Sparsity Realization in User-Side Multilayer RIS

User-side reconfigurable intelligent surface (US-RIS)-aided communication has recently emerged as a promising solution to overcome the high hardware cost and physical size limitations of large-scale user side antenna arrays. This letter proposes, for the first time, a framework that realizes sparsity in multilayer US-RIS using two strategies, namely element-wise sparsity and geometric sparsity. The element-wise approach distributes a limited number of active elements irregularly across multiple layers, thereby exploiting additional spatial degrees of freedom and boosting the achievable rate. For further performance enhancement, a novel foldable RIS architecture leveraging geometric sparsity is proposed, achieving additional gains by optimizing the folding topology of its multilayer structure. Simulation results show that the proposed sparse architectures provide consistently higher achievable rates than existing designs.