BER Analysis and Optimization of Pinching-Antenna-Based NOMA Communications

This paper presents the first bit error rate (BER) analysis of a pinching-antenna (PA)-based non-orthogonal multiple access (NOMA) communication system. The PA is assumed to be able to be placed anywhere along the waveguide and serves two NOMA user equipment (UEs) in both uplink (UL) and downlink (DL) scenarios. Exact closed-form expressions for the average BER of each user are derived under practical imperfect successive interference cancellation (SIC). These expressions are then used to optimize the PA location for minimizing the overall average BER of both UEs. In the UL case, the interference between the users' channels introduces phase-dependent fluctuations in the BER cost function, making it highly non-convex with many local extrema. To address this challenge, a smoothing technique is applied to extract the lower envelope of the BER function, effectively suppressing ripples and enabling a reliable identification of the global minimum. In the DL case, a joint optimization of the PA location and NOMA power allocation coefficients is proposed to minimize the average BER. Simulation results verify the accuracy of the analytical derivations and the effectiveness of the proposed optimization methods. Notably, the UL results demonstrate that an optimally positioned PA can create the required received power difference between two equally powered UEs for reliable power-domain NOMA decoding under imperfect SIC.

On the Distribution of Matched Filtering with Continuous Aperture Arrays

Continuous aperture arrays (CAPAs) provide a theoretical upper bound on the performance of densely packed antenna arrays, but their analysis is limited by the lack of closed-form signal-to-noise ratio (SNR) distributions under realistic fading conditions. This paper derives accurate analytical expressions for the matched-filter SNR distribution of one-dimensional CAPAs in correlated Rayleigh environments under both the sinc and Jakes correlation models using the Karhunen-Loeve expansion. By applying a truncated hypoexponential model, we obtain accurate approximations for the probability density function and cumulative distribution function of the SNR that closely match simulations, including the outage probability region where precise characterization is critical. Compared to a standard gamma approximation, our approach provides significantly improved accuracy in this regime. Additionally, the CAPA system considered is shown to outperform discrete antenna arrays. The derived expressions enable tractable and accurate evaluation of CAPAs under practical channel models.

Dimensional Scaling Laws for Continuous Fluid Antenna Systems

Consider the signal-to-noise ratio (SNR) of a continuous fluid antenna system (CFAS) operating over a Rayleigh fading channel. In this paper, we extend traditional system assumptions and consider spatially coherent isotropic correlation, continuous positioning of the antenna rather than discrete, and the use of multi-dimensional space (1D, 2D and 3D). By focusing on the upper tail of the received SNR distribution (the high SNR probability (HSP)), we are able to derive asymptotically exact closed-form formulas for the HSP. Finally, these results lead to scaling laws which describe the increase in the HSP as we employ more dimensions and the optimal CFAS dimensions.

BER Analysis and Optimization for Continuous RIS-Enabled NOMA

This letter investigates a novel uplink (UL) system that integrates power-domain non-orthogonal multiple access (PD-NOMA) with a continuous reconfigurable intelligent surface (CRIS). We analyze the effective CRIS-assisted channels under spatially correlated fading to accurately approximate the characteristic function of the cascaded channel. This allows the derivation of an expression for the bit error rate (BER), a key performance metric for UL PD-NOMA. We further utilize the derived BER expressions to introduce a joint optimization framework that minimizes the average BER via UL power allocation and dynamic RIS partitioning among the users. The analytical results are validated by simulations, and show that the proposed optimization scheme eliminates the BER floors that are associated with UL NOMA. The results also confirm the superiority of the optimized CRIS-NOMA scheme over conventional orthogonal multiple access (OMA) and non-optimized UL NOMA schemes.

Level Crossing Rate Analysis for Optimal Single-user RIS Systems

We analyse the level crossing rate (LCR) of an uplink single-user (SU) reconfigurable intelligent surface (RIS) aided system. It is assumed that the RIS to base station (RIS-BS) channel is deployed as line-of-sight (LoS), and the user (UE)-RIS and UE-BS channels are correlated Rayleigh. For the optimal RIS reflection matrix, we derive a novel and exact analytical LCR expression for when the direct (UE-BS) channel is blocked, i.e. the RIS-only channel. Also, the existing exact expression for the direct-only channel (equivalent to classical maximal-ratio-combining (MRC)) suffers from extreme numerical precision problems when the BS has many elements. Therefore, we propose a new stable and accurate approximation to the LCR of the direct channel. The approximation is based on replacing any small similar eigenvalues of the channel correlation matrix by their average. We show that increasing the number of elements at the RIS or BS and decreasing channel correlation makes the LCR drop more rapidly for thresholds away from the mean SNR. Crucially, we find that RIS systems do not significantly amplify temporal variations in the channel. This is particularly beneficial for RIS systems considering the difficulty in acquiring channel state information (CSI).

Performance Characterization of Continuous Reconfigurable Intelligent Surfaces

We consider a reconfigurable intelligent surface (RIS) that can implement a phase rotation continuously over the whole surface rather than via a finite number of discrete elements. Such an RIS can be considered a design for future systems where advances in metamaterials make such an implementation feasible or as the limiting case where the number of elements in a traditional RIS increases in a given area. We derive the optimal RIS design for the single-user (SU) scenario assuming a line-of-sight (LoS) from the RIS to the base station (BS) and correlated Rayleigh fading for the other links. We also derive the associated optimal signal-to-noise ratio (SNR) and its mean, a bound on the mean spectral efficiency (SE), an approximation to the SNR outage probability and an approximation to the coefficient of variation for the investigation of channel hardening.

Phase Selection and Analysis for Multi-frequency Multi-user RIS Systems Employing Subsurfaces in Correlated Ricean and Rayleigh Environments

We analyse the performance of a reconfigurable intelligent surface (RIS) aided system where the RIS is divided into subsurfaces. Each subsurface is designed specifically for one user, who is served on their own frequency band. The other subsurfaces (those not designed for this user) provide additional uncontrolled scattering. We derive the exact closed-form expression for the mean signal-to-noise ratio (SNR) of the subsurface design (SD) when all channels experience correlated Ricean fading. We simplify this to find the mean SNR for line-of-sight (LoS) channels and channels experiencing correlated Rayleigh fading. An iterative SD (ISD) process is proposed, where subsurfaces are designed sequentially, and the phases that are already set are used to enhance the design of the remaining subsurfaces. This is extended to a converged ISD (CISD), where the ISD process is repeated multiple times until the SNR increases by less than a specified tolerance. The ISD and CISD both provide a performance improvement over SD, which increases as the number of RIS elements (N) increases. The SD is significantly simpler than the lowest complexity multi-user (MU) method we know of, and despite each user having less bandwidth, the SD outperforms the existing method in some key scenarios. The SD is more robust to strongly LoS channels and clustered users, as it does not rely on spatial multiplexing like other MU methods. Combined with the complexity reduction, this makes the SD an attractive phase selection method.