Efficient Beam Alignment for Millimeter Wave Single-Carrier Systems With Hybrid MIMO Transceivers

Abstract

Communication at millimeter wave (mmWave) bands is expected to become a key ingredient of next generation (5G) wireless networks. Effective mmWave communications require fast and reliable methods for beamforming at both the User Equipment (UE) and the Base Station (BS) sides, in order to achieve a sufficiently large Signal-to-Noise Ratio (SNR) after beamforming. We refer to the problem of finding a pair of strongly coupled narrow beams at the transmitter and receiver as the Beam Alignment (BA) problem. In this paper, we propose an efficient BA scheme for single-carrier mmWave communications.In the proposed scheme, the BS periodically probes the channel in the downlink via a pre-specified pseudo-random beamforming codebook and pseudo-random spreading codes, letting each UE estimate the Angle-of-Arrival / Angle-of-Departure (AoA-AoD) pair of the multipath channel for which the energy transfer is maximum. We leverage the sparse nature of mmWave channels in the AoA-AoD domain to formulate the BA problem as the estimation of a sparse non-negative vector. Based on the recently developed Non-Negative Least Squares (NNLS) technique, we efficiently find the strongest AoA-AoD pair connecting each UE to the BS. We evaluate the performance of the proposed scheme under a realistic channel model, where the propagation channel consists of a few multipath scattering components each having different delays, AoAs-AoDs, and Doppler shifts. The channel model parameters are consistent with experimental channel measurements. Simulation results indicate that the proposed method is highly robust to fast channel variations caused by the large Doppler spread between the multipath components.Furthermore, we also show that after achieving BA the beamformed channel is essentially frequency-flat, such that single-carrier communication needs no equalization in the time domain.

Active Learning and CSI Acquisition for mmWave Initial Alignment

“…A higher error exponent is shown across a wide range of raw SNR even when only 1-bit of information about the measurement is available to hieP M . The numerical simulations show a significant improvement on the spectral efficiency over the previous vanilla bisection algorithm of [1] and the random search algorithm modelled as a best case of [12], [13], demonstrating a first work of possible standalone mmWave communication.…”

“…While these early studies did not take the practical beam patterns into account, this logarithmic scaling was later also confirmed and reported in more practical systems with realistic arXiv:1812.07722v4 [cs.IT] 4 Sep 2019 Fig. 1: The active learning process of the AoA φ is to design the beams w t ∈ W S adaptively for the sequential collection of the observations y t , from which at the ending of the collection is to be used for the estimation of the AoA φ. and empirically precise beam patterns ( [1], [12], [13]) with the caveat of a sufficiently large SNR model. In particular, [1] carefully developed a hierarchical beamforming codebook which in the noiseless setting allows for an (adaptive) binary search over the angular space; increasing transmission power and/or time is then used to combat the measurement noise.…”

“…In particular, [1] carefully developed a hierarchical beamforming codebook which in the noiseless setting allows for an (adaptive) binary search over the angular space; increasing transmission power and/or time is then used to combat the measurement noise. The authors in [12], [13] showed that similar performance gains can also be achieved by a non-adaptive strategy. More specifically, the authors of [12] proposed random hash functions to generate a random beamforming codebook whose acquisition time, they showed, grows only logarithmically with target resolution/error probability.…”

“…The logarithmic scaling (of search time with angular resolution) could also be obtained when viewing the problem as that of sparse estimation with compressive measurements (see [14] and references therein). Indeed, the authors of [13] recover the signal direction with a non-negative least square estimate from Compressive Sensing by measuring the received power via a random beamforming codebook which hashes the angular directions similarly to [12].…”

Fast Beam Alignment for Millimeter Wave Communications: A Sparse Encoding and Phaseless Decoding Approach

“…Since the RF chain is expensive and power consuming, we have R ≪ N . Note that although a single receiver is considered in our paper, the extension of our scheme to the multi-user scenario is straightforward, in which case the base station periodically broadcasts a common codeword that is decoded by each user to extract its associated channel information [30]. Each user then sends the index of the beam corresponding to the selected angle-of-departure (AoD) to the base station via a random access control channel.…”