Beampattern Design for Transmit Architectures Based on Reconfigurable Intelligent Surfaces

In this work, we tackle the problem of beampattern design for a transmit system employing a large reconfigurable intelligent surface (RIS) to redirect radio frequency signals emitted by a few active antennas (sources). We begin by establishing a convenient signal model and discussing the impact of signal bandwidth, source-RIS channel, and system geometry on our derivations. Subsequently, we propose a joint optimization of the waveform emitted by each source and the phase shifts introduced by the RIS. The objective is to match a desired space-frequency distribution of the far-field radiation pattern, relevant to both radar and communication applications. We present a sub-optimal solution to this problem, subject to a constraint on the total power radiated by the sources and, optionally, on the constant modulus of the waveforms. The provided example demonstrates the effective beampattern shaping capabilities of this RIS-based transmit architecture. Specifically, for the same array size and the same desired radiation pattern, the resulting approximation error is comparable to that obtained with a fully-digital MIMO array, especially when constant-modulus waveforms are enforced, and significantly smaller than that of a phased array.