Deep Learning-based Compressive Beam Alignment in mmWave Vehicular Systems

TL;DR

A deep learning-based technique to design a structured compressed sensing matrix that is well suited to the underlying channel distribution for mmWave vehicular beam alignment achieves better beam alignment than standard CS techniques which use random phase shift-based design.

Abstract

Millimeter wave vehicular channels exhibit structure that can be exploited for beam alignment with fewer channel measurements compared to exhaustive beam search. With fixed layouts of roadside buildings and regular vehicular moving trajectory, the dominant path directions of channels will likely be among a subset of beam directions instead of distributing randomly over the whole beamspace. In this paper, we propose a deep learning-based technique to design a structured compressed sensing (CS) matrix that is well suited to the underlying channel distribution for mmWave vehicular beam alignment. The proposed approach leverages both sparsity and the particular spatial structure that appears in vehicular channels. We model the compressive channel acquisition by a two-dimensional (2D) convolutional layer followed by dropout. We design fully-connected layers to optimize channel acquisition and beam alignment. We incorporate the low-resolution phase shifter constraint during neural network training by using projected gradient descent for weight updates. Furthermore, we exploit channel spectral structure to optimize the power allocated for different subcarriers. Simulations indicate that our deep learning-based approach achieves better beam alignment than standard CS techniques which use random phase shift-based design. Numerical experiments also show that one single subcarrier is sufficient to provide necessary information for beam alignment.

Figures (14)

• Figure 1: Illustration of the ray tracing setup in which cars and trucks are randomly dropped in the two lanes of the urban canyon. Receivers are mounted on the top center of the low vehicle. The BS is mounted on a street-side lamp-post. The figure illustrates the top five strongest paths of the channel for a certain receiver. Our channel model includes the effect of multiple reflections that occur at the buildings and the vehicles.
• Figure 2: An illustration of the system model in 2D-CCS. The BS has a single RF chain and is equipped with a uniform planar phased array of size $N\times N$, and there is one single antenna at the receiver. The BS applies phase shift matrix in successive $M$ time slots. The $m$-th CS channel measurement is the projection of the channel on the phase shift matrix ${\mathbf{P}}[m]$.
• Figure 3: For the vehicular communication scenario in our simulations, the beamspace prior is non-zero over a small set in the space of 2D-DFT directions. The blue curves represent the LoS directions associated with vehicles on the two lanes. Random phase shift-based CS uses quasi-omnidirectional beams and does not exploit such an information.
• Figure 4: An illustration of how to implement 2D circular convolution using CNN. In Fig. \ref{['fig:convillus']}a, we show an implementation of circular convolution of two real matrices ${\mathbf{H}}_\mathrm R$ and ${\mathbf{P}}_\mathrm R$ by repeating ${\mathbf{H}}_\mathrm R$. Fig. \ref{['fig:convillus']}b demonstrates an example of a 2-channel CNN. The result sums up the product of $ac$ and $bd$. Fig. \ref{['fig:convillus']}c shows an example that a 2-channel CNN can achieve the product of two complex variables $a + \mathsf{j}b$ and $c + \mathsf{j}d$, where the left part of the correlation in Fig. \ref{['fig:convillus']}c is the real component and the right is imaginary. Lastly, Fig. \ref{['fig:convillus']}d combines the idea in Fig. \ref{['fig:convillus']}b and Fig. \ref{['fig:convillus']}c and demonstrates how to implement 2D circular convolution between two complex matrices.
• Figure 5: Channel measurements in 2D-CCS are realized using convolutional filters $\mathbf{P}_{\mathrm{R}}$ and $\mathbf{P}_{\mathrm{I}}$. Using end-to-end learning, the base matrix in 2D-CCS, i.e., $\mathbf{P}=\mathbf{P}_{\mathrm{R}}+\mathsf{j} \mathbf{P}_{\mathrm{I}}$, is optimized for compressively measuring the channel and maximize the probability of beam alignment. The fully connected layers are optimized to predict the optimal beam direction based on the compressive channel measurements.