Subspace Estimation and Decomposition for Large Millimeter-Wave MIMO Systems

Abstract

Abstract-Channel estimation and precoding in hybrid analogdigital millimeter-wave (mmWave) MIMO systems is a fundamental problem that has yet to be addressed, before any of the promised gains can be harnessed. For that matter, we propose a method (based on the well-known Arnoldi iteration) exploiting channel reciprocity in TDD systems and the sparsity of the channel's eigenmodes, to estimate the right (resp. left) singular subspaces of the channel, at the BS (resp. MS). We first describe the algorithm in the context of conventional MIMO systems, and derive bounds on the estimation error in the presence of distortions at both BS and MS. We later identify obstacles that hinder the application of such an algorithm to the hybrid analog-digital architecture, and address them individually. In view of fulfilling the constraints imposed by the hybrid analog-digital architecture, we further propose an iterative algorithm for subspace decomposition, whereby the above estimated subspaces, are approximated by a cascade of analog and digital precoder/combiner. Finally, we evaluate the performance of our scheme against the perfect CSI, fully digital case (i.e., an equivalent conventional MIMO system), and conclude that similar performance can be achieved, especially at medium-to-high SNR (where the performance gap is less than 5%), however, with a drastically lower number of RF chains (∼ 4 to 8 times less).

Single-Carrier Modulation Versus OFDM for Millimeter-Wave Wireless MIMO

“…It is easy to show that optimization problems (21) and (22) are not convex optimization problem; inspired by [26], we thus resort to the Block Coordinate Descent for Subspace Decomposition (BCD-SD) algorithm, that basically is based on a sequential iterative update of the analog part and of the baseband part of the beamformers. The algorithm's recipe, whose complexity is tied to the third power of the number of RF chains, is reported in Algorithm 1.…”

“…In fact, it is sufficient to consider an auxiliary channel which is a simplified version of the actual channel in the sense that only a portion of the actual channel memory and/or a limited number of impairments are present. In particular, we will use the auxiliary channel law (26), where the sum of the interference and the thermal noise z(n) is assimilated to Gaussian noise with a proper covariance matrix. The transceiver models are compared in terms of ASE without taking into account specific coding schemes, being understood that, with a properly designed channel code, the information-theoretic performance can be closely approached.…”

A Sequential Subspace Method for Millimeter Wave MIMO Channel Estimation

“…By using the knowledge of sparse signal reconstruction, orthogonal matching pursuit (OMP) [8] and sparse Bayesian learning (SBL) [9] were motivated to estimate the sparse mmWave channel in angular domain. Alternatively, if the channel is rank-sparse, it is possible to directly extract sufficient channel subspace information for the precoder design [10], [11], [16]. These subspace-based methods employ the Arnoldi iteration [16] to estimate the channel subspaces and knowledge of matrix completion [10], [11] to estimate the low-rank mmWave channel information.…”

“…Though the sparse signal reconstruction [8], [9] and matrix completion [10], [11] techniques can reduce the channel use overhead compared to traditional beam alignment techniques, the training sounders of these techniques [8]- [11] are predesigned and high-dimensional, which leads to the fact that these works suffer from explosive computational complexity as the size of arrays grows. To reduce the computational complexity, the adaptive training techniques have been investigated in [4], [16], [17], where the training sounders can be adaptively designed based on the feedback or two-way training. But these adaptive training techniques could not guarantee the performance on mean squared error (MSE) and/or subspace estimation accuracy.…”

“…Compared to the existing channel estimation techniques in arXiv:2003.11738v1 [eess.SP] 26 Mar 2020 [8]- [11], the training sounders of the proposed approach are adaptively designed to reduce the channel use overhead and computational complexity. Moreover, the proposed approach is open-loop, thus it has no requirements of feedback and twoway channel sounding compared to priori adaptive training techniques [4], [16], [17]. The main contributions of this paper are described as follows:…”