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Blind IRS Beamforming Using Only Received Signal Power Measurements
Tao Wang, Xiaohui Zhang, Pengfei Lv, Hehe Ban, Yiwei Guo, Ming Yi
TL;DR
Accurate CSI is challenging to obtain in IRS-aided systems, motivating blind beamforming from received-power samples. The paper estimates channel phase differences through least squares and uses them to configure IRS phases; simulations show gains over CSM for larger quantization levels at the same order of computational complexity.
Problem
Accurate CSI acquisition in IRS-aided systems is challenging, while CSM compares conditional sample means without fully using the information in sampled power measurements.
Source: §I · p. 1Method
The proposed blind method formulates a least-squares problem to estimate relative phase differences between the direct and IRS-reflected channels from received-power samples.
Source: §I · p. 1, A. Problem Statement and Theoretical… · p. 3, B. From Sampled Data to Phase… · p. 3Results
At K = 8 and K = 16, the proposed method gains +2.4 dB and +3.5 dB over CSM, respectively, and is equivalent to CSM at K = 2.
Source: C. Performance Evaluation and Discussion · p. 5, §VI · p. 6Takeaways & Limitations
For K > 2, the method outperforms CSM while retaining the same order of computational complexity, O(TNK).
Source: §I · p. 1, §VI · p. 6
Abstract
from arXiv · showhide
This paper proposes a novel blind beamforming strategy for signal enhancement aided by an intelligent reflecting surface (IRS), using only samples of the received signal power. Unlike existing conditional sampling mean (CSM) based approaches, which rely solely on comparing the CSM values, the proposed algorithm fully exploits the information in the sampled data by constructing a least squares problem. This enables the estimation of the phase difference between the IRS-reflected channel and the direct channel, ultimately yielding the optimal IRS phase configuration. The simulation results verify that, by fully leveraging the collected data, the proposed scheme outperforms the CSM-based method, especially when the number of IRS phase quantization levels is larger than 2, while incurring the same level of computational complexity.
I. INTRODUCTION
Accurate CSI is difficult to acquire in IRS-aided systems, motivating blind beamforming from received-power measurements. The paper proposes estimating channel phase differences from those samples and configuring IRS phases to enhance the signal.
I. INTRODUCTION
- Conventional IRS beamforming depends on accurate CSI, which is challenging because the direct link and noise can overwhelm weak reflections, I/Q components may be unavailable, and estimation can be costly.The paper notes I/Q support limitations in protocols such as 5G.Source: §I · p. 1
- The proposed blind algorithm uses a least-squares problem to estimate phase differences from received-power samples, fully exploiting data also used by CSM.The estimated differences guide IRS phase shifts that compensate for them.Source: §I · p. 1
- At K = 2 phase-quantization levels, the proposed algorithm is theoretically equivalent to CSM; for K > 2, it achieves superior performance, with simulations showing significant gains especially at larger K while maintaining the same order of computational complexity, O(TNK).Source: §I · p. 1
II. SYSTEM MODEL
- The system model represents the received signal using the transmitted symbol, a direct channel, IRS-cascaded channels with applied phase shifts, and additive noise.Each IRS element selects its phase shift from a discrete set of K quantization levels.Source: §II · p. 2
- The receiver collects received-power measurements over T independent trials with random IRS phase configurations, and the method selects phase shifts using only this sampled dataset.The objective is to maximize received SNR using the dataset.Source: §II · p. 2
III. EXISTING SCHEMES
The section frames existing schemes as IRS-configuration approaches that rely on differing levels of channel knowledge.
III. EXISTING SCHEMES
- The benchmark schemes represent different IRS-configuration approaches with varying channel-knowledge requirements.Source: §III · p. 2
A. CPP with CSI
The section contrasts a perfect-CSI upper-bound method with a CSI-free heuristic that chooses the best observed configuration.
A. CPP with CSI
- CPP aligns each reflected channel with the background channel, then projects the continuous-phase solution to the nearest feasible discrete phase.Its perfect, instantaneous CSI requirement is often impractical in real systems.Source: A. CPP with CSI · p. 2
B. Random-Max Sampling (RMS)
- RMS selects the single phase-shift vector that produced the highest received power among T random trials, so its performance depends on trial count.Increasing T raises the chance of sampling a near-optimal configuration but increases sampling overhead.Source: B. Random-Max Sampling (RMS) · pp. 2–3
C. CSM Algorithm
The section describes CSM’s per-element phase selection and its finite-sample limitation, then introduces Phase Estimation (PE) beamforming using sampled received power to estimate channel phase differences and configure the IRS.
C. CSM Algorithm
- CSM selects each IRS element’s phase by maximizing the conditional sample mean of received power for that element and phase.It uses conditional statistics from the dataset rather than a single received-power sample.Source: C. CSM Algorithm · p. 3
- With limited samples, CSM’s comparison of conditional means only partially uses the sampled data, which can limit performance, especially for large K.With T = Ω(N^2(log N)^3) samples, the CSM configuration theoretically converges with high probability to the CPP solution.Source: C. CSM Algorithm · p. 3
IV. PROPOSED BLIND BEAMFORMING SCHEME
- PE beamforming estimates the relative phase difference between the background channel and each IRS-reflected channel from sampled received power, then configures phase shifts to compensate for those differences.It operates on the sampled dataset and requires no prior CSI.Source: §IV · p. 3
A. Problem Statement and Theoretical Foundation
The section relates conditional received-power statistics to the phase difference between the background and IRS-reflected channels. It then uses empirical power measurements to fit a least-squares model and estimate that phase difference.
A. Problem Statement and Theoretical Foundation
- The objective is to estimate each IRS-reflected channel’s phase difference from noisy empirical observations of a statistic that depends on the unknown difference through a cosine.The phase difference is between the background channel and the n-th equivalent cascaded channel.Source: A. Problem Statement and Theoretical… · p. 3
B. From Sampled Data to Phase Difference Estimation
- The empirical observation models the phase-dependent power contrast as a cosine of the phase level offset by Δn, plus observation noise.The method computes empirical unconditional and conditional sample means before forming the observations.Source: B. From Sampled Data to Phase… · p. 3
- A linear least-squares problem estimates intermediate coefficients A and B from the K empirical observations.The cosine and sine bases for the standard discrete phase set are orthogonal, yielding closed-form least-squares solutions.Source: B. From Sampled Data to Phase… · p. 3
- The phase difference is recovered from the fitted coefficients with a four-quadrant arctangent, using only the empirical observations.The stated relation is tan Δn = B/A.Source: B. From Sampled Data to Phase… · p. 4
C. IRS Phase Configuration Based on Phase Estimation
The estimated phase difference is mapped to the nearest permitted discrete IRS phase so the direct and reflected signals are co-phased. The section also establishes equivalence to CSM for two phase levels and equal-order computational complexity.
C. IRS Phase Configuration Based on Phase Estimation
- The continuous phase shift for an IRS element is chosen to align its reflected signal with the background channel.The phase-estimation procedure then selects the nearest phase allowed by the discrete constraint.Source: C. IRS Phase Configuration Based on… · p. 4
- For each IRS element, the algorithm maps the estimated phase difference into [0, 2π), selects the discrete phase with minimum circular distance, and applies that phase.Applying the selection across all N elements yields the final phase configuration, which aims to co-phase the direct and IRS-reflected paths and maximize received power and SNR.Source: C. IRS Phase Configuration Based on… · p. 4
- For K = 2, the proposed algorithm is theoretically equivalent to CSM because its estimation formula reduces to the CSM decision rule.The derivation gives B* = 0 and A* = 4β0βnP cos Δn + (ϵ2 − ϵ1).Source: C. IRS Phase Configuration Based on… · p. 4
- The proposed method and CSM have the same O(TNK) computational complexity.The least-squares solution adds only O(K) operations per IRS element after the shared conditional sample-mean calculations.Source: C. IRS Phase Configuration Based on… · p. 4
V. NUMERICAL RESULTS
The section evaluates the proposed blind beamforming scheme’s achievable SNR against benchmark methods, focusing on the effects of K, N, and T.
A. Simulation Setup
The simulations use fixed default system parameters and model the background and cascaded channels with large-scale path loss, small-scale fading, and specified antenna and IRS gains.
A. Simulation Setup
- The default parameters are P = 30 dBm, σ2 = −90 dBm, N = 200, K = 8, and T = 2000, with a 3 GHz carrier.Tx, IRS, and Rx are fixed at [50, -100, 20], [-10, -10, 0], and [0, 0, 0] meters.Source: A. Simulation Setup · p. 4
- Tx and Rx are isotropic with gains Gt = Gr = 1; each IRS element is a square patch with side length λ/2.The IRS receiving gain is π and its reflecting-link gain is 1.Source: A. Simulation Setup · p. 4
- The background channel’s large-scale fading amplitude is specified using the Tx–Rx distance d0 and path loss exponent a0.The distances are calculated from the fixed node coordinates.Source: A. Simulation Setup · pp. 4–5
- The background link uses path loss exponent a0 = 4, while both cascaded hops use a1 = a2 = 2; small-scale fading is i.i.d. CN(0, 1).The cascaded large-scale fading amplitude is the product of the Tx-to-IRS and IRS-to-Rx hop amplitudes.Source: A. Simulation Setup · p. 5
B. Benchmark Schemes
The evaluation compares the proposed method with channel-informed, statistical, instantaneous, random, and no-IRS benchmarks.
B. Benchmark Schemes
- CPP with perfect CSI uses ideal continuous phase shifts projected to the discrete phase set and serves as the performance upper bound.It assumes perfect knowledge of all channel coefficients.Source: B. Benchmark Schemes · p. 5
- CSM selects, for each IRS element, the discrete phase shift with the highest conditional sample mean of received power.Source: B. Benchmark Schemes · p. 5
- RMS chooses the trial’s phase vector with the highest instantaneous received power, while Random independently selects uniform phase shifts and No-IRS uses only the direct link.Average SNR is evaluated over 1000 independent Monte Carlo trials.Source: B. Benchmark Schemes · p. 5
C. Performance Evaluation and Discussion
Across the evaluated settings, the proposed scheme improves on CSI-free benchmarks, with gains over CSM increasing at larger phase-quantization levels. Its performance also depends on the number of sampling trials relative to the IRS size.
C. Performance Evaluation and Discussion
- At K = 8 and 16, the proposed algorithm exceeds CSM by 2.4 dB and 3.5 dB, respectively, while both perform identically at K = 2.Fig. 2 reports average SNR versus K; the proposed least-squares method estimates relative phase from the sampled data, whereas CSM selects the largest conditional mean.Source: C. Performance Evaluation and Discussion · p. 5
- The proposed scheme outperforms CSM, RMS, and Random across evaluated IRS-element counts N, while its gap to the CPP upper bound widens as N increases.The passage attributes the widening gap to the fixed sample count T increasingly limiting performance.Source: C. Performance Evaluation and Discussion · pp. 5–6, Figure 3 · p. 6
- As T increases, the proposed scheme converges toward the CPP upper bound and maintains an advantage over benchmarks; RMS improves more slowly.The stated explanation is that RMS’s brute-force sampling does not systematically extract and leverage channel information as the least-squares approach does.Source: Figure 4 · p. 6, C. Performance Evaluation and Discussion · p. 6
VI. CONCLUSION
The conclusion presents a blind IRS beamforming algorithm that estimates channel phase differences from received-power samples using least squares.
VI. CONCLUSION
- The algorithm estimates phase differences between channels by solving a least-squares problem using only received signal power samples.Source: §VI · p. 6
- The method is equivalent to CSM for K = 2 and achieves superior performance for K > 2, with gains increasing as K grows.Source: §VI · p. 6
- The reported computational complexity remains O(TNK); multi-user and broadband extensions are identified as future work.Source: §VI · p. 6