Tensor-Based Channel Estimation for Massive MIMO-OFDM Systems

Abstract

Channel estimation is a crucial problem for massive multiple input multiple output (MIMO) systems to achieve the expected benefits in terms of spectrum and energy efficiencies. However, a considerable number of pilots are usually distributed over a large number of time-frequency resources using orthogonal frequency division multiplexing (OFDM) to effectively estimate a large number of channel coefficients in space and frequency domains, sacrificing spectral efficiency. In this paper, by assuming MIMO-OFDM transmission, we start by proposing a tensor-based minimum mean square error (MMSE) channel estimator that exploits the multidimensional nature of the frequency-selective massive MIMO channel in the frequency-domain, being a low-complexity alternative to the well-known vector-MMSE channel estimation. Then, by incorporating a 3D sparse representation into the tensor-based channel model, a tensor compressive sensing (tensor-CS) model is formulated by assuming that the channel is compressively sampled in space (radio-frequency chains), time (symbol periods), and frequency (pilot subcarriers). This tensor-CS model is used as the basis for the formulation of a tensor-orthogonal matching-pursuit (T-OMP) estimator that solves a greedy problem per dimension of the measured tensor data. The proposed channel estimator has two variants which may either resort to a joint search per tensor dimension or to a sequential search that progressively reduces the search space across the tensor dimensions. The complexities of the different tensor-based algorithms are studied and compared to those of the traditional vector-MMSE and vector-CS estimators. Our results also corroborate the performance-complexity tradeoffs between T-MMSE and T-OMP estimators, both being competing alternatives to their vector-based MMSE and OMP counterparts.

Tensor-Based Channel Estimation for Millimeter Wave MIMO-OFDM With Dual-Wideband Effects

“…We first consider the special case with negligible wideband-effects and apply a successive beam training strategy to perform the channel estimation procedure. 5 When the phase shifts (17) approximate to ones, i.e., the array size or system bandwidth is not large enough, the steering vectors in (16) approximate those in (14), and the channel matrix (17) at the kth subcarrier within an arbitrary time slot simplifies to…”

“…The main drawbacks of the TALS and its modified versions [34], [35] are: (i) the convergence speed of this iterative method is relatively slow, which incurs high burden of computational complexity; (ii) the alternating result heavily depends on the initialization state, which may converge to a biased local optimal solution. Moreover, the TALS method does not consider the intrinsic structure of factor matrices, which are usually a priori known to the system [13]- [17]. By exploiting the Vandermonde nature of B (3) , we develop an improved channel parameter estimation scheme aided by the SCPD algorithm according to Theorem 1.…”

“…A denoising-aided deep learning network was introduced to implement the CSI acquirement in [12]. Moreover, tensor-based signal processing schemes have been exploited for the design of channel estimators [13]- [17].…”

“…Moreover, large bandwidths of frequency-selective systems induce to the frequencywideband effect. However, most of the existing works [6]- [17] have not jointly considered the spatial-and frequency-wideband (dual-wideband) effects. In practice, there exist numerous challenges caused by dual-wideband effects in wideband MIMO systems.…”

Tensor completion-based 5G positioning with partial channel measurements

“…However, this reshaping does not account for the multidimensional grid structure inherent in the data [9] . The joint use of tensor modeling and CS techniques for channel estimation in massive MIMO systems has been addressed recently [2,16]. Alternatively, tensor decomposition-based subspace methods are proposed in [5,25].…”