1.1 Need and motivation

Wireless communication technology has evolved significantly, leading to data-driven fifth-generation (5G) networks that offer high data rates, low latency, and enhanced connectivity [1,2]. As research progresses toward sixth-generation (6G) systems expected around 2030, the focus extends beyond high rate communication to high resolution sensing through shared spectrum and hardware. 6G combines communication and sensing into a single wireless infrastructure to provide intelligent, immersive, and context-aware applications [3]. This deep integration, termed Integrated Sensing and Communication (ISAC), is going to back 6G technology [4]. Unlike previous generations that focused solely on enabling human-to-human or machine-to-machine data exchange, 6G envisions a cyber-physical ecosystem where the wireless network not only facilitates communication but also acts as a ubiquitous, high-resolution radar-like sensor [5]. This means that 6G base stations (BSs), user devices, and access points (APs) will be capable of simultaneously sensing their environment and transmitting data over the same frequency spectrum [6]. This convergence blurs the lines between traditional communication and radar systems, enabling a wide range of new capabilities such as precise localization, object tracking, activity recognition, and environmental mapping [7].

1.2 ISAC frameworks

The sensing-assisted communication (SAC) framework enhances the reliability of wireless links by embedding radar-like sensing functions, which significantly reduce the overhead of repetitive beam training and channel estimation in high-mobility environments. Previous efforts mostly focused on using sensing capabilities to increase communication efficiency [8]. But in the context of 6G, sensing is seen as an essential service in addition to communication, especially for newly developed environment-aware applications [9]. Researchers have proposed exchanging sensing measurements across dispersed devices or a central fusion node to enable high-precision sensing channels wireless [10]. The paradigm is prevalent in several fields, including linked autonomous cars, over-the-air computation, IoT, and extended reality (XR). For instance, AI-driven edge intelligence transmits large volumes of sensory data between edge nodes and central servers for real-time, accurate perception tasks like object recognition and scene interpretation. Conventional networks rely on dispersed sensors and centralised data fusion, whereas communication aided sensing (CAS) uses device-free wireless sensing inherent in 6G [11]. This enables BSs or RSUs to simultaneously gather and communicate environmental data to end-users, reducing the need for additional sensors. The procedure consists of a sensing process (SP) where the BS records target observations, and a communication process (CP) where users receive the collected sensory data [12]. ISAC systems use the communication-assisted sensing (CAS) architecture to improve connection, environmental awareness, and reduce latency and deployment costs.

1.3 Our contribution

The spectrum and hardware overhead owing to increasing data traffic and device density are the main challenges in modern 6G networks. A unified framework integrating sensing and communication has become vital in achieving intelligent, spectrum-efficient and environment-aware connectivity. This paper proposes a centralized ISAC framework to perform joint communication and high-resolution sensing. Through a hybrid signal transmission model and realistic channel characterization, the framework enhances detection reliability, localization accuracy, and spectrum utilization under practical deployment conditions. The main contributions of this work are summarized as follows:

• A centralized ISAC system is designed within a C-RAN environment, integrating multiple transmit and receive APs to enable cooperative multi-static sensing and simultaneous downlink communication.
• The numerical formulations of channel modeling involving communication and sensing signals are provided. The model incorporates both line-of-sight (LoS) and non-line-of-sight (NLoS) propagation environments with spatial correlation, path loss, fading, and interference, providing a realistic and credible evaluation of system performance.
• Three localization methods, namely, Time of Arrival (TOA), Time Difference of Arrival (TDOA), and Direction of Arrival (DOA) are implemented and analyzed for estimating target locations under noise and synchronization uncertainties.
• The localization RMSE is evaluated for different number of receivers under different noise and angular standard deviations
• A radar based target detection model based on hypothesis testing (Neyman–Pearson) is developed to investigate the impact of SNR, antenna diversity, and radar cross-section (RCS) variations on probability of detection, considering realistic target fluctuation models, Swerling models.

3.1 Channel modeling

3.2 Communication channel model

A block fading model is used where the channel remains constant within a coherence time and changes independently across blocks. The channel vector from transmit AP q to UE u is denoted as

(3)

where is the spatial correlation matrix capturing the effects of path loss, shadowing, and antenna correlation. The full channel vector from all N_tK transmit antennas to UE u is defined as:

(4)

The path loss is modeled as:

(5)

where is the path loss exponent. For f = 3500 MHz and d = 50 m, the path loss is approximately 91.5 dB. Shadow fading is modeled as a log-normal distribution with 8 dB standard deviation. Minimum mean square error (MMSE) channel estimation is performed uplink pilot symbols.

3.3 Sensing channel model

A line-of-sight (LOS) channel is considered between the APs and a target located at , with azimuth angle ϕ and elevation angle . The antenna array response vector is given by:

(6)

The composite channel from all transmit APs to the target is:

(7)

where denotes the path loss for the link from AP q to the target.

3.4 Interference channel model

The interference at the sensing receive APs consists of both LoS components from other APs and non-line-of-sight (NLoS) clutter. While known LoS and static NLoS paths from permanent structures are pre-estimated and canceled, dynamic NLoS paths from moving objects are modeled as unknown interference [32]. The unknown NLoS channel between transmit AP q and receive AP r is represented by . Correlated Rayleigh fading channels are used for the NLoS channels which are modeled using Kronecker model.

(8)

where has independent and identically distributed (i.i.d.) entries, and , are spatial correlation matrices with correlation coefficient .

4.1 Localization

This section presents the localization techniques to estimate the position of a user node [33]. Let the source node whose location is to be estimated be the target node and the other M sensors that collect the measurements be the receivers.

A widely adopted technique is Time of Arrival (TOA), which measures the propagation delay between the target and each receiver. Provided the target and receivers are time-synchronized, multiplying the delay by the signal’s propagation speed yields the target-receiver distance. These distances enable multilateration methods to estimate the target’s position [34]. However, maintaining precise synchronization between a mobile target and multiple receivers is often impractical. To address this, Time Difference of Arrival (TDOA) methods are employed, wherein only the receivers must share a common time reference. By analyzing differences in signal arrival times, hyperbolic constraints are formed whose intersection yields the target’s estimated location. TDOA techniques are particularly effective for real-time localization in dynamic environments [35]. When receiver nodes are equipped with antenna arrays, they can estimate the Direction of Arrival (DOA) of the received signal. These angular measurements, combined with the known receiver positions, facilitate geometric triangulation, even in environments affected by multipath propagation. Modern localization systems often adopt hybrid approaches that integrate multiple modalities such as TOA, TDOA, DOA, Received Signal Strength (RSS), inertial sensor data, and heterogeneous radio technologies. Such fusion strategies mitigate the limitations of individual techniques, enhance robustness in NLoS conditions, and improve localization accuracy in complex environments.

The problem of localizing a target node in a two-dimensional Euclidean space using TOA, TDOA and DOA measurements from M spatially distributed receivers is addressed next. Let the unknown position of the target be (x,y), and the known location of the m^th receiver be , where .

4.2 TOA-based localization

Assuming perfect synchronization and LoS propagation, if the target transmits a signal at a known reference time t = 0, the TOA at the m^th receiver is given by:

(9)

where c denotes the speed of light. The propagation distance is:

(10)

This implies that the target lies on a circle centered at with radius d_m. With at least three such distances (), the target’s position can be uniquely determined via trilateration under ideal conditions [36].

In practice, TOA measurements are corrupted by noise, multipath effects, and bandwidth limitations. The noisy measurement is modeled as:

(11)

where represents additive white Gaussian noise (AWGN).

Each measurement defines an annular region around each receiver, and the intersection of these annuli provides an estimate of the target’s location. Estimation techniques such as Least Squares (LS), Maximum Likelihood (ML), or Bayesian filters are employed to refine localization [37].

Confidence intervals for the measured distance can be constructed as:

(12)

where γ is a confidence multiplier.

Computational complexity analysis.

Let M be the number of receivers and L be the number of signal samples. TOA localization involves estimation of signal arrival times followed by position estimation. At each of the M receivers, correlation or matched filtering is used for the TOA estimation over L received samples, resulting in a complexity of . Once the propagation delays are estimated, the target position is obtained using trilateration through LS or ML estimation. This involves solving a low-dimensional nonlinear optimization problem which incurs a computational cost of , where I denotes the number of iterations required for convergence. Therefore, the overall computational complexity of the TOA-based localization approach scales as .

4.3 TDOA-based localization

TDOA methods eliminate the need for target-receiver synchronization by requiring synchronization only among the receivers. The arrival time at the m^th receiver is:

(13)

where δ denotes the unknown transmission time offset.

Using receiver 1 as the reference, the TDOA is:

(14)

Multiplying by c yields the range difference:

(15)

Each such equation defines a hyperbola with foci at receivers m and 1. The noisy range difference measurement is:

(16)

where .

Define the measurement vector:

(17)

and the theoretical range difference vector:

(18)

The observation model is:

(19)

where the covariance matrix has:

• Diagonal entries: ,
• Off-diagonal entries: for .

Thus,

(20)

The ML estimate of the target coordinates are obtained as

(21)

This non-convex optimization problem is typically solved via iterative algorithms such as gradient descent, Gauss-Newton, or expectation-maximization, requiring careful initialization.

Localization accuracy is assessed using the Root Mean Square Error (RMSE) given by:

(22)

Computational complexity analysis.

In the TDOA-based localization approach, the computational complexity is mainly influenced by the estimation of time differences and the nonlinear position estimation process. The TDOA measurements are obtained through cross-correlation of the received signals across M synchronized receivers, resulting in a computational cost of , where L denotes the number of signal samples. The subsequent localization is formulated as an ML or weighted LS problem involving the inversion of an covariance matrix and iterative optimization, which incurs a complexity of , with I denoting the number of iterations. Consequently, the overall computational complexity of the TDOA-based localization method scales as .

4.4 DOA-based localization

Direction-of-Arrival (DOA), also known as Angle-of-Arrival (AOA), localization estimates the position of a target using angular information measured at multiple sensor nodes [38]. In a two-dimensional space, for M receivers positioned at known coordinates , and a target located at unknown coordinates (x,y), the DOA at the m-th receiver is:

(23)

Each measured angle defines a line extending from each receiver. The intersection point of at least two such lines (assuming non-collinear receivers) provides the target’s estimated location through triangulation [39]. In practice, DOA measurements are corrupted by angular noise, modeled as:

(24)

The complete observation model is expressed as:

(25)

where is the theoretical DOA vector.

The Maximum Likelihood (ML) estimate is obtained by minimizing the Mahalanobis distance:

(26)

where .

Due to the nonlinearity of the function, the estimation problem is non-convex and typically solved using grid search or iterative optimization algorithms.

Localization accuracy improves with:

• Reduced angular noise variance ,
• Greater spatial diversity in receiver placement.

In three-dimensional scenarios, both azimuth and elevation angles are required. Systems using uniform linear arrays (ULAs) provide only azimuthal data, necessitating at least three receivers for localization due to conical ambiguity.

DOA techniques eliminate synchronization requirements but require multi-antenna arrays, making them hardware-intensive. When combined with TOA or TDOA methods, DOA enhances overall localization accuracy and robustness.

Computational complexity analysis.

In the DOA-based localization approach, the computational complexity is dominated by the estimation of the direction of arrival using antenna array processing and the subsequent geometric localization. For subspace-based DOA estimators, the computation of the sample covariance matrix using K antenna elements and L samples requires operations, followed by an eigenvalue decomposition (EVD) with complexity . Additionally, angular search over G points incurs a complexity of . Once the DOA estimates are obtained, the target position is determined via triangulation or ML estimation with negligible overhead compared to array processing. Therefore, the overall computational complexity of the DOA-based localization approach scales as .

4.5 Target detection

Target detection is a fundamental task in radar-based sensing systems, where the objective is to determine the presence or absence of an object at a specific location. Unlike localization methods in which the target actively transmits, radar-based detection relies on transmitting known waveforms and analyzing their reflections from passive targets.

A key parameter governing detectability is the radar cross section (RCS) which characterizes how strongly a target reflects incident electromagnetic energy and is modeled using Swerling models. Consider L complex baseband samples y[1],...,y[L] collected during a single detection interval. Under the Swerling 1 model the target’s complex radar-cross-section (RCS) coefficient remains constant across the L samples, such that . While in Swerling 2 model, the target’s RCS fluctuate rapidly such that at each symbol time it takes a new realization as . Denoting the additive receiver noise samples by and average received power by P_R, the binary hypotheses in model-1 becomes

(27)

For a given false alarm probability , the detection probability can be maximized using Neyman-Pearson detector.

(28)

where γ is the detection threshold, L is the number of samples, and is the noise variance. For a desired false-alarm level α, the threshold is set as

(29)

With effective SNR , normalized threshold , the closed form of detection probability is

(30)

6.1 Integration with edge AI and 6G digital twin

From a deployment perspective, the proposed centralized ISAC framework can be extended by integrating edge AI and 6G digital twin technologies.

• Edge intelligence deployed at the C-RAN edge cloud can process sensing and communication data in real time, enabling learning-assisted localization, target detection, beam management and environment awareness under mobility and NLoS conditions. This significantly reduces latency and fronthaul overhead while enhancing system responsiveness in dense and dynamic environments [40].
• 6G digital twin can maintain a virtual representation of the physical environment, network topology and target dynamics by continuously ingesting sensing data from ISAC nodes [41]. This enables predictive sensing, proactive resource allocation and performance optimization without disrupting live network operations, facilitating self-configuration and self-healing capabilities [42].
  Such a synergy between ISAC, edge AI and digital twins aligns with the vision of intelligent, self-aware, and autonomous 6G networks and further enhances the practical applicability of the proposed framework.

6.2 Future directions

Future work focuses on addressing key practical challenges in ISAC-based 6G networks, including accurate 3D localization, reliable operation under high mobility scenarios and device synchronization issues.

• 3D localization: The localization model can be extended to 3D positioning for applications such as aerial vehicles, drone-assisted sensing, and indoor–outdoor integrated networks. To achieve high-precision 3D localization under multipath conditions, future work will focus on joint estimation of azimuth and elevation angles, elevation-aware beamforming, exploitation of planar or 3D antenna arrays and multi-node ISAC cooperation in complex NLoS environments [43].
• High mobility scenarios: Fast channel variations, severe Doppler effects in high-mobility scenarios and beam misalignment can degrade both communication and sensing accuracy [44]. Future work may incorporate mobility-aware beam tracking, Doppler-resilient waveforms and learning-assisted prediction at the edge to enable robust localization and target detection in vehicular and aerial environments.
• Device synchronization issues: The fundamental limitation particularly for TOA- and TDOA-based localization is the device synchronization. Practical deployments must address clock offsets, phase noise and hardware impairments across distributed access points [45]. Future research will explore synchronization-free localization techniques, joint clock-offset estimation, cooperative timing alignment and sensing-assisted synchronization to mitigate these effects.