Which Channel in 6G, Low-rank or Full-rank, more needs RIS from a Perspective of DoF?

Reconfigurable intelligent surface (RIS), as an efficient tool to improve receive signal-to-noise ratio, extend coverage and create more spatial diversity, is viewed as a most promising technique for the future wireless networks like 6G. As you know, RIS is very suitable for a special wireless scenario with wireless link between BS and users being completely blocked, i.e., no link. In this paper, we extend its applications to a general scenario, i.e., rank-deficient channel, particularly some extremely low-rank ones such as no link, and line-of-sight (LoS, rank-one). Actually, there are several potential important low-rank applications like low-altitude, satellite, UAV, marine, and deep-space communications. In such a situation, it is found that RIS may make a dramatic degrees of freedom (DoF) enhancement over no RIS. By using a distributed RISs placement, the DoF of channel from BS to user in LoS channel may be even boosted from a low-rank like 0/1 to full-rank. This will achieve an extremely rate improvement via spatial parallel multiple-stream transmission from BS to user. In this paper, we present a complete review of making an in-depth discussion on DoF effect of RIS.

💡 Research Summary

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The paper investigates how reconfigurable intelligent surfaces (RIS) can dramatically increase the degrees of freedom (DoF) of wireless links that are rank‑deficient, such as completely blocked (no‑link) or pure line‑of‑sight (LoS) channels, which are typical in emerging 6G scenarios like low‑altitude UAV, satellite, marine, and deep‑space communications. The authors first model a three‑node system consisting of a base station (BS) with M antennas, an RIS with N elements, and an IoT device with K antennas. The direct channel matrix H may have rank 0 (blocked) or 1 (LoS), while the cascaded channels G_BR and G_RU are controllable through the RIS phase‑shift matrix Θ.

For a single RIS, the paper shows analytically that if G_BR and G_RU are rich (i.i.d. Gaussian) or even LoS but not collinear with the BS‑device line, the composite channel G_BR Θ G_RU + H can achieve full rank K. In the blocked case, RIS creates a non‑zero rank (0 → 1) and, with sufficiently scattered reflected paths, can raise the rank to K, enabling K parallel streams. In the LoS case, RIS lifts the rank from 1 to 2, and with multiple RIS elements the rank can again reach K. Simulations using maximum‑ratio transmission (MRT) and phase alignment confirm rate gains of 1.6× (M=64) to 2.3× (M=128) over the RIS‑free baseline.

The most novel contribution is the distributed multi‑RIS architecture. By placing J RISs at carefully chosen geometric positions so that their spatial signatures are weakly correlated (angles θ_ij and φ_ij designed per the paper’s formulas), the summed cascaded channel ∑_j G_j_BR Θ_j G_j_RU + H achieves rank K even when each individual RIS provides only a rank‑1 path. Consequently, the system can support J + 1 independent streams; for K=4, four RISs yield four DoF. Numerical results show that increasing the number of RISs from one to four raises the achievable rate by roughly 0.7, 1.9, 2.7, and 3.5 times, respectively, under a total power constraint and realistic noise levels (RIS noise σ_r² = −90 dBm).

Implementation aspects such as RIS power supply, control signaling, and realistic distances (BS‑RIS ≈ 82 m, RIS‑IoT ≈ 28 m, BS‑IoT ≈ 100 m) are incorporated. Beamforming at the BS (null‑space projection), phase alignment at the RIS, and zero‑forcing at the receiver are employed to realize the theoretical gains.

In conclusion, RIS can create new DoF in channels that would otherwise be unusable for multi‑stream transmission. Distributed RIS deployment further scales DoF linearly with the number of surfaces, offering robust rate improvements even in high‑noise environments. These findings position RIS—especially in a distributed configuration—as a key enabler for the massive connectivity, high data rates, and extreme‑environment resilience envisioned for future 6G and IoT networks.