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Waveform Design and Performance Analysis for Full-Duplex Integrated Sensing and Communication

Zhiqiang Xiao, Yong Zeng

arXiv:2108.06449v1eess.SP

TL;DR

Monostatic ISAC must jointly support radar sensing and communication despite pulsed-radar blind ranges and limited communication rates. The paper proposes full-duplex time multiplexing of classic radar pulses with dedicated communication signals, improving communication and detection when self-interference is effectively suppressed.

  • Problem

    Conventional pulsed radar has near-target blind ranges, while information embedding provides limited communication capability for monostatic ISAC.

  • Method

    The proposed full-duplex waveform time-multiplexes classic pulsed radar transmission with dedicated communication signals and analyzes sensing under residual self-interference.

  • Results

    45–92 dB of self-interference cancellation is required to maintain PD ≥99% as target distance increases from 100 m to 1350 m.

  • Takeaways & Limitations

    With sufficiently powerful self-interference cancellation, the scheme can improve communication rate and target-detection probability relative to pulsed radar with information embedding.

Abstract

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Integrated sensing and communication (ISAC) is a promising technology to fully utilize the precious spectrum and hardware in wireless systems, which has attracted significant attentions recently. This paper studies ISAC for the important and challenging monostatic setup, where one single ISAC node wishes to simultaneously sense a radar target while communicating with a communication receiver. Different from most existing schemes that rely on either radar-centric half-duplex (HD) pulsed transmission with information embedding that suffers from extremely low communication rate, or communication-centric waveform that suffers from degraded sensing performance, we propose a novel full-duplex (FD) ISAC scheme that utilizes the waiting time of conventional pulsed radars to transmit dedicated communication signals. Compared to radar-centric pulsed waveform with information embedding, the proposed design can drastically increase the communication rate, and also mitigate the sensing eclipsing and near-target blind range issues, as long as the self-interference (SI) is effectively suppressed. On the other hand, compared to communication-centric ISAC waveform, the proposed design has better auto-correlation property as it preserves the classic radar waveform for sensing. Performance analysis is developed by taking into account the residual SI, in terms of the probability of detection and ambiguity function for sensing, as well as the spectrum efficiency for communication. Numerical results are provided to show the significant performance gain of our proposed design over benchmark schemes.

I. INTRODUCTION · II. SYSTEM MODEL AND PROPOSED FULL-DUPLEX ISAC WAVEFORM

The paper targets monostatic ISAC by combining dedicated radar and communication waveforms through full-duplex operation, addressing the low communication rate of radar-centric designs and degraded sensing of communication-centric waveforms. It defines collocated and separated system architectures and prepares the waveform formulation by reviewing conventional pulsed radar and radar-centric information embedding.

  • I. INTRODUCTION · II. SYSTEM MODEL AND PROPOSED FULL-DUPLEX ISAC WAVEFORM: The study addresses monostatic ISAC, where one node simultaneously senses a radar target and communicates with a receiver using separate transmit and receive antennas.The system includes collocated and separated target–receiver architectures.
  • I. INTRODUCTION: Existing monostatic approaches rely on half-duplex pulsed transmission with information embedding or communication-centric waveforms, respectively suffering extremely low communication rate or degraded sensing performance.Communication-centric ISAC commonly uses OFDM or OTFS waveforms, whose random nature can degrade sensing.
  • I. INTRODUCTION: The proposed FD-ISAC waveform time-multiplexes dedicated sensing and communication signals, increasing communication spectrum efficiency and mitigating eclipsing and near-target blind-range issues when SI is suppressed.It preserves the classic radar waveform for improved autocorrelation compared with communication-centric waveforms.
  • I. INTRODUCTION: The proposed low-complexity design requires no complicated optimization and includes conventional pulsed radar and continuous communication waveforms as special cases through power control.The design exploits the FD capability of the ISAC node to multiplex sensing and communication waveforms.
  • I. INTRODUCTION: Residual SI is incorporated into analytical performance evaluation through derived sensing metrics, including probability of detection and ambiguity function, and communication metrics, including symbol error rate and spectrum efficiency.The analysis indicates that detection probability can exceed conventional pulsed radar depending on SIC capability.
  • II. SYSTEM MODEL AND PROPOSED FULL-DUPLEX ISAC WAVEFORM: The FD-ISAC system supports collocated and separated architectures, including a UAV-follower scenario and a V2X scenario involving a roadside unit, surrounding vehicle, and pedestrian.The separated architecture senses one target while communicating with a different receiver.
  • II. SYSTEM MODEL AND PROPOSED FULL-DUPLEX ISAC WAVEFORM: The transmitted baseband waveform is formulated over one radar coherent processing interval using total bandwidth B, pulse repetition intervals, and per-PRI waveforms x_k(t).The paper next reviews conventional radar-only pulsed waveforms and radar-centric ISAC with low-rate information-symbol embedding before presenting x_k(t).

A. Conventional Pulsed Waveform · B. Pulsed Radar with Information Embedding

Conventional monostatic radar uses HD pulsed transmission to avoid SI, but this creates blind-range and resolution–energy limitations. Embedding PSK symbols across pulse repetition intervals enables communication without radar performance loss, yet supports only very low spectrum efficiency.

  • A. Conventional Pulsed Waveform: HD pulsed radar alternates pulse transmission and echo reception, switching off its receiver during transmission to avoid self-interference.The waveform is characterized by pulse duration T_p, pulse repetition interval T, and duty cycle ρ = T_p/T.
  • A. Conventional Pulsed Waveform: Continuous-wave radar avoids pulsed operation but incurs severe self-interference, forcing reduced transmit power and restricting sensing to nearby targets.The conventional CW waveform corresponds to duty cycle ρ = 1.
  • A. Conventional Pulsed Waveform: A 1-µs pulse produces an approximately 150-m blind range, making conventional pulsed radar unsuitable for nearby-target ISAC applications such as UAV swarms or V2X.Targets within the minimum detectable range cannot be detected because the radar requires recovery time when switching from transmission to reception.
  • A. Conventional Pulsed Waveform: Unmodulated pulses impose a resolution–energy tradeoff because BT_p = 1, whereas pulse compression achieves N = BT_p ≫ 1 through waveform modulation.Pulse compression preserves bandwidth-based range resolution while increasing pulse energy relative to the unmodulated-pulse constraint.
  • A. Conventional Pulsed Waveform: Pulse-compressed fast-time codes are designed for favorable sensing autocorrelation and spectrum properties, including Barker, MPS, maximal-length, Frank, polyphase Barker, and LFM codes.For LFM pulses, the fast-time code is c[n] = exp(jπn^2/N).
  • B. Pulsed Radar with Information Embedding: Radar-centric ISAC embeds M-ary PSK symbols across successive pulse repetition intervals, adding information transmission without compromising radar performance.Embedding symbols over fast-time codes is also possible, but it degrades radar autocorrelation and spectrum properties.
  • B. Pulsed Radar with Information Embedding: PSK information embedding supports only very low communication spectrum efficiency because typical pulsed radars have ρ ≪ 1 and N ≫ 1.The limitation follows from transmitting information through radar pulses rather than using the waiting intervals.

C. Proposed FD-ISAC Waveform · III. SENSING PERFORMANCE ANALYSIS · A. Received Radar Echo

The proposed FD-ISAC waveform transmits dedicated communication signals during each radar PRI’s waiting interval while retaining radar signaling, improving communication efficiency but requiring effective self-interference cancellation. Its received echo model incorporates target reflection, residual self-interference, Doppler, and AWGN for subsequent sensing analysis.

  • C. Proposed FD-ISAC Waveform: The FD-ISAC node transmits dedicated communication signals during the radar waiting interval T−T_p, using otherwise idle time for high-rate communication.The waveform also supports information embedding over the radar pulse, allowing low-rate control messages and high-capacity payload transmission to coexist.
  • C. Proposed FD-ISAC Waveform: The transmitted waveform combines radar signaling with a dedicated signal g_k(t) of bandwidth B and communication power P_c, which may differ from radar power P_r.The dedicated signal contains J = B(T−T_p) ≫ 1 symbols per PRI.
  • C. Proposed FD-ISAC Waveform: With ρ ≪ 1, the proposed waveform’s communication spectrum efficiency significantly outperforms information embedding and approaches log_2 M, the pure-communication benchmark.This follows because the dedicated signal occupies most of each PRI’s duration outside the radar pulse.
  • C. Proposed FD-ISAC Waveform: The proposed design’s sensing and communication performance depends critically on effective suppression of residual self-interference in practical full-duplex systems.The subsequent analysis explicitly incorporates residual self-interference rather than assuming ideal cancellation.
  • A. Received Radar Echo: After clutter suppression, the received radar echo over one CPI contains the delayed Doppler-shifted target reflection, self-interference through coefficient β, and complex Gaussian noise.The target coefficient is α = α̃e^−j2πf_dτ, with delay τ and Doppler shift determined by target motion.
  • A. Received Radar Echo: For each PRI, the received signal is y_k(t) = αx_k(t−τ)e^j2πf_dkT + βx_k(t) + n_k(t), combining target echo, self-interference, and AWGN.The self-interference propagation delay is neglected because it is typically very small or can be estimated and compensated offline.
  • A. Received Radar Echo: Within one PRI, fdT ≪ 1 permits omission of fast-time Doppler phase variation, so velocity estimation requires Doppler processing across the CPI’s slow-time dimension.The resulting per-PRI model preserves the Doppler phase progression across PRI index k.

B. Signal Processing and Probability of Detection · 1) Sampling:

The paper models radar sensing through sampling, self-interference cancellation, matched filtering, Doppler processing, and target detection. Sampling projects each PRI’s received waveform onto orthonormal basis functions, yielding a finite-dimensional vector model with radar echoes, self-interference, and projected noise.

  • B. Signal Processing and Probability of Detection: Radar sensing follows sampling, self-interference cancellation, matched filtering, Doppler processing, and target detection.These procedures are illustrated in Fig. 3.
  • 1) Sampling:: For each PRI k, the received waveform y_k(t) is projected onto N + J orthonormal basis functions to obtain an (N + J)-dimensional vector.The basis functions are ψ(t − lT_c), with l ranging from 0 to N + J − 1.
  • 1) Sampling:: Each sampled component is defined by the inner product y_k[l] = ⟨y_k(t), ψ(t − lT_c)⟩ for 0 ≤ l ≤ N + J − 1.The inner product uses complex conjugation in its function definition.
  • 1) Sampling:: The projected noise samples are modeled as independent CSCG variables with distribution CN(0, N_0), producing a noise vector n_k ∼ CN(0, N_0I_(N+J)).The samples span k = 0, …, K − 1 and l = 0, …, N + J − 1.
  • 1) Sampling:: With bandwidth B, the sensing time resolution is T_c = 1/B, and delay τ is approximated by n_τT_c where n_τ = round(τB).For 0 < τ ≤ T − T_p, the detectable delay bins satisfy 1 ≤ n_τ ≤ J.
  • 1) Sampling:: The sampled received vector is expressed using radar-echo and self-interference vectors together with projected noise.The vector model specifies y_k ∈ C^(N+J)×1 and distinguishes the echo and SI components.
  • 1) Sampling:: Because the monostatic radar knows its transmitted waveform, self-interference can in principle be cancelled by subtracting the corresponding transmitted-signal component.This cancellation relies on the known waveform at the radar receiver.

2) SIC:

The SIC analysis models residual self-interference after practical cancellation and derives matched-filter detection performance through radar-echo SINR. The resulting unified expression captures target-range effects, special radar cases, and power-control implications under imperfect SIC.

  • Residual SI Model: The residual SI model accounts for receiver saturation and imperfect antenna-separation, analog, and digital cancellation, with strength controlled by ǫ ≪1.Residual SI is represented by a random CSCG vector after multiple SIC stages.
  • Matched-Filter Detection: Matched filtering is used because it maximizes radar-detection output SNR, with parallel filters applied across range bins.The analysis then focuses on the range-Doppler bin containing the target.
  • Radar SINR Analysis: The unified SINR expression incorporates residual SI and includes pulsed and CW radar as special cases, while FD operation enables nearby-target sensing.For nearby targets, residual SI affects SINR; for farther targets, echoes arrive after radar-pulse transmission and incur no SI, and perfect SIC equalizes both cases.
  • Power Allocation: When SIC is poor, the FD-ISAC scheme mitigates residual SI by reducing communication power Pc while increasing radar power Pr, unlike constant-envelope CW schemes.Residual SI becomes especially relevant for higher-power long-range CW sensing.
  • Radar Processing: After matched filtering, Doppler processing across K coherent processing intervals estimates target Doppler frequency fd and radial velocity vd for each range bin.The matched-filter outputs form a J ×K range-slow-time data matrix.

4) Doppler processing:

Doppler processing applies a slow-time DFT to matched-filter outputs for each range bin, mapping target motion to range-Doppler bins. Integrating K PRIs coherently increases the peak SINR by K times before detection is performed.

  • Doppler processing: The Doppler processor computes a DFT of slow-time matched-filter data separately for each range bin.For the target range bin nτ, processing uses the matched-filter outputs yk across k = 0, · · · , K − 1.
  • Doppler processing: Doppler frequencies are assigned to bins, with negative and positive values representing targets moving away from and toward the radar receiver, respectively.The ground-truth Doppler frequency is represented through a Doppler-bin index q.
  • Doppler processing: K-PRI Doppler processing provides a coherent integration gain that increases the target-bin peak SINR by K times relative to one PRI.This gain results from Doppler processing across the K PRIs in each CPI.
  • Doppler processing: After Doppler processing, detection decisions are made for each range-Doppler bin, including the bin (nτ, q) containing the target.The signal output is characterized according to whether the target exists or not.

5) Target Detection:

The section formulates monostatic target detection as binary hypothesis testing with a linear detector, deriving adaptive false-alarm thresholds and a residual-SI-aware detection probability. The resulting expression applies across pulsed and continuous-wave radar waveforms and depends on output SINR rather than the transmitted waveform.

  • Target Detection: The detector uses binary hypothesis testing with a linear detection rule and a predetermined threshold.
  • Target Detection: Under H0, the detector output follows a Rayleigh distribution, while under H1 it follows a Rician distribution.
  • Target Detection: The threshold is adjusted for each range-Doppler bin because residual self-interference makes σϕ delay-dependent, preserving a fixed probability of false alarm.
  • Target Detection: The unified probability-of-detection expression uses the first-order Marcum Q-function and increases monotonically with output SINR, independently of transmitted waveform.

C. Ambiguity Function Analysis

The ambiguity-function analysis shows that range resolution is primarily governed by within-PRI autocorrelation, while Doppler resolution depends on waveform structure across PRIs. Because the proposed FD-ISAC scheme preserves the radar pulse and confines communication effects to random cross-correlation and autocorrelation terms, it can avoid the high instantaneous ACF peak-to-sidelobe levels associated with communication-centric waveforms when sensing quality is prioritized.

  • Ambiguity Function Analysis: Range estimation is mainly determined by each PRI’s autocorrelation, whereas Doppler estimation depends primarily on the waveform across the K PRIs.The analysis therefore focuses on the autocorrelation function for range performance over 0 ≤ τ ≤ T − T_p.
  • Ambiguity Function Analysis: The radar pulse typically provides good and constant autocorrelation for range sensing, while dedicated communication signals contribute cross-correlation and autocorrelation terms.At zero delay, the waveform autocorrelation is χ_k(0, 0) = P_rT_p + P_c(T − T_p).
  • Ambiguity Function Analysis: Unlike conventional radar waveforms, ISAC autocorrelation is random because communication symbols and waveforms randomize the cross-correlation and autocorrelation components.This randomness directly affects instantaneous range-sensing behavior.
  • Ambiguity Function Analysis: Communication-centric radar waveforms may produce high instantaneous ACF peak-to-sidelobe levels, resulting in poor range-sensing performance.The passage contrasts this behavior with the proposed FD-ISAC scheme when better sensing capability is desired.

IV. COMMUNICATION PERFORMANCE ANALYSIS

The section derives communication performance for the proposed FD-ISAC scheme by modeling received signals across radar and dedicated communication intervals. It characterizes embedded PSK detection and dedicated-signal spectrum efficiency under channel, noise, and power constraints.

  • Communication signal model: Each PRI receiver signal combines radar pulses carrying PSK symbols with a dedicated communication signal.The received waveform is described before and after ADC in discrete time.
  • Embedded PSK communications: Known radar fast-time codes enable matched-filter demodulation of embedded PSK symbols with processing gain proportional to code length N.The resulting output SNR depends on channel magnitude, radar transmit power, pulse duration, code length, and noise bandwidth.
  • Embedded PSK communications: For M-ary PSK, the embedded-symbol error probability is determined by the matched-filter output SNR and Gaussian Q-function.The error probability is explicitly a function of radar pulse transmit power Pr.
  • Dedicated communication transmission: Dedicated communication transmission is modeled as an AWGN channel with independent complex Gaussian signaling and noise.The signaling variable satisfies S ∼ CN(0, 1), while the noise has variance N0.
  • Dedicated communication transmission: The dedicated signal’s achievable spectrum efficiency depends on communication power Pc and a pre-log factor for its time occupancy.The pre-log factor accounts for the fraction of time occupied by dedicated communication signals.

V. NUMERICAL RESULTS AND DISCUSSIONS

Numerical results show that FD-ISAC can improve sensing–communication performance over benchmark waveforms when self-interference cancellation is sufficiently strong. It also substantially extends detection range while preserving better radar autocorrelation than communication-centric transmission.

  • Self-interference cancellation: 45 dB to 92 dB SIC is required to maintain PD ≥99% as target distance increases from 100 m to 1350 m.Farther targets produce weaker echoes, requiring stronger self-interference cancellation.
  • Sensing–communication tradeoff: At ϵ = −80 dB, increasing communication rate degrades PD, whereas at ϵ = −95 or 110 dB, PD improves with communication spectrum efficiency.The proposed FD-ISAC combines PSK embedding and dedicated communication transmission, producing a sensing–communication tradeoff under weak SIC and mutual benefits under stronger SIC.
  • Sensing–communication tradeoff: Sufficiently powerful SIC enables FD-ISAC to provide mutual benefits for radar sensing and wireless communication as communication transmit power increases.Radar-echo SINR versus Pc corroborates the probability-of-detection trends.
  • Detection-range comparison: 950 m detection range at PD ≥99% is achieved by FD-ISAC, versus 700 m for CW SC-Commun under the stated peak and average power constraints.The comparison uses Pc = 0.01 W, Pr = 0.91 W, ρ = 0.1, average power 0.1 W, and SIC factor ϵ = −80 dB.
  • Autocorrelation comparison: HD pulsed LFM has good, constant ACF with maximum PSL 13.2 dB at time-bandwidth product N = 100, while communication-centric waveforms incur sensing-resolution limitations.The ACF comparison evaluates HD LFM, FD-ISAC, and CW SC-Commun for range estimation.

VI. CONCLUSION

The paper proposes a full-duplex waveform for monostatic ISAC that time-multiplexes a classic pulsed radar waveform with dedicated communication signals. It derives sensing and communication performance metrics and evaluates the scheme numerically against benchmark waveforms.

  • The proposed FD-ISAC design flexibly time-multiplexes a classic pulsed radar waveform with dedicated communication signals.
  • The analysis derives the probability of detection, ambiguity function, and communication spectrum efficiency of the proposed waveform.
  • Extensive numerical results compare the proposed scheme with various benchmark waveforms.

APPENDIX A PROOF OF (16) · APPENDIX B PROOF OF (18)

The appendices prove equations (16) and (18) by evaluating matched inner products across separate cases, using the pulse expression and the autocorrelation property of ψ(t). Combining the resulting case-specific expressions establishes each equation.

  • APPENDIX A PROOF OF (16): Equation (16) is proved by separately evaluating k[l] = ⟨x_k(t), ψ(t − lT_c)⟩ across two cases.The proof begins by considering two cases for the inner product defining k[l].
  • APPENDIX A PROOF OF (16): The proof of (16) uses p(t) from (3) and the autocorrelation function R_ψ(t) = δ(t).These identities simplify the case-specific inner-product calculations.
  • APPENDIX A PROOF OF (16): Combining the expressions in (61) and (62) yields equation (16).The two case results are combined to complete the proof.
  • APPENDIX B PROOF OF (18): Equation (18) is proved by evaluating ⟨x_k(t − τ), ψ(t − lT_c)⟩ from (13) across three cases.The proof organizes the delayed matched inner product into three separate cases.
  • APPENDIX B PROOF OF (18): One case in the proof of (18) gives P_cT_c s_k[l − N − n_τ] for N + n_τ ≤ l ≤ N + J − 1.This expression is the case-specific result stated in (65).
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