Multilinear Singular Value Decomposition for Millimeter Wave Channel Parameter Estimation

Abstract

Fifth generation (5G) cellular standards are set to utilize millimeter wave (mmWave) frequencies, which enable data speeds greater than 10 Gbps and sub-centimeter localization accuracy. These capabilities rely on accurate estimates of the channel parameters, which we define as the angle of arrival, angle of departure, and path distance for each path between the transmitter and receiver. Estimating the channel parameters in a computationally efficient manner poses a challenge because it requires estimation of parameters from a high-dimensional measurement -particularly for multi-carrier systems since each subcarrier must be estimated separately. Additionally, channel parameter estimation must be able to handle hybrid beamforming, which uses a combination of digital and analog beamforming to reduce the number of required analog to digital converters. This paper introduces a channel parameter estimation technique based on the multilinear singular value decomposition (MSVD), a tensor analog of the singular value decomposition, for massive multiple input multiple output (MIMO) multi-carrier systems with hybrid beamforming. The MSVD tensor estimation approach provides a computationally efficient method and is shown to closely match the Cramer-Rao bound (CRB) of parameter estimates through simulations. Limitations of channel parameter estimation and communication waveform effects are also studied.

Tensor completion-based 5G positioning with partial channel measurements

“…2, we show the relation between the different defined vectors and the UE position. Rearranging the terms in (16)…”

“…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].…”

“…Standard 5G positioning algorithm is based on either CS approaches [17], which express the sparsity in an appropriate domain, or on tensor decomposition, where the dominant higher-order singular values can be related to the dominant signal paths [21,24]. Recently, a joint tensor decomposition and compressed sensing based multidimensional channel parameter estimation method is proposed in [16]. However, these methods do not account for the training overhead.…”

5G Positioning and Mapping With Diffuse Multipath

“…Standard 5G mmWave channel estimation is based on either compressive sensing approaches [18], which express the sparsity in an appropriate domain, or on tensor decompositions, where the dominant higher-order singular values can be related to the dominant signal paths [19], [20]. A joint tensor decomposition and compressed sensing based multidimensional channel parameter estimation method is proposed in [21]. However, these methods do not account for the intra-cluster spread of angles or delay.…”

Tensor Dictionary Manifold Learning for Channel Estimation and Interference Elimination of Multi-User Millimeter-Wave Massive MIMO Systems

“…However, for each dimension, one dimensional search is required and the complexity of the spectral search may still be unacceptably high for real-time problems. In [32], a multilinear singular value decomposition (MSVD) method is used for channel parameter estimation. The Tucker form of the MSVD enables paths to be extracted based on signal energy.…”