The setup is shown on Fig. 1. A simplifying assumption in deriving the solution is that all communication paths are going through the RIS and the direct links between the transmitters (Txs) and receivers (Rxs) are blocked. It is assumed that there are no other uncontrollable paths, including reflected ones, going between the Txs and the Rxs. This has a pedagogic justification, as it helps to understand how to control the controllable paths; the effects of the uncontrollable paths can only be cancelled if it is not strong and otherwise be treated as an extra interference, as also investigated in Section VI with results. There are K*K combinations of propagation paths between the i-th Tx and j-th Rx. Intuitively, only K of them should be preserved to carry signals for the cases i=j, while the other K*(K-1) need to be forced to zero. To be able to do that, the RIS needs to have at least N>=K*(K-1) controllable coefficients, if both the amplitude and the phase of the coefficients can be controlled. With phase control only, the minimum number of reflection coefficients would be N>=2K(K-1). The problem is rigorously studied and illustrated with plenty of simulation results.  

Here are some reflections of the authors upon their work.

JSAC: Your work can be seen as a way to engineer the environment and achieve an efficient space division multiple access (SDMA). Which environments are not favorable to your proposal and how would you detect that in practice?

Indeed, the reconfigurable intelligent surface (RIS) gives us a way to engineer the wireless propagation environment. However, the RIS can only engineer the reflection paths. So, if the direct paths between the transmitters and receivers are too strong (as compared to the reflection paths), then the RIS may not be able to completely cancel the existing interference patterns in the direct paths. Of course, an RIS can still help in terms of reducing the interference level as much as possible, even if the interference cannot be completely removed.

The question of how to detect such an unfavorable environment touches upon the important issue of channel estimation in the presence of RIS. If perfect channel state information is available, then a simple way to detect such an unfavorable environment is to run the proposed alternating projection algorithm then to check the resulting interference level. But a more important question is how to estimate the multiuser interference channel coefficients in a wireless propagation environment involving RISs. Due to the large number of elements at the RIS, the length of pilots required can be significant. This is a challenging and important area for future investigation.

JSAC: A more general question on the RIS and your approach - what do you see as a main challenge towards wide adoption of RIS, especially in standardization?

The first challenge is the better modelling of the RIS. We need to understand the device physics of the meta-surfaces and the electromagnetic interaction between the RIS and the propagation environment. The model adopted in this paper is rather simplistic. A better model must come from prototyping, performing measurements, and comparing the measurements with solving the full wave equation around each RIS element.  A second challenge is how to perform channel estimation in an RIS-assisted system. In many applications (e.g., in this work), the number of RIS elements needs to be very large (hundreds or even thousands) in order to achieve good performance. But this makes channel estimation a rather difficult task given the limited pilot overhead. A third challenge is computational: The optimal reconfiguration of the RIS is a high-dimensional optimization problem, which needs to be re-solved in every channel coherence interval. 

One possible solution to the challenges mentioned above is to use modern machine learning techniques.  For example, we have shown in a previous work ‘’Learning to reflect and to beamform for intelligent reflecting surface with implicit channel estimation’’ [IEEE JSAC 39(7), July 2021] that it is possible to use a graph neural network to directly optimize the RIS based on the received pilots without explicit modelling of the channel. This is a promising direction for future work.

From a standardization perspective, the main issue is to define the control protocol between the access-point and the RIS controller, which are connected via wired or wireless communications links. Further, in a cellular network, an RIS optimized for one cell can also affect the propagation environment of the adjacent cells. Therefore, coordination between the base stations (BSs) and the RIS controllers is important. Moreover, practical application scenarios can involve multiple RISs deployed by different operators, possibly from different vendors. The design of the protocols between these multiple BSs and possibly multiple RIS controllers is a relevant problem from a standardization perspective.