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Spatial Modulation for Joint Radar-Communications Systems: Design, Analysis, and Hardware Prototype

Dingyou Ma, Nir Shlezinger, Tianyao Huang, Yariv Shavit, Moshe Namer, Yimin Liu, Yonina C. Eldar

arXiv:2003.10404v2eess.SP

TL;DR

DFRC designs must balance radar and communication performance, while optimized joint waveforms can require channel and target knowledge and complex optimization. SpaCoR uses GSM-driven antenna allocation to combine separate waveforms; experiments report improved equal-rate BER and radar angular resolution versus fixed allocations.

  • Problem

    Existing DFRC approaches trade radar performance or communication rate, while optimized joint waveforms require channel and target knowledge and computationally complex optimization.

    Source: §I · p. 1

  • Method

    SpaCoR uses GSM to allocate antenna elements between separate radar and communications waveforms according to the transmitted message, embedding bits in antenna selection.

    Source: §I · pp. 1–2

  • Results

    At the same data rate, SpaCoR improves BER over fixed-allocation SMX, while dynamic antenna switching improves radar angular resolution and reduces sidelobe levels versus fixed allocation.

    Source: 4) Fix2 Scheme · p. 7, B. Communications Subsystem Evaluation · p. 12

  • Takeaways & Limitations

    A dedicated hardware prototype using over-the-air signaling demonstrates the feasibility of the SpaCoR DFRC system.

    Source: §VII · p. 13

Abstract

from arXiv · show

Dual-function radar-communications (DFRC) systems implement radar and communication functionalities on a single platform. Jointly designing these subsystems can lead to substantial gains in performance as well as size, cost, and power consumption. In this paper, we propose a DFRC system, which utilizes generalized spatial modulation (GSM) to realize coexisting radar and communications waveforms. Our proposed GSM-based scheme, referred to as spatial modulation based communication-radar (SpaCoR) system, allocates antenna elements among the subsystems based on the transmitted message, thus achieving increased communication rates by embedding additional data bits in the antenna selection. We formulate the resulting signal models, and present a dedicated radar processing scheme. To evaluate the radar performance, we characterize the statistical properties of the transmit beam pattern. Then, we present a hardware prototype of the proposed DFRC system, demonstrating the feasibility of the scheme. Our results show that the proposed GSM system achieves improved communication performance compared to techniques utilizing fixed allocations operating at the same data rate. For the radar subsystem, our experiments show that the spatial agility induced by the GSM transmission improves the angular resolution and reduces the sidelobe level in the transmit beam pattern compared to using fixed antenna allocations.

I. INTRODUCTION

SpaCoR combines dedicated radar and communications waveforms with GSM-based antenna allocation, embedding data in antenna selection while supporting spatial agility. The design addresses trade-offs in existing DFRC approaches and is evaluated under constraints including simultaneous operation in separate frequency bands.

I. INTRODUCTION

  • Prior DFRC strategies trade radar performance or communication rate, while optimized joint waveforms require channel and target knowledge and computationally complex optimization.Radar-waveform index modulation can preserve radar performance but typically has lower data rates than dedicated communication signals.Source: §I · p. 1
  • SpaCoR uses GSM to allocate antenna elements between separate radar and communications waveforms according to the message, embedding data bits in antenna selection.The message-dependent allocation induces spatial agility; the paper analyzes radar performance under this design.Source: §I · pp. 1–2
  • At the same data rate, SpaCoR improves BER over fixed-allocation systems, and its spatial agility improves radar angular resolution.The prototype experiments compare SpaCoR with fixed antenna allocations.Source: §I · p. 2
  • The prototype uses a 16-element two-dimensional antenna and evaluates actual passband waveforms with over-the-air signaling.The hardware implementation is presented as demonstrating practical feasibility.Source: §I · p. 2

II. SPACOR SYSTEM MODEL

  • The system uses a phased array for pulse-radar sensing while communicating; radar is primary, and only the communications receiver requires channel state information.Transmission and reception use time-division duplexing, with communication transmitted during radar transmission.Source: A. System Design Guidelines and… · p. 2

A. System Design Guidelines and Constraints

  • Separate frequency bands permit simultaneous, spectrally orthogonal operation, while each antenna element transmits only radar or communications signaling per pulse repetition interval.The design avoids multiband transmission to maintain power efficiency and targets a low-complexity joint structure.Source: A. System Design Guidelines and… · pp. 2–3

B. SpaCoR System

SpaCoR dynamically assigns antennas to radar or communications across symbol slots, embedding message bits in antenna selection while retaining dedicated waveforms. This addresses fixed allocation’s limits on radar beam patterns and communication data rates.

B. SpaCoR System

  • Fixed subarrays produce a wider radar mainlobe or higher sidelobes than a full-array radar, while leaving spatial diversity unused for communication.Fix1 keeps the allocation static during a pulse; Fix2 randomizes it between radar pulses.Source: B. SpaCoR System · p. 3
  • SpaCoR changes antenna assignments between communication symbol slots, using transmitted bits to select antennas while radar and communication waveforms occupy distinct bands.Each element transmits only one waveform at a time, avoiding multiband transmission; the prototype uses a two-dimensional antenna surface, while the system model focuses on a one-dimensional array.Source: B. SpaCoR System · p. 3
  • Across many time slots, each antenna probes with high probability, so SpaCoR’s expected transmit beam pattern approaches the full-array pattern.The antenna allocation changes between symbol slots, rather than only between radar pulses.Source: B. SpaCoR System · p. 3

1) Generalized Spatial Modulation:

  • GSM combines spatial index modulation with multi-antenna transmission, conveying information through both antenna selection and transmitted constellation symbols.In each PRI, K symbol slots convey K · R bits; the paper focuses on phase shift keying to maintain constant-modulus waveforms.Source: 1) Generalized Spatial Modulation · pp. 3–4

C. Communications Subsystem

  • At the same constellation order, GSM embeds additional bits per symbol in antenna selection, enabling a higher data rate or sparser constellations at the same rate.The receiver need not know the communication channel at the transmitter; available CSI may be used for spatial precoding.Source: 1) Generalized Spatial Modulation · p. 3, B. SpaCoR System · p. 3

2) Communications Receiver Operation:

The communication receiver detects sparse GSM inputs using channel state information, then separates antenna-selection bits from constellation bits. The radar subsystem models echoes from dynamically allocated antennas and samples them during the pulse’s receive interval.

2) Communications Receiver Operation:

  • Because radar and communications use distinct bands, the communication input is a sparse vector with M_c_T active entries, and the modeled channel is linear and memoryless.The received communication symbol is modeled as y(c) = Hx + w(c).Source: 2) Communications Receiver Operation · p. 4
  • With full channel state information, the receiver applies maximum a-posteriori detection to recover each GSM symbol, then reads selection bits from the detected support and constellation bits from its nonzero entries.For white Gaussian noise, the detector becomes a minimum-distance rule; direct search is used in the experiments when the candidate set is relatively small.Source: 2) Communications Receiver Operation · p. 4

D. Radar Subsystem

  • SpaCoR assigns M − M_c_T antennas to radar at each symbol slot and changes those assignments across the K slots of a pulse.The radar signal model uses a phased array steered with element-specific weights and a narrowband approximation.Source: R TPRI · pp. 4–5, D. Radar Subsystem · p. 4

R TPRI

  • Radar echoes are sampled during the pulse’s receive interval at a rate meeting the Nyquist criterion, with the sampled signal model extended to multiple targets.The target parameters include reflection factor, spatial frequency, and delay.Source: R TPRI · p. 5
  • Sub-Nyquist sampling for SpaCoR is left for future study, although generalized sampling methods have been used in prior work.The paper’s described receiver samples at Nyquist rate or above.Source: R TPRI · p. 5

1) Radar Detection:

The radar detector estimates target delay, spatial frequency, and reflection factor by formulating the received samples as a sparse recovery problem on discretized delay and spatial-frequency grids.

1) Radar Detection:

  • The delay grid spans the known target-delay interval with spacing δτ ≤ 1/Br, and the spatial-frequency grid spans [−π, π) with spacing δϑ ≤ 2π/M.P uniformly spaced delay points and Q equally spaced spatial-frequency points are used.Source: 1) Radar Detection · p. 5
  • Target recovery is formulated as sparse recovery of a vector whose nonzero entries encode target reflection factors at grid points in delay and spatial frequency.The model assumes targets lie on the discretized grids and that the number of targets L is much smaller than the number of grid locations P Q.Source: 1) Radar Detection · p. 5
  • The sparse optimization can be solved with compressed-sensing methods, including greedy approaches and l1-norm optimization.The optimization constraint parameter ϵ is related to the noise level.Source: 1) Radar Detection · p. 5

III. RADAR PERFORMANCE ANALYSIS

The radar analysis defines a delay-direction transmit beam pattern from echo correlations and examines its statistics under SpaCoR’s message-dependent antenna allocation. The pattern is averaged over communication symbols within a pulse and compared with full-array and fixed-allocation patterns.

A. Transmit Beam Pattern

  • SpaCoR’s delay-direction transmit beam pattern is computed by correlating target echoes with reference-direction echoes and averaging across the radar pulse.The analysis uses a unit-reflectivity target and focuses on the echo at one receive antenna without loss of generality.Source: §III · p. 5, A. Transmit Beam Pattern · p. 6

III. RADAR PERFORMANCE ANALYSIS

  • The analysis uses a two-dimensional delay-direction pattern to characterize radar resolution and mutual interference between targets.SpaCoR’s pattern varies across communication symbols, so the analysis takes correlation over the symbols transmitted within a pulse.Source: §III · p. 5

A. Transmit Beam Pattern

  • Because antenna indices are random under message-dependent allocation, the resulting transmit beam pattern is random and is analyzed against full-array and fixed-subset patterns.The phase term that disappears under the magnitude operation is omitted from the subsequent expression.Source: A. Transmit Beam Pattern · p. 6

B. Comparison of Different Antenna Allocation Schemes

The full-array radar beam pattern provides a deterministic baseline. SpaCoR’s randomized antenna allocation yields an expected beam pattern matching that baseline up to a constant factor, while its finite-pulse pattern varies with the communication-driven antenna selections.

1) Full Antenna Array:

  • The full-array baseline uses deterministic antenna indices, producing a deterministic beam pattern whose mainlobe width sets resolution and whose sidelobes affect clutter interference and nearby-target coupling.The full array is used as the basis for comparison with SpaCoR and fixed-allocation patterns.Source: 1) Full Antenna Array · p. 6, B. Comparison of Different Antenna… · p. 6

2) SpaCoR:

  • SpaCoR’s beam pattern is random because communication data determine the selected radar antennas; increasing K reduces its variance and the likelihood of deviation from the mean pattern.The variance discussion concerns a single radar pulse with a finite number of symbols.Source: 2) SpaCoR · pp. 6–7
  • SpaCoR’s expected beam pattern matches the full-array radar pattern up to a constant factor, giving the same average sidelobe-to-mainlobe ratio over many pulses.The equality is stated for the expected pattern; the long-pulse average approaches it when communicated bits are i.i.d.Source: 2) SpaCoR · pp. 6–7
  • With K = 12 and two radar antennas, a SpaCoR realization has mainlobe width and sidelobe levels similar to the full-array pattern using four elements.The comparison is illustrated in Fig. 4(a) and Fig. 4(b).Source: 2) SpaCoR · p. 7

3) Fix1 Scheme:

Fix1 and Fix2 provide fixed-allocation comparisons for SpaCoR: Fix1 uses a deterministic radar sub-array, while Fix2 randomizes the allocation between pulses. The hardware prototype includes a 16-element array, FPGA boards, a PC server, and a radar echo generator.

3) Fix1 Scheme:

  • Fix1’s reduced radar sub-array produces a wider mainlobe than the full-array pattern.The comparison uses the same settings as the full-array and SpaCoR patterns in Fig. 4.Source: 3) Fix1 Scheme · p. 7

4) Fix2 Scheme:

  • Fix2 randomizes the radar/communication sub-arrays once per radar pulse; its expected pattern matches SpaCoR’s, but its maximum variance is K times SpaCoR’s.The variance comparison is for a given pulse width and is evaluated at τd = 0.Source: 4) Fix2 Scheme · p. 7

A. Overall System Architecture

  • The prototype has a 16-element two-dimensional array split into eight transmit and eight receive elements, two FPGA boards, a PC server, and a radar echo generator.The PC configures and processes signals; the echo generator simulates target reflections.Source: A. Overall System Architecture · p. 8, §IV · p. 8
  • The PC-generated waveform passes through the transmit FPGA and antenna array; echoes are simulated by the REG, while communication signals and radar echoes are received and processed by the PC.The transmit FPGA converts the waveform to analog and passband; the receive FPGA digitizes down-converted signals.Source: A. Overall System Architecture · p. 8

B. System Parameterization

System parameterization first reserves enough transmit elements for radar detection, then allocates the remainder to communications. The prototype generates joint waveforms by encoding GSM antenna choices in communication chips inserted into the radar waveform.

1) Number of Elements Allocated for Radar:

  • The radar element count is set to meet the detection-range requirement, after which the remaining transmit elements are assigned to communications.The minimum radar allocation is determined using the radar equation.Source: 1) Number of Elements Allocated for… · p. 8

2) Number of Chips Divided:

  • K should increase to reduce beam-pattern variance, but satisfy K^2 < BrTr and 1/Tc < Bc to avoid chirp-chip bandwidth expansion and meet the flat-channel assumption.Here Tc = Tr/K, and Bc is the communication-channel coherence bandwidth.Source: 2) Number of Chips Divided · p. 8

C. Generation of the JRC Waveform

  • The waveform generator maps data blocks into GSM symbols and antenna allocations, then inserts communication chips into the radar waveform according to the allocation bits.The combined waveform encodes antenna allocation in each time slot, avoiding complex high-speed switching devices.Source: C. Generation of the JRC Waveform · p. 9

2) DFRC Tx Board:

  • The prototype uses a 16-element two-dimensional antenna array, with eight transmit waveforms converted to analog, up-converted, amplified, and forwarded to the array.The transmitter uses an FPGA, DAC card, and up-conversion card.Source: 1) Antenna Array · p. 9, 2) DFRC Tx Board · p. 9

V. PROTOTYPE REALIZATION

  • The transmit FPGA receives digital JRC waveforms from the PC server and interfaces them to the antenna through digital-to-analog conversion and passband up-conversion.The system uses a dedicated transmitter board for this signal chain.Source: 2) DFRC Tx Board · p. 9

3) DFRC Rx Board:

The prototype digitizes received radar echoes and communication signals for PC processing, and uses a radar echo generator to simulate configurable targets. Its GUI configures experiments and displays radar and communication results; the reported evaluation combines hardware experiments and simulations.

3) DFRC Rx Board:

  • The receive board down-converts and digitizes radar echoes and received waveforms, then forwards digital streams to the server for software processing.The board uses an FPGA, two ADC cards, and an RF down-converter.Source: 3) DFRC Rx Board · p. 9

4) REG:

  • The REG captures transmitted waveforms, applies configurable delays and Doppler shifts, and retransmits them to simulate up to six targets within 10 kM range and 190 kHz Doppler.Target parameters are configured through the PC application.Source: 4) REG · p. 10

5) Data Processor:

  • The PC data processor processes radar echoes and detects communication symbols, with configurable target profiles available for experiments.The processor is a 64-bit laptop with four CPU cores and 16 GB RAM.Source: 5) Data Processor · p. 10

B. GUI: Configuration, Control and Display

VI. NUMERICAL EVALUATIONS

  • The numerical evaluation uses hardware experiments and simulations; multiple-target radar detection is evaluated with the prototype, while the remaining evaluations are simulations.The prototype supports eight antennas, but the experiments use M = 4 elements.Source: §VI · p. 10

A. Radar Subsystem Evaluation

SpaCoR combines GSM communications with changing radar antenna allocations, and the evaluations report radar and communication gains over fixed-allocation schemes. The section examines angular resolution, clutter hit rate, BER, and achievable rate, then concludes that the approach is feasible in a hardware prototype.

1) Radar Angular Resolution:

2) Sidelobe Level:

  • SpaCoR’s angle-estimate hit rate approaches the full array’s and exceeds both fixed-allocation methods across the considered signal-to-clutter ratios.Fix1 has the lowest hit rate at all considered SCR values; SpaCoR’s lower beam-pattern variance than Fix2 is associated with lower sidelobes and less clutter sensitivity.Source: 2) Sidelobe Level · p. 12, Figure 12 · p. 12

B. Communications Subsystem Evaluation

  • At equal data rates, GSM-based SpaCoR has better BER than fixed-allocation SMX, with its BER curve decreasing faster as SNR increases.GSM conveys additional bits through antenna-index selection, allowing less dense constellations, at the cost of increased receiver decoding complexity.Source: B. Communications Subsystem Evaluation · p. 12, Figure 14 · p. 12
  • GSM’s mutual information indicates improved achievable rate over SMX, while the compared schemes’ maximum rates require high SNR for reliable transmission.The maximum mutual information is 6 bits per symbol for GSM-QPSK and SMX-8PSK, and 8 bits per symbol for GSM-8PSK and SMX-16PSK.Source: B. Communications Subsystem Evaluation · p. 12, Figure 15 · p. 13

VII. CONCLUSIONS

  • SpaCoR’s hardware experiments and simulations show gains over fixed antenna allocations in radar resolution and sidelobe level, as well as communication BER and achievable rate.The prototype uses over-the-air signaling.Source: §VII · p. 13

APPENDIX

The appendix proof treats the selected radar antenna combination as uniformly random and uses that assumption to derive the expected transmit delay-direction beam pattern.

APPENDIX

  • For each time slot, the radar antenna indices are randomized from the antenna-combination set and modeled as uniformly distributed over it.This distribution is used in the expected beam-pattern derivation.Source: A. Proof of Theorem 1 · p. 13
  • The proof formulates the expected transmit delay-direction beam pattern from the randomized antenna selection.The passage introduces the expectation calculation after defining the selection distribution.Source: A. Proof of Theorem 1 · p. 13
  • The expectation calculation simplifies because the antenna-index combinations are uniformly distributed and each array index occurs equally often in the summation.The proof states that the expectation does not depend on the time-slot index.Source: A. Proof of Theorem 1 · p. 13

B. Proof of Proposition 1

The supplied proof passages introduce the transmit beam-pattern variance and begin deriving it using the random antenna-selection model.

B. Proof of Proposition 1

  • The proof identifies the variance of the transmit beam pattern as the quantity being derived.The supplied passage introduces the variance expression without stating its resulting form.Source: B. Proof of Proposition 1 · p. 13
  • The derivation invokes the uniform distribution of antenna selections to evaluate an expectation term.The proof notes that the sum can be decomposed into constant terms.Source: B. Proof of Proposition 1 · pp. 13–14
  • The proof also specializes the expression to chirp waveforms and uses it with an earlier result to establish the stated relation.The supplied text does not provide the relation’s full expression.Source: B. Proof of Proposition 1 · p. 14

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