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Robust MIMO Beamforming for Cellular and Radar Coexistence
Fan Liu, Christos Masouros, Ang Li, Tharmalingam Ratnarajah
TL;DR
The paper addresses radar–communication spectrum sharing by designing downlink MU-MIMO beamforming that preserves communication requirements while improving radar detection. It replaces the non-convex objective with a lower-bound optimization and extends the design to imperfect CSI. Simulations show a radar–communication performance trade-off and validate the approach under perfect and imperfect CSI.
Problem
Spectrum sharing requires coordinating downlink MU-MIMO communication with colocated MIMO radar while maintaining communication performance and radar detection capability.
Method
The paper maximizes radar detection probability under user-SINR and base-station power constraints, using a monotonicity-based lower bound and robust upper-bound or weighted minimization for CSI errors.
Results
Simulations validate the proposed beamforming approach for coexistence under both perfect and imperfect CSI and reveal a trade-off between radar and communication performance.
Takeaways & Limitations
The proposed beamformer facilitates coexistence by optimizing radar performance for a target communication SINR and transmit-power budget while accounting for CSI errors.
Abstract
from arXiv · showhide
In this letter, we consider the coexistence and spectrum sharing between downlink multi-user multiple-input-multiple-output (MU-MIMO) communication and a MIMO radar. For a given performance requirement of the downlink communication system, we design the transmit beamforming such that the detection probability of the radar is maximized. While the original optimization problem is non-convex, we exploit the monotonically increasing relationship of the detection probability with the non-centrality parameter of the resulting probability distribution to obtain a convex lower-bound optimization. The proposed beamformer is designed to be robust to imperfect channel state information (CSI). Simulation results verify that the proposed approach facilitates the coexistence between radar and communication links, and illustrates a scalable trade-off between the two systems' performance.
I. INTRODUCTION
Spectrum sharing is motivated by pressure to access spectrum used by radar systems, while prior coexistence methods include opportunistic sharing, null-space projection, and optimization-based designs. This letter designs beamforming that maximizes radar detection probability under communication and power constraints, including imperfect CSI.
- Spectrum sharing is studied as an enabling solution because additional spectrum is sought from bands occupied by air-surveillance and weather-radar systems.
- Prior MIMO radar–communication coexistence methods include Null Space Projection and optimization subject to power, capacity, or communication constraints.
- The proposed beamforming maximizes radar detection probability while guaranteeing each downlink user's SINR and the base station's transmit-power budget.
- The design handles imperfect communication and interference CSI through two optimization approaches transformed into semidefinite programs and solved using semidefinite relaxation.
II. SYSTEM MODEL
The system is a TDD downlink MU-MIMO link sharing a frequency band with a colocated MIMO radar. The model specifies communication and radar signals, channel assumptions, radar detection, and the interference affecting users and radar.
- An N-antenna base station serves K single-antenna users while a MIMO radar with M_t transmit and M_r receive antennas operates on the same frequency band.
- The user signal model includes communication channels, radar interference channels, beamforming vectors, symbols, and receiver noise over L symbol snapshots.
- Radar transmit and receive steering vectors describe the target response, with the model specializing to M_r = M_t = M and a_R(θ) = a_T(θ) = a(θ).
- The channels H, F, and G are modeled as mutually independent flat Rayleigh-fading channels estimated by the base station from pilot symbols.
- In typical TDD downlink operation, users remain silent during base-station transmission, so the radar receives interference from the base station.
- Under the Neyman–Pearson criterion and GLRT, radar detection probability depends on a non-central chi-square distribution, while base-station interference affects radar detection.
III. PROPOSED BEAMFORMING OPTIMIZATION
The optimization maximizes radar detection performance subject to per-user SINR and base-station power constraints. It first treats perfect CSI, then introduces upper-bound and weighted minimization approaches for norm-bounded CSI errors.
- The design objective is to maximize radar detection performance while satisfying every user's received SINR requirement and the base station's transmit-power budget.
- The formulation is developed first for perfect CSI and then extended using upper-bound minimization and weighted minimization with norm-bounded CSI errors.
A. Beamforming for Perfect CSI
For perfect CSI, the radar-detection optimization is relaxed because its objective is non-concave. Monotonicity of detection probability in the non-centrality parameter yields a lower-bound formulation that can be solved efficiently using semidefinite relaxation.
- The perfect-CSI problem imposes each user's required SINR and the base station's power budget while optimizing radar detection performance.
- The detection-probability derivation remains applicable after whitening the interference-plus-noise covariance, which is nonidentity under the proposed model.
- Because radar detection probability increases monotonically with the non-centrality parameter ρ, the objective can be reformulated in terms of ρ.
- The non-concave objective is replaced by a lower-bound relaxation based on positive-definite interference and radar-response matrices.
- The relaxed problem remains non-convex but is equivalent to minimizing total base-station interference power at the radar and can be solved using semidefinite relaxation.
B. Upper Bound Minimization for Imperfect CSI
The paper models CSI uncertainty with norm-bounded errors and uses worst-case interference constraints to obtain a robust upper-bound minimization problem. Dropping the rank constraint converts the resulting formulation into an SDP solvable by SDR.
- CSI uncertainty: CSI is represented as estimated channel vectors plus error vectors constrained within spherical uncertainty sets.The uncertainty model reflects quantization and feedback errors, with the base station knowing only error-norm bounds.
- Upper-bound formulation: The method upper-bounds each radar antenna’s interference power when the interference channel is only partially known.The total interference objective is then optimized using these bounds.
- Robust communication constraints: Worst-case constraints bound radar-to-user interference under uncertainty in the communication and radar interference channels.The formulation uses the triangle inequality and the S-procedure to enforce robustness.
- Solution method: Dropping the rank constraint transforms the non-convex formulation into a standard semidefinite program solvable by semidefinite relaxation.This provides the computational route for the upper-bound minimization design.
C. Weighted Minimization for Imperfect CSI
Weighted minimization interpolates between minimizing actual interference with known channels and minimizing transmit power with unknown channels. Its weighting increases with CSI uncertainty, while upper-bound minimization is a special case.
- Motivation: Upper-bound minimization may avoid strong interference yet perform poorly across realizations of the interference channel G.This motivates weighting the interference and transmit-power terms according to channel knowledge.
- Weighted formulation: The weighted formulation combines estimated interference power with uncertainty determined by the norm bound δ_gm.The same constraints as P3 are retained.
- Weight selection: The weight function φ(δ_g1, ..., δ_gm) increases with the error bounds, so greater uncertainty places more emphasis on transmit-power minimization.This interpolates between the partially known, perfectly known, and unknown interference-channel cases.
- Numerical comparison: Figure 2 compares average detection probability against SINR level and radar SNR for different beamformers and CSI conditions.The SINR plot fixes δ2 = 2 × 10^-3, P0 = 32dBm, and P_FA = 10^-5; the radar-SNR plot fixes Γ = 20dB with the same δ2 and P_FA.
IV. NUMERICAL RESULTS
Monte Carlo simulations evaluate the proposed designs under complex Gaussian channels, a ULA radar, and common uncertainty settings. The results show a radar–communication trade-off and favorable performance for robust and weighted designs.
- Simulation setup: The simulations use standard complex Gaussian channel entries, a unit-power ULA radar, and common uncertainty bounds across channels.The main settings are N = 8, K = 4, M = 4, δ2 = 2 × 10^-3, and P_FA = 10^-5.
- Detection-performance trade-off: Detection probability decreases as the communication SINR requirement Γ increases, exposing a trade-off between radar and downlink communication performance.Robust H + F and weighted minimization remain close to the perfect-CSI detection performance, whereas upper-bound minimization suffers a significant loss when δ is small.
- Power budget: Larger P0 produces higher detection probability for the proposed methods because the feasible domain is extended.The comparison is reported for the radar-SNR experiments with Γ = 20dB.
V. CONCLUSION
The paper introduces beamforming for MU-MIMO communication and MIMO-radar coexistence while optimizing radar performance under communication SINR and base-station power constraints. Robust upper-bound and weighted minimization address CSI errors, and simulations reveal the radar–communication trade-off.
- Conclusion: The proposed beamformer maximizes radar performance for a target communication SINR and base-station transmit-power budget.The design is intended to facilitate coexistence between downlink MU-MIMO communication and MIMO radar.
- Conclusion: Upper-bound and weighted minimization make the optimization robust to CSI errors.Numerical simulations evaluate both the coexistence trade-off and the effectiveness of the proposed approach.