Deep Learning-Based CS under IQ imbalance For Channel Estimation of mmWave phased arrays

Introduction

In this repository, we approach the problem of IQ imbalance in channel estimation of mmWave phased arrays from a compressed sensing (CS)/neural network point of view.

We refer the interested reader to the pdf file Data_Compression__Deep_Learning_Based_CS_under_IQ_Imbalance.pdf for a full report on the problem and the approach.

We are able to find a remarkably small neural network solution, able to completely negate the effects of IQ imbalance, as well as faithfully reconstruct the signal for a range of SNR. Plots of NMSE for various models are shown below

Additionally, we are able to restrict the values of the CS matrix even further, to a discrete set defined by $q \in { \pm \pi, \pm \frac{1}{2}\pi, 0}$ corresponding to a 5-bit limited resolution phased-array antenna, allowing the deployment on low-cost and complexity phased-array antenna setup! The results are shown below.

Below we show how a signal is reconstructed using the algorithm

Methodology

We use autoencoder based compressed sensing to reconstruct the chanel from limited measurements, allowing us to find a good approximation of the original channel of size 100 from just 40 measurements!

A visual representation of the measurement model is given below

where we model a phased-array antenna setup via a compressed sensing matrix. A known symbol is sent through the channel, resulting in the vector $h$, which is measured at $N$ timesteps where at each timestep the phased array setup is adjusted. The phased-array setup is then modelled as a restricted CS matrix, where all values are restricted to $e^{jq}$.

This matrix is trained via the Pytorch architecture via an autoencoder setup shown below

We then add noise, reduce the amount of measurements and add IQ imbalance. The IQ imbalance is a result of an imbalance in the phase and amplitude of the local oscillator (LO) at the receiver (RX) end. A schematic is given below, courtesy of ¹

Footnotes

1. A. -A. A. Boulogeorgos, V. M. Kapinas, R. Schober and G. K. Karagiannidis, "I/Q-Imbalance Self-Interference Coordination," in IEEE Transactions on Wireless Communications, vol. 15, no. 6, pp. 4157-4170, June 2016, doi: 10.1109/TWC.2016.2535441. ↩