Multiple Signal Classification Based Joint Communication and Sensing System

Joint communication and sensing (JCS) has become a promising technology for mobile networks because of its higher spectrum and energy efficiency. Up to now, the prevalent fast Fourier transform (FFT)-based sensing method for mobile JCS networks is on-grid based, and the grid interval determines the resolution. Because the mobile network usually has limited consecutive OFDM symbols in a downlink (DL) time slot, the sensing accuracy is restricted by the limited resolution, especially for velocity estimation. In this paper, we propose a multiple signal classification (MUSIC)-based JCS system that can achieve higher sensing accuracy for the angle of arrival, range, and velocity estimation, compared with the traditional FFT-based JCS method. We further propose a JCS channel state information (CSI) enhancement method by leveraging the JCS sensing results. Finally, we derive a theoretical lower bound for sensing mean square error (MSE) by using perturbation analysis. Simulation results show that in terms of the sensing MSE performance, the proposed MUSIC-based JCS outperforms the FFT-based one by more than 20 dB. Moreover, the bit error rate (BER) of communication demodulation using the proposed JCS CSI enhancement method is significantly reduced compared with communication using the originally estimated CSI.

FD capability, as detailed in [10]. Therefore, the self-leakage between arrays is ignored and not considered in the signal model in this paper. One BS array is used for transmitting the DL JCS signal, and the other is used for consistently receiving echoes of the JCS signal. MUE receives the JCS signal to demodulate the communication data, while BS receives the echoes to estimate the AoAs, ranges, and velocities. Moreover, we consider that both BS and MUE receive the superimposed co-channel interference from multiple reflected interference sources (ISs). The MUE is equipped with one UPA for receiving the communication signal. The array sizes of the BS and MUEs are P t × Q t and P r × Q r , respectively. where ϕ k is the azimuth angle, and θ k is the elevation angle. We use A p,q to denote the (p,q)th antenna element, and A 0,0 to represent the reference antenna element. Then, the phase difference between A p,q and A 0,0 is expressed as a p,q (p) = exp −j 2π λ d a (p cos ϕ sin θ+q sin ϕ sin θ) ,

B. UPA Model
where λ = c/f c is the wavelength of the carrier, c is the speed of light in vacuum, and f c is the carrier frequency.
The steering matrix for K far-field signals is then represented as which is a matrix of dimension P Q × K.

C. DL JCS Signal and Channel Model
In this paper, we consider the JCS system using OFDM-based signals. The transmitting signal is s D (t) = where P t is the DL transmit power, d n,m is the mth baseband OFDM symbol of the nth subcarrier, ∆f is the subcarrier interval, T = T s + T g , T s = 1 ∆f is the duration of OFDM symbol, T g is the guard interval, M s and N c are the number of OFDM symbols and subcarriers, respectively, and Rect (t/T ) is the rectangular window function of duration T . When the DL preamble signal for beam alignment and CSI estimation is transmitted, d n,m is replaced by the preamble symbols, denoted byd n,m , which is known and deterministic to both BS and MUE. When the DL data signal is transmitted, d n,m ∈ Θ QAM is a random symbol, where Θ QAM is the constellation of quadrature amplitude modulation (QAM). Note that d n,m is known to BS but unknown to MUE.
Next, we present the JCS channel model. As illustrated in Fig. 1, the DL JCS channel comprises a communication channel and an echo sensing channel.
• The JCS communication channel consists of a line-of-sight (LoS) path and several nonline-of-sight (NLoS) scattering paths.
• The JCS echo sensing channel consists of the echo path from MUE as a scatterer, and the echo paths from other scatterers which may or may not contribute to the communication channel. Since the signals after multiple reflections are much smaller than those with only one reflection, we only consider echoes directly reflected from scatterers.
Then, the JCS sensing echo and communication channels at the nth subcarrier of the mth OFDM symbol are defined as [5], [8] where p T X,l is the AoD of BS's JCS transceivers, a(p T X,l ) ∈ C PtQt×1 is the corresponding transmit steering vectors as given in (2), L is the number of scatterers, l = 0 is for the direct path between BS and MUE, l = 1, · · · , L − 1 is for the reflected paths involved the lth scatterer.
Moreover, i = S and i = C represent the echo sensing and communication channels, respectively; p S RX,l and p C RX,l are the AoAs of BS's echo receiver and the MUE's communication receiver, respectively; and α S,n,m,l and α C,n,m,l are the channel fading for the lth sensing echo path and communication path, respectively. 1) JCS Echo Sensing Channel: When i = S, a(p S RX,l ) ∈ C PtQt×1 is the receive steering vector for the lth echo sensing path, as given in (2). Since the mmWave array is typically small, p S RX,l = p T X,l . Moreover, α S,n,m,l is the fading factor for the lth echo (when l = 0, MUE acts as a scatterer), which is given by where f s,0,1 = 2v r,0,1 λ and τ s,0 = 2d 0,1 c are the echo Doppler frequency shifts and time delay between BS and MUE, with v r,0,1 and d 0,1 being the corresponding radial relative velocity and the distance, respectively; f s,l,1 = 2v r,l,1 λ and τ s,l = 2d l,1 c are the echo Doppler frequency shifts and time delay between BS and the lth scatterer, with v r,l,1 and d l,1 being the corresponding radial relative velocity and distance, respectively. Moreover, b S,l = λ 2 (4π) 3 d l,1 4 β S,l , and β S,l is the random reflection fading factor of the lth scatterer, following the complex Gaussian distribution with zero mean and variance σ 2 Sβ,l . 2) JCS Communication Channel: When i = C, a(p C RX,l ) ∈ C PrQr×1 is the receive steering vector for the lth communication path, as given in (2). Moreover, α C,n,m,l is the fading factor for the lth path, and is expressed as where f c,d,0 = v r,0    and time delay between BS and scatterer, and between the scatterer and MUE of the lth NLoS path, respectively, with v r,l,2 and d l,2 being the radial relative velocity and distance between the lth scatterer and MUE, respectively; b C,0 = λ 2 (4πd 0 ) 2 is the propagation loss of the LoS path, and b C,l = λ 2 (4π) 3 d l,1 2 d l,2 2 β C,l is the path fading factor of the lth NLoS path with β C,l being the scattering factor of the lth scatterer. Here, β C,l is the random reflecting factor of the scatterer in the lth path, which is assumed to follow the complex Gaussian distribution with zero mean and variance σ 2 Cβ,l . Due to the existence of b C,l , the LoS path is much stronger than the NLoS path for mmWave.
Note that H C,n,m is unknown and needs to be estimated by utilizing the DL preambles,d n,m .
The parameters of H S,n,m are unknown, and BS has to estimate the AoA, range and Doppler in H S,n,m . Since BS acts as both the sensing transmitter and receiver, both d n,m andd n,m can be used for DL sensing. Moreover, l = 0 represents a special path, for which the echo time delay and Doppler are twice of those in the communication channel, which is the theoretical basis for the JCS CSI enhancement method to be introduced in Section III-B.

D. JCS Received Signal Model
In this subsection, we present the expressions for DL JCS received signals.

1) DL Communication Received Signal:
The frequency-domain DL communication signal received by MUE at the mth OFDM symbol of the nth subcarrier is expressed as y C,n,m = P t d n,m (w RX ) H H C,n,m w T X + n X C,n,m , where w T X ∈ C PtQt×1 and w RX ∈ C PrQr×1 are the JCS transmit and communication receive beamforming (BF) vectors, respectively; w T X 2 2 = w RX 2 2 = 1. In this paper, the lowcomplexity least-square (LS) method is used to generate w T X and w RX for BF. BS utilizes the known DL preambles, i.e., d n,m =d n,m , to conduct beam alignment with MUE. When beam alignment is completed, w T X = c 1 [a T (p T X,0 )] † and w RX = c 2 [a(p RX,0 )] † , where c 1 and c 2 are both arbitrary complex values with modulus 1, [·] † is the pseudo-inverse operation,p T X,0 ≈ p T X,0 , andp RX,0 ≈ p C RX,0 . Simultaneously, the unknown communication CSI, (w RX ) H H C,n,m w T X , can be estimated by processing the received preambles.
Moreover, n X C,n,m = n C,n,m +ξ C,n,m is the sum of noise and interference, n C,n,m = (w RX ) H n C,n,m and ξ C,n,m = (w RX ) H x C,n,m are transformed noise and interference, the dimensions of n C,n,m and x C,n,m are both P r Q r × 1, n C,n,m is Gaussian noise vectors with each element following , and x C,n,m is the reflected interference signals from other network devices. We assume there are N ic ISs, and the reflected fading for each IS follows a Gaussian distribution.
Since the superimposed one of multiple random OFDM signals is noise-like, the pth element of x C,n,m can be given as where P i,c is the power of incident signal from the ith IS, and β I i,p ∼ CN (0, 1).
. Further, we define the communication SINR (C-SINR) as where h C,n,m = (w RX ) H H C,n,m w T X is the gain of DL communication signal at each antenna element.
2) DL Echo Sensing Received Signal: The echo signal that BS receives for the mth OFDM symbol at the nth subcarrier is given by y S,n,m = P t d n,m H S,n,m w T X +n X S,n,m = P t d n,m L−1 l=0 (α S,n,m,l )χ T X,l a(p S RX,l ) +n X S,n,m , (10) where χ T X,l = a T (p T X,l )w T X represents the gain of the DL JCS transmit BF, n X S,n,m = n S,n,m + x S,n,m is the sum of noise and interference, n S,n,m is the Gaussian noise vector with each element following CN (0, σ 2 N ), x S,n,m is the superimposed interference vector for N is reflected ISs, and the dimensions of n S,n,m and x S,n,m are P t Q t × 1. Similar to x C,n,m , the pth element of x S,n,m can be given as where h S,n,m,l = α S,n,m,l χ T X,l is the gain of DL echo sensing signal at each antenna element.
By defining s n,m,l = √ P t d n,m α S,n,m,l χ T X,l and s n,m = [s n,m,l ]| l=0,1,...,L−1 , (10) can be expressed in the matrix form as where A S,RX = [a(p S RX,l )]| l=0,1,...,L−1 is the steering matrix stacked by steering vectors of L echoes, A S,RX ∈ C PtQt×L , and s n,m ∈ C L×1 . By stacking all the M s OFDM symbols with N c subcarriers, we have

III. DL JCS SIGNAL PROCESSING
In this section, we demonstrate the signal processing for DL JCS sensing and communication, which is shown in Fig. 3. We first present the sensing signal processing scheme, and then elaborate on the JCAS CSI enhancement method.

A. JCS Sensing Signal Processing
In this subsection, we first present the conventional MUSIC method for estimating the 2D AoAs, and then introduce the novel MUSIC-based range and Doppler estimation method.

1) JCS MUSIC 2D Angle Detection:
First, the correlation matrix of Y S is obtained as By applying eigenvalue decomposition to R X , we have where Σ x is the real-value eigenvalue diagonal matrix in descending order, and U x is the orthogonal eigen matrix. Calculate the average of eigenvalues and denote it as m x . Let α t be a preset threshold, which is determined as elaborated in Appendix A. Then, the number of echo paths is determined as the number of eigenvalues no smaller than α t m x , denoted by N x .
Construct U N = U x (:, N x + 1 : P t Q t ) 1 as the noise subspace basis. We then use it to obtain the spatial angular spectrum function as [12] f a (p; where p = (ϕ, θ) is the 2D angle, and a (p) is given in (2). The spatial spectrum is represented The maximum points of S a (p; U N ), i.e., the minimum points of f a (p; U N ) are the estimated AoAs [13]. We first find N x local maximum points of S a (p; U N ) using a grid searching method with relatively large granularity, then we use the Newton descent method to identify the accurate minimum point of f a (p; U N ) by inputting the above local maximum points as initial points for iteration.
2) JCS Range and Doppler Detection: After the AoAs are obtained, through BF at the AoA of interest, the filtered received signal at the nth subcarrier of the mth OFDM symbol can be expressed as where w t,n,m,k =(w RX,S,k ) H n X S,n,m is the transformed noise and interference with zero mean and variance σ W 2 , RX,l,k = (w RX,S,k ) H a(p S RX,l ) is the receive BF gain, and w RX,S,k is the receive BF vector for the kth AoA, k ∈ [0, 1, ..., N x − 1]. Note that RX,k,k is typically larger than RX,l,k (l = k) due to the narrow beam feature of mmWave. By substituting (6) into (18), we obtain (19).
In (19), there are independent complex exponential functions for range and Doppler, i.e., e −j2πn∆f ( r l c ) and e j2πf s,l,1 mT , respectively. Here, we define the range and Doppler steering vectors as respectively. The range and Doppler steering matrices are defined as where A r ∈ C Nc×L , and A f ∈ C Ms×L . Stackȳ S,n,m,k into a matrixȲ S where Ȳ S n,m =ȳ S,n,m,k , then erase the communication where the division is element-wise, andH S ∈ C Nc×Ms .
According to (19),H S can be expressed by A r as where On the other hand, the transpose ofH S , i.e., H S T , can be presented by A f as where The range and Doppler can be estimated via the autocorrelation ofH S and H S T , which are given by respectively. Denote the noise subspaces of R X,r and R X,f as U x,rN and U x,f N , respectively.
Theorem 1. The minimum of U x,rN H a r (r) 2 2 , denoted by r s,l , is linked to the range via r s,l = 2d l,1 . The minimum of U x,f N H a f (f ) 2 2 corresponds to the Doppler value, f s,l,1 .
Proof. The proof is presented in Appendix C.
By applying eigenvalue decomposition to R X,r and R X,f , we have where Σ x,r and Σ x,f are the real-value diagonal matrices of eigenvalues in the descending order, and U x,r and U x,f are the corresponding eigenvector matrices.
We use m x,r to denote the mean value of Σ x,r , and then set the threshold α t,r using the method in Appendix A by replacing Σ x with Σ x,r . The number of targets in the AoA of interest, N x,r , is then determined as the number of eigenvalues no smaller than α t,r m x,r . Then, the noise subspace basis for range estimation is derived as U x,rN = U x,r (:, N x,r + 1 : N c ). Since the number of targets is the same for both Doppler and range estimation, the noise subspace basis for the Doppler estimation can be derived as U x,f N = U x,f (:, N x,r + 1 : M s ).
We use U x,rN and U x,f N to derive the range and Doppler spectrum functions as respectively. The range and Doppler spectra can be given by respectively.
The maximum points of S r (r; U x,rN ) and S f (f ; U x,f N ), i.e., the minimum points of f r (r; U x,rN ) and f f (f ; U x,f N ), are the range and Doppler estimation values, denoted byr s,l andf s,l , respectively. The distance, d l,1 , and radial velocity, v r,0,1 , between BS and the target are given bŷ The minimum of f r (r) and f f (f ) can be identified using a two-step Newton descent method.
We first find the local maximum points of S r (r) and S f (f ) with large-granularity grid searching.
Then, we use the Newton descent method to find the accurate minimum points of f r (r) and f f (f ) using the above local maximum points as the initial points. The iterative expression for the Newton descent method is derived as follows.
By applying the Taylor series decomposition to f r (r) and f f (f ), and taking their first order derivative over r and f , respectively, we obtain ∂f r (r) ∂r and By setting the above first-order derivative to be 0, the iterative descent expression for range and Doppler estimation can be given by respectively. From (29), the first-order and second-order derivatives of f f (f ) and f r (r) are expressed as ∂f r (r) ∂r ∂f f (f ) ∂f =2Re{a (1) where a (1) r (r), and a

B. JCS Communication Signal Processing
By substituting (5) into (8), and taking into consideration that w T X and w RX in (8) where h C,n,m = b C,0 RX,0 χ T X,0 e j2πmTsf c,d,0 e −j2πn∆f τ c,0 is the real communication channel response, and RX,0 = (w RX ) H a(p C RX,0 ) and χ T X,0 = a T (p T X,0 )w T X are the BF transmitting and receiving gains. In the CSI estimation, d n,m =d n,m , and we denote y C,n,m =ȳ C,n,m as the received signal. The CSI estimated with the LS method is expressed as [14] h C,n,m =ȳ where w C,n,m = Output: Filtered sequence [h C,n,m ]| n=0,··· ,Nc−1 .
Step 2: respectively. Based on the prior information obtained by JCS sensing, we propose a Kalman filter-based JCS CSI enhancement method to improve CSI by leveraging the sensing estimation results of JCS.
For the mth OFDM symbol,ĥ C,n,m can be regarded as the observation of h C,n,m as given in (41). Since b C,0 is unchanged for the same OFDM symbol. The state transfer of h C,n,m is given by The Kalman filter algorithm that utilizesΦ = [ĥ C,n,m ]| n=0,··· ,Nc−1 to recursively derive the estimation of Φ = [h C,n,m ]| n=0,··· ,Nc−1 is presented in Algorithm 1, with the details of the Kalman Filter algorithm referenced to [15]. Note that we obtain h C,n,m = e −j2πn∆f τ c,0 h C,0,m from (42), based on which we can further estimate the initial observation variance as After

IV. PERFORMANCE ANALYSIS OF THE JCS PROCESSING
In this section, the analytical MSE results of AoAs, range, Doppler, and location estimation of the proposed MUSIC-based JCS processing are derived using the perturbation method.

A. Analysis of 2D Angle Detection MSE
From (13), the noise term N t can be treated as the perturbation to the useful signal, which is expressed as where Y S,R = A S,RX S is the useful signal. The singular value decomposition of Y S,R can be expressed as where U 0 is the noise subspace basis, and U 0 H Y S,R = 0. Further, we have U 0 H A S,RX = 0.
With noise as perturbation, Y S can be expressed as whereΣ 0 = ∆Σ 0 ,Σ s = Σ s + ∆Σ s , andŨ 0 = U 0 + ∆U 0 . Here,Ũ 0 andŨ s are both orthogonal unitary matrices, andŨ H 0 Y S =∆Σ 0Ṽ H 0 . In the high SINR regime, solving the perturbation problem is equivalent to seeking the optimal ∆U 0 to minimize Ũ H 0 Y S 2 subject to the constraintŨ H 0Ũ 0 = I [13]. By substituting (44) The second-order perturbation (∆U 0 ) H N t and U 0 H Y S,R =0 can be discarded. By using the LS method [13], ∆U 0 can be presented as The MUSIC 2D angle estimation result is distorted by the noise perturbation, which is expressed asp k = p k + ∆p k , where p k is the actual value of AoA. Apply Taylor series decomposition to f a (p k ;Ũ 0 ) in (16), and take the first three terms. Applying first-order derivative to the truncated Taylor series, we have By setting (49) to be 0, we can obtain where H p (p k ;Ũ 0 ) = ∂ 2 fa(p k ;Ũ 0 ) With the perturbation expression, we can obtain From (16), we have where vec(·) is to vectorize a matrix, a p (p) and a (2) p (p) are the first-order and second-order derivatives of a(p) over p, respectively, which can be derived from (2).
Since U 0 H A S,RX = 0, we can obtain We use H p0 to represent H p (p k ; U 0 ). By substituting (55) and (56) into (51) and (52), (50) can be rewritten as Discarding the perturbation terms that are higher than second-order in (57), we can rewrite (57) as where the perturbation expression of ∆G p is derived in Appendix D as By substituting (59) and (56) into (58), we can obtain ∆p k as shown in (60).
The MSE of angle estimation can be expressed as  (25), is rewritten asH whereH S,p = A r S r,s is the useful signal. The singular value decomposition ofH S,p is where U r,s and U r,0 are orthogonal unitary matrices, and U r,0 HH S,p = 0. We further obtain U r,0 H A r = 0.
By treating W tr as a perturbation term,H S can be decomposed as

C. Analysis of Location MSE
The location of the target can be obtained after the AoA, p k = (ϕ k , θ k ), and the range, r k , are detected. The expression for the actual location is given by p loc (r k , ϕ k , θ k ) = (x k , y k , z k ) = (r k sin θ k cos ϕ k , r k sin θ k sin ϕ k , r k cos θ k ).
With the AoA and range estimation perturbation, ∆p k = (∆ϕ k , ∆θ k ) and ∆r k , the location of the target is Comparing (81) with (82) and discarding the second-order perturbation, we can represent the perturbation of x, y, and z axes coordinates as ∆x .
Finally, the location error can be expressed as

D. Cramer-Rao bound of JCS Sensing
We further derive the Cramer-Rao bound (CRB) to characterize the minimum lower bound for sensing. Based on the signal model presented in Section II-D2, the echo signal of the lth target received by the (p, q)th antenna element at the nth subcarrier of the mth OFDM symbol is y p,q S,n,m,l = P t d n,m α S,n,m,l χ T X,l a p,q (p l ) + n p,q S,n,m + x p,q S,n,m , where α S,n,m,l = b S,l e j2πmTs2v s,l /λ e −j2πn∆f 2r s,l /c is given as (6), v s,l = v r,l,1 and r s,l = d l,1 are the radial relative velocity and distance between BS and the lth target, respectively; a p,q (p l ) is given in (1), p l = p T X,l = (ϕ l , θ l ) is the 2D AoA of the lth target; χ T X,l is the transmitting BF gain; n p,q S,n,m and x p,q S,n,m are the noise and interference at the (p, q)th antenna element. Let n X,p,q S,n,m n p,q S,n,m + x p,q S,n,m , then n X,p,q S,n,m is independent and identically distributed, following CN (0, σ 2 W ), where σ 2 W = P IS + σ 2 N . Let ψ = (r s,l , v s,l , ϕ l , θ l ) be the set of estimation parameters. Then, the distribution of y p,q S,n,m,l is p(y; ψ)= 1 πσ 2 W e − y− √ Ptdn,mα S,n,m,l χ T X,l ap,q(p l ) 2 2 /σ 2 Because there are N c M s P t Q t independent symbols used for estimation, the joint distribution of these symbols is (n,m,p,q) y p,q n,m −sn,mα S,n,m,l ap,q( where ρ = ( 1 πσ 2 W ) NcMsPtQt , and s n,m = √ P t d n,m χ T X,l . Note that d n,m is independent and identically distributed with E( d n,m 2 2 ) = 1. According to [16], [17], the CRB of ψ i , ψ i ∈ (r s,l , v s,l , ϕ l , θ l ), is given by  With (89) and (90), the sensing CRBs are derived as (q cos ϕ l sin θ l −p sin ϕ l sin θ l ) 2 , C θ l = λ 2 8π 2 d 2 a γ S NcMs p,q (p cos ϕ l cos θ l +q sin ϕ l cos θ l ) 2 , where γ S is the S-SINR as given in (11).

E. Complexity Analysis and Comparison
In this section, we analyze and compare the complexity of the proposed MUSIC-based JCS method with the conventional FFT-based methods. We consider three schemes: Scheme 1 is the proposed MUSIC-based method; Scheme 2 is the original FFT-based method in [6]; and Scheme 3 is the Code-division OFDM (CD-OFDM) FFT-based method in [8]. It can be seen that Scheme 2 has the lowest complexity. The complexity of Scheme 3 increases due to the additional code-division multiplex processing. The complexity of our proposed MUSIC-based JCS method has the highest complexity to achieve super-resolution detection.

V. NUMERICAL AND SIMULATION RESULTS
In this section, we present extensive simulation results for the proposed MUSIC-based JCS processing method, with comparison to the Schemes 2 and 3 as described in Section IV-E, and verify them against the analytical performance bounds derived in Section IV. We also compare the BER results of communication demodulation for the proposed JCS CSI enhancement method with those in conventional communication systems.

A. System Setup
The system setup largely follows the specification in the 3GPP Vehicles-to-Everything (V2X) applications [18]. The carrier frequency is 63 GHz, the antenna interval, d a , is half of the wavelength, the sizes of antenna arrays of BS and MUE are P t ×Q t = 8×8 and P r ×Q r = 1×1,

B. Sensing Performance
We first demonstrate the sensing spectra of schemes 1, 2, and 3. The normalized range spectrum and radial velocity spectrum are shown in Figs. 4(a) and 4(b), respectively. The S-SINR is γ S,n,m = −20 dB. For range estimation as shown in Fig. 4(a), the peak to sidelobe ratio (PSLR) of scheme 1 is about 26 dB. By contrast, the PSLRs of schemes 2 and 3 are both around 10 dB.
For radial velocity estimation as shown in Fig. 4  the AoA estimation MSE decreases as the receiving signal power increases. As the S-SINR is larger than −27 dB, the AoA estimation MSE is less than 0.5 square degrees. Since the range of azimuth angle, ϕ k , is larger than the elevation angle, θ k , the MSE of ϕ k is larger than θ k at first. With S-SINR becoming large enough, the MSE of ϕ k approaches that of θ k .  achieves better location MSE than scheme 3. The gaps between scheme 1 and scheme 3 are not so large in the high SINR regime. This is because the AoA estimation error dominates the location MSE. More specifically, E{(r s,l − r s,l ) 2 } is smaller than 10 −1 m 2 , while the error of location as shown in (83), (84), and (85) can be much larger than E{(r s,l − r s,l ) 2 }, because they are related to r s,l .

C. Communication Performance
We  , according to (9) and (11) under the assumption γ IN C = γ IN S = 3 dB. Due to the CSI estimation error caused by noise and interference, the BER for case B is significantly larger than that for case A. As C-SINR increases, the BER for case C decreases rapidly and becomes lower than that for case B after C-SINR is larger than 20 dB. This is because the JCS CSI enhancement method exploits the accurate sensing results and improves the estimated CSI. By comparing case D with cases B and C, we can see that the BER for case D is much larger, which indicates that the FFT-based JCS sensing results are not helpful for improving the CSI and for communication. Referring to the sensing MSEs of the MUSIC-based and the FFT-based JCS in Fig. 5(b), we can see that the more accurate the sensing results are, the better CSI enhancement performance is, as the accuracy of range estimation directly determines the accuracy of A in Algorithm 1. This is also the reason that the BER for case C decreases rapidly when the sensing MSE becomes sufficiently low.

VI. CONCLUSION
In this paper, we proposed a novel JCS system that can achieve accurate AoA, range, and velocity estimation based on improved MUSIC algorithms, together with improved communication performance. Compared with the conventional FFT-based sensing method, our proposed [ where P i is the power of the ith incident signal, σ 2 N is the noise power. We define the differential vector of v [v ∆ ] k /(N − (N − 1)/2 ), andv is close to 0. Therefore, the number of detected targets is determined asL where ε is a parameter used to avoid false detection caused by a small error. In the simulation, we set ε = 1.
Therefore, α t is set as α t = [v x ]L/m x . It is a key parameter and has an important impact on sensing accuracy. When α t is too large, the selected noise subspace will include part of the signal subspace, and thus the target may be missed; when α t is too small, the noise subspace is not selected completely, and thus large noise may be taken into the signal space. [v x ] i /(N c − 1). On one hand, since U x,rN is the noise subspace of R X,r , we have