Joint Radar-Communications Waveform

• Joint radar-communications waveform is a dual-function signal designed to support both radar sensing and wireless communications under shared spectral and hardware constraints.
• It employs diverse strategies including communications-based reuse, radar-centric embedding, and dedicated co-design to balance tradeoffs like PAPR, interference, and latency.
• Advanced designs optimize key metrics such as ambiguity functions, SINR, and BER using methods like adaptive power allocation, chirp shaping, and convex or manifold optimization.

Searching arXiv for the cited JRC waveform papers to ground the article in current arXiv records. A joint radar-communications waveform is a transmitted signal, or a coordinated family of signals, designed so that the same RF emission supports both radar sensing and wireless communications. In the contemporary literature, the topic spans communication-centric waveform reuse, radar-centric data embedding, dedicated dual-function waveform design, and coexistence-oriented co-design. The common objective is simultaneous sensing and signaling under shared spectral and hardware constraints, but the literature also repeatedly stresses that no single waveform simultaneously optimizes radar detection probability, sensing accuracy and resolution, parameter estimation of range, Doppler, and angle, data rate and BER, latency and reliability, spectral efficiency, robustness to interference, hardware reuse, low-complexity implementation, and low cost/power (Ma et al., 2019).

1. Taxonomy and conceptual scope

The broadest organizing framework is the four-part taxonomy that divides existing methods into coordinated separated signals transmission, communications waveform-based schemes, radar waveform-based schemes, and joint waveform design. In coordinated separated transmission, radar and communications use distinct signals but are coordinated in time, frequency, or space. In communications waveform-based schemes, a communications waveform is reused as the radar probing waveform. In radar waveform-based schemes, communication information is embedded into a radar waveform. In joint waveform design, a dedicated dual-function waveform is optimized directly for both tasks (Ma et al., 2019).

Before examining specific waveform families, it is useful to distinguish the design philosophies they encode. Communication-centric schemes typically preserve the communications stack and extract sensing from preambles, pilots, or known symbol structure. Radar-centric schemes preserve radar-friendly signaling such as constant envelope, stepped frequency, or chirp structure, and place communications into waveform choice, tone ordering, or secondary modulation. Dedicated co-design methods treat the waveform, beamformer, receive filter, or covariance as optimization variables from the outset. Coexistence-oriented work occupies a related but distinct position: it may jointly optimize a communication beamformer and a radar waveform covariance without collapsing them into a single transmitted waveform (Liu et al., 2018, Liu et al., 2019, Liu et al., 2021, Liu et al., 2024).

Category	Defining idea	Representative examples
Coordinated separated signals transmission	Distinct radar and communications signals, coordinated in time, frequency, or space	OFDM subcarrier partitioning and beamforming coexistence (Ma et al., 2019)
Communications waveform-based schemes	A communications waveform is reused for sensing	OFDM IRCW (Liu et al., 2018), CCDT (Berggren et al., 2022), IEEE 802.11ad (Han et al., 2022)
Radar waveform-based schemes	Data are embedded into a radar waveform	Dynamic-length FSK (Han et al., 15 Sep 2025), triangle/V-LFM (Sümen et al., 2022), frequency permutations (Senanayake et al., 2021)
Joint waveform design	A dedicated dual-function waveform or covariance is optimized directly	Constant-modulus DFRC (Liu et al., 2019), STAP-SLP MIMO-DFRC (Liu et al., 2021)

This taxonomy also clarifies a recurrent ambiguity in the literature. Some works described as joint radar-communications actually study waveform reuse, some study symbol embedding in legacy radar signals, and some study spectrum-sharing cooperation. A plausible implication is that comparisons must be conditioned on architecture: a standard-compatible waveform reuse scheme and a fully optimized DFRC waveform do not solve the same design problem.

2. Signal models, objectives, and evaluation criteria

Across the literature, joint radar-communications waveform design is grounded in a small number of recurring signal models. One representative radar-centric model is the train of single-tone subpulses used in dynamic-length FSK: $$s_{L}(t) = \sum_{l=0}^{L-1} p(t-lT)\exp\!\big(j\omega_l (t-lT)\big),$$ where $L$ is the number of subpulses, $T$ is the subpulse repetition interval, and each $\omega_l$ is selected from an $M$-ary FSK alphabet. Another representative communication-centric model is the integrated OFDM waveform

$$s(t)=\sum_{n=0}^{N_s-1}\sum_{m=0}^{N_c-1} a_m c_{m,n} e^{j2\pi(f_c+m\Delta f)t}\, \mathrm{rect}\!\left(\frac{t-nT_s}{T_s}\right),$$

whose main design variable is the power allocation vector $\mathbf p=[p_0,\ldots,p_{N_c-1}]^T$ with $p_m=|a_m|^2$ (Han et al., 15 Sep 2025, Liu et al., 2018).

The metrics used to judge these waveforms vary with task. Radar-side analyses repeatedly use the ambiguity function, the Fisher information matrix, CRLBs for delay and Doppler, output SINR, and covariance- or beampattern-based criteria. Communications-side analyses use data information rate, BER or SER, constructive-interference QoS constraints, distortion MMSE, and secrecy rate. A particularly explicit information-theoretic formulation combines radar conditional mutual information and communications data information rate into a weighted normalized objective, while clutter-aware DFRC work maximizes radar output SINR subject to symbol-level QoS and waveform constraints (Liu et al., 2018, Liu et al., 2021).

The role of time-bandwidth structure appears repeatedly. In dynamic-length FSK, the paper invokes

$$\mathrm{CRLB}_{\omega} = \frac{1}{C\sigma_t^2}, \qquad \mathrm{CRLB}_{\tau} = \frac{1}{C\sigma_\omega^2},$$

with $\sigma_t^2 = L^2T^2/12$, so Doppler estimation improves monotonically with increasing $L$0. In OFDM IRCW, the weighted objective is built from $L$1 for radar and $L$2 for communications, so subcarrier power becomes the principal tradeoff variable. In adaptive mmWave virtual-waveform design, the communication metric is recast as a distortion MMSE so that radar CRB and communications distortion can be optimized on a comparable error-like scale (Han et al., 15 Sep 2025, Liu et al., 2018, Kumari et al., 2019).

Waveform constraints are equally central. Constant modulus or low PAPR is treated not as a secondary implementation issue but as a defining property of several JRC families. FSK is emphasized for unit baseband PAPR, CCDT can achieve $L$3 dB discrete-time PAPR with suitable sequences, and constant-modulus MIMO-DFRC formulations impose $L$4 or $L$5 entrywise. These constraints tie the abstract waveform problem directly to saturated power amplifiers, power-limited platforms, and mmWave or radar front ends (Han et al., 15 Sep 2025, Berggren et al., 2022, Liu et al., 2019, Liu et al., 2021).

3. Communications-waveform reuse

Communication-centric JRC schemes treat an existing communications waveform as the sensing signal. In robust OFDM integrated radar and communications waveform design, a single pulsed OFDM waveform carries communications symbols and simultaneously probes a frequency-selective radar-target response. Radar performance is measured by conditional mutual information between the observed radar signal and the target impulse response, communications performance is measured by OFDM data information rate, and the robust design maximizes the worst-case weighted sum over uncertainty classes for the radar combined propagation-target response and the communications channel. Because the objective is monotone increasing in both radar and communications subcarrier CNRs, the worst case is attained at the lower bounds, which yields a convex power-allocation problem with a closed-form KKT solution (Liu et al., 2018).

Other communication-centric designs emphasize ambiguity-function shaping rather than subcarrier power allocation. The multicarrier chirp-based CCDT waveform writes the periodic ambiguity function in closed form and shows that its modulus AF is the periodic modulus AF of the transmit sequence evaluated at an effective delay depending jointly on $L$6, $L$7, and the chirp rate $L$8. By choosing the sequence and chirp rate appropriately, the waveform can realize a ridge-like AF along delay, a ridge-like AF along Doppler, or near-thumbtack behavior. The paper also shows that random PSK symbols yield a thumbtack-like AF in expectation, and that CCDT can be realized as DFT-s-OFDM plus a unitary frequency-domain chirp filter (Berggren et al., 2022).

Standard-compatible reuse is represented by IEEE 802.11ad-based radar imaging. In that line of work, the waveform itself is not redesigned; instead, the Golay complementary sequences in the SC PHY preamble are exploited for delay estimation, LS-based Doppler estimation is performed from framewise radar-channel estimates, and a roadside unit forms an ISAR image while maintaining a mmWave V2I link. The paper explicitly classifies its contribution as waveform reuse rather than waveform co-design, and derives a sensing chain from the preamble and the communication beam-alignment structure (Han et al., 2022).

A further communication-centric variant is adaptive virtual waveform design for mmWave WLAN-like JCR. There the design variable is not the preamble waveform itself but the non-uniform placement of a small number of preambles across a CPI. The pairwise differences of physical preamble positions generate a difference co-waveform with many virtual preambles, improving velocity estimation accuracy with only a small reduction in communication data rate. The paper evaluates radar CRB and communication DMMSE, and studies uniform, nested, and Wichmann virtual waveforms; it reports that the optimal virtual waveform achieves significant performance improvement as compared to a uniform waveform (Kumari et al., 2019).

A plausible implication of these communication-centric papers is that the sensing function is often extracted from structure already present in the communications layer: preambles, Golay sequences, slow-time placement, pilot-like chirp filters, or subcarrier power distribution. The attraction is backward compatibility or near-backward compatibility, but the recurring limitations are also explicit: OFDM has high PAPR and can require high-rate ADCs, 802.11ad sensing depends strongly on the preamble, and virtual-preamble methods mainly target velocity estimation rather than a full radar design space (Ma et al., 2019, Liu et al., 2018, Han et al., 2022, Kumari et al., 2019).

4. Radar-waveform embedding and radar-centric families

Radar-centric JRC designs begin from a waveform already favored by radar hardware or sensing geometry and then embed communications into it. A clear example is dynamic-length $L$9-ary FSK. Communications operates exactly as ordinary symbol-by-symbol FSK, while the radar does not commit in advance to a fixed waveform length. Instead, the transmitter keeps sending FSK subpulses continuously, the radar-side controller updates the histogram $T$0 and the spectrum-flatness metric

$T$1

and the current contiguous block is declared a radar waveform once $T$2 and $T$3. The result is a dynamic-length constant-envelope FSK JCR waveform with unchanged conventional FSK communication receiver, stabilized delay performance through spectrum-flatness control, and a Brownian-motion approximation for the random waveform length (Han et al., 15 Sep 2025).

Chirp-based radar-centric embedding appears in the THz inter-satellite triangle/V-LFM waveform. Each communication bit selects one of two composite chirp pulses: triangle LFM for bit $T$4 and V-LFM for bit $T$5. The same pulse also contains both up- and down-chirp components, so the radar function can combine the resulting beat frequencies to estimate range and radial velocity and mitigate the delay-Doppler ambiguity of ordinary FMCW/LFM for moving targets. The paper’s stated application is low-orbit inter-satellite links with space debris sensing at $T$6 GHz, $T$7 MHz chirp bandwidth, and $T$8 chirp duration (Sümen et al., 2022).

Stepped-frequency permutation signaling provides a different radar-centric route. The waveform uses a classical stepped-frequency radar burst, but the order of the $T$9 orthogonal tones is chosen from the $\omega_l$0 permutations, and that permutation is the communication symbol. The mapping from bits to permutations is performed by the Lehmer code; the communication receiver can achieve optimum performance with much less operational complexity by using the Hungarian algorithm rather than exhaustive search; and the radar side is characterized through the ambiguity function, Fisher information matrix, and accurate approximations to the CRLBs on delay and Doppler estimation errors (Senanayake et al., 2021).

A related line of work addresses the fact that radar matched filtering usually requires exact knowledge of the transmitted waveform, including the embedded data. Composite-modulation JRC waveforms solve this by separating an internal modulation from an external modulation. In the $\omega_l$1-ary formulation, the internal modulation maps $\omega_l$2 bits to one of $\omega_l$3 orthogonal signals $\omega_l$4, while an external phase sequence $\omega_l$5 shapes the radar response. After a bank of internal matched filters and summation, the radar processing becomes independent of the unknown information under ideal orthogonality, the ambiguity function resembles that of the phase-coded external sequence, and a new parameter, dissimilarity, is defined to evaluate detection-performance robustness to unknown embedded information (Quan et al., 2020).

The bistatic extension adopts a two-layer waveform with two orthogonal signals $\omega_l$6 and $\omega_l$7, uses an external phase code such as a 13-Barker sequence, and designs a joint detection process whose output is independent of the information bits. In multi-path environments, the same joint detection stage also provides CSI for a judgement-reconstruction equalization method. The paper reports that the SER of the proposed system is similar to that of binary frequency shift keying, and that the SNR requirement in multi-path environments is less than $\omega_l$8 dB higher than in single-path environment to reach a SER of $\omega_l$9 (Quan et al., 2020).

Receiver design becomes a central issue when the transmitter switches among several communication-bearing radar waveforms across PRIs. In that setting, generalized fully coherent closed-form receiver design formulates the condition

$M$0

and derives two closed-form solutions, one for linear convolution and one for circular convolution, so that all waveform/filter pairs yield the same output response while suppressing range sidelobes. The paper’s significance is receiver-side: it disputes the claim that fully coherent response is unattainable for more than two waveforms and shows that coherent slow-time radar processing can be restored under waveform diversity (Zubair et al., 2021).

5. Fully co-designed waveform, beamforming, and covariance optimization

Dedicated co-design methods treat the waveform, beamformer, receive filter, or covariance as primary optimization variables. In constant-modulus dual-functional radar-communication waveform design under orthogonality constraints, the transmitted waveform matrix $M$1 is optimized to jointly minimize downlink multi-user interference and deviation from an orthogonal radar waveform. The central formulation is

$M$2

subject to $M$3 and $M$4. The paper solves the $M$5-subproblem in closed form by SVD and the constant-modulus $M$6-subproblem on the complex circle manifold via Riemannian conjugate gradient, within an alternating minimization loop (Liu et al., 2019).

The STAP-SLP-based MIMO-DFRC framework extends co-design into clutter-aware space-time optimization. There the same transmitted waveform, the same antenna platform, and the same processing chain serve both radar sensing and multi-user communications. The radar objective is output SINR in the presence of signal-dependent clutter, the communications constraints are symbol-level constructive-interference QoS inequalities, and the waveform can be constrained to be constant modulus, PAPR-bounded, similar to a reference waveform, or constant-modulus plus similarity. The paper concentrates the joint waveform/filter problem into a waveform-only problem by substituting the MVDR-optimal receive filter, then solves the nonconvex waveform problem by majorization-minimization and nonlinear equality constrained ADMM (Liu et al., 2021).

Joint design can also couple waveform structure and analog beamforming. In adaptive and fast combined waveform-beamforming design for mmWave automotive JCR, the waveform variable is the preamble length parameter $M$7, the beamforming variable is the power-split parameter $M$8, and frame-to-frame circulant shifts of the transmit beamformer are optimized to minimize compressed-sensing coherence in the Doppler-angle domain. The radar metric is normalized MSE of the sparse channel estimate, the communications metric is distortion MSE, and the final design is posed as a weighted average optimization over $M$9. The resulting scheme estimates short- and medium-range radar channels with a low normalized MSE at the expense of a small degradation in the communication distortion MSE (Kumari et al., 2020).

A distinct but related thread is coexistence-oriented co-design. In robust secure radar-communication coexistence, the communication base station and the radar are separate systems in the same band. The optimized variables are the communication beamforming covariance $$s(t)=\sum_{n=0}^{N_s-1}\sum_{m=0}^{N_c-1} a_m c_{m,n} e^{j2\pi(f_c+m\Delta f)t}\, \mathrm{rect}\!\left(\frac{t-nT_s}{T_s}\right),$$0 and the radar waveform covariance $$s(t)=\sum_{n=0}^{N_s-1}\sum_{m=0}^{N_c-1} a_m c_{m,n} e^{j2\pi(f_c+m\Delta f)t}\, \mathrm{rect}\!\left(\frac{t-nT_s}{T_s}\right),$$1. The objective is worst-case secrecy rate under imperfect CSI, while radar performance is maintained by a covariance mismatch constraint $$s(t)=\sum_{n=0}^{N_s-1}\sum_{m=0}^{N_c-1} a_m c_{m,n} e^{j2\pi(f_c+m\Delta f)t}\, \mathrm{rect}\!\left(\frac{t-nT_s}{T_s}\right),$$2 and INR constraints at the radar receiver. The paper solves the robust problem by a two-layer cooperative algorithm based on semidefinite relaxation, the Charnes-Cooper transformation, and the S-lemma (Liu et al., 2024).

These fully co-designed formulations are the most expressive, but the literature is equally explicit about their cost. They rely on convex or manifold optimization, on CSI or clutter statistics, and on algorithmic pipelines such as SVD projection, RCG, MM, neADMM, OMP, or semidefinite programming. This suggests that their main advantage is not standard compatibility but tradeoff control.

6. Applications, recurring tradeoffs, and unresolved issues

The applications covered by the literature are unusually broad. Automotive systems motivate much of the taxonomy because radar and communications may occupy similar or overlapping spectral ranges, especially at mmWave, and because autonomous vehicles require both sensing and V2X connectivity (Ma et al., 2019). Other papers target low-power IoT and LPWAN-like settings through constant-envelope FSK (Han et al., 15 Sep 2025), low-orbit inter-satellite links and space debris sensing through THz chirp signaling (Sümen et al., 2022), geosynchronous bistatic SAR imaging with a DSSS-QPSK communication waveform (Lian et al., 18 Aug 2025), and roadside vehicular ISAR using IEEE 802.11ad (Han et al., 2022).

Despite their diversity, the same tradeoffs recur. Constant-envelope and low-PAPR waveforms such as FSK, FMCW/LFM, DFT-sequence CCDT, and many radar-centric DFRC designs are attractive for saturated power amplifiers, but they generally give up spectral efficiency relative to multicarrier communications-centric waveforms (Han et al., 15 Sep 2025, Berggren et al., 2022, Sümen et al., 2022). Communication-centric reuse of OFDM or 802.11ad preserves communications operation and standard compatibility, but radar often depends on preamble structure, known symbols, or motion compensation, and OFDM specifically is associated with high PAPR and wideband hardware burden (Liu et al., 2018, Han et al., 2022, Ma et al., 2019). Radar-centric embedding preserves radar functionality and often keeps the communications receiver simple, but the payload alphabet can be modest, as in binary chirp-shape modulation or orthogonal-signal selection (Sümen et al., 2022, Quan et al., 2020).

Uncertainty and variability are another common theme. Dynamic-length FSK stabilizes delay estimation by monitoring spectrum flatness but introduces random radar processing latency and variable Doppler quality unless bounded (Han et al., 15 Sep 2025). Robust OFDM design gains worst-case performance at the cost of some best-case performance (Liu et al., 2018). STAP-SLP MIMO-DFRC shows that PAPR relaxation improves radar SINR, while similarity to a reference waveform preserves radar structure but reduces waveform freedom (Liu et al., 2021). Adaptive virtual-waveform design shows that sparse, non-uniform preamble placement can reduce the radar-communications tradeoff, but the advantage depends on target count and SNR, and conventional virtual-preamble-count heuristics converge to the MMSE-based solution only for a small number of targets and a high signal-to-noise ratio (Kumari et al., 2019).

Several unresolved issues are stated explicitly. The vehicular survey notes that there is no unified radar-communications performance metric, which makes rigorous cross-method comparison difficult (Ma et al., 2019). The CCDT paper states that whether comparable thumbtack behavior can be achieved with random QAM remains open (Berggren et al., 2022). The bistatic orthogonal-signal paper identifies Doppler performance as future work (Quan et al., 2020). The STAP-SLP paper points to robustness to CSI errors, clutter mismatch, hardware impairments, and low-complexity real-time implementation as open problems (Liu et al., 2021). The GEO SA-Bi SAR work is a feasibility-driven integrated waveform-and-receiver demonstration rather than a complete waveform-optimization theory, and it leaves synchronization, Doppler-spread communication channels, and quantitative sensing-communications tradeoff analysis open (Lian et al., 18 Aug 2025).

Taken together, the literature presents joint radar-communications waveform design not as a single waveform family but as a design space structured by architectural choice. Communication-centric reuse, radar-centric embedding, dedicated co-design, and coexistence-oriented optimization each remain active because they optimize different combinations of sensing fidelity, communications simplicity, hardware efficiency, robustness, and implementability.