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Foundations of MIMO Radar Detection Aided by Reconfigurable Intelligent Surfaces
Stefano Buzzi, Emanuele Grossi, Marco Lops, Luca Venturino
TL;DR
The paper addresses target detection in RIS-aided MIMO radar across monostatic, bistatic, LOS, and NLOS configurations. It develops a general signal model and GLRT-based phase-shift design, then analyzes how deployment conditions affect detection. The key result is that RISs are most beneficial when placed near the radar transmit and receive arrays.
Problem
The paper studies under which conditions RISs can improve MIMO-radar target detection across configurations with different direct and RIS-assisted paths.
Method
The paper derives a general multipath signal model, a GLRT receiver, and phase-shift optimization that maximizes detection probability at fixed false-alarm probability.
Results
Near-field radar-RIS deployment yields large performance gains, while far-field deployment offers only marginal gains; gains nearly double when both RISs view the target.
Takeaways & Limitations
RISs should be placed as close as possible to the radar transmitter and receiver to limit indirect-link path loss and improve detection performance.
Abstract
from arXiv · showhide
A reconfigurable intelligent surface (RIS) is a nearly-passive flat layer made of inexpensive elements that can add a tunable phase shift to the impinging electromagnetic wave and are controlled by a low-power electronic circuit. This paper considers the fundamental problem of target detection in a RIS-aided multiple-input multiple-output (MIMO) radar. At first, a general signal model is introduced, which includes the possibility of using up to two RISs (one close to the radar transmitter and one close to the radar receiver) and subsumes both a monostatic and a bistatic radar configuration with or without a line-of-sight view of the prospective target. Upon resorting to a generalized likelihood ratio test (GLRT), the design of the phase shifts introduced by the RIS elements is formulated as the maximization of the probability of detection in the location under inspection for a fixed probability of false alarm, and suitable optimization algorithms are proposed. The performance analysis shows the benefits granted by the presence of the RISs and shed light on the interplay among the key system parameters, such as the radar-RIS distance, the RIS size, and location of the prospective target. A major finding is that the RISs should be better deployed in the near-field of the radar arrays at both the transmit and the receive side. The paper is concluded by discussing some open problems and foreseen applications.
I. INTRODUCTION
The paper develops RIS-aided MIMO-radar target detection across monostatic, bistatic, LOS, and NLOS configurations. It models RIS phase-shift design through GLRT-based detection optimization and finds that near-field deployment offers the strongest gains.
- I. INTRODUCTION: RISs are nearly-passive, low-cost planar structures whose individually controlled elements redirect incident waves without amplification.Their focusing mechanism resembles a phased array while avoiding radio-frequency amplification chains, processing delay, and added noise.
- A. Contribution and paper structure: The paper studies how RIS placement can boost MIMO-radar detection while preserving wide-sector illumination and receive-side focusing.It emphasizes the dependence of redirected-wave coverage on incident power and the radar-RIS distance.
- A. Contribution and paper structure: The proposed signal model covers monostatic and bistatic radar, LOS and NLOS operation, and up to four transmitter-target-receiver paths using up to two RISs.The forward RIS assists target illumination, while the backward RIS assists echo capture.
- A. Contribution and paper structure: The GLRT-based design maximizes detection probability for a fixed false-alarm probability, with forward and backward RIS phase shifts optimized independently.Closed-form phase shifts are available when the radar-RIS links are in the far field; near-field cases require optimization algorithms.
- A. Contribution and paper structure: Far-field radar-RIS deployment provides only a marginal gain, whereas near-field deployment can produce a large performance gain.The analysis varies radar-RIS distance, RIS size, and inspected-target location; gains nearly double when both RISs view the target compared with one surface.
A. Geometric parameters
The geometric model describes planar transmit, receive, and RIS arrays in a Cartesian reference system, together with path lengths and angular parameters. Its assumptions retain wavefront curvature on radar-RIS hops while using far-field approximations for target-related hops.
- A. Geometric parameters: Transmit, receive, and reflecting arrays lie on the (y, z)-plane, with elements oriented toward the positive x-axis.Azimuth and elevation are defined relative to the local Cartesian reference system.
- A. Geometric parameters: The model specifies target range and azimuth/elevation angles from the radar transmitter and forward RIS reference elements.It also defines path length and departure/arrival angles between radar-transmitter and forward-RIS elements.
- A. Geometric parameters: The same geometric quantities are defined at the receive side, using modified notation for the receiver and backward RIS.The parameters are summarized in Figure 1.
- B. Design assumptions: The assumptions include narrowband waveforms, uncoupled array elements, and LOS propagation on radar-RIS, radar-target, and RIS-target hops.Narrowband operation makes target-echo delays unresolvable.
- B. Design assumptions: Radar-RIS links may be near-field, so phase curvature is retained there, while radar-target and RIS-target links are assumed far-field and their phase curvature is neglected.The target is also assumed to see the radar array and RIS in the far field, with a shared aspect-angle condition when both illuminate or observe it.
C. Received signal
After range gating and matched filtering, the received data are modeled as a known target signature scaled by an unknown response plus Gaussian noise. The signature combines direct and RIS-assisted paths through tunable forward and backward phase shifts.
- C. Received signal: Range gating projects each receive-element signal onto delayed transmit waveforms, producing vectorized samples for the inspected resolution cell.The delay is tied to the cell’s distance from the transmitter and receiver.
- C. Received signal: The received vector follows r = eα + w, where e is the known target signature, α is the unknown target response, and w is additive Gaussian noise.The signature depends on target location, system geometry, and RIS phase shifts.
- C. Received signal: The target signature contains up to four transmitter-target-receiver paths and up to two RIS bounces.Unit-modulus vectors specify the tunable phase shifts of the forward and backward RIS elements.
- C. Received signal: The scalar and matrix channels encode element gains, reflecting-element RCS, path loss, and phase delay for direct and RIS-assisted links.Absent RISs are represented by zero indirect-channel coefficients and channel matrices.
- C. Received signal: The transmit and receive target signatures superpose direct and indirect steering vectors weighted by their corresponding direct and two-hop channel coefficients.The resulting full signature has a Kronecker structure.
D. Channel model
The channel model separates RIS-assisted propagation into scalar reference channels, normalized radar-RIS matrices, and element-level bistatic RCS. It is designed to support the detection methodology across channel models satisfying the received-signal representation.
- D. Channel model: The proposed design methodology is independent of the adopted radar-target and radar-RIS-target channel models when the received signal retains the specified form.The paper notes that exact RIS-assisted channel modeling remains non-trivial and debated.
- D. Channel model: Scalar channels are modeled using radar-equation quantities including transmit/receive element gains, RIS-element bistatic RCS, and path-loss factors.Additional loss factors account for attenuation along the corresponding paths.
- D. Channel model: Normalized channel matrices describe radar-transmitter-to-forward-RIS and backward-RIS-to-radar-receiver links relative to reference-element scalar channels.Their entries incorporate gain, bistatic RCS, path loss, and phase delay.
- D. Channel model: Each RIS element’s bistatic RCS is modeled through effective aperture and transmit-gain terms with cosine-shaped scan loss in azimuth and elevation.The model treats the RIS as reciprocal and sets the RCS to zero outside the stated angular range.
III. SYSTEM DESIGN
The receiver uses a GLRT for target presence and selects RIS phase shifts and a receive filter to maximize SNR, thereby maximizing detection probability for a fixed false-alarm probability.
- Detection receiver: The GLRT distinguishes target presence from absence using a detection threshold selected for the desired probability of false alarm.The threshold satisfies Pfa = e^−η.
- Detection receiver: The receive filter and RIS phase shifts are jointly selected to maximize SNR at the inspected location and detection probability.For fixed RIS phases, the optimal receive filter is matched to the signal to be detected.
- RIS design: The indirect steering vectors are modified to create constructive alignment among RIS-reflected and direct signals during target illumination and observation.This passive beamforming mechanism provides SNR gains at both the transmit and receive sides.
- RIS design: RIS phase-shift design maximizes the forward and backward reflected-signal norms under unit-modulus constraints on every RIS element.The forward and backward designs are expressed as separate constrained optimization problems.
A. Optimization of the phase shifts of the RIS
The phase-shift problems are optimized using closed-form solutions in rank-one cases and iterative or relaxed methods when the associated quadratic program is more general.
- Closed-form solution: When rank(Q̄) = 1, the unit-modulus phase-shift problem has a closed-form solution based on factorizing Q̄ as āb̄^T.This case occurs when the radar transmitter and forward RIS are mutually far-field, or when one array has a single element.
- General case: For rank(Q̄) > 1, the phase-shift design becomes a strongly NP-hard complex quadratic program.The formulation introduces a positive-semidefinite matrix before applying solution procedures.
- General case: Alternate maximization updates one unit-modulus entry at a time and guarantees convergence because the bounded objective increases monotonically.Its complexity is O(N̄_s^2) per iteration after an initial O(N̄_s^3) cost.
- General case: The randomized method provides a π/4-approximation in expectation, with the same ratio holding with exponentially increasing probability as sample count grows.Its complexity depends on the method used to solve the relaxed problem and includes matrix-square-root evaluation.
B. Far-field deployment of the RISs
Far-field RIS deployment enables simplified plane-wave analysis but generally provides only marginal SNR gains when a direct path exists, because two-hop attenuation dominates.
- Far-field model: In the mutual far-field configuration, radar-RIS channels are approximated as plane waves and the corresponding channel matrices simplify to rank-one forms.The steering vectors describe the radar-to-RIS and RIS-to-radar geometry.
- Performance implication: When the direct path is present, additional far-field RIS paths provide only a marginal SNR gain because RIS area cannot compensate for radar-RIS attenuation.This conclusion applies when γ̄_rγ̈_r ≠ 0.
- Performance implication: The forward and backward RISs should instead be placed near and as close as possible to the radar transmit and receive arrays.The paper identifies near-field deployment as the preferable configuration for significantly improving performance.
- Scope of far-field deployment: A far-field RIS can remain competitive when its indirect path reaches a location that the direct path cannot serve.The paper gives disconnected users and otherwise blind radar spots as examples despite double-fading attenuation.
C. Mono-static radar with a bi-directional RIS
For a monostatic radar using one RIS in both directions, the same phase vector can be imposed to simplify hardware, but this is optimal only under transmit–receive symmetry.
- Monostatic configuration: The monostatic configuration uses the same RIS for transmission and reception, with equal element counts, distances, angles, and RIS responses on both sides.The shared phase-vector constraint is then imposed for hardware simplification.
- Phase-shift design: The shared phase vector is optimized under unit-modulus constraints by maximizing the squared norm of the received signal response.The resulting problem is given for a single phase vector x.
- Phase-shift design: Forcing x̄ = ẍ is optimal with reciprocal RIS and identical reciprocal transmit and receive arrays, but sub-optimal under transmit–receive asymmetry.In the asymmetric case, the paper uses one-phase-at-a-time iterative optimization.
- Phase-shift design: The per-phase objective is solved numerically through zeros of a derivative containing first- and second-harmonic sine terms.The alternating procedure converges because its bounded objective increases monotonically at every iteration.
D. More insights on the radar and RIS interplay
RISs give an MIMO radar additional design freedom through programmable reflections and a modified field of view, but their operation must be chosen before transmission. The paper’s design enhances SNR at one desired location, while multiple-location steering remains an alternative criterion.
- RIS phase shifts and a modified field of view provide an RIS-aided MIMO radar with additional degrees of freedom.
- Because RIS programming precedes waveform transmission, the system engineer must determine the surfaces’ operation in advance.
- The proposed design selects both RIS phase-shift sets to enhance SNR at one desired location.
- Forward and backward RISs could instead be steered toward multiple, possibly different locations, for scenarios involving multiple targets.
IV. PERFORMANCE ANALYSIS
The performance examples evaluate an RIS-aided bistatic radar using specified optimization algorithms and repeated random initializations. The two algorithms produced similar objective-function values in the reported examples.
- Algorithms 1 and 2 are implemented with Kmax = 200, ϵ = 10^-5, and 100 random initialization points.
A. System geometry
The study uses a bistatic radar geometry with planar radar and RIS arrays and evaluates RIS-assisted SNR gains, echo contributions, bandwidth constraints, and surface-size effects as radar–RIS spacing and target placement vary.
- System geometry: The considered geometry is a 3 GHz bistatic radar with linear transmitter and receiver arrays aided by forward and/or backward RISs.
- System geometry: The arrays share a plane containing their centers and the prospective target, which is fixed at P2 or moved along P1–P3.
- SNR evaluation: The baseline comparison is radar operation alone, while RIS configurations include forward-only, backward-only, and combined forward-and-backward deployment.
- Impact of the radar-RIS distance: Closer radar–RIS arrays yield larger SNR gains, whereas gains become negligible as the arrays are separated; far-field design can be detrimental at short distances.
- RIS size: SNR gain increases with reflecting-surface size, with Fig. 6 parameterizing the comparison by √Ns.
- Impact of the radar-RIS distance: With both RISs, the Radar→RIS→Target→Radar echo exceeds Radar→Target→RIS→Radar, while the two-RIS four-hop echo dominates only at very small spacing and fades faster with distance.
- Bandwidth constraint: The maximum bandwidth preserving unresolved target-echo delays decreases as radar–RIS spacing or the number of propagation hops increases.
C. Impact of the RIS size
RIS size strongly affects the SNR gain in RIS-aided MIMO radar: larger surfaces strengthen indirect echoes, while sufficiently large near-field deployments can make RIS assistance clearly beneficial.
- RIS size and propagation regime: SNR gain increases as the reflecting surfaces get larger, but gains remain marginal while √Ns < 8 because the radar and RIS arrays are in each other’s far-field.The advantage of one or two RISs becomes evident as √Ns grows beyond this regime.
- Echo contributions: Indirect echoes become progressively stronger with RIS size and eventually dominate the direct echo when both RISs are employed.The comparison considers the four echoes and their superposition as Ns varies.
- Deployment trade-offs: A reflecting surface becomes competitive only when its size sufficiently offsets the stronger attenuation of the indirect radar-RIS path.RIS deployment is also constrained by cost and installation requirements.
- Target position: For a target moved from P1 to P3, simultaneous use of two RISs can provide substantial gains over intervals where both surfaces can illuminate or observe the target.The forward RIS is ineffective from 0–5 Km and the backward RIS from 15–20 Km in the examined geometry.
- Hardware simplification and receiver size: Equal forward and backward phase shifts incur only marginal SNR losses, while the SNR gain decreases as the number of receive elements increases.This simplifies hardware for a monostatic configuration, although a better receiver reduces the reward from a nearby RIS.