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Blind Interference Suppression in IRS-Aided Wireless Systems: A Statistical Channel Ratio Estimation Approach

Tao Wang, Xiaohui Zhang, Hehe Ban, Pengfei Lv, Yiwei Guo, Ming Yi

arXiv:2609.38845v1eess.SP

TL;DR

Non-cooperative interference is difficult to suppress with IRSs when CSI and interferer cooperation are unavailable. This paper estimates relative channel ratios from received-power measurements and uses them to optimize IRS phases; simulations report suppression within a few dB of the interference-free case, with unbiased estimation feasible for K ≥ 3.

  • Problem

    IRS interference suppression is underexplored in non-cooperative settings where the interferer provides no pilots, making conventional channel estimation infeasible.

    Source: §I · p. 2

  • Method

    The framework estimates relative reflected-to-direct interference-channel ratios from received-power measurements under random IRS configurations, then applies greedy or iterative IRS phase optimization.

    Source: §I · p. 2

  • Results

    Simulations suppress strong interference to within a few dB of the ideal interference-free case, and unbiased ratio estimation is feasible when K ≥ 3.

    Source: §I · p. 2, §VI · p. 11

  • Takeaways & Limitations

    Received-power statistics provide a CSI-free basis for configuring an IRS against non-cooperative interference.

    Source: §I · p. 2

    Unbiased estimation is impossible with binary phase shifters (K = 2); at least three phase levels are required.

    Source: §I · p. 2, C. Scalar Calibration via Iterative… · p. 6

Abstract

from arXiv · show

This paper addresses the problem of suppressing non-cooperative interference in intelligent reflecting surface (IRS)-aided wireless links without any channel state information (CSI) or cooperation from the interferer. We propose a fully blind framework that relies solely on received signal power measurements. A key insight is that nulling the aggregate interference channel requires only the complex ratios between the IRS-reflected paths and the direct interference link, rather than absolute CSI. We develop a novel estimation algorithm that obtains unbiased estimates of these channel ratios using only power samples collected under random IRS configurations. Theoretically, we prove that unbiased estimation is feasible when the number of discrete phase levels $K\geq 3$, and establish the Cramer-Rao lower bounds (CRLBs) for both the phase offset and amplitude ratio estimates, thus providing design guidance. Based on the estimated ratios, we propose two low-complexity IRS phase optimization algorithms: a one-shot greedy method and an iterative variant that mitigates error propagation from weakly reflecting elements. Simulations demonstrate that the proposed schemes can suppress strong interference to within a few dB of the interference-free upper bound, offering a practical, CSI-free solution for robust wireless communications in contested spectral environments.

I. INTRODUCTION

The introduction frames non-cooperative interference suppression as a gap in IRS research because conventional channel estimation depends on CSI or cooperation unavailable in this setting. The paper proposes using received-power statistics to estimate relative channel ratios and configure the IRS for suppression.

I. INTRODUCTION

  • Existing IRS work emphasizes enhancing desired-link SNR, while suppressing non-cooperative interference remains underexplored under discrete phase shifts and passive-element constraints.Conventional channel-estimation methods are infeasible when the interferer supplies no pilots and its symbols are random and unknown.Source: §I · p. 1
  • Prior blind and power-measurement approaches require pilots, prescribed frame structures, shared codebooks, blocked direct links, or measurements that may exceed channel coherence time.The cited power-measurement methods estimate slowly varying channel autocorrelations rather than instantaneous CSI.Source: §I · pp. 1–2
  • Relative complex ratios of reflected paths to the direct interference channel suffice to null aggregate interference, avoiding a need for absolute CSI.The proposed framework estimates these ratios from received-power measurements under random IRS configurations.Source: §I · p. 2
  • The proposed estimator obtains unbiased channel-ratio estimates from received-power measurements without CSI; unbiased estimation is impossible with K = 2 phase levels, while K = 4 is sufficient.The paper also derives Cramér–Rao lower bounds for the estimation error.Source: §I · p. 2
  • Two linear-complexity IRS phase-optimization algorithms—a greedy method and an iterative method designed to mitigate estimation-error propagation—are evaluated in simulations.The schemes suppress strong interference to within a few dB of the ideal interference-free case and outperform naive benchmarks.Source: §I · p. 2

A. Signal Model

  • The UE measures instantaneous interference power by suspending its legitimate transmission, because the unknown random interference symbol prevents estimating the composite interference channel from the interference signal alone.The signal model includes direct and IRS-reflected interference paths, with IRS phase shifts drawn from a discrete set.Source: A. Signal Model · p. 3

B. Problem Formulation

The formulation minimizes aggregate interference using discrete IRS phase shifts and received-power measurements. It relies on relative channel ratios, which can be estimated from power differences under random phase configurations.

B. Problem Formulation

  • The objective is to choose discrete IRS phases that minimize aggregate interference power using only received-power measurements.The phase of each element must belong to the discrete set ΦK.Source: B. Problem Formulation · p. 3
  • With static channels, the optimization can be expressed in terms of normalized array gain rather than the original channel coefficients.The channel coefficients are decomposed into amplitude and phase components.Source: B. Problem Formulation · p. 3
  • The ratio γn and phase offset ∆n describe the nth reflected path relative to the direct interference link.γn is the relative amplitude; ∆n is the phase difference.Source: B. Problem Formulation · p. 3
  • Nulling the aggregate interference requires only the complex ratios between reflected paths and the direct interference link, not global CSI.The ratios encode each reflected path’s relative amplitude and phase.Source: B. Problem Formulation · p. 3

III. PROPOSED ALGORITHM FOR ESTIMATING γne−j∆n

  • The estimation dataset consists of received-power samples paired with random IRS phase configurations, collected over T trials.The UE configures the IRS and measures the corresponding received power for each trial.Source: §III · p. 3
  • A pre-defined phase codebook can replace stochastic phase generation to improve sampling efficiency and reduce hardware switching latency.This is presented as a practical option for selecting configurations.Source: §III · p. 3

A. Theoretical Foundation

  • The differential statistic Jnk is the difference between conditional and unconditional expected received power for a given IRS phase state.Its theoretical relationship depends on the relative amplitude and phase to be recovered.Source: A. Theoretical Foundation · p. 4

B. Estimation via Least Squares

The estimator fits received-power differences across discrete phase states to recover channel ratios. A fixed-point calibration estimates direct-link power, while the unbiasedness result requires at least three phase levels.

B. Estimation via Least Squares

  • The empirical differential statistic subtracts the unconditional received-power mean from the conditional mean for each discrete phase state.The resulting observations are modeled as a cosine response with finite-sample noise.Source: B. Estimation via Least Squares · p. 4
  • For K ≥ 3, the least-squares estimator yields unbiased estimates of the complex channel ratios from empirical conditional-mean differences.The phase offset is obtained from the fitted coefficients, and the amplitude ratio is estimated using direct-link power calibration.Source: B. Estimation via Least Squares · p. 4, C. Scalar Calibration via Iterative… · p. 5

C. Scalar Calibration via Iterative Approximation

  • The algorithm estimates direct-link power Q by alternating amplitude-ratio updates with power-scalar updates until the relative change falls below a tolerance.This avoids relying on IRS absorption and produces an asymptotically unbiased estimate of Q.Source: C. Scalar Calibration via Iterative… · pp. 4–5
  • At K = 2, the orthogonality conditions fail, so the phase and amplitude estimates become biased and cannot be disentangled by the stated regression model.The binary phase resolution does not adequately excite the underlying sinusoidal model.Source: C. Scalar Calibration via Iterative… · pp. 5–6

D. Cramér–Rao Lower Bound Analysis

The section derives Cramér–Rao lower bounds for estimating phase difference and channel amplitude ratio, showing how system parameters affect estimation accuracy.

D. Cramér–Rao Lower Bound Analysis

  • The analysis derives CRLBs for phase-difference and channel-amplitude-ratio estimates to characterize fundamental estimation accuracy limits.The bounds indicate how key system parameters affect estimation performance.Source: D. Cramér–Rao Lower Bound Analysis · p. 6

1) CRLB Expressions:

The CRLB expressions depend on the interference-symbol distribution, with separate cases considered for constant-modulus and complex Gaussian interference.

1) CRLB Expressions:

  • The CRLBs are evaluated for constant-modulus and complex Gaussian interference symbols, and the expressions are simplified in the high-INR regime.For constant-modulus interference, the supplied expressions are for the phase-offset and amplitude-ratio estimates.Source: 1) CRLB Expressions · p. 6

2) Impact of System Parameters:

The CRLB analysis links estimation accuracy to sample size, phase resolution, IRS size, reflected-path strength, and interferer power. It also identifies a practical trade-off between phase resolution and hardware cost.

2) Impact of System Parameters:

  • Both estimation variances scale inversely with T, while increasing K lowers the CRLB through the factor (1 −1/K); the benefit diminishes rapidly for K > 4.The authors identify K = 4 as a favorable trade-off between hardware cost and estimation performance.Source: 2) Impact of System Parameters · p. 6
  • More IRS elements provide greater interference-suppression degrees of freedom but require proportionally larger training overhead to maintain per-element estimation accuracy.The bounds rise with the number of elements because more channel parameters must be estimated.Source: 2) Impact of System Parameters · p. 6
  • The CRLB for phase-offset estimation is inversely proportional to γ_n^2, so elements with stronger reflected paths relative to the direct path permit more accurate phase estimates.This relationship motivates the improved phase-optimization algorithm described in Section IV-B.Source: 2) Impact of System Parameters · p. 7
  • Under the high-INR assumption, larger P2 raises the effective estimation INR and consequently lowers the CRLB, although P2 does not appear explicitly in the approximations.The stated assumption is that the interference power dominates the noise power.Source: 2) Impact of System Parameters · p. 7

IV. INTERFERENCE SUPPRESSION BASED ON CHANNEL RATIO ESTIMATION

The phase-configuration problem is discrete and costly to solve exhaustively, so the paper uses a low-complexity greedy search. It orders elements by estimated relative amplitude and optimizes their phases one at a time.

IV. INTERFERENCE SUPPRESSION BASED ON CHANNEL RATIO ESTIMATION

  • With K = 4 and N = 200, exhaustive search would require evaluating about 1.6 × 10^120 phase combinations, making it infeasible for practical system sizes.The finite phase set makes the optimization a non-convex discrete problem.Source: §IV · p. 7

A. Greedy Element-wise Optimization Algorithm

  • The greedy method sorts IRS elements by descending estimated γ̂_n, then optimizes each phase over Φ_K while holding previously optimized phases fixed.Each candidate phase is assessed against the current cumulative channel response.Source: A. Greedy Element-wise Optimization… · p. 7
  • The element-wise search reduces the optimization cost to O(NK), compared with exhaustive evaluation of all K^N phase vectors.The algorithm prioritizes larger estimated relative-amplitude ratios before configuring weaker elements.Source: A. Greedy Element-wise Optimization… · p. 7, §IV · p. 7

B. Iterative Optimization Algorithm

The iterative method addresses error propagation from low-γ_n elements by configuring higher-confidence elements first and re-estimating ratios for those still unoptimized. Under a fixed sample budget, it retains the one-shot method’s asymptotic complexity order.

B. Iterative Optimization Algorithm

  • Because phase-estimation errors are larger for low-γ_n elements, applying the one-shot method to every element can let those errors propagate and degrade suppression.The iterative scheme first configures high-confidence elements, updates the effective background channel, and re-estimates ratios for the remaining elements.Source: B. Iterative Optimization Algorithm · p. 8
  • Each iteration prioritizes remaining elements by estimated γ̂_n, stops an element’s search early if no phase reduces power, updates the background channel, and collects new samples for re-estimation.The process repeats until all elements are optimized or I_max is reached; any remaining elements are handled with the one-shot algorithm in the final iteration.Source: B. Iterative Optimization Algorithm · p. 8

1) Algorithm 1:

The channel-ratio estimation step has complexity O(NKT), and it governs the total cost of the one-shot greedy approach in typical configurations. The iterative approach retains that asymptotic order under a fixed sample budget; simulations use specified channel and benchmark settings.

1) Algorithm 1:

  • Algorithm 1 processes T power samples and computes K conditional sample means for each of N elements, giving complexity O(NKT).Source: 1) Algorithm 1 · p. 8

2) Algorithm 2:

  • When T is sufficiently large, Algorithm 1 dominates the sorting and phase-search costs, so the one-shot approach including estimation has total complexity O(NKT).Sorting costs O(N log N), and the per-element phase search costs O(NK).Source: 2) Algorithm 2 · pp. 8–9

3) Algorithm 3:

  • Under a fixed total sample budget, Algorithm 3 has the same O(NKT) asymptotic complexity order as Algorithm 2 while mitigating error propagation from low-γ_n elements.Source: 3) Algorithm 3 · p. 9

V. NUMERICAL RESULTS

  • Defaults are N = 200 IRS elements, K = 4 phase-quantization levels, T = 20000 total samples, and Algorithm 3 Imax = 3; proposed schemes are compared with no-interference, perfect-estimation, and random-min-sampling benchmarks.Source: §V · p. 9
  • Figures 2 and 3 plot SINR against sample size T and interference power P2, respectively.Source: Figure 2 · p. 10, Figure 3 · p. 10

A. SINR Performance Evaluation

The simulations show that the proposed methods suppress strong interference and approach the interference-free bound, while performance depends on sample size, IRS size, phase resolution, and deployment geometry. In multi-UE settings, performance is affected by other IRSs mainly when the inter-UE distance is very small.

A. SINR Performance Evaluation

  • For T > 4000, Algorithm 3 consistently outperforms Algorithm 2 by prioritizing high-confidence elements and re-estimating the remaining ones.Perfect estimation closely approaches the No Interference bound, while RMS performs poorly and Random Phase is comparable to Without IRS.Source: A. SINR Performance Evaluation · p. 10
  • Over 20 dB gain at P2 = 50 dBm is achieved by Algorithm 3 under strong interference.The conclusion reports that the proposed schemes can also achieve SINR within a few dB of the interference-free upper bound.Source: A. SINR Performance Evaluation · p. 10, §VI · p. 11
  • With fixed T, increasing N first improves proposed-algorithm SINR, but performance later saturates and declines as per-element estimation error grows.The Perfect Estimation scheme instead improves rapidly with N and converges to the No Interference bound.Source: Figure 4 · p. 10, A. SINR Performance Evaluation · p. 11
  • At K = 2 the proposed algorithms perform poorly, while K ≥4 yields significantly higher, comparable performance; K = 4 is sufficient for near-optimal suppression.The passage attributes the K = 2 result to unbiased channel-ratio estimation being infeasible at that phase resolution.Source: Figure 5 · p. 10, A. SINR Performance Evaluation · p. 11

B. Performance in Multi-UE Scenarios

  • In the two-UE scenario, proposed-scheme performance degrades only when d21 < 1 m; for typical inter-UE distances above 1 m, other-IRS effects are negligible.The evaluation fixes d11 at 0.5 m and uses d21 as an approximation of inter-UE distance.Source: B. Performance in Multi-UE Scenarios · p. 11, Figure 6 · p. 11

APPENDIX

The appendix models the empirical conditional-mean observations used in Algorithm 1 and characterizes their finite-sample noise. It gives separate received-power variance cases for constant-modulus and complex-Gaussian interference.

A. Observation Model and Noise Statistics

  • The empirical conditional mean difference has expectation Jnk = C cos(kω −∆n), with C = 2β0βnP2.Its estimation noise is the difference between the empirical observation and this expected value.Source: A. Observation Model and Noise… · p. 12
  • For sufficiently large T and uniformly random phase configurations with |Tn,k| ≈T/K, the observation noise is modeled as zero-mean Gaussian.The variance is derived from the conditional and unconditional sample-mean variances.Source: A. Observation Model and Noise… · p. 12

B. Fisher Information and CRLB Derivation

The CRLB derivation models the K observations as Gaussian and uses their Fisher information to bound estimation of the amplitude and phase parameters. It then transforms the bound for C into a bound for the amplitude ratio γn.

B. Fisher Information and CRLB Derivation

  • The K observations are modeled as i.i.d. Gaussian with mean C cos(kω −∆n) and variance σ2ϵ, for parameter vector [C, ∆n]T.The derivation proceeds from this likelihood to the Fisher Information Matrix.Source: B. Fisher Information and CRLB… · p. 12
  • For K ≥3, cosine and sine orthogonality makes the Fisher Information Matrix diagonal, and each unbiased estimator’s CRLB is the corresponding diagonal entry of its inverse.The appendix invokes the discrete phase set’s orthogonality condition in simplifying the matrix.Source: B. Fisher Information and CRLB… · p. 12
  • Estimating γn is equivalent to estimating C with a known scale factor, so its CRLB follows by transforming the bound for C.The transformation uses γn = βn/β0 = C/(2β2 0P2).Source: 1) CRLB for Phase Difference ∆n:  · p. 12
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