Non-Reciprocal Beyond-Diagonal RIS

Secure Full-Duplex Wireless Communication System

System Architecture

NR-BD-RIS UE1 UE2 UE3 Secure Communication Flow

Key Benefits

  • Breaks channel reciprocity for enhanced security
  • Supports multiple non-aligned beam directions
  • Prevents eavesdropping through signal suppression
  • Outperforms R-BD-RIS and D-RIS in sum-rate
  • Enables secure full-duplex wireless functionality
  • Provides real-time interference management

Algorithm Flow

Initialize Φ, P, W
Update ι (auxiliary)
Update τ (auxiliary)
Update P (precoders)
Update W (combiners)
Update Φ (via PDD)
Check Convergence
Output Solution

Performance Statistics

<10
BCD Iterations
<80
PDD Iterations
32
Typical RIS Elements
20
Transmit Power (dBm)

System Parameters

Parameter Value Description
Transmit Power 20 dBm Per FD user
Noise Power -80 dBm Background noise
Path-loss (RIS) ζ₀=-30dB, ε=2.2 Via RIS channel
Path-loss (Direct) ε=3.3 Direct channel
Rician Factor κ=5 Channel fading
RIS Elements 8-56 (M=32) Reflecting elements

Optimization Mathematics

Matrix Definition Purpose
A ∑αₖ|τₖ|²H*ᵣₑf,ₖwₖwₖᴴH⊤ᵣₑf,ₖ User interference
B ∑Hᵣₑf,ᵢ₋₁pᵢpᵢᴴHᴴᵣₑf,ᵢ₋₁ Precoder interference
C₁ ∑αₖ√(1+ιₖ)τₖ*Hᵣₑf,ₖ₋₁pₖwₖᴴH⊤ᵣₑf,ₖ Signal enhancement
Δ Kᴴ_gRᴴ_g[A⊤⊗B]RgKg + 1/(2ρ)KᴴgKg Optimization matrix

Performance Comparison

NR-BD-RIS (solid) R-BD-RIS (dashed) D-RIS (dotted) Sum-Rate Performance Number of RIS Elements

Security Features

One-way communication enforcement
Multi-user interference suppression
Eavesdropping prevention mechanisms
Real-time threat detection
Physical layer security protocols

Computational Complexity

Total: O(I_BCD × G × I_outer × I_inner × M_g² × M⁴)
BCD Framework: O(K²M²) per iteration
Precoder Update: O(K(M² + I_b N³))
Combiner Update: O(KN³)
PDD Method: O(GM_g²M⁴) (most intensive)
Non-reciprocal BD-RIS further enhances capability by breaking circuit reciprocity and channel reciprocity, enabling secure one-way communication among FD devices while suppressing signals from all other users.

Convergence Analysis

Algorithm 1 (BCD): Converges in <10 iterations
Algorithm 2 (PDD): Converges in <80 iterations
Constraint satisfaction: ||Φ-Ψ||∞ < 10⁻⁶
Penalty scaling: c ∈ (0.7, 0.95)
Objective function: Monotonic non-decreasing
Optimality: Guaranteed local optimum

Applications & Future Extensions

Physics-Compliant Modeling
Advanced structural scattering models for realistic RIS behavior
Multi-User Optimization
Sum-rate region optimization for large-scale deployments
Group-Connected Architectures
Enhanced BD-RIS designs for improved performance
MIMO Integration
Full-duplex MIMO system integration capabilities
Enhanced Security
Advanced physical layer security protocol development
Real-Time Implementation
Hardware acceleration and real-time processing systems