Sequential Learning of CSI for MmWave Initial Alignment

Abstract

MmWave communications aim to meet the demand for higher data rates by using highly directional beams with access to larger bandwidth. An inherent challenge is acquiring channel state information (CSI) necessary for mmWave transmission. We consider the problem of adaptive and sequential learning of the CSI during the mmWave initial alignment phase of communication. We focus on the single-user with a single dominant path scenario where the problem is equivalent to acquiring an optimal beamforming vector, where ideally, the resulting beams point in the direction of the angle of arrival with the desired resolution. We extend our prior by proposing two algorithms for adaptively and sequentially selecting beamforming vectors for learning of the CSI, and that formulate a Bayesian update to account for the time-varying fading model. Numerically, we analyze the outage probability and expected spectral efficiency of our proposed algorithms and demonstrate improvements over strategies that utilize a practical hierarchical codebook.

Variational Hierarchical Posterior Matching for mmWave Wireless Channels Online Learning

“…We start this section by first reviewing the details of the vanilla HiePM scheme [7], showing that knowledge of the channel gain α as well as the noise variance σ 2 is necessary to make such a search strategy usable in practice. We then detail our main contribution, which consists of augmenting HiePM with a novel variational model comparison based approximate inference framework [10] to account for the uncertainties about α and σ 2 B and thus overcome the shortcomings, as detailed in the introduction, of the vanilla HiePM and modified HiePM schemes proposed in [7] and [9] respectively.…”

“…Chiu et al have shown in that contribution that using posterior matching [8] together with hierarchical beam search [4] can significantly reduce the initial access acquisition time while keeping the corresponding misalignment probability relatively low, provided that the channel's complex gain and operating signal-to-noise ration (SNR) are fully known to the communicating devices. These limiting constraints were relaxed in [9] by proposing to augment HiePM with extra simplifying assumptions on the statistical properties of the channel's CSI and then to use either a sampling scheme or a linear filtering scheme (Kalman filter) to learn it in parallel to running HiePM. Although this latter extension of the vanilla HiePM makes it robust with respect to uncertainties on the channel's CSI, it still presents some limitations.…”

“…Our contribution, in this work, which we dub "Variational HiePM (V-HiePM)" will address shortcomings of proposals in both of the aforementioned works [7], [9]. Specifically, we will augment HiePM with a variational approximate inference model [10] that will:…”

“…The first and second order moments of α are the only assumed known values in our model 8. In the above, CN (•; µ, λ) denotes the complex Gaussian pdf with mean µ and precision λ, Γ(•; a, b) denotes the Gamma pdf with shape and rate parameters a and b 9. Note that (10) and (11) can be re-written, after performing some algebra, in a recursive format w.r.t their terms involving summation over measurements epochs.…”

Deep Active Learning Approach to Adaptive Beamforming for mmWave Initial Alignment

“…It is shown that the hiePM algorithm in [6], which is mainly devised from the algorithms for sequential noisy search strategies [7] and Bayesian active learning from imperfect labelers [8,9], can achieve better performance as compared to the bisection algorithm in [5]. While the original hiePM algorithm is restricted to the scenario that the fading coefficient of the single-path channel is known at the BS, the recently proposed variants of hiePM extend the results to the more realistic case in which the fading coefficient is unknown, either by using Kalman filter tracking of the fading coefficient in [10] or by using the variational Bayesian inference framework in [11].…”