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Uplink Sensing in Perceptive Mobile Networks with Asynchronous Transceivers

Zhitong Ni, J. Andrew Zhang, Xiaojing Huang, Kai Yang, Jinhong Yuan

arXiv:2011.09098v1eess.SP

TL;DR

Asynchronous, physically separated transceivers create timing and carrier-frequency offsets that make uplink sensing ambiguous. The paper combines CACC, mirrored-MUSIC, and multidomain AoA estimation; simulations demonstrate estimation of actual delay and Doppler values and high-resolution AoAs with few receiving antennas.

  • Problem

    With separated asynchronous transceivers, timing and carrier-frequency offsets create ambiguity in sensing delay and Doppler.

    Source: §II · p. 4

  • Method

    The scheme uses CACC to mitigate offsets, mirrored-MUSIC to handle mirrored outputs, and an improved MUSIC algorithm for AoA estimation.

    Source: §I · p. 2, §VII · p. 12

  • Results

    Simulations demonstrate that mirrored-MUSIC estimates actual delays and Doppler frequencies, while the scheme obtains high-resolution AoAs with a small number of receiving antennas.

    Source: §VII · p. 12

  • Takeaways & Limitations

    The proposed scheme provides high-accuracy sensing parameter estimation with asynchronous transceivers and a small number of receiving antennas.

    Source: §VII · p. 12

    When targets have close delays and Doppler frequencies, similar basis vectors can respond to multiple AoAs, causing some lower-gain AoA estimates to be missed.

    Source: §V · p. 9

Abstract

from arXiv · show

Perceptive mobile network (PMN) is a recently proposed next-generation network that integrates radar sensing into communication. One major challenge for realizing sensing in PMNs is how to deal with spatially-separated asynchronous transceivers. The asynchrony between sensing receiver and transmitter will cause both timing offsets (TOs) and carrier frequency offsets (CFOs) and lead to degraded sensing accuracy in both ranging and velocity measurements. In this paper, we propose an uplink sensing scheme for PMNs with asynchronous transceivers, targeting at resolving the sensing ambiguity and improving the sensing accuracy. We first adopt a cross-antenna cross-correlation (CACC) operation to remove the sensing ambiguity associated with both TOs and CFOs. Without sensing ambiguity, both actual propagation delay and actual Doppler frequency of multiple targets can be obtained using CACC outputs. To exploit the redundancy of the CACC outputs and reduce the complexity, we then propose a novel mirrored-MUSIC algorithm, which halves the number of unknown parameters to be estimated, for obtaining actual values of delays and Doppler frequencies. Finally, we propose a high-resolution angles-of-arrival (AoAs) estimation algorithm, which jointly processes all measurements from spatial, temporal, and frequency domains. The proposed AoAs estimation algorithm can achieve significantly higher estimation accuracy than that of using samples from the spatial domain only. We also derive the theoretical mean-square-error of the proposed algorithms. Numerical results are provided and validate the effectiveness of the proposed scheme.

I. INTRODUCTION

PMN applies joint communication and radar sensing in mobile networks, but uplink sensing with separated asynchronous transceivers faces unresolved timing, frequency, and AoA challenges. The paper proposes a broadband scheme combining CACC, mirrored-MUSIC, and multidomain AoA estimation.

I. INTRODUCTION

  • Asynchrony between separated sensing receiver and transmitter introduces timing and carrier-frequency offsets, creating sensing ambiguity and degrading delay and Doppler accuracy.Most recent JCAS papers assume perfect synchronization, while cognitive-radio work discussed interference but did not provide an effective parameter-estimation method.Source: §I · p. 2
  • Prior CACC methods leave mirrored unknown parameters that obscure Doppler signs, while add-minus suppression can be weak in rich multipath unless static paths dominate dynamic paths.Earlier approaches to higher-resolution AoA estimation either target narrowband systems or lack joint estimation of AoAs with delay and Doppler.Source: §I · p. 2
  • The proposed scheme combines CACC for timing and frequency offsets, mirrored-MUSIC for delay and Doppler estimation, and multidomain MUSIC for high-resolution AoA estimation.The AoA algorithm combines spatial, temporal, and frequency measurements; the scheme targets physically separated asynchronous transceivers and OFDM modulation.Source: §I · p. 2
  • The scheme is scoped to a single static UE and a line-of-sight path between that transmitter and the base station.The introduction presents physically separated uplink sensing as a near-term option requiring minimal network changes, given full-duplex technology's immaturity.Source: §I · pp. 1–2
  • The paper introduces mirrored-MUSIC to process actual and mirrored CACC parameters, halving unknown variables without approximation and reducing complexity relative to conventional MUSIC.The authors also note potential applications to harmonic retrieval, ESPRIT, and the matrix pencil method.Source: §I · p. 2
  • The proposed MUSIC-based AoA estimator combines spatial, temporal, and frequency measurements to improve resolution over spatial-only estimation.It addresses ambiguity of basis vectors by selecting multiple peaks from MUSIC outputs.Source: §I · p. 2

II. SYSTEM AND CHANNEL MODELS

The system uses uplink OFDM preambles from a fixed, known UE to sense targets at a static base station with a limited antenna array. Its channel and signal model includes a dominant LOS path, target-reflected paths, and time-varying offsets from asynchronous clocks.

II. SYSTEM AND CHANNEL MODELS

  • The base station uses uplink signals from a specific fixed, known UE for both communication and sensing, with a limited N-antenna array.The model assumes a dominant LOS path and L NLOS paths reflected or refracted from targets; the LOS delay and AoA are known, and its Doppler is zero.Source: §II · p. 3
  • The sensing input is the OFDM preamble, which precedes data in each packet and can also support communication synchronization and channel estimation.The packet contains one preamble in the model, and the proposed scheme also applies to systems with similar signal structures, such as WiFi.Source: §II · p. 3
  • When multiple UEs are present, the scheme requires UE 1 to have an available segment of interleaved subcarriers; the model simplifies by assigning it the whole preamble.Each OFDM symbol has G subcarriers and a cyclic prefix; the described packet structure places the preamble before data.Source: §II · p. 3
  • Packets are sent at equal intervals, but absent clock-level synchronization leaves a time-varying TO and CFO mixed with propagation delay and target Doppler.The model assumes packet-level synchronization may be achieved; these offsets vary over time and can make delay and Doppler vary across packets.Source: §II · pp. 3–4
  • The model represents the base-station array response using each path's AoA and adds zero-mean complex AWGN to the received signal.For simplicity, transmitted preamble symbols are assumed to have unit power.Source: §II · pp. 3–4

III. CACC FOR MITIGATING TOS AND CFOS

The CACC stage uses cross-antenna correlation to mitigate timing and frequency offsets before estimating target delays and Doppler frequencies. Filtering its outputs removes an invariant component, leaving sensing parameters without those offsets, although residual side products motivate later processing.

III. CACC FOR MITIGATING TOS AND CFOS

  • Cross-correlating signals from different receiving antennas mitigates both TO and CFO, which otherwise mix with actual delay and Doppler.The method selects the antenna with the largest average received power as its reference antenna.Source: §III · p. 4
  • The 2D-FFT of the target-dependent CACC component produces an impulse centered around each target's delay and Doppler, while an invariant component does not vary with subcarrier or packet index.The power of one additional component is stated to be significantly lower than that of the other three.Source: §III · p. 4
  • A 2D high-pass filter removes the invariant CACC component, yielding outputs that contain actual sensing parameters without TOs and CFOs.Because the LOS delay is assumed known, the resulting delay estimates are relative to that LOS delay.Source: §III · p. 4
  • The CACC output retains mirrored side products, so conventional estimation of actual and mirrored components together would require twice as many samples.The paper notes that separating the actual component from its side product is challenging.Source: §III · p. 5
  • The authors report that their adopted CACC signal has smaller input error than AMS, which may fail when many paths create rich multipath.The input error arises from a residual component in the CACC output.Source: §III · p. 5

IV. MIRRORED-MUSIC FOR ESTIMATING PROPAGATION DELAYS AND DOPPLER FREQUENCIES

The section introduces mirrored-MUSIC for estimating conjugated variables from signals like the CACC-derived signal. By exploiting redundancy in the conventional formulation, it halves the unknown variables without approximation and improves performance over conventional MUSIC.

IV. MIRRORED-MUSIC FOR ESTIMATING PROPAGATION DELAYS AND DOPPLER FREQUENCIES

  • Mirrored-MUSIC directly estimates conjugated variables from signals of the form used in the CACC method.The algorithm is also framed as a solution to problems where test basis vectors have mirror symmetry.Source: §IV · p. 5
  • Conventional MUSIC uses basis vectors in the signal matrix’s null space to test candidate parameters.A candidate parameter is identified by checking whether its basis vector falls into that null space.Source: §IV · p. 5
  • By exploiting redundancy in the doubled-parameter matrix, mirrored-MUSIC halves the unknown variables without approximation and performs better than conventional MUSIC.The conventional construction requires twice as many parameters because of the side product.Source: §IV · p. 5

A. Proposed Mirrored-MUSIC Algorithm

The algorithm exploits mirror symmetry in CACC-derived signal vectors to estimate delay and Doppler using fewer basis vectors. It forms mirrored vectors, estimates the two parameter types in parallel, and tests only half-ranges.

A. Proposed Mirrored-MUSIC Algorithm

  • The side product mirrors delay and Doppler signs, but the AoA terms do not share this symmetry.This symmetry reduces the delay and Doppler estimates to L parameters each.Source: A. Proposed Mirrored-MUSIC Algorithm · p. 5
  • The algorithm adds each signal vector to its reversed version to form two types of mirrored vectors.One vector sequence is indexed across m and the other across g.Source: A. Proposed Mirrored-MUSIC Algorithm · p. 5
  • The resulting signal vectors have L basis vectors, rather than the 2L required by conventional MUSIC because of the side product.The P and Q ranges are chosen so that at least L mirrored vectors are linearly independent.Source: A. Proposed Mirrored-MUSIC Algorithm · pp. 5–6
  • Delay and Doppler are estimated in parallel from separate matrices P and Q, each formed by stacking signal vectors and decomposing the matrix with SVD.P is related to Doppler and Q to delay; the matrices have rank L.Source: A. Proposed Mirrored-MUSIC Algorithm · p. 6
  • Mirror symmetry limits Doppler and delay searches to 0–1/TA and 0–T, respectively, while retaining the same quantization interval.The Doppler interval between adjacent tests is 1/[TA(P + 1)]; delay tests use T/(Q + 1).Source: A. Proposed Mirrored-MUSIC Algorithm · p. 6

B. Pair Matching and Doppler Frequency’s Sign Determination

The initial delay and Doppler estimates are not paired by target, and Doppler signs remain unknown. The method uses CACC combining gain to iteratively pair estimates and determine each Doppler sign.

B. Pair Matching and Doppler Frequency’s Sign Determination

  • The initial estimates leave both target pairing and Doppler signs unresolved, producing 2L^2 candidate pairs.Delay is positive by default, while each Doppler estimate has two possible signs.Source: B. Pair Matching and Doppler… · p. 6
  • The method selects the Doppler-delay candidate with maximum combining gain from the CACC outputs to identify a matching pair and Doppler sign.Only one of the two opposite Doppler values matches the actual value according to the combining-gain criterion.Source: B. Pair Matching and Doppler… · p. 7
  • After selecting a pair, it removes that pair and its mirrored Doppler candidate, then repeats until all L pairs are matched.The iterative selection reduces the candidate set and determines Doppler signs alongside the delay-Doppler matches.Source: B. Pair Matching and Doppler… · p. 7

C. Performance Analysis

The analysis characterizes mirrored-MUSIC error through perturbations of the signal null space and examines computational complexity. It also identifies a reference-antenna choice that suppresses perturbation variance.

C. Performance Analysis

  • The performance analysis uses perturbation methods for Doppler estimation, with delay performance derived similarly.At high SNR, Doppler estimation error is approximated using a Newton-method analysis of the perturbed null spectrum.Source: C. Performance Analysis · p. 7
  • The CACC operation makes the entries of perturbation matrix Ψ non-independent Gaussian variables, complicating the analysis.The error analysis models the signal block as the signal of interest plus perturbations from high-pass filtering and AWGN.Source: C. Performance Analysis · p. 7
  • The section compares the computational complexity of the two algorithms in Table I.The supplied table caption identifies computational complexity as the comparison's scope.Source: Table I · p. 8
  • Fixing the reference antenna index n0 can suppress Ψ variance and improve sensing performance.The proposed choice minimizes the low-pass component of the 2D-FFT across antenna indices; the information of interest is in the high-pass components.Source: C. Performance Analysis · p. 8

D. Complexity Analysis

The complexity analysis finds that conventional MUSIC has twice the overall complexity of mirrored-MUSIC, because it requires twice as many candidates.

D. Complexity Analysis

  • Delay and Doppler frequency are estimated in parallel in Algorithm 1.The analysis focuses on Doppler frequency without loss of generality.Source: D. Complexity Analysis · p. 8
  • The main Doppler-estimation computations are an SVD of a (P+1)×(M−P) matrix and evaluation of the objective function.Other steps are described as having much lower complexity.Source: D. Complexity Analysis · p. 8
  • Conventional MUSIC has twice the overall complexity of mirrored-MUSIC because it requires a doubled number of candidates.The comparison is summarized in Table I.Source: D. Complexity Analysis · p. 8

V. HIGH RESOLUTION AOAS ESTIMATION

The proposed high-resolution AoA method combines spatial, temporal, and frequency-domain measurements. It addresses basis-vector ambiguity that can arise when target delays or Doppler frequencies are close.

V. HIGH RESOLUTION AOAS ESTIMATION

  • Combining spatial measurements with time- and frequency-domain measurements enlarges the effective spatial response for high-resolution AoA estimation.The method is intended for settings where one-shot spatial measurements are insufficient, such as a base station with few antennas.Source: §V · p. 8
  • The method assumes Algorithm 1 has already estimated delays and Doppler frequencies, leaving the integrated signal vector dependent only on NLOS AoAs.The paper states that without those estimates, the parameters are mixed together and can be difficult to obtain simultaneously.Source: §V · p. 8
  • The method forms an enlarged matrix from measurements across indices m and g, with columns combining spatial responses with frequency-domain or time-domain signals.The two columns of C′[m, g] represent spatial-plus-frequency and spatial-plus-time measurements, respectively.Source: §V · p. 9
  • The constructed matrix has rank 4L but its basis vectors correspond to only L+1 AoAs, and the known LOS AoA means positive-index basis vectors need not be tested.The positive-index vectors correspond to the known LOS AoA at the base station.Source: §V · p. 9
  • The narrowband method in does not address broadband cases where close delays or Doppler frequencies can cause lower-gain AoA estimates to be missed.Similar delay- and Doppler-associated basis vectors can respond to multiple different AoAs.Source: §V · pp. 8–9
  • Multiple objective-function peaks address basis-vector ambiguity, and the equivalent spatial dimension sets a maximum of C(N−1) detectable AoAs.When several peaks occur, the selection procedure retains one AoA using the stated comparison with already determined AoAs.Source: §V · p. 9
  • The paper derives a theoretical AoA-estimation error using a perturbation of the matrix and its null-space.The analysis writes C as Cs + Ψ′ and the null-space as a perturbed null-space.Source: §V · p. 9
  • The complexity analysis identifies the SVD of C and objective-function evaluation as main computations, with other steps having lower complexity.The SVD matrix has dimension C(N−1)×2C1.Source: §V · p. 9

VI. SIMULATION RESULTS

Simulations characterize CACC signal construction and test delay, Doppler, and AoA estimation. The proposed methods outperform the compared alternatives in delay and AoA estimation and detect multiple targets.

VI. SIMULATION RESULTS

  • The simulations use a 3 GHz carrier, 256 subcarriers, 128 MHz bandwidth, 128 preamble packets, and a four-element ULA.Unless otherwise stated, the setup has one LOS path and three NLOS paths reflected or refracted from three targets.Source: §VI · p. 10
  • The CACC spectrum contains a low-pass component without target information and mirrored high-pass side products; a high-pass filter removes the low-pass component.The side products contain target parameters with opposite signs.Source: §VI · p. 10
  • The Butterworth filter outperforms LOS-path removal for L=1 and L=3, while ξ_n[m, g] error approaches a fixed level for multiple targets.The MSE of ξ_n[m, g] reflects constructed high-pass-signal accuracy and affects subsequent sensing-parameter estimation; for L=1, it falls linearly with SNR.Source: §VI · p. 10, Figure 4 · p. 10
  • The proposed mirrored-MUSIC achieves lower delay NMSE than AMS and conventional MUSIC, and its simulated NMSE closely matches theory.An error floor remains for mirrored-MUSIC and conventional MUSIC because of error in ξ_n[m, g]; larger bandwidth can improve delay performance.Source: Figure 5 · p. 10, §VI · p. 11
  • For 3–10 targets, mirrored-MUSIC yields much lower delay NMSE than conventional MUSIC and AMS; at one target, their NMSEs are nearly equal.NMSE rises as target count increases, with a declining growth rate as delays become closer and separable into groups.Source: §VI · p. 11
  • Detection probability rises toward one and false-alarm rate falls toward zero as SNR increases; more targets reverse both trends.Targets are counted as detected when NMSE is below 10^-3; the sum of detection probability and false-alarm rate is below one because a target may have multiple estimates.Source: §VI · p. 11, Figure 7 · p. 11
  • The proposed AoA algorithm outperforms H-MUSIC and H-ESPRIT, with simulated RMSE matching theoretical values.It combines spatial, temporal, and frequency measurements; the comparison simplifies the hybrid-array methods to one receiving antenna per array.Source: §VI · pp. 11–12, Figure 8 · p. 11

VII. CONCLUSION

The paper concludes that its uplink scheme supports high-accuracy sensing with asynchronous transceivers and few receiving antennas. It also identifies possible extensions of its algorithms to other signal-analysis problems.

VII. CONCLUSION

  • The proposed scheme combines CACC, mirrored-MUSIC, and multi-domain AoA estimation for uplink sensing with asynchronous transceivers and few receiving antennas.The conclusion reports accurate multiple-target detection and performance above the state of the art, with little infrastructure modification and no need for advanced hardware such as full-duplex transceivers.Source: §VII · p. 12
  • Mirrored-MUSIC may extend to mirrored-signal problems such as harmonic retrieval, while the AoA method may extend to similar multi-domain measurement problems.The mirrored-MUSIC idea may also extend to ESPRIT and the matrix pencil method.Source: §VII · p. 12

APPENDIX A PROOF OF THEOREM 1

The appendices characterize CACC components and estimation error, derive the variance terms used to select a receiving antenna, and analyze the basis vectors used in (30).

APPENDIX A PROOF OF THEOREM 1

  • The proof distinguishes integer m′ and g′ from continuous ωf and ωτ values in [−π, π], while the variant component’s 2D-FFT is impulsive but much weaker than other components.The variant component is therefore described as negligible.Source: Appendix A · p. 12

APPENDIX B THE ERROR OF ξn[m, g]

  • Without the noise term, ξn[m, g] error is mainly due to the variant part of ˜ρ(2)n[m, g]; invariant components can be largely suppressed by high-pass filtering.Source: Appendix B · p. 12
  • AMS yields larger ξn[m, g] errors than the method in (8), with errors up to ρ(2)n[m, g] and additional error from approximating Dn[m, g] and In[m, g].AMS assumes |α0| ≫ |αl| and estimates Dn[m, g] as the mean of yn[m, g].Source: Appendix B · pp. 12–13

APPENDIX C THE VARIANCE OF Ψ

  • The variance analysis selects receiving antenna index n0 to minimize δn0, which minimizes the variance of each entry of Ψ.The variance expression includes interference after high-pass filtering and a noise term after CACC.Source: Appendix C · p. 13

APPENDIX D PROOF OF (30)

  • For (30), the basis vectors across g acquire phase shifts set by ¯τl′; the second column uses the corresponding expression with ¯fD replacing ¯τ.Source: Appendix D · p. 13
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