Virtual LoS Links: Concepts & Techniques

• Virtual LoS links are communication channels that mimic direct line-of-sight by reconfiguring blocked paths using techniques like ESPAR antennas and intelligent reflecting surfaces.
• Techniques such as randomized basis-pattern excitation, passive redirection, and multi-hop relaying restore deep fading diversity and enhance path reliability.
• Applications span spectrum sharing, urban FSO backhaul, and cellular enhancements, with design guidelines optimizing spectral efficiency and network robustness.

Virtual line-of-sight (LoS) links are communication links in which a physical propagation path blocked by objects or obstacles is electronically or optically reconfigured—using devices such as electronically steerable antennas or intelligent reflecting surfaces—so that the link exhibits the statistical or functional properties of a direct LoS channel. Techniques to achieve this include randomized basis-pattern excitation (virtual antennas), passive surface redirection, and multi-hop relaying, each restoring or emulating beneficial channel characteristics such as deep fading diversity, reduced blockage, and enhanced path reliability in otherwise non-LoS or LoS-dominated interference scenarios.

1. Principles of Virtual Line-of-Sight Link Creation

Virtual LoS links are constructed either by inducing artificial fluctuations in otherwise static LoS interference channels or by “bouncing” the electromagnetic or optical signal around obstructions to create a controllable propagation path with LoS-like properties. In wireless spectrum-sharing systems, this is achieved via ESPAR antennas equipped with multiple orthonormal “dumb” basis patterns, where randomized phasing across these patterns transforms a Rician (strong-LoS) channel into a Rayleigh-equivalent virtual channel, restoring beneficial deep-channel fades (Alaa et al., 2014). In urban free-space optical (FSO) networks, virtual LoS paths are realized by strategically deploying optical intelligent reflecting surfaces (OIRS) that redirect amplified signals from relays to bypass blockages, functionally emulating a line-of-sight connection even when the physical path is obstructed (Shang et al., 3 Nov 2025). In cellular and mmWave networks, IRS-reconfigured virtual LoS links are dynamically established when direct LoS is blocked, by rerouting the signal through passive surfaces to maintain service continuity (2403.07337).

2. Channel Modeling and Statistical Properties

The statistical transformation of channel fading characteristics underpins the concept of virtual LoS links. In the spectrum-sharing context, the native LoS interference channel is modeled as Rician,

$$h_i(k) = \sqrt{\bar{\gamma}_i}\Big[\sqrt{\frac{K_i}{K_i+1}}e^{j\phi_i} + v_i(k)\Big],$$

with $K_i$ the K-factor and $v_i(k)\sim \mathcal{CN}(0,1/(K_i+1))$. When random-weighting of $M$ basis patterns from an ESPAR antenna is applied, the aggregate LoS component becomes a sum of randomly rotated phasors: $$\bar l_{sp}(k) = \sqrt{\frac{\bar{\gamma}_{sp}K_{sp}}{K_{sp}+1}}\cdot \frac{1}{\sqrt{M}}\sum_{m=0}^{M-1} e^{j(\phi_{sp,m}+\theta_m(k))}.$$ For moderate $M$ (e.g., $M\geq5$), this sum is approximately circular complex Gaussian (Central Limit Theorem), and the virtual channel is Rayleigh faded, providing the ergodic statistical diversity required for optimal dynamic spectrum access (Alaa et al., 2014).

In OIRS-based FSO systems, each hop is modeled by cascaded fading channels: atmospheric turbulence (Gamma-Gamma), geometric misalignment (Hoyt law), and path attenuation. The key link, OIRS-assisted reflection, results in a composite channel $h_2$ whose PDF is derived in closed-form using Meijer-G functions: $$f_{h_2}(h) = \sum_{k=0}^{N_k} C_{2,k} G_{2k+1,2k+3}^{2k+3,0}\left[\dots\right],$$ enabling exact performance analysis for outage, BER, and capacity under virtual LoS relay operation (Shang et al., 3 Nov 2025).

3. Architectures for Realizing Virtual Line-of-Sight Links

3.1 Electronically Steerable Parasitic Arrays (ESPAR)

A single-RF-chain ESPAR antenna with $M$ basis patterns is used at transmitters or receivers. Arbitrary phasing of these basis patterns, with amplitudes fixed at $1/\sqrt{M}$ and phases chosen independently from $\text{Unif}[0,2\pi]$, creates $M$ “virtual dumb antennas.” Each basis pattern samples a distinct, fixed spatial signature, and randomized excitation transforms fixed LoS components into fast-fading equivalents (Alaa et al., 2014).

3.2 Intelligent Reflecting Surfaces (IRS) and OIRS

IRS/OIRS are passive or active surfaces deployed in the environment (e.g., on rooftops). When direct LoS is blocked, an IRS is scheduled to establish a new path, provided both the transmitter-IRS and IRS-receiver links are unblocked. In FSO systems, the architecture consists of a source, relay (HAP), IRS, and receiver arranged to bypass obstacles, with IRS phase shifters programmed to “bend” the signal around obstacles, establishing the virtual LoS (Shang et al., 3 Nov 2025, 2403.07337).

3.3 Markovian Reconfiguration in Mobile Networks

The serving user–base station link is modeled as a three-state Markov chain: direct-LoS (L), IRS-reconfigured-LoS (R), and non-LoS (N). Upon blockage, the system probabilistically selects an IRS-reconfigured path if at least one suitable IRS is available, maintaining LoS-like performance despite obstacles (2403.07337).

4. Performance Metrics and Analytical Frameworks

4.1 Spectral and Outage Capacity

In spectrum-sharing, the opportunistic (Rayleighized) interference channel recovers the classic underlay ergodic capacity scaling,

$$C = E_{\Gamma} \left\{\log_2\left[1+\frac{\gamma_s P_s(\Gamma)}{1+\gamma_{ps}\bar{\gamma}_p}\right]\right\},$$

with water-filling subject to peak and average interference constraints (Alaa et al., 2014). For OIRS-assisted FSO, ergodic capacity and outage probability are expressed in closed-form via Fox-H and Meijer-G functions, enabling precise performance quantification under arbitrary turbulence, misalignment, and relay settings (Shang et al., 3 Nov 2025).

4.2 Mobility and Reliability Enhancements

In mobile networks, the probability of LoS → NLoS drop and handover (HO) rates are derived using Markov transition probabilities $P_{ij}$ and the geometry of blockage and IRS deployment. IRS deployment at realistic densities ($\lambda_i\approx93\,\mathrm{km}^{-2}$, $D=100$ m) can reduce NLoS drop probability by 70% and handover rate by 67% compared to networks without IRS—outperforming direct increases in BS density at far lower cost (2403.07337).

4.3 End-to-End SNR and Diversity

For multi-hop OIRS-assisted FSO, the end-to-end SNR $\gamma$ is given by

$$\gamma = \frac{\gamma_{H1}\gamma_{H2}}{\gamma_{H2} + C},$$

with its distribution derived in terms of multivariate Fox-H functions. The high-SNR outage scales as $OP\asymp K\overline{\gamma}^{-\mathcal{G}_d}$ with diversity order

$$\mathcal{G}_d = \min\left\{ \frac{\alpha_1}{r_1}, \frac{\beta_1}{r_1}, \frac{\eta_s^2}{r_1}, \frac{\alpha_2}{r_2}, \frac{\beta_2}{r_2}, \frac{(1+q_g^2)\omega}{2q_gr_2}\right\},$$

which allows diversity optimization through choice of relay gain, IRS deployment, and detection scheme (Shang et al., 3 Nov 2025).

5. Design Guidelines and Practical Considerations

Optimal deployment parameters for virtual LoS architectures differ by technology but share the common feature that beyond moderate hardware complexity (e.g., $M\approx5$ basis patterns, IRS densities $\sim$ tens/km$^2$) additional deployment yields only diminishing returns for reliability and handover reduction (Alaa et al., 2014, 2403.07337). Practical ESPAR-based virtualization requires only one RF chain and a small number of reactive loads for reconfigurable weight control; IRS/OIRS surfaces should be positioned and controlled to maximize unblocked coverage regions and to satisfy geometric constraints on feasible reflecting paths. Tuning beam-width, alignment accuracy, and relay gains is crucial under atmospheric and urban turbulence. Closed-form and asymptotic analytical results facilitate rapid dimensioning and optimization of such deployments for spectral efficiency, mobility robustness, and reliability (Shang et al., 3 Nov 2025).

6. Applications and Broader Implications

Virtual LoS links are foundational for spectrum underlay, compact device-to-device (D2D) communications, urban FSO backhaul, NLoS cellular coverage, and low-cost, robust mobile connectivity. These technologies enable mobile terminals and access points to overcome LoS blockage and static interference using low-complexity hardware or passive environmental augmentation. The underlying frameworks and formulas provided—in terms of transition probabilities, channel PDFs, and high-SNR scaling laws—allow for rigorous design, analysis, and trade-off evaluation in scenarios ranging from opportunistic spectrum sharing to dense urban wireless and FSO deployments (Alaa et al., 2014, Shang et al., 3 Nov 2025, 2403.07337).