System design and frame structure

In Fig. 1, a sketch representing an example of the investigated scenario is illustrated. Four nodes are adopted for the ease of simplicity. Each node comprises an operational configuration to facilitate radar and communication features. N ₁ emerges as a pivotal actor with an active radar alongside a separate communication receiver, driven by the dual functionality of target detection and concurrent communication engagement with other nodes, such as N ₂. Meanwhile, N ₂, equipped with its dedicated communication receiver, operates to capture the signal from N ₁ and extracts the information sent from N ₁ to enable data exchange for their signal properties and traffic status of the surroundings. Simultaneously, N ₃ and N ₄, on the other hand, are characterized by the activation of their radar transceivers, eliciting a deliberate generation of interference aimed at N ₂.

Figure 1.

Exemplary scenario in automotive applications. N ₁ represents the node that is responsible for radar and communication transmission. N ₂ is the node where the valuation of communication data takes place. N ₃ and N ₄ illustrate a possible interference events aimed at N ₂. The blue line represents communication transmission, while the black and green counterparts represent the detection in the surroundings. Red lines illustrate possible interference events.

The signal frame for the proposed CaCS-based radar systems consists of two sub-frames. Initially, a preamble-based chirp signal is transmitted to ensure synchronization between the transmitter of one node and the receiver of another. This synchronization section includes a predetermined number of up- and down-chirps [Reference Alabd, Benjamin Nuss, Li, Diewald and Zwick14] and is adjusted at the beginning for each sensor transmitting in the same environment. Following this, the signal used for CaCS-based radar systems is transmitted to achieve both communication and sensing functionalities. A sequence of multiple modulated chirps, denoted as $Q_\mathrm{rc}$ with index ${q_\mathrm{rc}~\in~\{0,1,\dots, Q_\mathrm{rc}-1\}}$, a time duration $T_\mathrm{C}$, and equal pauses between each, is transmitted to enable relative speed estimation at the radar receiver. An exemplary chirp sequence with a time repetition interval $T_\mathrm{RRI}$ and a duration of ${T^\mathrm{rc}_\mathrm{Seq}=Q_\mathrm{rc}T_\mathrm{RRI}}$ is depicted in Fig. 2. As illustrated, the communication symbols are modulated in a narrow sector at the upper part of each chirp, within a limited bandwidth $B_\mathrm{com}$ and time duration $T_\mathrm{com}$. These communication symbols are assigned to different phases according to quadrature phase shift keying. Moreover, at the beginning of the frame, a set of up- and down-chirps is allocated for synchronization within the duration $T^\mathrm{sync}_\mathrm{Seq}$. This structure ensures efficient synchronization and accurate relative speed estimation, thereby enhancing the overall performance of the CaCS-based radar systems.

Figure 2.

Representation of CaCS-based radar system. Structure of the transmit CaCS-based signal, including the pattern for the synchronization and the dedicated chirps for both radar and communication functionalities [Reference Alabd, Dittmer, Nuss, Li, Giroto de Oliveira, Diewald and Zwick1].

Interference on graph

Radar sensors on different vehicles face challenges from various sources of interference in the environment. For this purpose, a graph-based approach is employed to clarify the degree of interference between the nodes using principles from graph theory [Reference Khoury, Ramanathan, McCloskey, Smith and Campbell8, Reference Tovar Torres and Waldschmidt15, Reference Yu, Bar-Noy, Basu and Ramanathan16]. The nodes are modeled as a graph to represent the aforementioned CaCS-based systems with either radar or communication functionality, and edges illustrate interference between nodes. A graph, denoted as $G = (V, E)$, consists of a set of vertices $V = \{v_1, \ldots, v_N\}$ and a set of edges $E \subseteq V \times V$, representing connections between vertices. The edge set E contains tuples $(v_i, v_j)$ for which nodes v_i and v_j are connected, where the number of edges is $|E| = M$. A graph can be categorized as directed if its edges have a defined direction or undirected with no specified orientation for the edges. Undirected graphs are investigated since the sensors can cause interference and simultaneously be a victim. The graph-based interference modeling for CaCS-based nodes is developed based on multiple critical factors, including signal duration, bandwidth, transmit power, and FoV. Signal duration refers to the temporal extent of sensor signals, dictating the duration of potential interference events. A realistic-based scenario is shown in Fig. 3, where sensors emit periodic signals with finite durations, within the investigated bandwidth and limited transmitted power. Interference occurs when signals overlap in time and frequency with enough strength, leading to potential disruptions in sensor readings during the signal processing. Additionally, the FoV range of sensors is incorporated into the modeling framework. The FoV defines the angular coverage of sensor measurements, representing the spatial extent to which sensors can detect objects. Interference is considered between sensors whose operational ranges intersect within the FoV angle range of each other.

Figure 3.

Interference analysis of CaCS-based systems according to graph and color concepts. (a) Graph-based illustration of a scenario with 3 vehicles and 12 nodes from the perspective of the radar transceiver. (b) Graph-based illustration of a scenario with 3 vehicles and 12 nodes from the perspective of the communication receiver. (c) Graph-based illustration of a scenario with 10 vehicles and 40 nodes from the perspective of the radar transceiver with color mapping, leading to 3 unique colors. (d) Graph-based illustration of a scenario with 10 vehicles and 40 nodes from the perspective of the communication receiver with color mapping, leading to 2 unique colors. However, only the desired vehicle is illustrated since the scenario spanned widely in (c) and (d). (e) Comparison of interference occurrence between radar $\mathrm{int}_\mathrm{rad}$ and communication $\mathrm{int}_\mathrm{com}$ cases. (f) Probability of error occurrence based on interference grade for radar and communication.

Since the proposed CaCS nodes also comprise a communication part with limited bandwidth $B_\mathrm{com}\lt \lt B$,this allocation might restrict the amount of information that can be transmitted, but at the same time the interference event based on the same criteria of the limited bandwidth. In contrast, the radar part typically operates with access to a broader frequency spectrum, spanning about $B = {4}\,\mathrm{GHz}$ within 79–81 GHz. This wide bandwidth allows radar signals to occupy a larger portion of the frequency spectrum, enabling high-resolution sensing and detection capabilities. However, radar detections can be restricted by interference events. Therefore, employing techniques to mitigate the effects of interference is a vital feature for safe monitoring of the environment. For example, a scenario with 3 vehicles with four sensors in each leads to 12 nodes in the scenario. The distance threshold for interference is set at 150 m, defining the maximum allowable distance between nodes for interference to occur. Each sensor generates signals for communication and sensing purposes. These signals have specific durations, with each node generating 128 chirps. For example, signal durations range from 10 to 100 μs, with an interval of 2 μs between consecutive chirps. Each sensor operates within a defined center frequency range, randomly assigned between 76 and 81 GHz. The receiver in the network has a bandwidth limitation of 100 MHz, constraining the communication bandwidth. Furthermore, the sensors have a defined FoV, with an angle range of −80 to 80^∘, dictating the angular span over which each sensor can perceive its environment. As depicted in Fig. 3(a) and (b), the interference between CaCS nodes with radar functionality can occasionally be severe, where five interference cases are introduced. On the other hand, if the interference is investigated within the communication section, merely one interference event is observed for the same parameters above. An extension of the scenario with 10 vehicles, each equipped with 4 sensors leads to 40 nodes in the scenario. In Fig. 3(c), the connections between nodes are performed and illustrated based on interference that occurred from the perspective of node 8. Since the bandwidth and time duration of the investigated radar signal is considerable compared with the communication section, node 8 undergoes five interference cases, where $|E^{8}_\mathrm{rad}| = 5$. To minimize or mitigate this impact, a coloring approach on the graph is recommended to coordinate the resources between the nodes with a degree of orthogonality C relative to the number of unique colors applied to the graph [Reference Yu, Bar-Noy, Basu and Ramanathan16]. According to this approach, two connected nodes cannot possess the same color, leading to three colors with $C_\mathrm{rad} = 3$. On the other hand, Fig. 3(d) depicts the same investigation from the perspective of the communication receiver. In this case, node 8 can merely undergo two interference cases with $|E^{8}_\mathrm{com}| = 2$, and two colors $C_\mathrm{com} = 2$ are needed to coordinate the scenario. It should be mentioned that the number of edges E and colors C are usually presented according to the complete graph. However, only one node has been considered for the sake of simplicity. Overall, the results indicate the importance of establishing communication between the CaCS-based nodes. Since the impact of interference on communication is so minimal, the nodes can communicate beforehand and adjust their parameters to avoid distorting their radar functionalities. Furthermore, the impact of interference on node 8 is analyzed further in Fig. 3(e) and (f). The occurrence of interference for radar and communication functionalities $\mathrm{int}_\mathrm{rad}$, $\mathrm{int}_\mathrm{com}$ caused by other nodes in the surroundings is illustrated in Fig. 3(e). In this term, the interference in communication at node 8 occurred about ${7}{\%}$ compared with its radar counterpart, which occurred about ${68}{\%}$ among $n_\mathrm{snap} = 100$ snapshots. Figure 3(f) depicts the probability of interference occurrence relative to the number of interferers in the scenario. For node 8, about ${85}{\%}$ of the snapshots undergone no interference for $\mathrm{int}_\mathrm{com}$ and less than ${35}{\%}$ for its radar counterpart, where eight interferers might contribute to those effects in some rare cases, less than ${5}{\%}$. It should be noted that the orientation of the investigated nodes has been arbitrarily chosen, and concrete information regarding the automotive scenario can lead to lower interference impacts on radar and communication functionalities. Besides, the decision to have interference in the scenario has been connected with the geometrical location of the nodes, the power level of the interferers, and the overlapping of their signal in the time-frequency plane within the receiver bandwidth of the investigated node.

Correlation approach

According to the study presented in [Reference Alabd, Dittmer, Nuss, Li, Giroto de Oliveira, Diewald and Zwick1], a promising approach to synchronize the transmitter and receiver of communicating CaCS nodes in an interfering environment involves creating a codebook that incorporates the parameters of the signals. This codebook-based method enables the detection of interference at the beginning of the procedure, with synchronization applied in subsequent steps. The two-stage interference detection and synchronization method begins with chirp rate estimation of the signals, where the slopes are assigned within the predetermined codebook. Initially, the interference is identified by comparing incoming signals with the entries in the codebook, allowing for the quick detection of potential conflicts. Once interference is detected, the next step comprises applying correlation to the chosen detected patterns within the codebook. This correlation process synchronizes the receiver of one CaCS node with one of the desired transmit signals, facilitating reliable communication. This method offers several advantages, where the system can quickly identify and resolve interference events. Besides, the use of chirp rate estimation enhances the robustness in environments with high levels of signal interference.

Chirp rate estimation

In this framework, all the signals overlapping within one evaluated time duration $T_\mathrm{C}$ can be detected if each adopts a unique chirp rate. The detected chirp rates are estimated using the fast quadratic phase transform (FQPT) [Reference Ikram, Abed-Meraim and Hua18], in which an adaption from the conventional discrete Fourier transform (DFT) is adopted to estimate the slopes of the receive signals within the limited bandwidth on the communication receiver, as depicted in Fig. 5. After filtering the input signal according to $B_\mathrm{com}$ within the longest time duration of the investigated signals, the desired one and interferers in the baseband can be given as

(1)\begin{align} s(t) &= e^{(2\pi f_c^\mathrm{com} t + \pi \mu t^2 + \phi)}, \quad 0 \leq t \lt T_\mathrm{com} \end{align}

(2)\begin{align} i_j(t) &= e^{(2\pi f_{c_j} t + \pi \mu_j t^2 + \phi_j)}, \quad 0 \leq t \lt T_j \end{align}

Figure 5.

Exemplary detection of three different chirp signals with unique slopes $\{\mu_1$, µ ₂, $\mu_3, \mu_4\}$ [Reference Alabd, Dittmer, Nuss, Li, Giroto de Oliveira, Diewald and Zwick1].

where $T_\mathrm{com}$ is the time duration of the communication section, µ is the chirp rate, $f_c^{\mathrm{com}}$ is the center frequency of the communication section, and ϕ is the initial phase. Besides, T_j is the time duration of the interferer, $f_{c_j}^{\mathrm{com}}$ is the center frequency of the interferer, µ_j is the chirp rate of the interferer, and ϕ_j is the initial phase. $T_\mathrm{com}$ and T_j are adjusted to have the same length in samples to be added together as

(3)\begin{align} s_\mathrm{in}(t) = s(t) + i_j(t). \end{align}

After the received signal related to $B_\mathrm{com}$ in Fig. 4 at the receiver side, only N samples of the received signal are employed to estimate the investigated chirp rates. The parameters can be evaluated regarding the following equation:

(4)\begin{align} s_\mathrm{cr}(k,\Gamma) &= \sum_{n=0}^{N-1} s_\mathrm{in}(n)~z^{(\Gamma)}~{W_N^{kn}} + w(n), \end{align}

where $s_\mathrm{in}(n)$ is the sampled signal at the output of the filter dedicated to the modulation bandwidth $B_\mathrm{com}$, $s_\mathrm{cr}(k,\Gamma)$ represents the output of the first stage of the proposed method. $z^{(\Gamma)}=e^{-\mathrm{j}\frac{2\pi\Gamma\Delta}{N}n^2}$ represents the chirp function and ${W_N^{kn}}~=~e^{-\mathrm{j}\frac{2\pi kn}{N}}$ is the Fourier factor. w(n) is the noise, $k,n = 0,..., N-1$, as introduced in DFT, and $\Gamma = 0,...,\frac{N}{\Delta}-1$, where Δ is an incremental step introduced for the estimation of the chirp rates dependent on the slopes assigned in the investigation.

Correlation-based synchronization

As a next step upon extracting the number of the signals transmitted in the same time duration, the start point of the frame is detected according to a modified version of the Schmidl & Cox algorithm [Reference Schmidl and Cox19], as proposed in [Reference Khoury, Ramanathan, McCloskey, Smith and Campbell8, Reference Martinez, Kumar, Chafii and Fettweis20]. Since the investigation focuses on analyzing the impact of interfering signals on the desired frame synchronization, the proposed algorithm in [Reference Khoury, Ramanathan, McCloskey, Smith and Campbell8] is explored based on [Reference Marey and Steendam21], where the investigation in [Reference Marey and Steendam21] presented the impact of narrowband interferers on the desired signals. After that, a set of different up- and down-chirps are adopted based on the parameters of a reference codebook within the sampled receiver bandwidth $B_\mathrm{com}$. In this context, the received signal is correlated with each set of up- and down-chirps deployed from the codebook. Figure 6 illustrates an exemplary output of the correlator according to the desired signal that should be synchronized at the receiver side to deliver the communication data afterward. The frequency offset $\Delta f_\mathrm{i}$ of the first set can be calculated dependent on the difference between the maximum correlation peaks of the up- and down-chirps $\Delta C_\mathrm{i}$, which are represented in samples

(5)\begin{align} \Delta f_\mathrm{i} &= \Big(\Delta C_\mathrm{i}\cdot\frac{1}{f_\mathrm{s}}-T_\mathrm{C}\Big)\cdot\mu, \end{align}

Figure 6.

Exemplary time shift τ at the output of the correlator for four successive up and down-chirps, composing one preamble dedicated to synchronization correlated with the reference signals. Red peaks represent the output of the correlator concerning the up-chirps, whereas blue counterparts are the output related to down-chirps. For simplicity, only the peaks for one assigned signal are illustrated [Reference Alabd, Dittmer, Nuss, Li, Giroto de Oliveira, Diewald and Zwick1].

where µ is the chirp rate, $T_\mathrm{C}$ is the chirp duration, and $f_\mathrm{s}$ represents the sampling frequency. Furthermore, a modified version of the study in [Reference Martinez, Kumar, Chafii and Fettweis20] is adopted to accomplish high accuracy in terms of frequency estimation. For accurate time estimation in each time duration, the delay $\Delta t$ in samples relative to each correlation peak can be calculated by:

(6)\begin{align} \Delta t_\mathrm{i}\cdot f_\mathrm{s} &= C_\mathrm{i} - \Big(\frac{\Delta f_\mathrm{i}}{f_\mathrm{s}}\Big). \end{align}