Active Learning and CSI Acquisition for mmWave Initial Alignment

Abstract

Millimeter wave (mmWave) communication with large antenna arrays is a promising technique to enable extremely high data rates due to large available bandwidth in mmWave frequency bands. In addition, given the knowledge of an optimal directional beamforming vector, large antenna arrays have been shown to overcome both the severe signal attenuation in mmWave as well as the interference problem. However, fundamental limits on achievable learning rate of an optimal beamforming vector remain.This paper considers the problem of adaptive and sequential optimization of the beamforming vectors during the initial access phase of communication. With a single-path channel model, the problem is reduced to actively learning the Angle-of-Arrival (AoA) of the signal sent from the user to the Base Station (BS). Drawing on the recent results in the design of a hierarchical beamforming codebook [1], sequential measurement dependent noisy search strategies [2], and active learning from an imperfect labeler [3], an adaptive and sequential alignment algorithm is proposed.For any given resolution and error probability of the estimated AoA, an upper bound on the expected search time of the proposed algorithm is derived via Extrinsic Jensen-Shannon Divergence. The upper bound demonstrates that the search time of the proposed algorithm asymptotically matches the performance of the noiseless bisection search up to a constant factor, in effect, characterizing the AoA acquisition rate. Furthermore, the upper bound shows that the acquired AoA error probability decays exponentially fast with the search time with an exponent that is a decreasing function of the acquisition rate.Numerically, the proposed algorithm is compared with prior work where a significant improvement of the system communication rate is observed. Most notably, in the relevant regime of low (−10dB to +5dB) raw SNR, this establishes the first practically viable solution for initial access and, hence, the first demonstration of stand-alone mmWave communication.

Sequential Learning of CSI for MmWave Initial Alignment

“…In this work we focus on relative performance, although the physical properties corresponding to this range of raw SNR (like cell size, and bandwidth) can be defined as in ( Fig. 6 in [8]).…”

“…This work follows most closely [7], where a fixed size hierarchical codebook and a bisection algorithm for sequentially selecting beamforming vectors to obtain the AoA are proposed. Our prior work [8], which proposes a fully adaptive initial alignment method based on posterior matching, theoretically characterizes an upper-bound on the probability of error in the AoA acquisition under a known static fading coefficient α, and shows a significant improvement in the system communication rate over [7] and random beamforming method of [4]. For a slightly mismatched estimate of the fading coefficient α (i.e.…”

“…The idea is to mitigate the effects of imperfect channel knowledge under a dynamic channel by augmenting the detection of the AoA to include simultaneous estimation of α for a given user. We propose two algorithms that work with the searching methods of our prior work [8] in order to fully learn the CSI (AoA and α). Specifically, the contributions of the paper are as follows:…”

“…• First, we propose a direct extension of our prior work [8] to be robust to a time-varying fading model by adapting the posterior matching based strategy to include estimation of α. • In light of excessive computations required to compute a Baysian posterior, we develop a heuristic approximation with low memory complexity.…”

“…This strategy compliments the sequential detection of AoA with estimation of the fading coefficient via a Kalman filter. • The proposed algorithms are compared to our prior work [8] and the bisection algorithm of [7] using the performance measures of outage probability and expected spectral efficiency. Numerically, we show improvements over [7] and [8], which suggests promising performance by our strategies for combining the learning of the AoA of the fading coefficients in the relevant regime of low (−10dB to +5dB) raw SNR.…”