SWISS: Spectrum Weighted Identification of Signal Sources for mmWave Systems Ziming Cheng * , Jingyue Huang * , Meixia Tao * , and Pooi-Yuen Kam † ∗ Dept. of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China † Department of Electrical and Computer Engineering, National University of Singapore, Singapore Emails: {charlotte311, huangjingyue, mxtao}@sjtu.edu.cn, elekampy@nus.edu.sg Abstract—This paper considers the channel estimation prob- lem in millimeter-wave (mmWave) systems where a single- antenna user communicates with a massive multiple-input multiple-output (MIMO) base station (BS) in the uplink. Unlike many existing works which estimate the channel gain under the assumption that the number of channel paths is given a priori, we address first the problem of path-number identification. By taking the weighted discrete Fourier transform (WDFT) of the received noisy signal, we formulate an optimization problem to determine the optimum combination of DFT components in this weighted spectrum that leads to a time-domain reconstructed signal (the channel vector) that is at the minimum Euclidean distance from the received signal. Our algorithm, called SWISS (Spectrum Weighted Identification of Signal Sources), is an accurate and computationally efficient means for identifying the paths in the channel vector, providing the information needed for BS beamforming. Once the paths are identified, their individual directions-of-arrival (DoAs) and complex fading gains can be obtained easily. Simulation results for the case of no power leakage in the DFT are presented to demonstrate the effectiveness of SWISS. I. I NTRODUCTION Communication over millimeter wave (mmWave) bands from 30 to 300 GHz is a promising technology for 5G mobile networks to provide multi-gigabit communication services [1]. Beamforming with massive multiple-input multiple-output (MIMO) antennas in mmWave communications can further boost the transmission coverage and reliability. However, to exploit the beamforming gains, the transmitter must know the perfect channel state information (CSI). It is very challenging to obtain the accurate CSI with the deployment of large- scale antenna arrays. The conventional training strategy with orthogonal pilots [2] cannot be applied here since it requires that the minimum length of the training sequence must be equal to the number of transmit antennas, which causes severe overhead. Moreover, as the size of channel dimension increases, the matrix operations involved in channel estimation induce prohibitively high complexity in practical systems. Recent contributions to the channel estimation problem in mmWave massive MIMO communication, e.g., [3]–[6], mostly exploit the sparse nature of the mmWave channel This work was done while P. Y. Kam was a visiting professor at Shanghai Jiao Tong University, Shanghai, China. This work is supported by the National Natural Science Foundation of China under grants 61571299 and 61329101. to reduce the effective number of channel parameters. The authors in [3] consider the joint design of hybrid precoding and channel estimation, and propose a compressed sensing- based channel estimation method for the hybrid architecture. [4] develops an efficient channel estimation algorithm based on an overlapped beam pattern design. In [5], the authors propose a two-dimensional discrete Fourier transform (DFT)- based algorithm to estimate the angular information and the channel gain separately in a downlink 60GHz indoor system. The authors in [6] build a DFT-based spatial basis expansion model (SBEM) to decrease the parameter dimensions of the channel and propose a unified channel estimation strategy for multiuser time-division duplex (TDD)/frequency-division duplex (FDD) massive MIMO systems. Note that all the aforementioned works [3]–[6] assume that the number of paths is known a priori. Estimating the number of paths is critically important for reconstructing the actual channel. Given the similarity between direction- of-arrival (DoA) estimation and multiple-discrete-frequency signal estimation, the MUSIC algorithm [7] can be applied to estimate the number of paths and the corresponding DoAs. However, the singular value decomposition (SVD) method in the MUSIC algorithm works only if the complex channel gains of the paths are independently fast fading in time. For massive MIMO channel estimation, a block-wise constant fading channel model is more accurate and practical, which does not meet the independence requirement of the SVD method. Moreover, the SVD operation in MUSIC is of high computational complexity and is not practical for implemen- tation in large scale systems. Thus, in this paper, we develop a simple and effective algorithm to detect the number of paths accurately for a massive-MIMO, mmWave channel based on a block-wise constant fading model. This frequency-domain algorithm enables us to also estimate the DoA of each path and its complex fading gain. In this paper, we assume that the channel signal arriving at the BS from a single-antenna user consists of an unknown number of discrete paths, each with unknown complex am- plitude and DoA. By taking the DFT of the received signal, we can, in principle, determine its structure in the angular (frequency) domain, if not for the received additive white Gaussian noise (AWGN). Nevertheless, despite the presence of the AWGN, we can determine the optimum combination of