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Cooperative Ambient Backscatter Communications for Green Internet-of-Things

Gang Yang, Qianqian Zhang, Ying-Chang Liang

arXiv:1801.01249v1cs.IT

TL;DR

AmBC receivers traditionally treat the RF-source signal as interference and recover only the A-BD, motivating a cooperative design that recovers both signals. The paper develops CABC models, detectors, and closed-form BER analyses for flat-fading and OFDM frequency-selective channels, finding near-ML SIC performance and improved RF-source ML detection when the A-BD transmits more slowly.

  • Problem

    Existing AmBC receivers focus on A-BD information while treating the RF-source signal as unwanted interference, despite applications requiring recovery from both users.

  • Method

    The paper models CABC with multi-antenna reception, derives ML, linear, and SIC detectors for flat fading, and develops a low-complexity ML detector with closed-form BERs for both channel types.

  • Results

    SIC achieves near-ML detection when the signals have equal symbol periods, while backscatter enhances RF-source ML detection when the A-BD symbol period is longer.

  • Takeaways & Limitations

    CABC enables simultaneous recovery of RF-source and A-BD information, with the passive A-BD also assisting RF-source detection.

Abstract

from arXiv · show

Ambient backscatter communication (AmBC) enables a passive backscatter device to transmit information to a reader using ambient RF signals, and has emerged as a promising solution to green Internet-of-Things (IoT). Conventional AmBC receivers are interested in recovering the information from the ambient backscatter device (A-BD) only. In this paper, we propose a cooperative AmBC (CABC) system in which the reader recovers information not only from the A-BD, but also from the RF source. We first establish the system model for the CABC system from spread spectrum and spectrum sharing perspectives. Then, for flat fading channels, we derive the optimal maximum-likelihood (ML) detector, suboptimal linear detectors as well as successive interference-cancellation (SIC) based detectors. For frequency-selective fading channels, the system model for the CABC system over ambient orthogonal frequency division multiplexing (OFDM) carriers is proposed, upon which a low-complexity optimal ML detector is derived. For both kinds of channels, the bit-error-rate (BER) expressions for the proposed detectors are derived in closed forms. Finally, extensive numerical results have shown that, when the A-BD signal and the RF-source signal have equal symbol period, the proposed SIC-based detectors can achieve near-ML detection performance for typical application scenarios, and when the A-BD symbol period is longer than the RF-source symbol period, the existence of backscattered signal in the CABC system can enhance the ML detection performance of the RF-source signal, thanks to the beneficial effect of the backscatter link when the A-BD transmits at a lower rate than the RF source.

I. INTRODUCTION

The paper introduces cooperative ambient backscatter communication, enabling a receiver to recover information from both an RF source and an ambient backscatter device while using the backscatter device as a passive relay. It develops detection and BER analyses for flat-fading and frequency-selective channels.

  • Motivation and contribution: Conventional AmBC receivers recover only A-BD information, whereas CABC jointly recovers RF-source and A-BD information.The A-BD also passively assists recovery of the RF-source signal.
  • System model: The CABC model incorporates multiple receive antennas and combines spread-spectrum and spectrum-sharing perspectives for flat-fading channels.The received backscatter signal is the product of the RF-source and A-BD signals.
  • Receiver design: For flat fading, the paper derives optimal ML, linear, and SIC-based detectors; SIC detects the source, removes direct-link interference, detects the A-BD, and re-estimates the source.For frequency-selective fading over ambient OFDM carriers, it develops a low-complexity optimal ML detector.
  • Performance analysis: Closed-form BER expressions are obtained for the proposed detectors under both flat-fading and frequency-selective channels.The analysis covers the detector designs across both channel types.
  • Numerical findings: When signal symbol periods are equal, SIC achieves near-ML performance in typical scenarios; with a slower A-BD, backscatter can enhance RF-source ML detection.The enhancement is attributed to the beneficial backscatter link when the A-BD transmits at a lower rate.
  • Motivation and contribution: Direct-link interference is challenging because the direct channel is typically much stronger than the backscatter channel, while the two received data streams are mutually dependent.Treating the direct link as interference can severely degrade A-BD detection.

III. RECEIVER DESIGN FOR CABC UNDER FLAT FADING CHANNELS

This section develops ML and lower-complexity receiver designs for CABC under flat fading, exploiting the shared structure of the RF-source and backscatter signals.

  • The CABC receiver includes an optimal ML detector, suboptimal linear detectors, and SIC-based detectors for flat fading channels.
  • ML Detector: The original ML search grows exponentially with the RF-source modulation size |As|, producing extremely high complexity.
  • ML Detector: The low-complexity ML detector conditions each RF-source symbol estimate on every A-BD candidate, then selects the A-BD candidate using the conditional estimates.The final RF-source estimates correspond to the selected A-BD candidate.
  • ML Detector: The two-step ML detector reduces the search count to K|Ac||As|, but this remains large for large K or high-order modulation.

B. Linear Detectors

Linear and SIC-based detectors recover both RF-source and A-BD information by combining antenna observations and exploiting the stronger direct link.

  • Linear Detectors: Linear detectors use a block-diagonal decoding matrix with per-symbol matrices to extract RF-source and A-BD signals.
  • Linear Detectors: The proposed linear choices include maximum-ratio combining, zero-forcing, and minimum mean-square-error detectors.
  • SIC-Based Detectors: SIC first estimates the RF-source signal, subtracts its direct-link contribution, detects the A-BD signal, and then re-estimates the RF-source signal.
  • SIC-Based Detectors: The SIC variants are named MRC-SIC, ZF-SIC, and MMSE-SIC according to the first-step RF-source estimator.

IV. CABC UNDER FREQUENCY-SELECTIVE FADING CHANNELS

This section extends CABC to frequency-selective fading over ambient OFDM carriers, modeling delayed direct and backscatter links across multiple subcarriers and antennas.

  • Signal Model: The frequency-selective CABC model uses ambient OFDM signals, with the A-BD symbol period matched to the OFDM symbol period.
  • Signal Model: The model assumes block-fading multipath channels for the RF-source-to-reader, RF-source-to-A-BD, and A-BD-to-reader links.
  • Signal Model: The C-RX is synchronized to the direct-link arrival, while the backscatter link may arrive with a small delay d.
  • Signal Model: After cyclic-prefix removal, the receiver applies a DFT over a specified time window to obtain subcarrier observations.
  • Signal Model: The backscattered signal multiplies the low-rate A-BD signal c(n) with the high-rate OFDM spreading signal s_k(n), providing spreading gain N.
  • Signal Model: The frequency-domain received model represents direct-link and backscatter-link channel vectors across the M receive antennas, together with additive noise.

B. Optimal ML Detector

The OFDM detector exploits the same signal structure as the flat-fading case to obtain a low-complexity ML solution and closed-form BER analysis.

  • Optimal ML Detector: The frequency-selective signal model has the same structure as the flat-fading model, enabling a directly formulated low-complexity ML detector.
  • Optimal ML Detector: For each A-BD candidate c(n), the detector estimates each OFDM subcarrier symbol s_k(n) using the equivalent channel and MRC.
  • Optimal ML Detector: The detector then jointly selects the optimal A-BD signal and corresponding RF-source symbols across subcarriers.
  • Optimal ML Detector: The estimated A-BD signal benefits from both spreading gain and frequency diversity under frequency-selective fading.
  • BER Performance: The BER analysis assumes QPSK for the RF source and BPSK for the A-BD, while stating that the method generalizes to other modulation schemes.
  • BER Performance: The analysis treats K=1 for exposition and states that the BER derivation generalizes to K>1.
  • BER Performance: Closed-form BER expressions are given for ML detection of the RF-source and A-BD signals, with average BERs obtained by expectation over the channel.

3) BER Performance for Linear Detectors:

The paper derives closed-form BER expressions for MRC, ZF, MMSE, and SIC-based detectors in the CABC system, conditioned on the channel matrix H.

  • MRC detector: BER expressions are provided for MRC detection of the RF-source signal s(n) and A-BD signal c(n), conditioned on H.The corresponding expressions are stated in Proposition 1, with proofs deferred to Appendix B.
  • ZF and MMSE detectors: BER expressions are likewise derived for ZF and MMSE detectors when detecting s(n) and c(n).These results are stated in Propositions 2 and 3, with proofs given in Appendices C and D.
  • SIC-based detectors: SIC-based detectors analyze three stages: detecting s(n), detecting c(n), and re-estimating s(n).The BER of the first stage uses the corresponding MRC, ZF, or MMSE expression, while later-stage BERs account for the successive detection process.

B. Frequency-Selective Fading Channels

For frequency-selective fading over ambient OFDM carriers, the paper matches the A-BD and OFDM symbol periods and derives a low-complexity ML detector with BER analysis. Simulations show that backscatter can improve RF-source detection, while the A-BD rate-reliability tradeoff depends on the symbol-period ratio.

  • System setup: The A-BD symbol period equals the OFDM symbol period, which comprises N + Nc sampling periods, giving an A-BD data rate of RA-BD = fs/(N + Nc).This design supports the proposed OFDM-based frequency-selective fading model.
  • BER analysis: The BER of c(n) is generally small because its second detection step benefits from a large spreading gain N.The paper therefore focuses on the BER of s(n) in this subsection.
  • ML detection: A low-complexity optimal ML detector is analyzed using the composite channel matrix H formed from per-subcarrier direct and backscatter channels.Theorem 3 gives the BER of s(n) conditioned on H and the BER of c(n), with averaging over H yielding the average BER.
  • ML-detector results: At BER 10^-5, CABC provides around 1 dB SNR gain for s(n) over conventional direct-link SIMO when Δγ = −10 dB.The gain becomes larger as Δγ increases, while the low-complexity ML detector matches the original joint ML detector in the reported simulation.
  • Symbol-period ratio: Doubling K gives c(n) around 3 dB SNR gain but halves the A-BD data rate, demonstrating a reliability–rate tradeoff.For fixed Δγ, the BER of both s(n) and c(n) improves as K increases, while improvement for s(n) becomes smaller at larger K.

2) BER Comparison for Suboptimal Detectors:

The BER comparisons evaluate ML and suboptimal detectors across flat and frequency-selective fading, symbol-period ratios, relative powers, and delay conditions. SIC-based detectors approach ML performance in representative flat-fading settings, while channel delay and insufficient cyclic-prefix coverage degrade OFDM performance.

  • Flat fading: At Δγ = −10 dB, MMSE-SIC achieves near-ML performance for the RF-source signal, whereas MRC and MRC-SIC exhibit BER floors.ZF performs worse than MMSE because it forces signal interference to zero despite the direct-link signal being ten times stronger.
  • Flat fading: At Δγ = −10 dB, SIC-based detectors achieve almost the same BER as optimal ML detection for the A-BD signal.The SIC-based detectors also provide a 1.7 dB SNR gain over conventional ZF and MMSE detectors at BER 10^-2.
  • Frequency-selective fading: In frequency-selective fading, s(n) outperforms direct-link OFDM even when backscatter power is 10% of direct-link power.Increasing relative backscatter power further improves s(n) BER.
  • Frequency-selective fading: For Δγ = −10 dB, c(n) gains around 22 dB at BER 10^-2 over K = 1 flat-fading performance through spreading and diversity gains.The BER of c(n) is lower at higher backscatter-link power.
  • Delay and synchronization: When total channel delay exceeds the cyclic-prefix coverage, both BERs increase because inter-block and inter-carrier interference destroy subcarrier orthogonality.For d ≤ dmax = 9, BERs match the zero-delay case; delayed A-BD transmission mainly worsens s(n), while c(n) increases slightly.

APPENDIX A PROOF OF THEOREM 1

The proof derives BER expressions for the ML detector by conditioning on mutual estimates of the RF-source and A-BD symbols. It constructs sufficient statistics and evaluates Gaussian decision errors across symbol-estimation cases.

  • Conditional BER analysis: BER expressions account separately for correct and incorrect intermediate symbol estimates and combine the resulting conditional error probabilities.For QPSK, error contributions depend on whether one or both mapped bits are decoded incorrectly.
  • Estimating s(n) from c(n): The proof first estimates the RF-source symbol from the A-BD estimate using a sufficient statistic derived from the received signal model.The resulting ML estimate is obtained by quantizing the statistic.
  • Estimating c(n) from s(n): The proof then estimates c(n) from the RF-source ML estimate using a decision statistic whose threshold determines the binary ML output.The detector outputs c(n) = 1 when z(n) > 0 and c(n) = −1 otherwise.

APPENDIX B PROOF OF PROPOSITION 1

The proof derives Proposition 1 by analyzing MRC detection errors for the RF-source and backscattered signals under correct and incorrect intermediate decisions. Gaussian error probabilities are then combined using QPSK symmetry.

  • BER of c(n): For c(n), the proof derives separate BER contributions when the RF-source estimate is correct and incorrect, then combines them into Proposition 1.The two conditional cases are explicitly evaluated before obtaining the final BER expression.
  • BER of s(n): For RF-source detection, the proof decomposes complex estimation errors into real and imaginary components and derives the real-part error probability.QPSK symmetry gives the BER of s(n) from the identical real- and imaginary-part error rates.

APPENDIX C PROOF OF PROPOSITION 2

The proof derives Proposition 2 by writing ZF-based estimates for the RF-source and backscattered signals and evaluating their conditional Gaussian error probabilities. The final BER expressions combine these cases.

  • RF-source detection: The proof begins with the ZF estimate of the signal vector and derives the RF-source detecting SNR from the resulting effective noise term.The RF-source BER follows from the effective SNR expression.
  • A-BD detection: For c(n), the analysis conditions on correct and incorrect RF-source estimates and derives the corresponding Gaussian error probabilities.These conditional expressions are combined to obtain the BER in Proposition 2.

APPENDIX D PROOF OF PROPOSITION 3

The proof derives BER expressions for the RF-source and backscattered signals using MMSE estimates, Gaussian-distributed intermediate variables, and separate symbol cases.

  • MMSE detection produces estimated RF-source and backscattered signal vectors from channel-dependent expressions.
  • The detecting SNR for s(n) yields the BER expression in (39), while the two c(n) cases complete the proof of Proposition 3.
  • For bs(n) = s(n), the proof obtains the BER of c(n) by applying steps analogous to Theorem 1.
  • The proof analyzes the backscattered-signal variable bs(n) across three cases with specified probabilities.
  • For bs(n) ≠ s(n), the corresponding BER of c(n) is obtained from the Gaussian distribution of z(n) and its case-specific mean and variance.
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