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MAJoRCom: A Dual-Function Radar Communication System Using Index Modulation

Tianyao Huang, Nir Shlezinger, Xingyu Xu, Yimin Liu, Yonina C. Eldar

arXiv:1909.04223v1eess.SPcs.IT

TL;DR

MAJoRCom embeds communication messages in CAESAR’s frequency and spatial selections while preserving the radar functionality. Its achievable rate is comparable to dedicated communication waveforms, and low-complexity decoding balances reliability with computational burden.

  • Problem

    Index-modulation decoding can impose substantial computational burden, motivating simpler receiver methods for MAJoRCom.

  • Method

    MAJoRCom uses frequency and spatial index modulation inherent to CAESAR, with dimension-reduced codebook design and a low-complexity receiver.

  • Results

    MAJoRCom achieves a rate comparable to dedicated communication waveforms without affecting radar functionality, while its low-complexity decoder achieves comparable BER to optimal decoding.

  • Takeaways & Limitations

    The scheme turns CAESAR’s inherent radar randomness into communication capability without coexistence interference, using simpler decoding at a rate cost for codebook design.

Abstract

from arXiv · show

Dual-function radar communication (DFRC) systems implement both sensing and communication using the same hardware. Such schemes are often more efficient in terms of size, power, and cost, over using distinct radar and communication systems. Since these functionalities share resources such as spectrum, power, and antennas, DFRC methods typically entail some degradation in both radar and communication performance. In this work we propose a DFRC scheme based on the carrier agile phased array radar (CAESAR), which combines frequency and spatial agility. The proposed DFRC system, referred to as multi-carrier agile joint radar communication (MAJoRCom), exploits the inherent spatial and spectral randomness of CAESAR to convey digital messages in the form of index modulation. The resulting communication scheme naturally coexists with the radar functionality, and thus does not come at the cost of reduced radar performance. We analyze the performance of MAJoRCom, quantifying its achievable bit rate. In addition, we develop a low complexity decoder and a codebook design approach, which simplify the recovery of the communicated bits. Our numerical results demonstrate that MAJoRCom is capable of achieving a bit rate which is comparable to utilizing independent communication modules without affecting the radar performance, and that our proposed low-complexity decoder allows the receiver to reliably recover the transmitted symbols with an affordable computational burden.

I. INTRODUCTION

MAJoRCom embeds communication into CAESAR’s frequency and spatial agility, allowing radar and communication to share the radar scheme without affecting radar performance. The paper analyzes achievable rate and introduces lower-complexity decoding and codebook design for reliable recovery.

  • System concept: MAJoRCom extends CAESAR into a DFRC system by using frequency selections and antenna allocations for index modulation.The scheme combines frequency and spatial index modulation without requiring transmitter channel state information.
  • System concept: Communication is an inherent byproduct of the radar design, so the two functionalities coexist without cross interference or changes to radar power and waveform.Unlike approaches using dedicated communication waveforms or antennas, MAJoRCom embeds information in CAESAR’s existing spectral and spatial randomness.
  • Communication analysis: MAJoRCom’s maximal bits per pulse grow linearly with the number of transmit antennas and logarithmically with the number of available carrier frequencies.The rate analysis identifies increased radar agility, particularly more carrier frequencies, as contributing to achievable communication rate.
  • Evaluation: Numerical results show communication rates comparable to dedicated communication modules without affecting radar performance or radar resources.The paper positions narrowband transceivers and simple hardware as practical advantages of the scheme.
  • Receiver and codebook design: The proposed low-complexity decoder achieves comparable BER performance to the optimal decoder, while permutation codebooks further facilitate decoding at a cost in information rate.The decoder addresses the computational burden of optimal index-modulation decoding.

B. Information Embedding Scheme

MAJoRCom embeds digital information by exploiting CAESAR’s random carrier-frequency selection and antenna allocation. Each pulse combines frequency selection with spatial allocation to form communication codewords while retaining the radar waveform.

  • Information Embedding Scheme: CAESAR’s carrier-frequency and antenna-allocation randomness enables index and permutation modulation for digital communication.The scheme uses frequency indices and antenna assignments as information-bearing parameters.
  • Information Embedding Scheme: MAJoRCom applies the same information-embedding method independently on each pulse.More transmitted pulses convey more bits to the receiver.
  • Information Embedding Scheme: At each pulse, CAESAR selects K frequencies from M available frequencies and allocates antenna elements among them.The selected frequency subset and its antenna allocation jointly determine the transmitted codeword.
  • Information Embedding Scheme: Each selected frequency is assigned to exactly LK = LR/K antennas, with diagonal selection matrices uniquely describing the allocation pattern.The formulation assumes LR/K is an integer, though uneven allocations can be accommodated by adapting the method.
  • Information Embedding Scheme: For LR = 4 antennas and K = 2 frequencies, spatial permutation provides 6 possible allocation codewords.Each frequency is used by two antennas in this example.

3) Hybrid modulation:

Hybrid modulation combines frequency-subset selection with antenna-allocation patterns, allowing MAJoRCom to encode information through the radar transmission itself. The resulting signal uses the full antenna array and does not require transmitter-side CSI.

  • 3) Hybrid modulation:: Combining frequency and antenna selection creates a hybrid frequency-and-spatial index modulation scheme.The total codebook is formed by combining frequency-selection codewords with antenna-allocation patterns.
  • 3) Hybrid modulation:: The achievable bits per pulse are determined by the logarithm of the total number of hybrid codewords.Stirling’s approximation is used to characterize this quantity for large systems.
  • 3) Hybrid modulation:: The bit count grows linearly with LR and logarithmically with M when LR ≫ K and M ≫ K.Here LR is the antenna count and M is the number of available frequencies.
  • 3) Hybrid modulation:: Input bits are divided between selecting the frequency subset and selecting the antenna-allocation pattern.Fig. 3 illustrates this hybrid signaling process.
  • 3) Hybrid modulation:: MAJoRCom uses one carrier per transmit antenna and the complete antenna array, maximizing radar power and aperture without requiring transmitter CSI.The radar waveform remains a constant-modulus monotone signal.
  • 3) Hybrid modulation:: Embedding additional data into the radar waveform could increase communication rate but may degrade radar performance.This extension is left for future work.

III. COMMUNICATION PERFORMANCE ANALYSIS

The paper models MAJoRCom’s communication link and characterizes its achievable rate from the discrete radar-generated codebook. The analysis yields upper and lower rate bounds and supports numerical comparison with dedicated communication waveforms.

  • III. COMMUNICATION PERFORMANCE ANALYSIS: The communication receiver is modeled with a memoryless additive white Gaussian noise channel and observes sampled outputs across the available frequency range.The model includes receiver antennas, channel matrix H, and Gaussian noise.
  • III. COMMUNICATION PERFORMANCE ANALYSIS: MAJoRCom’s frequency codewords and baseband vectors represent the selected carrier frequencies in the sampled channel model.The receiver is assumed to know K, the steering vectors, the channel matrix H, and the noise distribution.
  • III. COMMUNICATION PERFORMANCE ANALYSIS: The rate analysis treats each radar waveform x as a channel input whose information is embedded through carrier frequencies and antenna allocations.This specializes index-modulation analysis to the statistical structure of MAJoRCom radar signals.
  • III. COMMUNICATION PERFORMANCE ANALYSIS: The achievable rate is characterized through single-letter mutual information for the memoryless channel.The equally likely codewords induce a Gaussian-mixture distribution at the receiver.
  • III. COMMUNICATION PERFORMANCE ANALYSIS: Because Gaussian-mixture differential entropy lacks a closed-form expression, the analysis provides a lower bound on the achievable rate.Proposition 1 states this lower bound using a bound on the differential entropy.
  • III. COMMUNICATION PERFORMANCE ANALYSIS: At sufficiently high SNR, the upper bound can be approached when the codewords are reliably distinguishable.The upper bound reflects the number of bits required to represent the available codewords.
  • III. COMMUNICATION PERFORMANCE ANALYSIS: In low SNRs, MAJoRCom achieves higher rates than individual dedicated communication waveforms without affecting radar performance.The information-theoretic analysis motivates a separate reduced-complexity decoder for practical receiver implementation.

IV. REDUCED DECODING COMPLEXITY IMPLEMENTATION

The paper addresses the computational burden of decoding MAJoRCom’s index-modulated messages. It presents an iterative sub-optimal decoder and a reduced codebook design, which can be used independently or together.

  • IV. REDUCED DECODING COMPLEXITY IMPLEMENTATION: Decoding can impose substantial computational burden even though MAJoRCom signal generation and transmission require relatively light computation.This motivates reduced-complexity receiver methods.
  • IV. REDUCED DECODING COMPLEXITY IMPLEMENTATION: The reduced-complexity decoder and modified codebook design are independent and may be applied separately or simultaneously.The codebook change may affect the radar beam pattern, but simulations report minimum influence on range, Doppler, and angle estimates.
  • IV. REDUCED DECODING COMPLEXITY IMPLEMENTATION: The optimal ML decoder jointly estimates selected frequencies and antenna allocations from the received signal.Equiprobable codewords and i.i.d. Gaussian noise make ML the minimum-error detector under the stated model.
  • IV. REDUCED DECODING COMPLEXITY IMPLEMENTATION: The ML optimization is generally NP-hard because it exhaustively searches over frequency indices and binary antenna-selection matrices.This produces high computational complexity for optimal index-modulation decoding.
  • IV. REDUCED DECODING COMPLEXITY IMPLEMENTATION: The paper designs a dedicated low-complexity decoder because all information is embedded in frequency selection and antenna allocation.Unlike many index-modulation schemes, MAJoRCom does not add digitally modulated symbols.
  • IV. REDUCED DECODING COMPLEXITY IMPLEMENTATION: The sub-optimal decoder initializes frequency estimates using sparse recovery, then alternates between recovering antenna allocations and refining frequencies.FFT followed by thresholding can provide the initial frequency estimate in suitable settings.
  • IV. REDUCED DECODING COMPLEXITY IMPLEMENTATION: When Tp is approximately n/∆f, FFT-based processing identifies the K active frequencies by ranking estimated row norms.For other pulse durations, a general sparse-recovery method can be used.

2) Spatial Decoder:

The spatial decoder recovers binary antenna-allocation vectors under a joint constraint, using either ML decoding or a sequential greedy alternative to reduce computation.

  • Spatial decoder: The decoder recovers each binary spatial-selection vector sequentially rather than treating the K vectors as independent linear problems.Each antenna is assigned to one frequency, imposing a joint constraint across the vectors.
  • Spatial decoder: The sequential recovery of each spatial vector uses exhaustive search over its feasible binary values.The non-conventional constraints and binary entries require exhaustive search for each selection step.
  • Spatial decoder: The proposed low-complexity decoder achieves BER performance comparable to the computationally complex ML decoder.This comparison is reported in the numerical analysis.
  • Spatial decoder: The method first obtains a coarse estimate of frequency indices and spatial selections, then can refine them through alternating updates.The refinement updates the frequency indices, spatial selections, and the estimate used in both recovery steps.

3) Frequency Refinement:

The frequency-refinement procedure recovers frequency indices after an initial sparse-recovery estimate and can replace exhaustive joint searches with sequential estimation.

  • Frequency Refinement: Algorithm 1 computes a sparse-recovery estimate, sorts row norms to recover frequency indices, and then applies ML or greedy spatial decoding.The algorithm takes YC, Ψ, and K as inputs and outputs estimated frequency indices and spatial selections.
  • Frequency Refinement: The exhaustive frequency search over distinct indices can be replaced by sequential frequency-code estimation to reduce computation.The frequency indices are distinct and selected from M possible indices.
  • Frequency Refinement: The sequential frequency method requires only 2 evaluations, substantially fewer than its exhaustive-search counterpart.The cited passage reports the reduced evaluation count without specifying the omitted exhaustive-search count.
  • Frequency Refinement: The decoder refines the estimate of the system matrix using recovered frequency indices and spatial selections before further greedy decoding.The refined matrix keeps recovered-frequency rows and sets the remaining rows to zero.

C. Codebook Design

The codebook design selects a subset of spatial allocation codewords to balance communication rate and decoding complexity while improving codeword distinguishability.

  • Codebook Design: The proposed codebook uses all frequency options while selecting Nb spatial codewords to balance achievable rate and receiver computational burden.The design changes the codebook rather than the frequency-index set.
  • Codebook Design: The authors reduce the design problem dimension and then construct a sub-optimal solution aimed at improving receiver distinguishability.The stated design goal is to make different codewords easier for the receiver to distinguish.
  • Design Criterion: The design objective maximizes the minimum distance between distinct codewords in the selected subset.This distance governs distinguishability, and the resulting optimization remains high-dimensional.
  • Design Criterion: The codebook-design optimization is NP-hard because the codewords obey an additional uniqueness constraint absent from standard binary codebooks.Consequently, standard Hamming-distance codebook designs cannot be used directly.

2) Dimension Reduction of the Constellation Set:

The constellation codewords are projected into a lower-dimensional real space while preserving their pairwise distances, enabling simpler visualization and distance calculations.

  • Dimension Reduction of the Constellation Set: PCA and SVD are used to project the original binary codewords into a real-valued plane while preserving codeword distances.The intrinsic dimension is estimated from the rank, represented by the number of nonzero singular values.
  • Dimension Reduction of the Constellation Set: The distance matrix is symmetric, has zero diagonal entries, and each row is a permutation of the first row.These properties reduce the computation needed to evaluate distances among possible allocation codewords.
  • Dimension Reduction of the Constellation Set: For LR = 4, K = 2 and LK = 2, six spatial selection patterns produce original codewords with KLR = 8 dimensions.The reduced representation makes the constellation convenient to visualize.
  • Dimension Reduction of the Constellation Set: The example’s three-dimensional constellation preserves the distance-matrix entries between codewords.The resulting constellation is depicted in Fig. 4.

3) Design of the Constellation Set:

MAJoRCom’s constellation and evaluation use frequency and antenna allocations to encode information while preserving the radar functionality. Achievable-rate comparisons assess this design against dedicated communication antennas under spatial-decay and Rayleigh channels.

  • Radar-performance trade-off: Reducing the number of antenna allocations can affect spatial agility, radiation patterns, and radar parameter accuracy, although simulations show minimal degradation.The affected parameters include range, Doppler, and angular estimates.
  • Evaluation scope: The study evaluates communication rates, decoder complexity, and reduced-cardinality codebook effects on radar performance.The numerical study refers to prior work for detailed CAESAR radar-performance analysis.
  • Achievable-rate evaluation: The evaluation compares achievable-rate bounds for MAJoRCom with communication-only allocations using one or two dedicated antennas under equal average power.The comparisons are made versus SNR for spatial exponential-decay and Rayleigh-fading channels.
  • Rate comparison: At relatively low SNR, MAJoRCom achieves higher rates than a dedicated communication antenna without impairing radar performance.For Rayleigh fading, it outperforms two dedicated communication antennas for SNRs not larger than 5 dB; dedicated antennas prevail as SNR increases.

B. Decoding Strategies

The decoding and codebook studies evaluate BER, distance-based codeword design, and radar impacts of reduced codebook cardinality. Low-complexity decoders approach maximum-likelihood performance, while codebook distances track the desired design objective.

  • Decoding Strategies: The proposed sub-optimal decoders achieve BER 10^-4 around -9 dB with ML estimation, versus -10 dB for global ML and a 3 dB gap for greedy decoding.The results average BER over 10^6 trials and compare iterative and non-iterative decoder variants.
  • Decoding Strategies: Low-complexity decoders scale similarly with SNR to the optimal ML decoder while substantially reducing receiver computational burden.Greedy refinement does not necessarily improve accuracy over the initial non-iterative estimate.
  • Codebook design: For LC = 4, the approximate Dist criterion has an approximately monotonic relationship with H-Dist, and the relationship becomes more distinct as receive antennas increase.Reducing Dist therefore proportionally reduces the desired H-Dist objective in the reported numerical study.
  • Codebook design: The reduced codebook is constructed by applying PCA, estimating intrinsic dimension LD = 7, clustering candidates into Nb classes, and selecting representatives nearest to class centers.The study evaluates Nb = 21, 23, and 25.
  • Radar-performance evaluation: Radar evaluation uses range-Doppler hit rate and target-angle RMSE over Monte Carlo trials with four targets and 32 radar pulses.The radar SNR is defined as 1/κ^2.

APPENDIX PROOF OF PROPOSITION 2

The appendix proves that the distance matrix R has symmetric structure and that every row is a permutation of its first row. The proof uses permutation matrices associated with codewords.

  • APPENDIX PROOF OF PROPOSITION 2: The distance matrix R has a zero main diagonal and is symmetric by its definition.These properties are stated directly before the row-permutation argument.
  • APPENDIX PROOF OF PROPOSITION 2: Each codeword i is induced by an LR × LR permutation matrix Σi acting on the reference antenna-selection structure.The inducing permutation matrix need not be unique.
  • APPENDIX PROOF OF PROPOSITION 2: The proof introduces G as the set of permutation matrices that fix the reference selection vectors for all k.This set captures the permutations preserving the reference codeword structure.
  • APPENDIX PROOF OF PROPOSITION 2: Because permutation matrices are orthogonal and codeword indices range over all codewords, each row of R is a permutation of the first row.The argument applies the permutation representation and the resulting identity in (44).
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