AirCons Algorithm for RIS Communications

• AirCons is a unified channel estimation technique that superimposes direct and RIS-reflected channels to reduce pilot and signaling overhead.
• The protocol segments training into Q periods with varied RIS configurations, using least-squares estimation and beamforming to meet multiuser SINR constraints.
• It achieves robust performance at low SNR, capturing up to 80% of RIS gain while minimizing complexity compared to traditional cascaded estimation methods.

The AirCons algorithm refers to a superimposed channel training protocol for reconfigurable intelligent surface (RIS)-assisted multiuser communications, which unifies acquisition of composite direct and reflected channels into a low-overhead, high-robustness end-to-end estimation framework. In contrast to traditional cascaded channel estimation approaches that separately estimate the direct link and the base station (BS)-RIS-user cascade, AirCons performs channel estimation on the full superimposed end-to-end channel over a small set of RIS phase-control periods, providing a fundamental complexity–performance trade-off and drastically reducing pilot and signaling overhead (An et al., 2021).

1. System Model and Problem Overview

The algorithm operates in time-division duplex (TDD) multiuser downlink scenarios where an M-antenna BS communicates to K single-antenna users via a passive RIS with N elements. The composite channel experienced by user k in phase period $q$ is:

$h_{q,k}^H = v_k^H \Phi_q U + h_{d,k}^H,$

with $U$ the BS-RIS channel, $v_k^H$ the RIS→user channel, $h_{d,k}^H$ the direct channel, and $\Phi_q$ the diagonal RIS phase-shift matrix for the $q$th period. The received signal at the BS during uplink training period $q$ is a superposition:

$Y_q = \sqrt{\alpha} H_q X + Z_q,$

where $H_q$ collects the end-to-end (superimposed) user channels, $X$ is an orthogonal pilot matrix, and $Z_q$ is noise.

This framework avoids explicit identification of the separate BS→RIS, RIS→user, and direct paths, targeting only the effective superimposed MIMO channel that depends on the RIS setting.

2. Protocol Description and Workflow

AirCons divides channel training into $Q$ periods, each corresponding to a chosen RIS phase configuration $\Phi_q$ held constant over $L=K$ slots. The workflow is:

1. Uplink training: All users send $L=K$-length orthogonal pilot sequences. The BS collects $Y_q$ for each period.
2. Per-period least-squares estimation: BS estimates $H_q$ via

$$\widehat{H}_{q,\mathrm{LS}} = \frac{1}{K\sqrt{\alpha}} Y_q X^H.$$

1. Beamforming computation: For each $q$, a downlink transmit beamformer $W_q$ is computed to meet multiuser SINR constraints, e.g., via classic power-minimization.
2. RIS configuration selection: For the $Q$ candidate phase settings, select the one minimizing total BS transmit power:

$\hat{q} = \arg\min_{q} \sum_{k=1}^K \|w_{q,k}\|^2.$

1. Operational phase: Use the selected $\Phi_{\hat{q}}$ for data transmission.

This avoids the need for explicit cascaded-channel inversion or per-RIS-element estimation.

3. RIS Phase Selection and Codebook Design

AirCons supports two families for RIS-phase codebooks:

• Random Phases: Each element's phase in $\Phi_q$ chosen independently $\sim \mathcal{U}[0,2\pi)$.
• Equi-partitioned Codebook: For each RIS element, its $Q$ phase values are set at the vertices of a regular $Q$-gon, maximizing mutual Euclidean distance between codewords and minimizing codebook correlation.

Selection among $Q$ candidate configurations is based on transmit-power minimization metrics over all $K$ users.

4. Theoretical Performance Analysis

For the single-input single-output (SISO, $M=K=1$) case, AirCons furnishes explicit received-power expressions:

• Received power under random-training:

$$P_u = P [\rho_r^2 + \rho_d^2 + \frac{\pi}{2} \rho_r \rho_d g(Q)],$$

with $\rho_r^2$, $\rho_d^2$ the RIS and direct link variances, and $g(Q)$ a function reflecting training diversity.

• For $N \to \infty$ RIS elements, the power ratio to optimal is asymptotic to $g(Q)^2$.
• The effect of channel estimation noise is explicitly characterized, with AirCons demonstrating mild error-propagation: only the final period selection is disturbed by noise, not each RIS element individually.

Explicit expressions for power, error, and bounds are given in [(An et al., 2021), Eq. (4-11–4-12), (4-23), (5-3), (5-20)].

5. Overhead, Complexity, and Robustness

AirCons reduces resource requirements as follows:

Method	Pilot Overhead	Signaling Complexity	Computational Effort
Cascaded-CE (DFT/ON/OFF)	$(N{+}1)K$ pilots	$N \log_2 B$ bits RIS control	$O(NKM)$
AirCons (Superimposed)	$QK$ pilots	$Q \log_2 Q$ bits	$Q$ MIMO LS, standard beamforming

Since pilots per training period are independent of RIS size $N$, and only $O(Q)$ bits control the RIS per block, the signalling and overhead are orders of magnitude lower. Only a small number ($Q=2{\sim}4$) of periods is generally needed to capture a substantial fraction of the available RIS gain—e.g., $50$-$80\%$ [(An et al., 2021), Secs. IV, Tables II–III].

Moreover, numerical studies show that at low SNR, AirCons exhibits increased robustness to estimation noise, outperforming traditional cascaded estimation methods in both SISO and multiuser/MIMO regimes [(An et al., 2021), Figs. 6–17].

6. Trade-Offs, Limitations, and Applicability

AirCons achieves a quantifiable balance between implementation complexity and channel estimation fidelity:

• At the cost of optimality (achieving up to $80\%$ of the RIS gain), it enables single-step estimation and selection with dramatically reduced overhead.
• Requires only $QK$ pilot symbols per training interval, making it scalable to large $N$ RIS systems.
• The method’s performance approaches traditional full cascaded estimation at higher SNR or with more training periods $Q$, but is significantly more robust at low SNR due to error isolation.
• The method is best suited for TDD multiuser downlink settings where direct link and BS-RIS-user paths can be considered stationary over the training interval, and the RIS can be rapidly reconfigured among $Q$ settings.

7. Generalizations and Impact

AirCons, by focusing on superimposed end-to-end channel estimation rather than full parametric decomposition, establishes a new paradigm for RIS-assisted systems and large-scale passive physical-layer reconfigurability. The framework’s minimization of pilot and control signaling renders it highly suitable for massive-RIS deployments, dense-user scenarios, low-power IoT, and future scaling of intelligent wireless infrastructure. Closed-form SISO analysis and extensive MISO/MIMO simulations in (An et al., 2021) corroborate its efficiency–accuracy tradeoff, making it a practical design tool in both academic and industrial RIS-enabled wireless research.