A Low-Complexity Structured Neural Network Approach to Intelligently Realize Wideband Multi-Beam Beamformers

Abstract

True-time-delay (TTD) beamformers can produce wideband squint-free beams in both analog and digital signal domains, unlike frequency-dependent FFT beams. Our previous work showed that TTD beamformers can be efficiently realized using the elements of the delay Vandermonde matrix (DVM), answering the longstanding beam-squint problem. Thus, building on our work on DVM algorithms, we propose a structured neural network (StNN) to realize wideband multi-beam beamformers using structure-imposed weight matrices and submatrices. The structure and sparsity of the weight matrices and submatrices are shown to reduce the computational complexity of the NN significantly. The proposed StNN architecture has $\mathcal {O} \boldsymbol {(p L M} \log \boldsymbol M)$ complexity compared to a conventional fully connected L-layers network with $\mathcal {O}(M^{2}L)$ complexity, where M is the number of nodes in each layer of the network, p is the number of sub-weight matrices per layer, and $M \gt \gt p$ . We show numerical simulations in the 24 to 32 GHz range to demonstrate the numerical feasibility of realizing wideband multi-beam beamformers using the proposed StNN architecture. We also show the complexity reduction of the proposed NN and compare that with fully connected NNs, to show the efficiency of the proposed architecture without sacrificing accuracy. The accuracy of the proposed NN architecture was shown in terms of the mean squared error, which is based on an objective function of the weight matrices and beamformed signals of antenna arrays, while also normalizing nodes. The proposed StNN’s robustness was tested against channel impairments by simulating with Rayleigh fading at different signal-to-noise ratios (SNRs). We show that the proposed StNN architecture leads to a low-complexity NN to realize wideband multi-beam beamformers, enabling a path for reconfigurable intelligent systems.