Millimeter-Wave Beamformed Full-Dimensional MIMO Channel Estimation Based on Atomic Norm Minimization

Abstract

The millimeter-wave (mmWave) full-dimensional (FD) MIMO system employs planar arrays at both the base station and user equipment and can simultaneously support both azimuth and elevation beamforming. In this paper, we propose atomic-norm-based methods for mmWave FD-MIMO channel estimation under both uniform planar arrays (UPA) and non-uniform planar arrays (NUPA). Unlike existing algorithms such as compressive sensing (CS) or subspace methods, the atomic-norm-based algorithms do not require to discretize the angle spaces of the angle of arrival (AoA) and angle of departure (AoD) into grids, thus provide much better accuracy in estimation. In the UPA case, to reduce the computational complexity, the original largescale 4D atomic norm minimization problem is approximately reformulated as a semi-definite program (SDP) containing two decoupled two-level Toeplitz matrices. The SDP is then solved via the alternating direction method of multipliers (ADMM) where each iteration involves only closed-form computations. In the NUPA case, the atomic-norm-based formulation for channel estimation becomes nonconvex and a gradient-decentbased algorithm is proposed to solve the problem. Simulation results show that the proposed algorithms achieve better performance than the CS-based and subspace-based algorithms.

An Overview of Enhanced Massive MIMO With Array Signal Processing Techniques

“…To avoid the enlarged problem size due to the vectorization-based atomic norm minimization in the 2D-angle scenarios, Tian et al [103] proposed a decoupled atomic norm minimization technique and its theoretical results were provided in [104]. Moreover, Tsai et al [105] proposed an atomic-norm-denoising-based method for mmWave FD-MIMO channel estimation. Tirkkonen et al [106] formulated mmWave MIMO channel estimation as atomic norm denoising problem and then designed the multi-user precoder.…”

User Selection for Millimeter Wave Non-Uniform Full Dimensional MIMO

“…For the digital transceiver, the proposed algorithm utilizes the correlation information between the users' channels to maximize the sum data rate. The non-uniform spacing of the NURA structure can reduce the channel correlation between the users since the spacing between two antenna elements in the array can be greater than the half wavelength [8]. However, it could not still be zero in the NURA for dense scenarios.…”

“…Eliminate the κ th 1 user channel fromĤ [n r , n c ] = size Ĥ 16: end while After the selection of K u users is completed through Algorithm 1, the ZF precoding is performed as given in (8) using the K u × N T dimensional resulting channel matrix of H.…”

“…Therefore, the performance of the downlink multiuser system can be enhanced by utilizing NURA at the base station (BS). For the mmWave communication systems, the NURA configuration has been examined in [8] by considering only the channel estimation aspects. For a multiuser system, the BS may not serve a large number of users simultaneously due to the hardware limitations.…”

Spectral and Energy Efficient Low-Overhead Uplink and Downlink Channel Estimation for 5G Massive MIMO Systems

“…It is also based on CS algorithms. To obtain the DL channel-vector, we employ classical narrowband ray-based mmWave channel model which is given by [ 30 , 31 ]: where is the DL channel-vector for j th user, that is also required by the BS for precoding and power allocation; is the number of resolvable paths from BS to j th UE; is the i.i.d complex-gain of the i -th propagation-path of the j -th UE having zero mean and unit variance; is the i -th path-AoD of the j -th UE; is the steering-vector representing the antenna-response of the i -th path of the j -th UE.…”