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Joint resource allocation and user association for multicell integrated sensing and communication systems
EURASIP Journal on Wireless Communications and Networking volume 2023, Article number: 64 (2023)
Abstract
The densification of the orthogonal frequency division multiplexing (OFDM) based fifthgeneration communication systems, as well as the requirement of integrating sensing and communication functionalities, has promoted the development of integratedsensingandcommunication (ISAC) dense cellular networks (DCNs). In the OFDMbased ISACDCN, multiple base stations simultaneously serve mobile users and sense targets based on the echo of downlink communication signals. In this paper, we establish the interference model in ISACDCN for sensing and communication. Focusing on the interference management of the ISACDCN, we investigate the multidimension resource allocation problem. In particular, we aim to maximize the network utility by jointly optimizing subband allocation, user association, and transmission power under the sensing signaltointerferenceplusnoise ratio constraint to be solved iteratively. The mixedinteger optimization problem is decoupled into three subproblems. Specifically, a greedy genetic subband allocation scheme is proposed for subband allocation to reduce total interference. We employ the successive convex approximation technique to transform the transmission power control subproblem and solve it via geometric programming. Simulation results illustrate the tradeoff between sensing and communication performances, and show that the proposed algorithm significantly improves the network utility and achieves higher detection probability.
1 Introduction
Integrated sensing and communication (ISAC) has been one of the research hotspots, due to its potential to reduce hardware costs and improve spectral efficiency. Researchers have been devoting their efforts to promoting the realization of ISAC technique [1]. As the waveform adopted by the fifthgeneration (5 G) new radio (NR) [2], the orthogonal frequency division multiplexing (OFDM) waveform has been used widely in modern communication systems, while it also has an excellent ambiguity function, which promotes its application in sensing [3,4,5]. Therefore, developing ISAC techniques based on OFDM waveform can simultaneously satisfy the communication requirement and provide sensing functionality with little change on the existing 5 G systems.
Motivated by the aforementioned advantages, some works have investigated ISAC design in the framework of 5 G NR systems [5,6,7,8,9,10]. In [5], the selfambiguity and crossambiguity functions of several synchronization signals and reference signals (RSs) in OFDM waveform were analyzed. In [6], RSs used for channel estimation in OFDM waveform were multiplexed as sensing signal. Considering the energy efficiency, RS density and power allocation between pilots and data symbols were optimized to minimize the total transmission power, while satisfying the communication and radar sensing requirements. In [7], the 5 G network was utilised to serve as the illumination source for passive bistatic radar to detect the target, which verifies the possibility of 5 Gbased passive bistatic radar. In [8], the base station (BS) was deployed as a monostatic sensor to estimate the targets’ ranges, speeds, and directions of arrival (DoAs) via beam scanning. The targets’ positions were then obtained based on the estimated ranges and DoAs. However, singlestation based sensing faces several problems, e.g., sensing blind areas, limited detection range, and poor robustness. To address this issue, in [9], the authors proposed a novel twophase framework for devicefree sensing in an OFDM cellular network to achieve ISAC, in which adjacent BSs are assigned orthogonal subbands to avoid significant intercell interference. A maximumlikelihood based algorithm was provided to deal with the target association issue to achieve multiBS cooperative sensing. Besides, based on the 5 G NR standard framework configuration, the authors in [10] proposed a staggered framework structure for ISAC cellular network to avoid selfinterference and realize the parallelism of sensing units and communication cells. However, in this scheme, discontinuous OFDM symbols used for sensing will reduce the speed measurement accuracy due to the reduction of coherent accumulation time.
Although the promising dense cellular networks (DCNs) significantly promote the capacity of wireless communication systems [11], as well as more robust and accurate sensing through multiBS cooperation. However, higher frequency reuse among different BSs results in much higher intercell interference (ICI), thereby degrading the performance of both communication and sensing functionalities. Facing this issue, there have been a lot of researches [12,13,14,15,16,17,18,19,20] on suppressing the ICI caused by FR in cellular networks. In general, physical separationbased frequency assignment and transmission power control are two underlying concepts for ICI mitigation [12]. Since the frequency assignment problem is an NP problem, metaheuristic algorithms such as Ant Colony Optimization [13], Differential Evolution [14] and Greedy algorithm [15], as well as branchandbound algorithm [16] were used to effectively solve this problem. In [17], the quality of service under various FR schemes, including partial FR, fractional frequency FR and soft FR, etc., were analyzed. In [18], the authors investigated joint subband and power allocation to improve intercell fairness in femtocell OFDM networks. Moreover, since users are distributed unevenly among cells, the load of BSs is imbalanced, which also leads to the degradation of system communication performance. Therefore, in [15] and [19], (partial) FR and user association schemes were jointly optimized to maximize the network utility or system throughput. In [20], the authors presented a loadaware and selfadapting frequency allocation scheme to cope with the changing traffic conditions.
However, the aforementioned studies only focused on improving communication performance, such as throughput, quality of service, and network utility, while the impact of interference on sensing still needs to be addressed. In [16], the authors studied the sensing interference management in multiple UAV networks through joint channel allocation and power control but did not consider the communication performance. In [21], the authors studied the issue of power control for cooperative ISAC networks under the sensing signaltointerferenceplusnoise (SINR) constraint, where the Lagrangian method was employed. Thus, in this paper, we aim to address the interference management of the OFDMbased ISACDCN via joint resource allocation and user association. In particular, both sensing and communication performances are taken into consideration. For communication performance, we adopt the network utility metric [22], which considers both sumrate and fairness among different users. For sensing performance, to improve the target detection probability, which is directly determined by the SINR of the received echo signals [23], we adopt the SINR of the echo signal received at each BS as the metric.
The main contributions of this paper are summarized as follows.

(1)
The interference models caused by FR in ISACDCN are analyzed from the perspectives of both communication and sensing. Thereafter, a joint resource allocation and user association problem is formulated with the aim of maximizing the network utility of the ISACDCN under both sensing signaltointerferenceplusnoise (SINR) and transmit power constraints.

(2)
The formulated highly nonconvex problem is decomposed into three subproblems, i.e., subband allocation, user association, and transmission power control subproblems, and an alternating optimization based algorithm is proposed to solve the original problem by iteratively solving the three subproblems. In particular, a greedy genetic algorithm (GRGA) is proposed to solve the subband subproblem, while the Hungarian algorithm and successive convex approximation (SCA) technique are utilized to solve the subproblems of user association and transmission power control, respectively.

(3)
The effectiveness of the proposed algorithm in improving the network utility and detection probability is verified through numerical simulation. Compared with both conventional and stateoftheart schemes, the proposed algorithm is able to significantly improve both network utility and detection probability. Moreover, the tradeoff between communication and sensing performances is also illustrated.
The rest of this paper is organized as follows. In Sect. 2, we introduce both system models and interference models of ISACDCN. Then, we formulate a problem of joint subband allocation, user association, and transmission power control in Sect. 3. The algorithm for solving the problem is presented in Sect. 4. Then we present the numerical simulation results as well as discussions in Sect. 5. Finally, we conclude the paper in Sect. 6.
The notations used in this paper are as follows. Lower case normal letters a denote scalars, lowercase bold letters \({\textbf{a}}\) denote column vectors and uppercase bold characters \({{\textbf{A}}}\) denote matrices. \({{\left( \cdot \right) }^{T}}\) represents the transpose.
2 System model
In this section, we first describe the OFDM based ISACDCN model, where multiple BSs simultaneously provide communication services to mobile users, and at the same time sense the targets based on the echo of DL communication signals. Subsequently, we introduce the interference models for both communication and sensing.
2.1 System description
We consider an OFDM based ISACDCN as shown in Fig. 1a, which consists of M BSs, denoted by \({\mathcal {M}} = \{1,\ldots ,M\}\), N (\(N > M\)) mobile users, denoted by \({\mathcal {N}} = \{1,\ldots ,N\}\), and T targets, denoted by \({\mathcal {T}} = \{1,\ldots ,T\}\). Due to the scarcity of spectral resource, we assume only K (\(K < N\)) orthogonal subbands are available, which are denoted by \(\mathcal {K} = \{1,\ldots ,K\}\). The bandwidth of each subband is denoted by B. The transmission power of the BSs are denoted as \({\textbf{p}}= [{p_1},\ldots ,{p_M}]\), where the ith element represents the power of the ith BS. In addition, a central station is deployed and connected to all BSs to perform resource allocation and signal processing [9].
The detailed signal transmission, reflection and interference are illustrated in Fig. 1b. The BSs provide communication services for users via OFDM signal in DL time slots. In a meantime, the DL communication signals are reflected by the targets and received by the BSs, based on which the ISACDCN can cooperatively estimate the targets’ locations [8] as well as velocities. The BSs marked with the same color are assigned the same subband. Such frequency multiplexing between BSs introduces interference to both communication and sensing.
Furthermore, we make the following assumptions for the remainder of this paper:

Each BS occupies one subband. \({w_{k,i}}=1\) denotes BS i is assigned with subband k and 0 otherwise, and \(\sum \limits _{k=1}^{K}{{{w}_{k,i}}=1,} \forall i\in {\mathcal {M}}\).

Each user is associated with one base station. \({u_{i,n}}=1\) denotes user n is associated with BS i and 0 otherwise, and \(\sum \limits _{i = 1}^M {{u_{i,n}} = 1,} \forall n \in {{\mathcal {N}}}\).

Each BS only focuses on the sensing results within a predetermined sensing range to improve the accuracy of cooperative sensing and reduce the appearance of ghost targets. In other words, the target appearing in a certain area is sensed by specific BSs. The sensing range of each BS is set as R.
2.2 Communication interference model
The timedomain signal in one OFDM symbol period transmitted by the ith BS is given by
where L denotes the IFFT size in OFDM modulation, and Q denotes the length of the cyclic prefix (CP).
The received signal at the nth user associated with the ith BS in the lth OFDM sample period is expressed as
where \({{h}_{i,n}}\) denotes the DL communication channel from the ith BS to the nth user, \({w_{k,i}} \in \left\{ {0,1} \right\}\), and \({{z}_{n}} \sim \mathcal{N}\left( {0,\sigma ^2} \right)\) denotes additive white Gaussian noise (AWGN) at the nth user. In addition, \({{h}_{i,n}}\) considers both the smallscale Rayleigh fading effect and path loss effect, and time domain expression is given by
in which \({{f}_{i,n}}\) is a Rayleigh random variable with zero mean and variance \({\sigma }_{r}^{2}\), \({{\rho }_{0}}\) denotes the path loss at the reference distance \({d}_{0}\) = 1 m, \({{d}_{i,n}}\) denotes the distance between BS i and user n, and \({{\tau }_{i,n}}={{{d}_{i,n}}}/c\), with c being the speed of light.
Therefore, the SINR of the received signal at the nth user in the lth OFDM sample period is expressed as [24]
Under static channels and flat transmission power spectral density, the optimal frequency allocation for one BS is equal allocation among its associated users [22]. Therefore, we assume that each user served by the same BS is assigned equal bandwidth. The bandwidth occupied by the user associated with the ith BS is expressed as
where \({u_{i,n}} \in \left\{ {0,1} \right\}\).
The data rate of user n associated with BS i is express as
which is determined by \({{\gamma }_{{{c}_{i}}}}\) and \(B_{i,n}\). According to (4), the communication SINR \({{\gamma }_{{{c}_{i}}}}\), is related to subband allocation, user association and transmission power. Moreover, \(B_{i,n}\), is related to the number of users served by BS i. Therefore, in this paper, we aim at reducing the cochannel interference and increasing the data rate through resource allocation, including subband and transmission power, as well as user association.
2.3 Sensing interference model
The echo signal received by the receive antenna of the ith BS is expressed as
where \({h}_{j,i}\) and \({h}_{j,t,i}\), respectively, denotes the complex channel of “BS jBS i” and “BS jtarget tBS i”, and \({{z}_{i}} \sim \mathcal{N}\left( {0,\sigma ^2} \right)\) denotes AWGN at the ith BS. The time domain expression of \({h}_{j,i}\) and \({{h}_{j,t,i}}\) is, respectively, given by
in which \(\psi\) denotes radar cross section (RCS), \({{\tau }_{j,i}}={d_{j,i}}/{c}\;\), \({{\tau }_{j,t,i}}={(d_{j,t}+d_{t,i})}/{c}\), and \({{f}_{{{d}_{j,t,i}}}}=({{v}_{t,j}}+{{v}_{t,i}}){{{f}_{c}}}/c\), with \({{v}_{t,j}}\), \({{v}_{t,i}}\) and \({{f}_{c}}\) denote the radial velocity of target t relative to BS j, the radial velocity of target t relative to BS i and the center carrier frequency, respectively.
In this paper, we mainly consider the direct interference among the BSs sharing the same subband, while the scattered interference is ignored due to its much lower power. In this case, (7) can be simplified as
in which \(\sum \limits _{j=1}^{M}{{{\textbf{w}}}_{i}}{\textbf{w}}_{j}^{H}{{h}_{j,i}}{{{x}_{j,l}}}\) denotes the interference among the BSs sharing the same subband. By applying pointwise division [4] and twodimensional DFT (2DDFT), the BS i can eliminate the impact of the communication data symbols \({{x}_{i,l}}\) and obtain the distance and speed information[25].
Generally speaking, cooperative sensing can be realized in two ways. One way is to directly upload the signals received by each sensing node to the center for joint signal processing [26], while the other way is to upload the data local processing results of each node, based on which the center conducts further processing, e.g., target association [9]. The latter scheme benefits from lower processing complexity, and therefore is considered in this paper. In other words, the ISAC BSs are considered to firstly sense the targets in a separate way, and then upload the processing results to the center. In order to guarantee the performance of cooperative sensing, the sensing performance of each node is required to satisfy a given threshold. Supposing the detection range of each BS is R, the SINR of the received echo signal is given by
where \(\chi\) denotes the correlation gain of the transmitted symbols [25] and \(\beta\) denotes the suppression gain for the direct interference. As BSs can share transmission signals through backhaul connections and obtain delay information between BSs by channel estimation. Therefore, the direct interference in the received superimposed signals can be suppressed by the extended cancellation algorithm (ECA)[27], which operates by subtracting appropriately weighted delayed copies of the reference signal from the received signal.
Based on the NeymanPearson criterion, utilizing the Generalized Likelihood Ratio Test (GLRT), the asymptotic detection probability is given as [28]
where \(P_ {F A}\) is the false alarm probability of sensing, \({\mathcal {F}}_{X_2^2({{\gamma }_{{{s}_{i}}}})}\) devotes the noncentral chisquared distribution function with two degrees of freedom and noncentrality parameter and \({{\gamma }_{{{s}_{i}}}}\), \({\mathcal {F}}_ {X_2 ^ 2}\) is the central chisquared distribution function with two degrees of freedom, with \({\mathcal {F}}_ {X_2 ^ 2} ^ { 1}\) being its inverse function. For given \(P_ {F A}\), the distribution of \(P_D\) follows noncentral chisquared distribution function with two degrees of freedom and noncentrality parameter \({{\gamma }_{{{s}_{i}}}}\). As can be readily seen from (12), the detection probability \(P_D\) is positively correlated with SINR \({{\gamma }_{{{s}_{i}}}}\) [28]. Therefore, we transform the detection probability metric into the SINR performance metric. According to (11), the SINR of the echo signal \({{\gamma }_{{{s}_{i}}}}\) is related to subband allocation and transmission power. Appropriate subband allocation and transmission control can improve the sensing SINR, thereby improving the detection probability.
3 Problem formulation
In this section, we formulate the problem of joint subband allocation, user association, and transmission power control. To be specific, we consider to maximize the network utility under the constraints of the echo signal SINR threshold, which is formulated as follows.
where \(\Gamma\) in the constraint (13a) denotes the SINR threshold of echo signal for sensing, and the constraint (13f) limits the BS transmission power.
4 Proposed method
To deal with the nonconvex and NPhard problem (12), we decompose it into three subproblems, i.e., subband allocation, user association, and transmission power control subproblems.
4.1 Subband allocation
With the fixed transmission power \({\textbf{p}}_{0}\) and user association strategy, the problem (13) can be simplified as the following subproblem.
The problem (14) is a 0–1 programming problem, and the objective function is nonconvex even for continuous \({\textbf{w}}\), which makes it challenging to solve. Nevertheless, notice that the network utility is mainly related to the SINR of each user with equal bandwidth allocation. Furthermore, with the transmission power fixed, according to (11), the SINR is only related to the intercell interference. Therefore, we propose to alternatively minimize the total intercell interference, which can be formulated as
Since there are totally \({{K}^{M}}\) different allocation schemes, it is extremely complex to solve the above subproblem via exhaustive searching. Besides, the greedy channel allocation algorithm [29] and lowcomplexity branchandbound based channel allocation [16] may result in a locally optimal solution, thereby increasing intercell interference and degrading network utility and sensing performance. Motivated by the ability of the genetic algorithm [30] in increasing the possibility of finding the optimal global solution, we proposed the subband allocation scheme based on the greedy genetic idea that combines the greedy algorithm and genetic algorithm [31] to reduce complexity and improve the sensing and communication performance.
Firstly, we represent the subband allocation of each BS by K base coding. For example, when \(M=4\) and \(K=2\), coding mode ‘2112’ means that BS 1, 2, 3, and 4 are assigned with subband 2, 1, 1, and 2, respectively. As the interference among different BSs to be addressed are dependent. Thus, we firstly pick K BSs in a greedy manner and assign them K different subbands, which avoids the uncertainty of weight due to dependence. Specifically, the two nearest BSs are selected and then the BS that is closest to the set of the selected BSs is selected one by one. The selected K BSs are assigned different subbands. Subsequently, for other BSs, we assign them subbands randomly, and generate \({{Q}_{1}}\) initial allocation schemes. The initial \({{Q}_{1}}\) allocation schemes are, respectively, represented by the above K base coding, and form \({{Q}_{1}}\) coding sequences. Unlike the onetoone mapping in [28], the same subband can be repeatedly allocated. Correspondingly, we define the fitness function of each allocation scheme as
The smaller the value of \({\mathcal {F}}\) is, the greater the fitness of the scheme is. Based on the fitness value, we select \({{Q}_{2}}\) schemes to be retained, in which the scheme with high fitness value has a high probability of being retained. Finally, the coding sequences of schemes retained are crossed and mutated to generate new candidate schemes. The specific steps of the algorithm are summarized in Algorithm 1.
4.2 User association
With given subband allocation scheme and fixed transmission power, the user association subproblem can be expressed as follows.
where \({u_{i,n}}=1\) means user n is associated with BS i and 0 otherwise. Note that for each n, only one \(u_{i,n}\) for all n’s is equal to 1, which means that the user can only be served by one BS. Therefore, for given subband allocation and transmission, the objective function of the problem (14) can be compactly and equivalently expressed as
By introducing \((N_{b}1)\) dummy BSs, the sum of severaltoone weight in (17, 18) can be transformed into the sum of onetoone matching weight [32]. Thus, the above problem is equivalent to
which is a bipartite matching problem by setting \(N_{b}=N\), and can be solved efficiently by the Hungarian algorithm, which has been proven superior to greedy and improved greedy algorithms for user association [33, 34].
4.3 Transmission power control
With given subband allocation scheme \({\textbf{w}}\) and user association scheme \({\textbf{u}}\), the transmission power control subproblem is expressed as follows.
Different from the power control based network utility maximization problem, the above problem cannot be solved via the conventional waterfilling type of solution [35] due to the existence of the sensing SINR constraint. Meanwhile, due to the nonconvexity of the objective function and constraints, problem (21) cannot be directly solved using CVX tools. Firstly, by introducing an auxiliary variable \(\varvec{\eta }=\left\{ {{\eta }_{1}},\cdot \cdot \cdot ,{{\eta }_{N}} \right\}\), the subproblem above can be reformulated as
However, problem (21) is still a nonconvex optimization problem due to the nonconvexity of constraint (21c). We employ SCA technique to address this issue. By applying the firstorder Taylor series expansion at the given point \({\widetilde{p}}\), the constraint (21c) can be approximated as
where \(\xi _{i,n}^{(a)}=\frac{\widetilde{\gamma }_{{{u}_{i,n}}}^{(a)}}{1+{\widetilde{\gamma }}_{{{c}_{i,n}}}^{(a)}}\) and \(\varepsilon _{i,n}^{(a)}=\log \left( 1+\widetilde{\gamma }_{{{c}_{i,n}}}^{(a)} \right) \xi _{i,n}^{(a)}\log \left( {\widetilde{\gamma }}_{{{u}_{i,n}}}^{(a)} \right)\), superscripts (a) and (\(a + 1\)) represent the ath and \((a + 1)\)th iteration, respectively.
Thereafter, the problem (21) can be transformed into the following form.
Theorem 1
Problem (23) can be solved by geometric programming (GP).
Proof
It can be seen from (11) that constraint (20a) is a posynomial function of \({\textbf{p}}\). Next, we prove that constraint (20c) is convex [36]. Constraint (20c) can be expressed as,
which is convex due to the convexity of \(\log \left( \cdot \right)\). The objective function of (22) and constraint (22b) are also convex. Therefore, the problem (22) is composed of posynomial function and convex functions, it can be solved by GP. \(\square\)
Therefore, the transmission power control subproblem (19, 20) can be solved by GP and successive convex approximation (SCA) technique.
4.4 Overall algorithm
Based on the aforementioned algorithms, we present the overall algorithm for solving the problem (13) in Algorithm 2. Specifically, we update subband allocation \({\textbf{w}}\), user association \({\textbf{u}}\) and transmission power \({\textbf{p}}\) by solving the subproblem (15), (17, 18) and (21), respectively. By iteratively updating the three variables in an alternative manner, the solution to the problem (13) can be obtained.
5 Simulation results and discussion
In this section, we verify the effectiveness of the proposed algorithms through numerical results. We assume that BSs are uniformly located in a 2dimension area of \(1.5*1.5\) km, while the users are randomly distributed in this area. Figure 2 shows an example of the subband allocation and user association results obtained by Algorithm 2, where the BSs marked with the same color share the same subbands, and the users are served by the associated BSs. Simulation parameters are listed in Table 1.
As far as we know, there have been no existing works studying the problem considered in this paper. Therefore, to show the superiority of the algorithms adopted to solve the three subproblems, we select the following four benchmark schemes for performance comparison:

(1)
Random channel allocation with user association (UA) and transmission power control (TPC), denoted as “Rand+UA+TPC”.

(2)
Fixed power, in which we set BSs working at maximum power, with GGSA proposed and UA, denoted as “GGSA+UA+FP”.

(3)
Power control for cooperative ISAC Networks in [21], with GGSA proposed and UA, denoted as “GGSA+UA+[21]”.

(4)
A lowcomplexity branchandbound algorithm channel allocation [16], where the initial solution also comes from the greedy algorithm, with UA and TPC, denoted as “[16]+UA+TPC”.
Specifically, for subband allocation, we compare the performance of Algorithm 2 with scheme (1) and scheme (4). For transmission power, scheme (2) and scheme (3) is set as benchmarks to illustrate the system performance improvement by the proposed transmission power control.
To begin with, we show the convergence of Algorithm 2 in Fig. 3. The network utility at iteration 0 corresponds to “Rand+UA+TPC”. It shows that the network utility achieved with the proposed Algorithm 2 increases quickly, and converges (the variation does not exceed 1%) after the first iteration.
In Fig. 4a, we present network utility achieved by different approaches under different sensing SINR thresholds. It can be seen that the network utility under all schemes increases with the number of available subbands. By using the proposed Algorithm 2 and the “[16]+UA+TPC” scheme, the network utility is improved compared with the “Rand+UA+TPC”,“GGSA+UA+FP” and “GGSA+UA+[21]” scheme. In particular, Algorithm 2 improves the network efficiency slightly higher than the “[16]+UA+TPC”, which verifies the effectiveness of the proposed GGSA. In addition, with fewer subbands allocable, the proposed Algorithm 2 improves the network utility more significantly than the “[16]+UA+TPC” scheme. Still, it has a feasible solution in a larger sensing SINR threshold. Compared with the “GGSA+UA+FP” and “GGSA+UA+[21]” scheme, the network utility increases under the proposed Algorithm 2 for both \(K=3\) and \(K=4\), which verifies the effectiveness of the proposed TPC algorithm. We also show the average data rate under different sensing SINR thresholds in Fig. 4b. Similarly, the proposed Algorithm 2 achieves best tradeoff between the average data rate and achievable sensing SINR.
Figure 5 depicts the detection probability [28] of three schemes under different sensing SINR thresholds. As Fig. 5 shows, with the sensing SINR threshold increasing, the detection probability also increases. For the same scheme, the detection probability of ’\(K=4\)’ is higher than that of ’\(K=3\)’. The proposed Algorithm 2 and “[16]+UA+TPC” scheme can reach a larger sensing threshold than the other schemes, and also have higher detection probability at the same achievable SINR threshold. With fewer allocable subbands, the proposed Algorithm 2 shows the best performance.
From Figs. 4 and 5, it can be observed that there exists a tradeoff between communication and sensing performances. For the “Rand+UA+TPC” scheme, with the increase of sensing SINR threshold, the network utility and average data rate show downward trends. By using Algorithm 2 and the“[16]+UA+TPC” scheme, the network utility can remain stable within a certain range of the singing SINR threshold. Nevertheless, when SINR is greater than a certain value, the network utility will also decline. On the other hand, the detection probability, increases with the increase of SINR for all cases, which shows the tradeoff between communication and sensing performances. In what follows, we take the case of \(K=3\) as an example to illustrate the above tradeoff.
In Fig. 6, we plot the cumulative distribution function (CDF) curves of transmission power based on 100 simulation results. Since the distribution of BSs is symmetrical, we select four BSs numbered 1, 2, 5, and 6 in Fig. 2 to represent the four types of BSs, namely, edge, general case 1, general case 2, and center. As shown in Fig. 6, when \(\Gamma =4\) dB, the power of the BS 6 in the center is lower than that of BS 1, BS 2, and BS 5. The reason is presented as follows. With a low sensing SINR threshold, more degrees of freedom (DoFs) are reserved to improve the communication performance. Since the central BSs are close to other BSs sharing the same subband, which brings about more significant intercell interference to the entire network than other BSs, decreasing their transmission power can significantly decrease the intercell interference and improve the overall network utility. However, when \(\Gamma =10\) dB, the central BSs require high transmission power to resist the interference from the neighborhood BSs working in the same subbands, thereby improving the SINR of echo signals. Therefore, we can see that the power of BS 6 in the center is greater than that of other BSs. In this case, the sensing performance has been improved, while the communication performance is sacrificed and the overall network utility decreases.
In a meantime, we can also see that the BS power distribution is more centralized with \(\Gamma =10\) dB than that with \(\Gamma =4\) dB. Specifically, for \(\Gamma = 10\) dB, the power of BS 1, BS 2, and BS 5 all lie in the range of 2.2\(\)2.225 W, while the power of BS 6 is around 2.9 W. As mentioned above, for a high sensing SINR threshold, e.g., \(\Gamma\) = 10 dB, the central BSs need large power to resist the interference of other BSs. At the same time, they cannot cause too much interference with other BSs. Therefore, the power optimization concentrates their power around a high power so that the power of other BSs is also around a certain value. Under the low sensing SINR constraint, the DoFs for communication optimization is high. The power of each BS can be adjusted with the result of user association to achieve higher network utility. Note that users’ locations are random, so user associations vary with each simulation. Therefore, the BSs’ power fluctuate in 100 simulations.
6 Conclusion
In this paper, we studied the ISAC design in OFDMbased ISACDCN. In this paper, we established the communication and sensing interference models in ISACDCN. To address the issue of interference management, we proposed an alternatingoptimizationbased algorithm for joint subband allocation, user association, and transmission power control. To reduce interference and improve the performance of communication and sensing, we proposed a greedy genetic subband allocation (GGSA) scheme to reduce total interference. Subsequently, the user association subproblem was converted to a minimumweighted bipartite matching problem and solved via the Hungarian algorithm. Moreover, the SCA technique was employed to convert the transmission control subproblem, which was then solved by GP. Simulation results show that the proposed algorithm significantly improves the network utility and achieves a higher sensing detection probability. Additionally, we analyzed the tradeoff between communication and sensing performance in detail. Although this paper focused on the NR systems, it can also be extended to the other ISAC systems, e.g. vehicular network [37], which is left for future work.
Abbreviations
 OFDM:

Orthogonal frequency division multiplexing
 ISAC:

Integrated sensing and communication
 DCN:

Dense cellular network
 DL:

Downlink
 SINR:

Signal to interference plus noise ratio
 GAGR:

Greedy genetic algorithm
 SCA:

Successive convex approximation
 5 G:

Fifthgeneration
 NR:

New radio
 RS:

Reference signal
 BS:

Base station
 DoA:

Directions of arrival
 FR:

Frequency reuse
 ICI:

Intercell interference
 UA:

User association
 TPC:

Transmission power control
 CDF:

Cumulative distribution function
 DoF:

Degrees of freedom
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This work was supported by the National Key R &D Program of China under Grant No. 2021YFB2900200, and the National Natural Science Foundation of China under Grant U20B2039.
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Zhang, J., Fei, Z., Wang, X. et al. Joint resource allocation and user association for multicell integrated sensing and communication systems. J Wireless Com Network 2023, 64 (2023). https://doi.org/10.1186/s13638023022641
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DOI: https://doi.org/10.1186/s13638023022641