and sensing model of the B-ISAC system and derive the metrics of communication and sensing performance respectively, i.e., communication rate and detection probability. We propose a joint beamforming scheme aiming to optimize the communication rate under sensing constraint and power budget. A successive convex approximation (SCA) based algorithm and an iterative algorithm are developed for solving the complicated non-convex optimization problem. Numerical results validate the effectiveness of the proposed scheme and associated algorithms.  The proposed B-ISAC system has broad application prospect in IoT scenarios.



Integrated sensing and communication (ISAC), backsactter communication (BackCom), passive tag.




§ INTRODUCTION

Integrated sensing and communication (ISAC) technology has recently emerged as a candidate technology of the next generation wireless network, which aims to integrate sensing and communication into one system to improve spectrum efficiency and hardware efficiency while providing sensing and communication service simultaneously<cit.>. As a promising technology for low-power communication, backscatter communication (BackCom) uses radio frequency (RF) tags to enable passive communication links by scattering RF signals to the reading device <cit.>. 

The combination of BackCom with ISAC promises to combine the advantages of both technologies to enable energy-efficient passive communication while improving the sensing performance, especially for internet of things (IoT) applications. The authors in <cit.> further considered the detection requirement of RF tags and developed a joint beamforming design for ISAC system with backscatter tags, which minimize the total transmit power while meeting the tag detection and communication requirements. In summary, research on on joint beamforming schemes for backscatter integrated sensing and communication is scarce and thus requires further exploration of this novel paradigm. Moreover, existing schemes only focus on the optimization of the energy consumption, however the optimization of communication rate is still remained to be explored.

In this paper, we propose a novel backscatter-ISAC  system and design a joint beamforming scheme to optimize communication rate under the sensing constraint and power budget. Specifically, we model the signals received at the tag, user equipment (UE), and access point (AP). Further, we establish the communication and sensing model and derive the metrics of communication and sensing performance respectively, i.e., communication rate and detection probability. Then, we propose a joint beamforming scheme aiming to optimize the UE communication rate while ensuring the tag is working normally. We develop a successive convex approximation (SCA) based algorithm and an alternating algorithm for the joint beamforming scheme. Extensive simulation validate the effectiveness of the proposed scheme and associated algorithms. 

The proposed B-ISAC system fully utilizes the passive back scatter
properties of RF tags to achieve low-power communication and sensing capabilities. It is expected to has broad application
prospect in IoT scenarios.

The remainder of this paper is organized as follows. Sec. <ref> introduces the B-ISAC system and signal model. The joint beamforming scheme for communication rate optimization is proposed in Sec. <ref>. Numerical results are presented in Sec. <ref>. Finally, the conclusions are drawn in Sec. <ref>.

Notation: In this paper, boldface lower-case and upper-case letters denote vectors and matrices respectively. ℝ and ℂ represent the real and complex sets respectively. |·|, ||·||, and ||·||_F are  absolute value, Euclidean norm, and Frobenius norm, respectively. ( ·)^-1 and ( ·)^† denote the inverse and pseudo inverse, respectively. ( ·)^T, ( ·)^*, and ( ·)^H represent transpose, complex conjugate, and Hermitian transpose, respectively. 𝔼( ·) represents statistical expectation. Re{·} returns the real part of a complex number. j is the imaginary unit, which means j^2=-1. 𝐈_N is the N× N identity matrix. 1=[1,1,…,1]^T∈ℝ^N. 𝐀≽0 means that 𝐀 is a positive semidefinite matrix. ⊙ represents the Hadamard product. diag(𝐚) returns a diagonal matrix, the vector composed of its diagonal elements is 𝐚. Tr(𝐀) and rank(𝐀) compute the trace and rank of matrix 𝐀 respectively. chol(𝐀) returns the Cholesky decomposition of matrix 𝐀. vec(𝐀) vectorizes matrix 𝐀 by column-stacking.


§ SYSTEM AND SIGNAL MODEL
 
 

 §.§ System Model

 
As shown in Fig. <ref>, the B-ISAC system is composed of an AP, a UE, and a passive tag. The AP facilitates communication service to the UE, while providing sensing and communication support for the tag. The tag receives the signal transmitted by the AP to decode downlink data and modulates the uplink data onto the backscattered signal to achieve two-way data transmission. At the same time, the AP receives the backscattered signal and carries out further processes to obtain sensing information, such as position, status and etc. For the UE, the backscattered signal from the tag can be regarded as interference.  

It is assumed that the AP is equipped with uniform linear transmit and receive arrays with N_t and N_r antenna elements, respectively. There is λ/2 inter-spacing between neighboring antenna elements, where λ is the carrier wavelength. Without loss of generality, we assume N_t ⩽ N_r. The tag and UE are equipped with a single antenna, respectively. It is also assumed that the self-interference between the transmit and receive arrays can be ignored.

𝐗∈ℂ ^N_t× L denote the transmitted signal at the AP, where L is the length of the transmitted signal such that L>N_t. 𝐗 can be expressed as

    𝐗=𝐖𝐒=𝐰_u𝐬_u^H+𝐰_t𝐬_t^H+𝐖_s𝐒_s∈ℂ ^N_t× L,

where the joint beamforming matrix 𝐖 and the data augmentation matrix 𝐒 are respectively given by

    𝐖   =[𝐰_u,𝐰_t,𝐰_1,𝐰_2,…,𝐰_N_t] ∈ℂ ^N_t× (N_t+2),
    𝐒   =[ 𝐬_u,𝐬_t,𝐬_1, 𝐬_2 …,𝐬_N_t] ^H∈ℂ ^(N_t+2)× L,

where 𝐰_u∈ℂ ^N_t×1 and 𝐰_t∈ℂ ^N_t×1 are beamforming vectors for the UE and tag, respectively. Vectors 𝐬_u∈ℂ ^L×1 and 𝐬_t∈ℂ ^L×1 are data streams for the UE and tag, respectively. The additional probing stream [𝐬_1,𝐬_2,...,𝐬_N_t]^H =𝐒_s∈ℂ^N_t× L  is introduced to extend the sensing degrees of freedom (DoF) of the transmit waveform. In this way, the DoF of the transmit waveform can be extended to its maximum value <cit.>. Note that these dedicated probing streams are deterministic and do not contain any information. Moreover, [𝐰_1,𝐰_2,...,𝐰_N_t] =𝐖_s∈ℂ^N_t× N_t is the dedicated auxiliary beamfoming matrix corresponding to the dedicated probing streams. 

It is assumed that there is no correlation between dedicated probing streams 𝐒_s and data streams [𝐬_u,𝐬_t]^H. When L is sufficiently large, the random sample covariance matrix of the random communication data streams [𝐬_u,𝐬_t]^H can be approximately considered to satisfy 1/L[𝐬_u,𝐬_t]^H[𝐬_u,𝐬_t] ≈𝐈_2. 
At the same time, the dedicated probing streams 𝐒_s is also elaborated to satisfy 1/L𝐒_s𝐒_s^H=𝐈_N_t. Therefore, 𝐒 satisfies

    1/L𝐒𝐒^H≈𝐈_N_t+2.

The sample covariance matrix of waveform 𝐗 is given by

    𝐑_𝐗=1/L𝐗𝐗^H≈𝐖𝐖^H∈ℂ ^N_t × N_t,

Then, the beam pattern of the transmit waveform is

    P( θ) = 𝐚^H( θ) 𝐑_𝐗𝐚( θ),

where 𝐚( θ)= [ 1,e^jπsinθ,e^2jπsinθ,...,e^( N_t-1 ) jπsinθ] ^T ∈ℂ ^1 × N_t represents the steering vector of the transmit array, and θ represents the azimuth angle with respect to the array.


 §.§ Backscatter Model

The signal 𝐲_t∈ℂ^1× L received by the tag is given by

    𝐲_t   =𝐡_f𝐗+𝐧_t
       =𝐡_f𝐰_u𝐬_u^H+𝐡_f𝐰_t𝐬_t^H+𝐡_f𝐖_𝐬𝐒_𝐬+𝐧_t,

where 𝐡_f∈ℂ ^1× N_t denotes the channel from the AP to tag, 𝐧_t∈ℂ ^1× L is the receiver noise vector at the tag, which is assumed to follow a zero-mean complex Gaussian distribution as 𝐧_t∼𝒞𝒩( 0,σ_t^2𝐈_L ). On the right hand side of (<ref>), the first part 𝐡_f𝐰_u𝐬_u represents the interference caused by the UE communication data, the second part 𝐡_f𝐰_t𝐬_t represents the desired signal for the tag, the third part 𝐡_f𝐖_𝐬𝐒_𝐬 represents the interference caused by the dedicated probing stream, and 𝐧_t is the noise vector. Therefore, the signal-to-interference-plus-noise ratio (SINR) of the signal received at the tag can be expressed as

    γ _t   =𝔼( 𝐡_f𝐰_t𝐬_t^H^2 )/𝔼( 𝐡_f𝐰_u𝐬_u^H^2 ) +𝔼( 𝐡_f𝐖_s𝐒_s ^2 ) +𝔼( 𝐧_t^2 )
       =|𝐡_f𝐰_t|^2/|𝐡_f𝐰_u|^2+𝐡_f𝐖_s ^2+σ _t^2.

Then, the tag modulates the uplink data onto the backscattered signal. The remodulated backscattered signal 𝐲_b∈ℂ ^1× L reflected by the tag is given by

    𝐲_b=   √(α)𝐲_t⊙𝐜_t
    
    =   √(α)𝐡_f𝐗⊙𝐜_t+√(α)𝐧_t⊙𝐜_t

where α is the backscatter modulation efficiency coefficient, and 𝐜_t is the uplink data satisfying 𝔼 [|𝐜_t|^2] =1.

Vector 𝐡_b∈ℂ ^N_r× 1 represents the channel from the tag to AP. Then, the backscattered signal received at the AP 𝐘_ap∈ℂ ^N_r × L can be expressed as

    𝐘_ap=   𝐡_b𝐲_b+𝐍_ap
    
    =   √(α)𝐡_b𝐡_f𝐗⊙𝐜_t+√(α)𝐡_b𝐧_t⊙𝐜_t+𝐍_ap

where 𝐍_ap∈ℂ ^N_r× L is the noise matrix at the AP, which is assumed as vec(𝐍_ap)∼𝒞𝒩( 0,σ_ap^2𝐈_N_rL). Then, we use a receive combine vector 𝐰_r∈ℂ ^1× N_r to combine the signal of N_r antennas. The combined signal 𝐲̃_ap∈ℂ ^1× L is given by

    𝐲̃_ap=   𝐰_r𝐘_ap
    
    =   √(α)𝐰_r𝐡_b𝐡_f𝐗⊙𝐜_t+√(α)𝐰_r𝐡_b𝐧_t⊙𝐜_t+𝐰_r𝐍_ap.

It is worth noting that the transmit signal 𝐗 is completely known to the AP, so 
the uplink data can be decoded using 𝐗. We denote 𝐂_t=diag( 𝐜_t). Consequently, the received SINR at the AP is 

    γ _ap   =𝔼( √(α)𝐰_r𝐡_b𝐡_f𝐗⊙𝐜_t ^2 )/𝔼( √(α)𝐰_r𝐡_b𝐧_t⊙𝐜_t ^2 ) +𝔼( 𝐰_r𝐍_AP ^2 )
       =α𝔼( 𝐰_r𝐡_b𝐡_f𝐗𝐂_t𝐂_t ^H𝐗^H𝐡_f^H𝐡_b^H𝐰_r^H)/α𝔼( |𝐰_r𝐡_b𝐧_t𝐂_t𝐂_t^H𝐧_t^H𝐡_b^H𝐰_r^H| ) +𝐰_r ^2σ _ap^2
       ( a )≈α𝐰_r𝐡_b𝐡_f𝐖𝐖^H𝐡_f^H𝐡_b^H𝐰_r^H/α |𝐰_r𝐡_b|^2σ _t^2+𝐰_r ^2σ _ap^2,

where (a) holds because of 𝔼(𝐂_t𝐂_t^H )=𝐈_L and 𝐗𝐗^H≈ L𝐖𝐖^H.
When the channel 𝐡_b is known to the AP, we could use equal gain combining vector, i.e., 𝐰_r=𝐡_b^H/𝐡_b.

Since 𝐗 is completely known to the AP, the SINR of the received signal at the AP is related to the sample covariance matrix of 𝐗, not just related to the signal 𝐰_t𝐬_t, which is different from <cit.>. In other words, communication signal 𝐰_u𝐬_u and dedicated probing stream 𝐖_s𝐒_s  can also help the tag to facilitate backscatter communication.


The data stream 𝐬_t contains a sequence that can activate the passive RF tag for data transmission. Therefore, in order to detect the tag and complete communication transmission, the SINRs at the tag and AP must be greater than a certain threshold to meet their respective sensitivity constraints.






 §.§ UE Communication Model

Let 𝐡_u∈ℂ ^1× N_t and h_tu∈ℂ represent  the channel between the AP and UE and the channel between the tag and UE, respectively. Then, the received communication signal at the UE 𝐲_u∈ℂ ^1× L can be expressed as

    𝐲_u=   𝐡_u𝐗+h_tu𝐲_b+𝐧_u
    
    =   𝐡_u𝐗+h_tu( √(α)𝐡_u𝐗⊙𝐜_t+√(α)𝐧_t⊙𝐜_t) +𝐧_u
    
    =   𝐡_u𝐰_u𝐬_u^H+𝐡_u𝐰_t𝐬_t^H+∑_i=1^N_t𝐡_u𝐰_i𝐬_i^H
       +h_tu√(α)𝐡_f𝐰_u𝐬_u^H⊙𝐜_t+h_tu√(α)𝐡_f𝐰_t𝐬_t^H⊙𝐜_t
       +∑_i=1^N_th_tu√(α)𝐡_f𝐰_i𝐬_i^H⊙𝐜_t+h_tu√(α)𝐧_t⊙𝐜_t+𝐧_u.

There are three parts in signal 𝐲_u, containing the signal 𝐡_u𝐗 from the AP, interference h_tu𝐲_b from tag, and 𝐧_u the noise vector at the UE, where 𝐧_u is assumed as  𝐧_u∼𝒞𝒩( 0,σ_u^2𝐈_L ). The SINR of the signal received by UE is given in (<ref>). Thus, the communication rate of UE can be expressed as


    R=log _2( 1+γ _u)




 §.§ Sensing Model


 Tag detection aims to determine whether the tag is present in the environment. The signal received by the AP can be used to perform a signal detection process. We formulate the tag detection problem as a hypothesis testing problem as follows,

    ℋ _0:𝐲̃_ap=𝐰_r𝐍_AP
    ℋ _1:𝐲̃_ap=[√(α)𝐰_r𝐡_b𝐡_f(𝐗+𝐧_t)]⊙𝐜_t+𝐰_r𝐍_ap,

where ℋ _0 means there is no backscatter signal from the tag, ℋ _1 means there is tag echo.
According to Neyman-Pearson criterion <cit.>, the following detector can be obtained

    Re{𝐲̃_ap (√(α)𝐰_r𝐡_b𝐡_f𝐗)^H }[ ℋ_1⩾; ℋ_0<;      ]  η,

where η is the detection threshold. The detection probability of the tag denoted as P_D is given by <cit.>

    P_D=1/2erfc{erfc^-1( 2P_F) -√(γ _ap)},

where erfc( x ) =2/√(π)∫_x^∞e^-t^2dt is  the complementary error function. P_F is the probability of false alarm. According to (<ref>), the tag detection probability P_D is a monotonically increasing function of γ _ap. Therefore, the SINR γ _ap of the echo signal can actually represent the ability to detect the tag of the B-ISAC system. In other words, the uplink communication capability of the tag is directly proportional to the ability of the tag detection.



§ JOINT BEAMFORMING SCHEME FOR COMMUNICATION RATE OPTIMIZATION
 
In this section, we focus on the beamforming design for optimizing the communication rate of the UE. we consider the case that the AP has detected the tag and has obtained the information of the channel 𝐡_b and 𝐡_f. We consider the problem of maximizing the communication rate of communication UE under the constraints of energy budget, SINRs at the tag and AP. The SINR constraint at the tag ensures that the tag remains activated, while the SINR constraint at the AP ensures the detection probability and uplink communication rate of the tag.
The optimization problem is given by

 
    ( 𝒫 _1 )     maximize_  𝐖      log _2( 1+γ _u) 
        subject to      γ _t⩾γ _tth
             γ _ap⩾γ _apth
             Tr( 𝐖𝐖^H ) ⩽ P_T,


 where γ _t⩾γ _tth is to set a threshold γ _tth for the to ensure the tag be activated,  γ _ap⩾γ _apth is to set a threshold γ _apth to ensure the uplink communication rate and remain the tag be detected. P_T is the total transmit power, Tr( 𝐖𝐖^H ) ⩽ P_T is a total power budget constraint for joint beamforming matrix.
 
Since only a single communication UE is considered, optimizing the rate is equivalent to optimizing the communication SINR γ _u. However, according to (<ref>), γ _u has a complicated fractional form. By introducing an auxiliary variables y, we can convert the fractional objective function into polynomial form by quadratic transform <cit.>. The new objective function ℱ( 𝐖,y ) is given by (<ref>). Then the optimization problem can be expressed as





 
    ( 𝒫 _1.1)     maximize_  𝐖,y      ℱ( 𝐖,y )
    
        subject to      γ _t⩾γ _tth
             γ _ap⩾γ _apth
             Tr( 𝐖𝐖^H ) ⩽ P_T,


where ℱ( 𝐖,y )  is a conditionally concave
function with respect to each variable given the other. Therefore, we can develop an alternating optimization method to solve this problem.

Update y: Given 𝐖, the optimization for the auxiliary variables y is a convex problem without constraints, given as

    ( 𝒫 _1.1.1)     maximize_  y      ℱ( 𝐖,y ).

Its optimal solution can be obtained straightforwardly by setting ∂ℱ/∂ y=0. The optimal y^* is given by (<ref>).

Update 𝐖: Given y, the optimization problem for updating 𝐖 can be expressed as 


 
    ( 𝒫 _1.1.2)     maximize_  𝐖=[𝐰_u,𝐰_t,𝐰_1,…,𝐰_N_t]       ℱ( 𝐖,y )
    
               subject to      γ _t⩾γ _tth
             γ _ap⩾γ _apth
             Tr( 𝐖𝐖^H ) ⩽ P_T.


Note that the objective function is concave with respect to 𝐖. The main challenge is the non-convex constraints  (<ref>) and (<ref>). According to (<ref>), the
(<ref>) can be rewritten as

    1/γ _tth|𝐡_f𝐰_t|^2⩾ |𝐡_f𝐰_u|^2+∑_i=1^N_t|𝐡_f𝐰_i|^2+σ _t^2.

By taking root square of both side of (<ref>), the constraint becomes a second-order cone form, which is given by

    √(1/γ _tth)Re{𝐡_f𝐰_t}⩾[   𝐡_f𝐰_u;   𝐡_f𝐰_1;   𝐡_f𝐰_2;        ⋮; 𝐡_f𝐰_N_t;     σ _t;          ] .

The original form of left hand side of (<ref>) after taking root square is √(1/γ _tth)| 𝐡_f𝐰_t|. While we find that any phase rotation does not affect the absolute value, i.e., | 𝐡_f𝐰_t|= | 𝐡_f𝐰_te^jθ|. Without changing the absolute value, we can always find a 𝐰_t  to make the 𝐡_f𝐰_t positive and real. Therefore, the constraint (<ref>) can be rewritten as (<ref>).

According to (<ref>), the constraint (<ref>) can be rewritten as 
 
    α/γ _apth|𝐰_r𝐡_b|^2  
    Tr( 𝐅𝐖𝐖^H ) ⩾[ √(α)|𝐰_r𝐡_b|σ _t;          𝐰_rσ_ap;                  ]^2 .

where 𝐅=𝐡_f^H𝐡_f.
Now, the main limitation for solving this problem is that constraint (<ref>) is not an affine constraint. In order to address this issue, we adopt successive convex approximation (SCA) based method <cit.> to solve it. Given a 𝐖^, the convex approximation of (<ref>) at 𝐖^ is given by
 
    α/γ _apth|𝐰_r𝐡_b|^2 Tr( 𝐅𝐖^𝐖^ H)
    
    +   α/γ _apth|𝐰_r𝐡_b|^2Tr[ 𝐖^H𝐅(𝐖-𝐖^)+𝐖^T𝐅^T(𝐖-𝐖^)^* ]
    
    ⩾   [ √(α)|𝐰_r𝐡_b|σ _t;          𝐰_rσ_ap;                  ]^2 .


The convex approximation problem of ( 𝒫 _1.1.2.1) can be written as follows,

 
    ( 𝒫 _1.1.2.1)     maximize_  𝐖      ℱ( 𝐖,y )
    
        subject to      (<ref>)
             (<ref>)
             Tr( 𝐖𝐖^H ) ⩽ P_T.



The SCA based algorithm for solving ( 𝒫_1.1.2.1) is summarized in Algorithm <ref>. Based on the above derivations, the optimal joint beamformer can be obtained by updating y and 𝐖 iteratively. The alternating joint beamforming design algorithm for communication rate optimization is summarized in Algorithm <ref>. With appropriate initialization of y and 𝐖 in the feasible space, we could iteratively update each variable until convergence.
 
 

 
 








§ NUMERICAL RESULTS
 
In this section, we present numerical results of the proposed beamforming schemes. We set the transmit and receive array with the same elements number, i.e., N_t =N_r=16. We assume that the noise power at the AP, tag, and UE are equal as σ _ap^2=σ _t^2=σ _u^2=-40 dBm. We use the line-of-sight (LOS) channel model in the simulation, which means that if the tag is at angle θ_k, the corresponding channel 𝐡_f is α_f𝐚(θ_k) and the channel 𝐡_b is α_b𝐛(θ_k). If the UE is at angle θ_j, the corresponding channel 𝐡_u is α_u𝐚(θ_j). 𝐚 and 𝐛 are the steering vector of the transmit and receive array respectively. α_f, α_b, and α_u are channel fading coefficients respectively.

First, we analyze the convergence of the proposed Algorithm <ref> and Algorithm <ref>. The convergence performance of the algorithms are presented in Fig. <ref>(a) and Fig. <ref>(b), respectively. The achievable communication rate versus the number of iterations under different setting is present in the figure. Algorithm <ref> converges after 10 iterations. In particular, after 5 iterations, the change of rate is already minor. Algorithm <ref> converges after 5 iterations. In particular, after 2 iterations, the change of rate is already minor. The above simulation results fully demonstrate the quick convergence performance of the proposed algorithms.

Then, we evaluate the beampattern of the proposed joint beamforming scheme for communication rate optimization (J.B.C). We set the transmit power of the AP as P_T=0 dBm, and set h_tu=0.5. We set the channels to 𝐡_f=0.8𝐚(π/4), 𝐡_b=0.8𝐛(π/4), and  𝐡_u=0.8𝐚(7π/10). The SINR threshold at the tag is set to γ_tth=15dB to ensure the tag is activated. The SINR threshold at the AP is set to γ_tth=12dB to make sure the tag can be detected and communicate with the AP. The beampattern of the proposed J.B.C scheme is presented in Fig. <ref>. J.B.C (Proposed, Overall Signal), J.B.C (Proposed, Communication Signal), J.B.C (Proposed, Tag Signal), and J.B.C (Proposed, Dedicated Probing Signal) are beampatterns of the overall signal, the communication signal, the tag signal, and the dedicated probing signal produced by the proposed J.B.C scheme (solving problem  ( 𝒫 _1 )) respectively. Orthogonal Beam is the full orthogonal beamforming scheme. We can observe that the communication beam forms a high gain beam at the communication UE direction and a notch at the tag direction. In order to maximize the UE communication rate, the tag signal and dedicated probing signal produce a high-gain beam in the tag direction and a notch in the communication direction.

The achievable communication rate with respect to the
transmit power under different settings is depicted in Fig. <ref>. We can also find that the communication performance of the proposed J.B.C scheme increases with the transmit power. We can also observe that the higher the SINR constraints, the lower the achievable communication rate, which reflects the power competition between the tag and UE.

In this work, we only consider the UE communication performance optimization in B-ISAC systems. The design for more task modes of B-ISAC systems is studied in <cit.>. In addition, the design of B-ISAC systems with multiple UEs and multiple RF tags is also a very interesting topic, which we leave as our future work.



§ CONCLUSION
 
We proposed an integrated BackCom and ISAC system called B-ISAC system in this work. We provided a theoretical analysis of the communication and sensing performance of the system. A joint beamforming scheme is designed to optimize the UE communication rate under the constraints of energy budget, SINRs at the tag and AP to ensure the tag sensing and communication performance. Moreover, efficient algorithms were developed for solving the complicated optimization problem. Simulation results validate the effectiveness of the proposed algorithms as well as illustrating the performance trade-off between communication and sensing performance. 




§ ACKNOWLEDGMENT

The work was supported in part by the National Natural Science Foundation of China under Grant 62388102, and the GuangDong Basic and Applied Basic Research Foundation under Grant 2022A1515010209. The corresponding author is Dr. Yuhan Dong.


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Hassan2016 A. Hassanien, M. G. Amin, Y. D. Zhang, and F. Ahmad, “Signaling strategies for dual-function radar communications: An overview,” IEEE Aerosp. Electron. Syst. Mag., vol. 31, no. 10, pp. 36–45, Oct. 2016.

Zhao2022 Z. Zhao, X. Tang, and Y. Dong, “Cognitive waveform design for dual-functional MIMO radar-communication systems,” in Proc. IEEE Global Commun. Conf. (GLOBECOM), Dec. 2022, pp. 5607–5612.

Liu2023 F. Liu, et al., “Seventy years of radar and communications: The road from separation to integration,” IEEE Signal Process Mag., vol. 40, no. 5,  pp. 106–121, Jul. 2023.

LiuX2020 X. Liu, T. Huang, N. Shlezinger, Y. Liu, J. Zhou, and Y. C. Eldar, “Joint transmit beamforming for multiuser MIMO communications and MIMO radar,” IEEE Trans. Signal Process., vol. 68, pp. 3929–3944, Jun. 2020.

Zhao2024 Z. Zhao, et al., “Joint beamforming scheme for ISAC systems via robust Cramér–Rao bound optimization,” IEEE Wireless Commun. Lett., vol. 13, no. 3,  pp. 889–893, Jan. 2024.

Niu2019 J. -P. Niu and G. Y. Li., “An overview on backscatter communications,” J. Commun. Inf. Networks , vol. 4, no. 2, pp. 1–14, Jun. 2019. 

Jiang2023 T. Jiang, et al., “Backscatter communication meets practical battery-free internet of things: A survey and outlook,” IEEE Commun. Surveys Tuts., vol. 25, no. 3, pp. 2021–2051, third quarter 2023.

Gala2023 D. Galappaththige, C. Tellambura, and A. Maaref., “Integrated sensing and backscatter communication,” IEEE Wireless Commun. Lett., vol. 12, no. 12, pp. 514–528, Dec. 2023. 

Luo2023 H. Luo, U. Demirhan, and A. Alkhateeb., “ISAC with backscattering RFID tags:
Joint beamforming design,” to appear in IEEE Intern. Commun. Conf. (ICC), arXiv:2401.09761. 

Biguesh2006 M. Biguesh, and A. B. Gershman, “Training-based MIMO channel
estimation: A study of estimator tradeoffs and optimal training signals,” IEEE Trans. Signal Process., vol. 54, no. 3, pp. 884–893, Feb. 2006.

Neyman1992 J. Neyman and E. S. Pearson, “On the problem of the most efficient tests of statistical hypotheses,” Philosophical Trans. the Royal Society of London, vol. 231, no. 694–706, pp. 289–337, 1992.

Tang2022 B. Tang and P. Stoica, “MIMO multifunction RF systems: Detection performance and waveform design,” IEEE Trans. Signal Process., vol. 70, pp. 4381-4394, Aug. 2022.

Shen2018 K. Shen and W. Yu, “Fractional programming for communication systems-part I: Power control and beamforming,” IEEE Trans. Signal Process., vol. 66, no. 10, pp. 2616–2630, May 2018.

Scutari2014 G. Scutari, F. Facchinei, P. Song, D. P. Palomar and J. S. Pang, “Decomposition by partial linearization: Parallel optimization of multi-agent systems,” IEEE Trans. Signal Process., vol. 62, no. 3, pp. 641–656, Feb. 2014.

Zhaoz2024 Z. Zhao, Y. Dong, T. Wei, X.-P. Zhang, X. Tang, and Z. Liu “B-ISAC: Backscatter integrated sensing and communication for 6G IoE applications,” arXiv:2407.19235.

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