---
title: Single-Carrier Joint Communication & Sensing
url: https://www.emergentmind.com/topics/single-carrier-joint-communication-and-sensing-jcas
type: topic
---

# Single-Carrier Joint Communication & Sensing

Searching arXiv for recent and directly relevant papers on single-carrier joint communication and sensing, including waveform design, detection, architecture, and learning-based methods.
Single-Carrier Joint Communication and Sensing (JCAS) denotes the class of integrated wireless systems in which communication is carried by a single-carrier signal—or by a narrowband, symbol-domain model that is directly compatible with single-carrier processing—while the same transmission is reused for sensing, target detection, localization, channel inference, or environmental perception. In recent arXiv literature, explicit single-carrier realizations include monostatic single-carrier QAM systems with neural sensing blocks and SC-IFDM waveforms merged with FMCW radar chirps, while several adjacent works contribute single-carrier-compatible detection, estimation, architectural, and optimization frameworks without deriving a dedicated single-carrier waveform [2403.02929][2503.12638][2404.12133].

## 1. Conceptual scope and position within JCAS taxonomy

JCAS is broadly framed as a 6G capability in which a wireless system uses the same spectrum, waveform, and hardware to both deliver data and sense the environment. The central motivation is reuse of spectrum, waveforms, and hardware resources, together with the observation that communication and sensing remain coupled by an inherent communication-sensing tradeoff rather than by a single universal objective [2602.09589]. Within that broader taxonomy, the survey literature classifies systems into communication-centric JCAS, sensing-centric JCAS, and dual-function JCAS. It also classifies integration by coexistence-based, cooperative, and joint or unified systems. Single-carrier JCAS is not treated as a dominant standalone branch in that taxonomy; instead, it appears as one implementation point inside the broader waveform and architecture design space [2602.09589].

This positioning matters because a recurrent misconception is that single-carrier JCAS is defined by one canonical waveform. The literature does not support that view. Some works are explicitly waveform-centric, such as SC-IFDM-FMCW integration, whereas others are single-carrier chiefly in the sense that they operate on time snapshots, covariance matrices, narrowband steering-vector models, or symbol-domain beamforming, without subcarrier-domain radar processing [2503.12638][2404.12133]. A second misconception is that single-carrier JCAS is only a PHY-layer modulation issue. Mobility-oriented 6G work instead places it on a continuum of convergence levels, from stand-alone sensing and communication to coexistence, cooperation, and full integration, with device-oriented sidelink, distributed processing, synchronization, privacy, and interference management all treated as first-class design constraints [2311.11623].

The attraction of single-carrier signaling in this context is consistently tied to lower PAPR, power-amplifier efficiency, and suitability for user equipment and uplink operation. That logic appears most explicitly in the SC-IFDM-based waveform literature and is echoed indirectly by the general JCAS survey’s emphasis on balancing high PAPR, low sidelobe levels, sensing quality, and communication efficiency [2503.12638][2602.09589].

## 2. Waveform constructions and orthogonal sensing embedding

The most explicit recent waveform proposal is the SC-IFDM-FMCW design of “Single-Carrier Waveform Design for Joint Sensing and Communication” [2503.12638]. Its central construction combines single-carrier interleaved frequency division multiplexing (SC-IFDM), described there as a 5G communication candidate signal, with FMCW radar chirps. The key observation is that an FMCW chirp is sparse in the SC-IFDM DFT domain. The waveform is built in three steps: SC-IFDM symbols are allocated alongside sparse FMCW components in the DFT domain; the joint structure is transformed back to the time domain; and a cyclic prefix is inserted while the FMCW component is phase-shifted so that chirp continuity is preserved across symbols [2503.12638].

The SC-IFDM time-domain signal is written as
$$
s^{\text{SC-IFDM}}(p)=\frac{1}{\sqrt{N}} \sum_{k=0}^{N-1} X^{\text{SC-IFDM}}(k,[p]_M)e^{j 2 \pi\frac{k}{MN}p},
$$
while the discrete FMCW chirp is modeled as
$$
s^{\text{FMCW}}(p)=e^{j\pi  \frac{ p^2 }{MN} } , \quad 0 \leq p<MN.
$$
When expressed in the SC-IFDM DFT structure, the chirp becomes nonzero only under the sparsity condition
$$
\left[\frac{M}{2} +l-k\right]_N=0,
$$
which enables orthogonal embedding into DFT positions that would otherwise be zero. The combined symbol is then
$$
X^{\text{comb}}(k,l)=
\begin{cases}
\sqrt{\boldsymbol{\psi}}\, s^{\text{FMCW}}(l)\omega_{k}^{l} ,&\left[\frac{M}{2} +l-k\right]_N=0 \\
X^{\text{SC-IFDM}}(k,l), & \text { otherwise } ,
\end{cases}
$$
where $\boldsymbol{\psi}$ is the FMCW power allocation parameter controlling the sensing-communication tradeoff [2503.12638].

A distinctive implementation issue is cyclic-prefix continuity. The paper shows that ordinary CP insertion would break chirp continuity, so the chirp is shifted by the CP duration in the DFT-domain index. This is not a cosmetic adjustment; it preserves the beat-frequency structure required by FMCW sensing and allows the radar receiver to process the analog mixed signal directly, without CP removal or extra digital processing [2503.12638]. The same paper also develops an enhanced channel estimation method in which the embedded FMCW chirp acts as a pilot in the DFT domain. Because the chirp is sparse, the pilot does not require guard bands between pilots and data, and the channel-estimation variance scales as
$$
\text{var}\{ \hat{Y}_1\}=\frac{\sigma_d^2 (\sum_{r=0}^{R-1}h_r^2) + \sigma^2 }{ \boldsymbol{\psi} M}.
$$
To resolve delay-Doppler ambiguity, the paper uses one up-chirp and one down-chirp, yielding the shift relations
$$
k_r-l_r=\alpha_1 N + \beta_1, \qquad
k_r+l_r=\alpha_2 N + \beta_2,
$$
from which both delay and Doppler shifts can be identified [2503.12638].

The reported simulations use $f_c = 77\,\mathrm{GHz}$, $200\,\mathrm{MHz}$ bandwidth, a $32 \times 32$ symbol size, and $100$ symbols. In that setting, SC-IFDM-FMCW approaches FMCW range and velocity RMSE at sufficiently large $\boldsymbol{\psi}/\sigma_d^2$, achieves BER comparable to OTFS-FMCW under perfect channel knowledge, and significantly outperforms OFDM-FMCW in both sensing and communication because OFDM-FMCW suffers from orthogonality loss and performs poorly in mobile channels [2503.12638].

A broader but OFDM-specific contrast is the MaRS design, which is not a single-carrier waveform but is important as a foil. Its main lesson is aperture-first sensing design: sensing quality is tied to time-frequency-space aperture rather than dense occupancy of all communication resources. This suggests that, even in single-carrier JCAS, sparse radar-friendly structure may be more consequential than dense waveform occupation, provided the resulting signal preserves the required aperture and receiver observability [2207.03241].

## 3. Detection, estimation, and receiver processing in single-carrier-compatible settings

A substantial portion of single-carrier JCAS research is not about waveform synthesis but about how sensing should be inferred from the shared transmission. “On Target Detection in the Presence of Clutter in Joint Communication and Sensing Cellular Networks” studies target-number detection in a bistatic cellular JCAS network using narrowband steering-vector models, time-slot observations, and sample-covariance eigenvalue analysis rather than OFDM-specific processing [2404.12133]. In that model, the sensing receiver forms
$$
\mathbf R_{T_s}=\frac{1}{T_s}\mathbf Y\mathbf Y^{\sf H},
$$
with the observation matrix
$$
\mathbf Y = \mathbf B_{\text{tar}}\mathbf X + \mathbf B_{\text{cl}}\widetilde{\mathbf X} + \mathbf V,
$$
where clutter is modeled by clustered scatterers and temporally correlated noise is represented through a Toeplitz covariance matrix $\mathbf{\Sigma}$ [2404.12133].

The detector is an eigenvalue-ratio test:
$$
\widehat K = \arg\max_{n=1,\ldots,K_{\max}}
\left\{ \frac{\lambda_n}{\lambda_{n+1}} > 1+\varepsilon \right\},
$$
with ordered eigenvalues $\lambda_1>\lambda_2>\cdots>\lambda_N$. The rationale is random-matrix-theoretic: target-induced rank-$K$ perturbations create outlier eigenvalues beyond the clutter-plus-noise bulks. The same paper compares time-division mode (TDM), with sensing fraction $\alpha$ and sensing horizon $T_s=\lfloor \alpha T\rfloor$, against concurrent mode (CM), with sensing power split $P_s=\delta P$. Its numerical findings are that target detection is successful even for moderate antenna and snapshot dimensions, transmit beamforming improves detection if beam pointing error is not too large, TDM generally outperforms CM for target detection, and the performance gap decreases as sensing fraction or sensing power is increased. Under temporally correlated noise and clutter, the proposed detector significantly outperforms MDL and AIC, while classical methods often miss the targets [2404.12133].

Uplink channel estimation provides a second single-carrier-compatible processing theme. “Sensing-aided Uplink Channel Estimation for Joint Communication and Sensing” uses sensing-derived AoA estimates as priors for CSI refinement [2211.04063]. Although its waveform model is OFDM, the core mechanism is spatial rather than subcarrier-specific: the least-squares channel estimate is post-processed by a sensing-aided Kalman filter that exploits the deterministic phase progression implied by the estimated AoA. From $\hat{\bf p}_{RX,l}^U=(\hat\varphi_l,\hat\theta_l)$, the spatial transition coefficients are
$$
\hat A_{P,l} = e^{-j\frac{2\pi d_a}{\lambda}\cos\hat\varphi_l\sin\hat\theta_l}, \qquad
\hat A_{Q,l} = e^{-j\frac{2\pi d_a}{\lambda}\sin\hat\varphi_l\sin\hat\theta_l},
$$
and the Kalman recursion refines the raw estimate through
$$
[{\bf \bar h}_C]_p = [{\bf \hat h}_C]_p^- + K_p\left([{\bf \hat h}_C]_p - [{\bf \hat h}_C]_p^-\right).
$$
The method applies column-wise and row-wise filtering, followed by an inverse pass to exploit the sensing information in both spatial directions. Its complexity is $\mathcal{O}(3N)$ versus $\mathcal{O}(N^3)$ for MMSE, and the reported BER under 4-QAM requires about $1.8$ dB less SNR than LS for the same BER while remaining only about $0.2$ dB worse than MMSE [2211.04063].

A hardware-oriented variant of this processing philosophy appears in “Low-complexity hardware and algorithm for joint communication and sensing,” which separates ToA and AoA estimation instead of performing 2D or 3D joint estimation [2309.06850]. The receiver combines a wideband analog beamforming branch for ToA with a narrowband per-antenna digital branch for AoA, and associates the two estimates through multiple non-coherent frames. The key operation is delay-conditioned coherent combining,
$$
\bar{H}_d(\hat{\tau}_\ell,m) = \sum_{i=0}^{F-1} \sum_{s} \hat{\alpha}_{(\ell,i)}^* e^{j2\pi \hat{\tau}_\ell s\Delta_f} \hat{H}_m(i,s\Delta_f),
$$
which makes the desired component combine coherently across frames while other components add mostly incoherently. The paper reports that, for $B_A=400$ MHz and $N=16$, the proposed front end uses $800$ MS/s versus $6.4$ GS/s for a fully digital baseline, with estimated ADC power reduced from $2.5$ W to $300$ mW [2309.06850].

## 4. Learning-based single-carrier JCAS and bound-informed training

Explicitly single-carrier learning-based JCAS is developed in “Loss Design for Single-carrier Joint Communication and Neural Network-based Sensing” [2403.02929]. The system is monostatic, uses a linear array with $K$ antennas, transmits single-carrier QAM symbols, and forms the transmitted matrix
$$
Y = v x^T,
$$
where the beamforming coefficients are $v_k = g_k e^{j\gamma_k}$. The sensing path is
$$
Z_s = T\, a_{\mathrm{Rx}}(\theta)a_{\mathrm{Tx}}(\theta)^T Y \,\mathrm{diag}(a_s) + N_s,
$$
with $T\in\{0,1\}$ and Swerling-1 reflectivity. Instead of operating on raw waveforms, the sensing network receives the autocorrelation matrix
$$
\mathrm{Corr}(Z_s,Z_s) := \frac{1}{N_{\text{win}}} Z_s Z_s^H \in \mathbb{C}^{K\times K},
$$
together with $N_{\text{win}}$ and $\mathrm{SNR}_s$ as auxiliary inputs [2403.02929].

The paper’s central contribution is loss normalization. Its multitask loss is
$$
L = (1-w_s)L_{\mathrm{comm}} + w_s L_{\mathrm{detect}} + w_s L_{\mathrm{angle}},
$$
but the plain angle-MSE term is replaced by the CRB-informed scaling
$$
L'_{\mathrm{angle}} = \frac{1}{N}\sum_{i=1}^N \frac{N_{\text{win},i}}{\sigma_{n,i}^2}(\theta_i-\hat\theta_i)^2.
$$
The motivation is that the Cramér–Rao bound for single-target AoA estimation depends strongly on snapshot count and noise, so the unnormalized loss produces unstable gradients across training samples. The reported effect is more stable convergence, lower AoA RMSE, and similar BMI relative to the unmodified loss. In the same study, the neural detector outperforms a Neyman–Pearson power detector and the neural AoA estimator outperforms ESPRIT at low sensing SNR, especially around $\mathrm{SNR}_s=-5$ dB [2403.02929].

The later extension “Neural Network-Based Single-Carrier Joint Communication and Sensing: Loss Design, Constellation Shaping and Precoding” broadens this framework into an autoencoder-like architecture with trainable beamformer, modulator, target detector, AoA estimator, and communication demapper [2509.26508]. It again uses a monostatic single-carrier architecture, now allowing either classical 16-QAM or geometrically shaped constellations. The beamformer learns from angular-region inputs, the sensing block again uses the correlation matrix $\mathrm{Corr}(\mathbf{z}_s,\mathbf{z}_s)$, and the communication objective is formulated through bit-wise mutual information (BMI). The paper shows that the communication BCE loss does not need SNR normalization because the SNR-dependent term is additive and independent of network weights, whereas the AoA loss again benefits from CRB-based scaling [2509.26508].

A notable result of that extension is the role of constellation shaping. As the sensing weight $w_s$ increases, the learned constellation becomes more PSK-like and more constant-envelope, improving sensing but reducing communication distance between constellation points. The paper also reports that the gap in sensing performance between classical and shaped modulation formats can be significantly reduced through multi-snapshot sensing. This is important because it shows that sensing-oriented modulation adaptation and sensing-oriented temporal accumulation are not interchangeable but can partially substitute for one another in practice [2509.26508].

## 5. Information-theoretic and multi-objective formulations

Single-carrier JCAS is also shaped by information-theoretic formulations that make the communication-sensing tradeoff explicit. “Rate Distortion Approach to Joint Communication and Sensing With Markov States: Open Loop Case” studies a single-transmitter JCAS system in which the transmitter both communicates and estimates a hidden Markov state from noisy observations [2501.15652]. Its key theorem states that the optimal sensing strategy is Bayesian filtering and that the open-loop capacity-distortion tradeoff is
$$
C^{(\textnormal{open})}(D)=\lim_{n\to\infty}\max_{P_{X^n}\in\overrightarrow{\mathcal{P}_D^{(n)}}\frac{1}{n}\sum_{i=1}^n I(X_i;Y_i\vert S_i).
$$
In the beam-pointing specialization, the state evolves according to a linear Gauss–Markov model and the Bayesian filter becomes a Kalman filter. The paper then compares beam switching, which time-shares between communication and sensing, with multi-beam transmission, which performs both simultaneously. The numerical result is clear: multi-beam outperforms beam switching in both stable and unstable systems, and the advantage becomes more pronounced at high communication rates and higher SNR [2501.15652].

At network scale, “Coverage and Rate of Joint Communication and Parameter Estimation in Wireless Networks” extends classical communication coverage probability and ergodic rate to sensing through mutual-information-based definitions [2210.02289]. Although its signal model is OFDM-like rather than single-carrier, its conceptual contribution is directly relevant to shared-waveform JCAS. It defines the sensing rate as
$$
R_{\rm rad} = \frac{I(Y;\Theta)}{T_{\rm CPI}},
$$
and a tractable sensing-efficiency proxy via Fisher information. Communication coverage is $P^0_U(\gamma \ge \tau_{\rm com})$, sensing coverage is $P^0_S(\Gamma_{\rm rad}\ge \tau_{\rm rad})$, and the combined JCAS coverage probability is a weighted spatial average over users and sensed objects. Its main numerical conclusion is that sensing SINR or efficiency improves monotonically or nondecreasingly with base-station density, whereas communication efficiency can peak at an intermediate density and then decrease [2210.02289].

A multi-objective beamforming formulation appears in “Multi-Objective Optimization for Joint Communication and Sensing in Multi-user MIMO Systems: Characterizing the Pareto Boundary” [2601.08152]. There the communication metric is mutual information and the sensing metric is the trace of the Fisher information matrix. The weighted-sum problem sweeps $\alpha\in[0,1]$ to generate the Pareto boundary, and the central structural result is Proposition 3.1: under independently distributed channels, the optimal solution satisfies $\operatorname{rank}(\mathbf{R}_i)=1$ for each user and $\operatorname{rank}(\mathbf{R}_0)=0$, meaning that no separate sensing beam is needed in the multi-user case. Joint beamforming is therefore optimal relative to independent communication and sensing beam design [2601.08152].

These formulations collectively show that single-carrier JCAS is not merely a waveform-coexistence problem. It is equally a rate-distortion problem, a coverage-and-interference problem, and a Pareto-optimization problem over sensing information and communication information.

## 6. Architecture, mobility, and distributed network operation

The architecture literature makes clear that waveform design alone is insufficient for single-carrier JCAS deployment. “Enabling Mobility-Oriented JCAS in 6G Networks: An Architecture Proposal” develops a device-oriented 6G JCAS architecture for vehicles and UAVs rather than a base-station-centric design [2311.11623]. Its relevance to single-carrier JCAS is indirect but substantial. It identifies four convergence levels—CL1 Separation, CL2 Coexistence, CL3 Cooperation, and CL4 Integration—and derives five Tech Cases spanning single-drone sensing, drone-swarm collaborative mapping, localization of non-cooperative emitters, vehicular communication-centric sensing, and cooperative vehicular radar. The proposed architecture is organized into four views: node view, functional view, data-flow view, and privacy and security view [2311.11623].

Several of its requirements are directly constraining for any single-carrier design. The system shall support a protocol to mitigate interference between sensing nodes; a sensing entity should be tunable to multiple carrier frequencies and adaptable bandwidths to reach CL2; the radar function should support cooperative operation where only preprocessed data such as point clouds or object lists is exchanged; and the system shall integrate sensing into a communication-capable platform to reuse communication signals, hardware, and infrastructure. The data-flow view distinguishes sensing data, control signals, and synchronization signals, and introduces three synchronization classes ranging from time-stamping to TX-RX clock synchronization. This implies that single-carrier framing, burst structure, and timing must remain compatible with distributed sensing quality requirements rather than only with link-level QoS [2311.11623].

Cell-free massive MIMO extends this architectural logic into centralized and distributed network optimization. “Power Allocation for Joint Communication and Sensing in Cell-Free Massive MIMO” studies downlink communication with multi-static sensing for single-target detection in a centralized C-RAN [2209.01864]. It derives a MAP ratio test detector for distributed AP observations and optimizes the power coefficients $\boldsymbol{\rho}$ to maximize sensing SNR subject to per-UE SINR and per-AP power constraints. The sensing SNR is written as a quadratic form $\gamma_s = \boldsymbol{\rho}^T A \boldsymbol{\rho}$, and the SINR constraints are reformulated as second-order cone constraints. The numerical finding is that, compared to communication-centric power allocation, the proposed scheme can increase detection probability under fixed false alarm probability both when additional sensing symbols are used and when only existing communication symbols are reused [2209.01864].

A related but distinct systems result appears in “Scalable Association of Users in CF-mMIMO: A Synergy of Communication, Sensing, and JCAS” [2506.01060]. This work is not waveform-level, but it shows that user association is itself a JCAS enabler. The scalable user association scheme uses AP masking, link prioritization, and mixed-integer optimization. For communication UEs the link metric is SNR, for sensing UEs it is SCNR, and for JCAS UEs it is
$$
\text{Joint}_{lk} = w_c \cdot \text{SNR}_{lk} + w_s \cdot \text{SCNR}_{lk}.
$$
In the reported simulation with $L=100$ APs and $K=30$ UEs, the average clutter count per link drops from approximately $44$ to approximately $1$, runtime decreases from about $0.0008$ s to about $0.0003$ s, and transmission delay decreases from an average of $196.39$ ns to $77.60$ ns [2506.01060]. For single-carrier JCAS, the implication is straightforward: even with a fixed waveform, sensing reliability depends strongly on which network links are activated and how clutter-prone associations are suppressed.

## 7. Limitations, related technologies, and unresolved research directions

The present literature does not support a narrow reading of single-carrier JCAS as a problem solved by replacing OFDM with a low-PAPR waveform. The survey literature instead frames JCAS as a multi-objective non-convex design problem over waveform, beamforming, resource allocation, optimization framework, and increasingly programmable propagation [2602.09589]. STAR-RIS is presented in that survey as enabling full-space programmable manipulation of electromagnetic waves through transmission and reflection, with element-wise coefficients satisfying
$$
\alpha_{n}^{t} + \alpha_{n}^{r} = 1.
$$
The survey’s waveform discussion is predominantly multicarrier-leaning, but its optimization tools—AO, FP, BCD, WMMSE, SDR, SCA, and QCQP—apply equally to single-carrier systems. A plausible implication is that single-carrier JCAS can use propagation control to compensate for reduced waveform flexibility, shifting some of the design burden from spectral shaping to environmental shaping [2602.09589].

Related RIS-assisted MIMO work strengthens that conclusion. “Joint Communication and Sensing in RIS-Assisted MIMO System Under Mutual Coupling” explicitly models the RIS response as
$$
\Theta = (\mathbf{\Upsilon}^{-1} - \mathbf{S})^{-1},
$$
rather than as an ideal diagonal phase matrix, and reports that physically consistent mutual-coupling modeling improves both communication MI and sensing FI relative to conventional RIS-assisted JCAS models [2601.08142]. “Full-Duplex-Enabled Joint Communications and Sensing with Reconfigurable Intelligent Surfaces” is not a single-carrier waveform paper either, but it shows that jointly designing full-duplex MIMO beamformers and RIS phases to be self-interference aware can significantly loosen the requirement for additional SI cancellation while respecting a CRB constraint [2306.10865]. These works indicate that, for single-carrier JCAS, the dominant practical bottlenecks may lie as much in self-interference, propagation control, and physical hardware realism as in modulation choice.

The survey on STAR-RIS-enabled JCAS identifies the main open challenges with unusual clarity: accurate and scalable CSI acquisition, coefficient coupling and hardware constraints, control signaling and latency overhead, robustness under environmental dynamics, joint interference management, energy and thermal constraints for active STAR-RIS, evaluation methodology and reproducibility, cross-layer design, and security, privacy, and sensing integrity [2602.09589]. Those challenges align closely with the mobility architecture literature, which emphasizes edge processing, synchronization precision classes, GDPR-compliant handling, PKI, post-quantum cryptography, and privacy-preserving processing near the sensor [2311.11623].

Single-carrier JCAS is therefore best understood not as a narrowly delimited modulation family but as a research direction at the intersection of low-PAPR waveform design, covariance-domain sensing, distributed synchronization, information-theoretic tradeoff analysis, neural and model-based inference, and architecture-level resource control. The explicit single-carrier waveform literature already demonstrates that orthogonal sensing embedding and low-complexity sensing reception are feasible, while the broader single-carrier-compatible literature shows that clutter-aware detection, sensing-aided CSI estimation, Bayesian filtering for dynamic states, distributed association, and privacy-aware mobility architectures are equally central to the field’s evolution [2503.12638][2404.12133][2501.15652].

Source: https://www.emergentmind.com/topics/single-carrier-joint-communication-and-sensing-jcas