PaperlayerView exact revision on arXiv

Source-linked AI summary

FRaC: FMCW-Based Joint Radar-Communications System via Index Modulation

Dingyou Ma, Nir Shlezinger, Tianyao Huang, Yimin Liu, Yonina C. Eldar

arXiv:2106.14671v1eess.SP

TL;DR

Vehicular DFRC seeks to combine environmental sensing and communications while balancing performance with hardware complexity. FRaC uses sparse-array, narrowband FMCW transmission with index modulation, and reports radar resolution comparable to wideband FMCW alongside improved communications outcomes over PM-only signalling.

  • Problem

    Vehicular DFRC needs a trade-off between radar and communications performance and hardware complexity, and existing schemes do not suit every application scenario.

    Source: §I · p. 1

  • Method

    FRaC combines sparse MIMO arrays and narrowband FMCW with index modulation across carrier and antenna selections, waveform permutations, and phase modulation.

    Source: §I · p. 2

  • Results

    FRaC achieves the same range, velocity, and angle resolutions as wideband FMCW radar, with increased rates and decreased BER compared with PM-only signalling.

    Source: §I · p. 2

  • Takeaways & Limitations

    FRaC reports comparable radar resolution with fewer RF modules and a lower radar-receiver sampling rate than wideband FMCW radar.

    Source: §I · p. 2, 4) Comparison of Hardware Complexity · p. 13

Abstract

from arXiv · show

Dual function radar communications (DFRC) systems are attractive technologies for autonomous vehicles, which utilize electromagnetic waves to constantly sense the environment while simultaneously communicating with neighbouring devices. An emerging approach to implement DFRC systems is to embed information in radar waveforms via index modulation (IM). Implementation of DFRC schemes in vehicular systems gives rise to strict constraints in terms of cost, power efficiency, and hardware complexity. In this paper, we extend IM-based DFRC systems to utilize sparse arrays and frequency modulated continuous waveforms (FMCWs), which are popular in automotive radar for their simplicity and low hardware complexity. The proposed FMCW-based radar-communications system (FRaC) operates at reduced cost and complexity by transmitting with a reduced number of radio frequency modules, combined with narrowband FMCW signalling. This is achieved via array sparsification in transmission, formulating a virtual multiple-input multiple-output array by combining the signals in one coherent processing interval, in which the narrowband waveforms are transmitted in a randomized manner. Performance analysis and numerical results show that the proposed radar scheme achieves similar resolution performance compared with a wideband radar system operating with a large receive aperture, while requiring less hardware overhead. For the communications subsystem, FRaC achieves higher rates and improved error rates compared to dual-function signalling based on conventional phase modulation.

I. INTRODUCTION

FRaC combines index modulation with sparse MIMO transmission and narrowband FMCW to target vehicular DFRC constraints. The paper situates this design against earlier DFRC approaches and reports radar and communications performance benefits.

I. INTRODUCTION

  • Vehicular DFRC still needs a trade-off between performance and hardware complexity, motivating FMCW-based IM for automotive systems,.The paper notes that existing DFRC strategies do not satisfy every vehicular scenario, while FMCW is commonly used in automotive radar for simplicity and low complexity.Source: §I · pp. 1–2
  • FRaC combines IM-based DFRC with sparse MIMO arrays and narrowband FMCW, adding PM bits to spatial and frequency IM.Random carrier and antenna selection, waveform assignment, and PM carry the digital message.Source: §I · p. 2
  • FRaC achieves the same range, velocity, and angle resolutions as wideband FMCW radar, while increasing communications rates and decreasing BER versus PM-only signalling.The comparison is to a wideband system with an equivalent large receiving aperture; FRaC also uses fewer RF modules and a lower radar-receiver sampling rate.Source: §I · p. 2

II. SYSTEM MODEL

  • The generic IM-based DFRC transmitter model uses weighted antenna waveforms for both radar sensing and communication, with transmission parameters conveying information.SpaCoR and MAJoRCom are presented as special cases of this model.Source: §II · p. 3, 2) MAJoRCom · p. 3

1) SpaCoR:

  • SpaCoR uses spatial modulation to allocate antenna elements between radar probing and communications, but its phased array and separate RF components raise cost and power use [15].It conveys information through communication waveforms and spatial IM while retaining the full antenna array for radar.Source: §I · p. 2, 1) SpaCoR · p. 3

2) MAJoRCom:

  • MAJoRCom conveys messages through spectral and spatial IM using radar waveforms, but relies on full-array phased-array transmission and does not exploit weights for additional information.Its hardware and power requirements are identified as potentially unsuitable for consumer-oriented vehicles.Source: 2) MAJoRCom · p. 3

B. Transmission Model of FRaC

FRaC transmits selected FMCW waveforms from a sparse antenna array and embeds data in carrier and antenna choices as well as PM symbols. Its message mapping combines those choices within each pulse repetition interval.

1) Dual Function Waveform Transmission:

  • FRaC activates K of P transmit antennas per pulse and sends different-carrier FMCW waveforms, with the transmit and receive arrays forming a MIMO radar.The active antennas can change between pulses under RF-switch control.Source: 1) Dual Function Waveform Transmission · p. 3
  • FRaC selects spectrally orthogonal FMCW carriers with spacing Δf = Bsub, where Bsub = κTp is the waveform bandwidth.A coherent processing interval contains N periodically transmitted pulses; each selected waveform also receives a PM symbol.Source: 1) Dual Function Waveform Transmission · p. 4

2) Information Embedding:

  • Each PRI carries PM bits plus IM bits encoded by carrier selection, antenna selection, and waveform permutation.The example uses two possible carriers, one selected carrier per pulse, and BPSK PM symbols; the figure distinguishes IM bits from PM bits.Source: 2) Information Embedding · p. 4, Figure 4 · p. 4

3) Comparison to SpaCoR and MAJoRCom:

FRaC differs from SpaCoR and MAJoRCom through sparse MIMO transmission, FMCW signalling, phase modulation, and separate transmit and receive arrays. Its radar receiver separates waveforms by de-chirping and uses compressed sensing to recover targets, with stated low-speed and narrowband assumptions.

3) Comparison to SpaCoR and MAJoRCom:

  • FRaC uses sparse MIMO arrays, FMCW signals, added phase modulation, and distinct transmit and receive arrays, unlike the full-array and shared-array designs of SpaCoR and MAJoRCom.The separate arrays are described as facilitating identification of nearby targets for automotive applications.Source: 3) Comparison to SpaCoR and MAJoRCom · p. 4
  • FRaC’s improved angular resolution is reported to translate into target-recovery gains over MAJoRCom.The comparison covers antenna architecture, angle resolution, information embedding, data rates, and target applications.Source: 3) Comparison to SpaCoR and MAJoRCom · p. 5

III. RADAR AND COMMUNICATIONS RECEIVERS

  • Radar and communications receiver models and processing algorithms are introduced in separate subsections.The radar receiver uses compressed-sensing-based detection.Source: §III · p. 5, A. Radar Receiver · p. 5

1) Radar Received Signal Model:

  • De-chirping mixes the received signal with transmit waveforms, then low-pass filtering separates the waveform transmitted by each selected element.The filter cutoff is set to B_sub.Source: 1) Radar Received Signal Model · p. 5
  • The radar signal model assumes far-field targets and a stop-and-go model; it neglects pulse-to-pulse and antenna-element migration under low-speed and narrowband conditions.The stated conditions are v_lNT_0 ≪ c/(2B_sub) and Q_rPd_R ≪ c/(2B_sub).Source: 1) Radar Received Signal Model · p. 5

2) Radar Processing:

Radar processing first forms a coarse range profile by pulse compression, then uses samples from a coarse range cell for compressed-sensing recovery of target parameters at enhanced resolution.

2) Radar Processing:

  • Radar processing has two stages: pulse compression creates a coarse range profile, then compressed-sensing recovery estimates target parameters from samples across one CPI.The recovered parameters are range, velocity, and angle.Source: 2) Radar Processing · p. 5
  • The coarse range profile is generated by applying an IDFT over G samples after pulse compression.The resulting profile has range resolution c/(2B_sub).Source: 2) Radar Processing · pp. 5–6
  • Samples from each coarse range cell are processed individually; the description focuses on targets within one selected cell.The stated maximum unambiguous range is c/(2Δf).Source: 2) Radar Processing · p. 6
  • Target recovery is formulated as sparse recovery from an underdetermined observation model because the target scene is sparse and the observation matrix has fewer rows than columns.The model is y^(r) = Ab + w^(r), and the targets are recovered by estimating b.Source: 2) Radar Processing · p. 6

B. Communications Receiver

The communications receiver section introduces the received-signal model and then presents maximum-likelihood and low-complexity methods for recovering the digital message.

B. Communications Receiver

1) Received Communication Signal:

The communications model assumes synchronized reception over a multipath channel whose tap coefficients remain fixed during the radar CPI. The transmit symbol vector encodes waveform and array choices, and the authors defer detailed channel-estimation procedures and analysis to future work.

1) Received Communication Signal:

2) Communications Decoder:

The receiver recovers the transmitted message by estimating the selected carriers, active transmit antennas, waveform permutations, and modulated phases. The section presents maximum-likelihood decoding and a lower-complexity successive orthogonal decoding method.

2) Communications Decoder:

  • The message is recovered by estimating carrier frequencies, active transmit antennas, waveform permutations, and modulated phases.These quantities are obtained through estimation of e_n.Source: 2) Communications Decoder · p. 7
  • The maximum-likelihood decoder minimizes error probability using full channel state information, including Ψ and the noise distribution.Under proper-complex white Gaussian noise, the rule becomes a minimum-distance detector.Source: 2) Communications Decoder · p. 7
  • ML recovery searches the entire set E, whose cardinality is 2^NTotal, motivating a lower-complexity decoder.The proposed successive orthogonal decoding method leverages orthogonality among transmit waveforms.Source: 2) Communications Decoder · p. 7
  • Successive orthogonal decoding first estimates carrier frequencies by matched filtering, then detects transmit antennas and modulated symbols.After carrier detection, the second-stage search is restricted to Esub, the subset consistent with the detected frequencies.Source: 2) Communications Decoder · pp. 7–8
  • The SOD search reduces computational complexity relative to ML by restricting the candidate transmission patterns to Esub.The passages express the reduction through the relative cardinalities of E and Esub.Source: 2) Communications Decoder · p. 8

IV. PERFORMANCE ANALYSIS OF RADAR SUBSYSTEM

The analysis characterizes FRaC’s three-dimensional ambiguity function under randomized antenna and subcarrier selection. It finds that FRaC’s range, velocity, and angle resolutions match those of wideband MIMO radar with equivalent bandwidth and aperture.

A. Ambiguity Function

  • For mathematical convenience, the analysis assumes relative narrow bandwidth, approximating ξ_n,k as 1.Resolution is calculated from half the width between the first two nulls in each dimension.Source: A. Ambiguity Function · p. 8
  • Because antenna and subcarrier choices vary with transmitted messages, FRaC’s ambiguity function is random across pulse repetition intervals.Its expected value is approached by averaging the ambiguity function over many coherent processing intervals.Source: A. Ambiguity Function · p. 8
  • The analysis extends stochastic ambiguity-function characterization to three dimensions, accounting for FRaC’s random subcarrier and active-antenna selections.Earlier cited studies considered two-dimensional ambiguity functions.Source: A. Ambiguity Function · p. 8
  • FRaC’s range, velocity, and angle resolutions equal those of wideband MIMO radar with bandwidth MΔf and PQr antenna elements.The result relates the randomized antenna selection and frequency division used for message embedding to the system’s resolution.Source: A. Ambiguity Function · pp. 8–9

B. Phase Transition Threshold

The section applies phase-transition analysis to relate FRaC’s waveform parameters to its maximum recoverable target count. It gives a threshold for high-probability recovery and identifies trade-offs among radar recovery, communications, and hardware complexity.

B. Phase Transition Threshold

  • The phase-transition analysis extends frequency-agile radar to spatial agility and FMCW signalling to characterize recoverable targets as waveform parameters vary.The FRaC radar receiver is formulated as a compressed-sensing problem.Source: B. Phase Transition Threshold · p. 9
  • For waveform parameters {N, K, M, P, Qr}, threshold L* marks the maximum target count recoverable with high probability.When the target count exceeds L*, the probability of exact recovery decreases dramatically.Source: B. Phase Transition Threshold · p. 9
  • The numerically tight phase-transition threshold can guide waveform design, and its simpler approximation is intended for L* much smaller than NMPQr.The approximation is reported to represent typical DFRC parameter settings faithfully.Source: B. Phase Transition Threshold · pp. 9–10
  • Increasing N, Qr, or K raises the maximum recoverable target count, whereas increasing M or P reduces it.The analysis attributes the N and Qr gains to more observations, and the M and P reductions to using a smaller portion of bandwidth or the transmit array.Source: B. Phase Transition Threshold · p. 10
  • Increasing P improves angle resolution and spatial-IM bits but lowers recoverable-target capacity, while increasing M improves frequency-IM bits but also lowers that capacity.Increasing K can improve both message cardinality and recoverable targets, with increased hardware complexity.Source: B. Phase Transition Threshold · p. 10

V. NUMERICAL EVALUATIONS

The radar evaluations show that FRaC attains wideband-like range, velocity, and angle resolution, and recovers closely spaced targets. Its hit-rate comparison shows a small low-SNR gap to wideband radar and better recovery than MAJoRCom for close targets.

1) Ambiguity Function:

  • 1.5 m range, 1 m/s velocity, and 14.48° angle resolutions match those of the wideband MIMO FMCW benchmark.The measured ambiguity-function mainlobe widths are nearly the same for the instantaneous and expected ambiguity functions.Source: 1) Ambiguity Function · p. 10

2) Target Recovery:

  • FRaC exactly recovers three adjacent targets without noise, while MAJoRCom fails to distinguish two targets sharing range and velocity.The two targets’ angle spacing is finer than MAJoRCom’s angle resolution.Source: 2) Target Recovery · p. 11, Figure 7 · p. 11
  • Hit rate counts successful range-velocity-angle recovery over 20,000 Monte Carlo trials of the three-target scenario.The simulated target echoes have equal normalized power.Source: 2) Target Recovery · p. 11
  • FRaC’s hit rate is 1 dB below wideband FMCW at low radar SNR, matches it above 14 dB, and outperforms MAJoRCom for close targets.MAJoRCom’s hit rate does not reach probability one as SNR increases because it cannot distinguish the close targets.Source: 2) Target Recovery · p. 11, Figure 8 · p. 12

3) Phase Transition Threshold:

The phase-transition simulations track the theoretical thresholds and show how waveform parameters affect recoverable-target capacity. The hardware comparison reports fewer RF modules and lower sampling and data requirements for FRaC than for wideband MIMO radar.

3) Phase Transition Threshold:

  • Recovery probability drops around the theoretical phase-transition thresholds; increasing K or N raises target capacity, while increasing M or P lowers it at fixed K.The evaluated parameters are transmit subcarriers K, carrier-set cardinality M, transmit antennas P, and pulses N per CPI.Source: 3) Phase Transition Threshold · p. 12, Figure 10 · p. 13

4) Comparison of Hardware Complexity:

  • FRaC uses K + Qr RF modules versus PQr for wideband MIMO, whose sampling rate is M times larger and which acquires PM/K more samples per pulse.The comparison targets the same radar resolutions.Source: 4) Comparison of Hardware Complexity · p. 13

B. Communications Subsystem Evaluation:

  • The communication evaluation compares FRaC with MAJoRCom and a PM-only system using achievable rate and uncoded BER, then compares ML and SOD decoders.The achievable-rate simulation uses 200 kHz bandwidth; BER evaluation uses 100 MHz.Source: B. Communications Subsystem Evaluation · p. 13

1) Achievable Rate:

FRaC’s communications results outperform PM-only signalling in achievable rate and BER, while its reduced-complexity SOD decoder trades complexity for a minor performance loss. The rate comparisons also show higher rates than MAJoRCom across the considered SNRs for the K2-BPSK configuration.

1) Achievable Rate:

  • At high SNR, FRaC-K2-BPSK and MAJoRCom approach 9 and 5 bits/pulse, respectively; FRaC rates also exceed PM-only FMCW at low SNR.FRaC-K2-BPSK rates are higher than MAJoRCom’s in all considered SNRs.Source: Figure 11 · p. 14

2) Bit Error Rate:

  • FRaC significantly outperforms PM-only signalling in BER; FRaC-K2-BPSK carries almost twice MAJoRCom’s bits with an SNR gap of merely 1 dB.The paper attributes the PM comparison to FRaC’s less-dense PM constellations because additional bits are conveyed through IM.Source: 2) Bit Error Rate · p. 14

3) Detector Comparison:

  • The SOD decoder reduces complexity relative to ML at the cost of a relatively minor performance loss.The cited comparison reports an approximately 2 dB SNR performance loss for the SOA decoder relative to ML.Source: 3) Detector Comparison · p. 14, Figure 13 · p. 14

VI. CONCLUSIONS

  • FRaC’s achievable-rate and BER performance outperform a system that only exploits PM.The conclusion describes FRaC as FMCW signaling with IM, sparse arrays, and narrowband waveforms.Source: §VI · p. 14

APPENDIX A. Proof of Theorem 1

The appendix derives the expected ambiguity function by averaging over randomized antenna and subcarrier indices. The Corollary 2 proof then simplifies its derivation by approximating L* and omitting terms from (32).

APPENDIX A. Proof of Theorem 1

  • Theorem 1’s proof forms the expected ambiguity function by averaging over randomized antenna and subcarrier index combinations.The index vectors are described as discrete uniform random variables.Source: Appendix A · p. 15
  • Uniform index distributions make each index occur equally often in the summation, supporting the expectation calculation.The proof states there are KΩmΩp summands and each index in the m and n summations occurs KΩmΩp/(MP) times.Source: Appendix A · p. 15

B. Proof of Corollary 2

  • The Corollary 2 proof approximates L* after ignoring the ln and L* terms in (32).The approximation is stated to hold under the proof’s specified conditions.Source: B. Proof of Corollary 2 · p. 15

Related papers

Loading 2106.14671v1…