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Joint Transmit and Receive Beamforming Design in Full-Duplex Integrated Sensing and Communications

Ziang Liu, Sundar Aditya, Hongyu Li, Bruno Clerckx

arXiv:2210.10904v2eess.SP

TL;DR

In mono-static ISAC, transmitter self-interference can drown radar echoes because communication frames are much longer than echo round-trip times. This paper jointly optimizes transceiver and user beamformers for communication, sensing, and SI suppression. Simulations report up to 60 dB residual-SI cancellation, along with better communication sum-rates and radar parameter estimation than the NSP method.

  • Problem

    In mono-static ISAC, transmitter SI can saturate the receiver or mask radar echoes because communication frames are typically much longer than echo round-trip times.

    Source: §I · p. 1

  • Method

    The paper jointly designs transceiver TX-RX beamformers, an uplink-user precoder, and a downlink-user combiner to optimize communication rates and radar beampattern power while penalizing residual SI.

    Source: §I · p. 2

  • Results

    Simulations show up to 60 dB residual SI suppression, with better uplink and downlink sum-rates and radar range-velocity and AoA estimation than the NSP method –[30].

    Source: §I · p. 3

  • Takeaways & Limitations

    The proposed design simultaneously addresses residual-SI suppression, communication rates, and transmit and receive radar beampattern power in FD ISAC.

    Source: §VI · p. 12

Abstract

from arXiv · show

Integrated sensing and communication (ISAC) has been envisioned as a solution to realize the sensing capability required for emerging applications in wireless networks, while efficiently utilizing the available spectral, hardware and energy resources. A commonly studied scenario in the ISAC literature involves a transceiver (e.g., a base station) serving a communication user, while simultaneously sensing targets from the reflected echo signals, by acting as a mono-static radar. However, as signal transmission durations are typically much longer than the radar echo round-trip times, the radar returns are drowned by the strong self interference (SI) from the transmitter - a phenomenon termed the echo-miss problem. A promising approach involves the ISAC transceiver to be full-duplex (FD), and in this paper we jointly design the transmit and receive beamformers at the transceiver, transmit precoder at the uplink user, and receive combiner at the downlink user to simultaneously (a) maximize the uplink and downlink rate, (b) maximize the transmit and receive radar beampattern power at the target, and (c) suppress the residual SI. Numerical results illustrate that the proposed design can effectively achieve up to 60 dB digital-domain SI cancellation, a higher average sum-rate, and more accurate radar parameter estimation compared with previous ISAC FD studies.

I. INTRODUCTION

In mono-static ISAC, transmitter leakage can mask radar echoes because communication frames are much longer than echo round-trip times. The paper models this echo-miss problem and jointly designs transmit and receive beamformers, user precoders, and a downlink combiner to balance communication, sensing, and residual-SI suppression.

I. INTRODUCTION

  • Communication frames can greatly exceed radar echo round-trip times, allowing transmitter SI to saturate the receiver or mask echoes even without ADC clipping—the echo-miss problem.For targets 100–1000 m away, the paper gives 1–10 μs echo RTTs versus a 10 ms 5G NR frame.Source: §I · p. 1
  • Unlike conventional SI cancellation that relies on SI and signal-of-interest uncorrelatedness, ISAC must suppress SI without distorting correlated radar echoes and uplink data.The paper identifies time-of-arrival and spatial angle-of-arrival differences as possible ways to distinguish SI from the signal of interest.Source: §I · p. 2
  • The paper jointly optimizes transceiver TX-RX beamformers, the uplink-user precoder, and the downlink-user combiner for both communication rates, radar beampattern power, and residual-SI suppression.Its objective includes post-beamforming SI residual as a penalty term.Source: §I · p. 2
  • Up to 60 dB of residual SI is suppressed, with better uplink and downlink sum-rates and radar range-velocity and AoA estimation than the NSP method –[30].The reported validation is by simulation.Source: §I · p. 3

A. Signal Model

  • The signal model assumes sufficient propagation- and analog-domain cancellation to avoid clipping, then designs beamformers to suppress residual SI while amplifying uplink symbols and radar returns.The downlink combiner estimates the downlink symbol; the transceiver receive beamformer filters its received signal to estimate the uplink symbol.Source: A. Signal Model · pp. 3–4
  • A common dual-functional transmit signal and beamformer avoid separate radar and communication beamformers, whose power allocation is not straightforward under a fixed transmit-power budget.With separate signals, residual SI would also need to be suppressed twice.Source: A. Signal Model · p. 4

B. Channel Model

The communication channels are modeled with large- and small-scale fading, using a Rician model for the small-scale component. Its line-of-sight component is represented using steering vectors for the link’s arrival and departure angles.

B. Channel Model

  • The uplink and downlink communication channels include large-scale fading and small-scale fading, with the latter modeled using a Rician fading matrix.The passage illustrates the model using the uplink channel.Source: 1) Communication Channel · p. 4
  • The Rician factor κ captures the proportion of direct-path (LoS) energy relative to scattered-path (NLoS) energy.Source: 1) Communication Channel · p. 4
  • Assuming antenna-array size is negligible relative to transceiver-user distance, the LoS channel component uses steering vectors for the transceiver’s AoA and the uplink user’s AoD.Source: 1) Communication Channel · p. 4

2) Radar Channel:

The radar channel assumes track-mode operation with a slowly varying mono-static echo channel; the paper also models residual digital self-interference and defines uplink and downlink rates. The downlink-rate model omits uplink interference under an assumed scheduling mechanism.

2) Radar Channel:

  • The radar channel uses a track model with an initial target-AoA estimate and assumes the mono-static transceiver’s radar channel varies slowly.The echo carries target AoA, range, and velocity information; mono-static operation makes AoA and AoD equal to θr.Source: 2) Radar Channel · p. 4
  • The radar attenuation factor includes round-trip path loss and radar cross-section, while Doppler frequency is fd = 2vfc/c.fc is the carrier frequency and c is the speed of light.Source: 2) Radar Channel · p. 4

3) Self-Interference Channel:

  • The analysis focuses on residual digital-domain SI, assuming effective analog cancellation prevents receive-chain ADC saturation.The SI channel may be obtained using classic estimation algorithms or machine-learning-based methods; the illustrative model is derived from experiments and has LoS and NLoS components.Source: 3) Self-Interference Channel · p. 4

1) Communication Rate:

  • The uplink rate is defined using the uplink SINR, while downlink rate ignores uplink interference under the assumption that scheduling manages it effectively.The passages introduce the uplink rate and SINR and state the corresponding scheduling assumption for the downlink rate.Source: 1) Communication Rate · pp. 4–5

2) Radar Beampattern Power:

The design uses transmit and receive beampattern power in the target direction as radar metrics and jointly optimizes them with communication rates under power and SI constraints. The resulting problem is difficult because of coupled variables and non-convex objective terms, motivating an iterative feasible-solution transformation.

2) Radar Beampattern Power:

  • Target-direction transmit and receive beampattern powers serve as proxies for radar SINR, enabling closed-form solutions for key subproblems that help Algorithm 1 converge faster.The paper notes that radar SINR’s fractional form is non-convex and difficult to bound, whereas beampattern power is tractable.Source: 2) Radar Beampattern Power · p. 5

3) Objective Function and Constraints:

  • The objective jointly weights uplink and downlink rates and target-direction transmit and receive beampattern powers, subject to transmit-power, receive-norm, and SI-suppression constraints.The SI constraint is w^H H_si p = 0; the receive constraint is ∥w∥2 = 1.Source: 3) Objective Function and Constraints · p. 5

A. Problem Transformation

  • Coupled beamformers, non-convex rate terms, and quadratic beampattern metrics make the optimization difficult; the paper transforms it for iterative solution with guaranteed convergence to a feasible solution.The transformation draws on PDD, weighted MMSE, and a reformulation of quadratic beampattern power.Source: 3) Objective Function and Constraints · p. 5, A. Problem Transformation · p. 5

1) Coupling Constraint Transformation by Penalty Term:

The transformation penalizes residual SI coupling, recasts communication rates through the rate–MSE relationship, and approximates beampattern powers with concave forms. These steps address the stated coupling and non-convexity difficulties in the joint design.

1) Coupling Constraint Transformation by Penalty Term:

  • The coupled SI constraint is replaced by a penalty term whose parameter β controls digital SI-suppression intensity, with lower β prioritizing SI suppression over communication and sensing performance.The penalty added to the objective is 1/(2β)∥w^H H_si p∥2^2.Source: 1) Coupling Constraint Transformation… · p. 5

2) Communication Rate Transformation by WMMSE Method:

  • The WMMSE method reformulates the uplink and downlink rate terms using the equivalence between rate and MSE matrix, with auxiliary variables ρu and ρd.The transformed objective is based on the rate-WMMSE relationship.Source: 2) Communication Rate Transformation… · p. 5

3) Beampattern Power Transformation:

  • The transmit beampattern power is approximated by a concave quadratic form, with equality in the bound when p reaches its transmit-power limit.The construction uses Zt(θr) = b(θr)b^H(θr) − VtI and drops the constant VtPd; the receive-power reformulation analogously uses Vr and equality when ∥w∥2 = 1.Source: 3) Beampattern Power Transformation · p. 6

B. Penalty-based Block Update Algorithm

The penalty-based block coordinate descent algorithm iteratively updates the design variables while holding the remaining blocks fixed. The supplied update steps use closed-form or convex subproblems, with bisection searches for the user precoder and transceiver beamformer updates.

B. Penalty-based Block Update Algorithm

6) Summary:

Algorithm 1 uses penalty-based block coordinate descent (BCD) updates and normalizes the receive beamformer after convergence. The formulation balances SI suppression, communications, and sensing while permitting closed-form BCD steps.

6) Summary:

  • Algorithm 1 iteratively updates the optimized variables by BCD and normalizes the receive beamformer after convergence to satisfy its power constraint.The updates use suitable initial values and stop when the objective converges.Source: 6) Summary · p. 7
  • The adopted SI constraint reflects that radar returns are weak and strongly correlated with residual SI, while enforcing stronger suppression can hurt communications and sensing.The paper presents its approach as a compromise between SI suppression and those performance costs.Source: 6) Summary · p. 7
  • The algorithm omits PDD’s outer loop because sufficiently small β can reduce residual SI below a suitable threshold without needless suppression.Further suppression would reduce communications and sensing performance and slow convergence.Source: 6) Summary · p. 7
  • The formulation permits closed-form solutions for each BCD step, unlike a radar-performance constraint formulation that would make such solutions difficult.Sensing can instead receive greater weight through α3 and α4.Source: 6) Summary · pp. 7–8
  • For K < min(Nt, Nr) downlink users, the design can extend to a multi-user scenario with a non-trivial nullspace for HsiP.This permits a nonzero receive beamformer w such that wᴴHsiP = 0.Source: 6) Summary · p. 8

C. Algorithm Implementation

The paper uses a centralized implementation of Algorithm 1, which requires sharing channel and target-direction information and distributing optimized variables. Decentralized implementation and alternative update orderings are left for future work.

C. Algorithm Implementation

  • Centralized execution requires channel state information and target direction at a controller, then distributes optimized variables to the transceiver and users.Decentralized implementation and alternative variable orderings or update rates are left for future work.Source: C. Algorithm Implementation · p. 8

A. Convergence Analysis

The convergence analysis shows that Algorithm 1’s objective is nondecreasing across BCD updates and bounded above, establishing convergence to at least a local optimum. Simulations also show convergence within a small number of iterations.

A. Convergence Analysis

  • The proof analyzes the original objective through a reformulation based on the rate-WMMSE relationship.The auxiliary variables are optimized with the other variables fixed in the reformulated objective.Source: A. Convergence Analysis · p. 8
  • The objective in (17a) is nondecreasing after each BCD update and bounded above, so Algorithm 1 converges to at least a local optimum.The upper bound follows from bounded rates and beampattern gains when both beamformers probe the target direction.Source: A. Convergence Analysis · p. 8
  • The simulated objective converges within a small number of iterations for different antenna counts and SI power levels.Fig. 2 plots objective and relative difference against iteration count; ζ ≤ ϵ is the stopping criterion.Source: A. Convergence Analysis · p. 8

B. Complexity Analysis

Algorithm 1 has polynomial complexity, and simulations evaluate SI cancellation, signal-of-interest preservation, and beampatterns. Across the reported settings, the design suppresses SI below the noise floor and shifts beam focus with the communications-versus-radar priority.

B. Complexity Analysis

  • Algorithm 1 has polynomial complexity, with step 8—the update of p—identified as the bottleneck under the stated antenna-dimension assumptions.The complexity expression is supplied in the passage, but its symbols are not fully recoverable here.Source: B. Complexity Analysis · p. 8

V. NUMERICAL EVALUATION

  • The evaluation uses 1000 Monte Carlo runs with perfect CSI and a 16-antenna transceiver, with SI power ranging from 10 to 60 dB above the noise floor.The simulated target is at (45°, 7.5 m, 20 m/s); uplink and downlink users have two antennas each.Source: §V · pp. 8–9

A. SI Power After Cancellation

  • Residual SI stays below the noise floor for SI power up to 60 dB as the priority parameter ϱ varies from 1 to 1000.Fig. 3 compares cancellation across priority and SI levels, with residual SI measured relative to the noise floor.Source: A. SI Power After Cancellation · p. 9, Figure 3 · p. 9
  • A positive SoI-over-SI power ratio indicates that radar echoes and uplink data are not drowned by SI; increasing ϱ raises that ratio as SI cancellation improves.The passage also reports that SI cancellation degrades as SI power increases.Source: A. SI Power After Cancellation · p. 9, Figure 4 · p. 9

B. Beampattern Power Performance

  • With 60 dB SI cancellation, increasing ϱ shifts transmit and receive beam focus toward communication users, while ϱ = 0.01 prioritizes the target.The plotted cases use ϱ = 1, 100, and 0.01; residual SI is −130.97, −197.37, and −108.48 dB, respectively.Source: B. Beampattern Power Performance · pp. 9–10, Figure 5 · p. 10

C. Sum-rate Performance

The joint design suppresses residual SI and supports communication and radar objectives, with reported gains in sum-rate and sensing performance. The section compares sum-rate across SI levels and evaluates range-velocity and angle sensing against alternative methods.

C. Sum-rate Performance

  • As SI power increases, sum-rate per unit time-frequency resource first falls and then flattens; increasing ϱ raises sum-rate, with FD communication and HD providing upper and lower bounds.The half-duplex comparison uses equal uplink and downlink resource allocation (δ = 0.5).Source: C. Sum-rate Performance · pp. 10–11, Figure 7 · p. 10

D. Sensing Performance

  • The proposed method suppresses residual SI in range-velocity sensing, whereas radar-only and communication-only methods leave SI interference that drowns the desired echo.The interference appears near the original point, at v = 0 m/s and r = 0 m.Source: D. Sensing Performance · p. 11, Figure 8 · p. 11
  • For angle sensing, the proposed method retains near-target output power comparable to radar-only and communication-only methods while producing less interference than NSP, especially near 0°.Its target-direction output power is close to radar-only, and its output power is similar to communication-only.Source: D. Sensing Performance · p. 11, Figure 9 · p. 11

VI. CONCLUSION

  • Up to 60 dB residual SI is suppressed digitally, and the design yields more accurate range, velocity, and angle estimates while outperforming NSP.The design jointly optimizes transceiver transmit and receive beamformers, the uplink precoder, and the downlink combiner using a BCD method.Source: §VI · p. 12

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