A Low-complexity Structured Neural Network Approach to Intelligently Realize Wideband Multi-beam Beamformers

TL;DR

This paper addresses the beam-squint problem in wideband beamforming by employing true-time-delay (TTD) beamformers realized through Vandermonde delay matrices (DVM). It introduces a structure-imposed neural network (StNN) that embeds the DVM factorization into trainable layers with sparse weight matrices, including a non-trainable delay layer and a recursive factorization strategy to reduce arithmetic from $O(M^2L)$ to $O(pLM\log M)$. The authors demonstrate numerically at 24–32 GHz that StNN can accurately realize wideband multi-beam outputs while significantly reducing trainable parameters and FLOPs, enabling real-time, hardware-friendly intelligent beamforming. This work provides a practical path to scalable, low-complexity beamforming for mmWave/wideband systems and highlights tunable trade-offs between factorization depth and accuracy in structured neural networks.

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 delay Vandermonde matrix (DVM), answering the longstanding beam-squint problem. Thus, building on our work on classical algorithms based on DVM, we propose neural network (NN) architecture 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 space and computational complexities of the NN greatly. The proposed network architecture has O(pLM logM) complexity compared to a conventional fully connected L-layers network with O(M2L) complexity, where M is the number of nodes in each layer of the network, p is the number of submatrices per layer, and M >> p. We will show numerical simulations in the 24 GHz to 32 GHz range to demonstrate the numerical feasibility of realizing wideband multi-beam beamformers using the proposed neural 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 using 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 NN architecture shows a low-complexity NN realizing wideband multi-beam beamformers in real-time for low-complexity intelligent systems.

Figures (3)

• Figure 1: ML-based architecture of multi-beam beamforming: In the offline training, we train the neural network to align the input data by the weight matrix to the desired output data. In real-time deployment: RF signals from the antennas and low noise amplifiers (LNAs) are beamformed utilizing the structure imposed neural network, i.e., StNN. Once the multibeams are formed they will be sent to the digital processor.
• Figure 2: StNN architecture for predicting the output of the TTD beamformers. $2N$ neurons in the input layer (separating real-vales and imaginary parts of the received vector $\tilde{x}$ giving $2N$ neurons in the input vector $\underbar{x} \in \mathbb{R}^{2N}$), $4pN$ neurons in the hidden layer, where $p, N \in \mathbb{Z}^+$, $4pN$ neurons in each hidden layers and $2N$ neurons in the output vector $\underbar{y} \in \mathbb{R}^{2N}$ resulting the beamformed vector $\tilde{y} \in \mathbb{C}^N$.
• Figure 3: The figures (a) and (b) show training and validation results of the StNNs based on the different frequencies (i.e. 24GHz, 27GHz, and 32GHz) for $N = 16$. These graphs are obtained referencing the "Models" listed in Table \ref{['tab:MSE vs N']}. When StNN is executed for 1900 epochs, it converges to MSE values of $10^{-5}$. These graphs are obtained using Python (Version-3.10) along with the Pytorch (version-2.5) framework, and compiled with Levenberg-Marquardt optimizer.

Theorems & Definitions (5)

• Remark 2.1
• Proposition 3.1
• proof
• Remark 3.2
• Remark 4.1