Spatial-Frequency Estimation for OFDM System with Coprime Array

Gang Shao,Lei Yin,Wen-Qin Wu,Chen-Yang Ding,Xiao-Yuan Zhang,Wang Zheng

doi:10.1155/2021/9998342

Abstract

Orthogonal frequency division multiplexing (OFDM) is the key technique of the communication system. In this paper, coprime array is designed in OFDM system to obtain joint direction of arrival (DOA) and carrier frequency offset (CFO) estimates. The proposed system can achieve beamforming and adaptive signal processing, reduce the multipath fading, and attain angle diversity. Meanwhile, coprime array has the advantages of extended array aperture, increased degrees of freedom, and reduced mutual coupling effect, which is adaptable in OFDM system. Moreover, this paper proposes a low-complexity parameter algorithm with superior performance, which first exploits propagator method (PM) as the initialization and then parallel factor (PARAFAC) method is employed for the accurate DOA and CFO estimation. Simulation results verify the effectiveness of the OFDM coprime array system and the proposed low-complexity multiparameter algorithm.

Highlights

Array signal processing is to arrange several sensors into sensor array to collect spatial signals and output discrete observation data related to signal sources [1]
The contributions of this paper are concluded as follows: (1) We model the problem of spatial-frequency estimation for Orthogonal frequency division multiplexing (OFDM) system with parallel factor (PARAFAC)
We summarize the merits of the proposed PMPARAFAC algorithm as follows: (a) The proposed algorithm initializes the carrier frequency offset (CFO) estimation by propagator method (PM). It needs no eigen decomposition which takes a great amount of calculation burden (b) Joint Direction of arrival (DOA) and CFO estimates can be obtained by the PARAFAC algorithm

Summary

Introduction

Array signal processing is to arrange several sensors into sensor array to collect spatial signals and output discrete observation data related to signal sources [1]. Reference [11] introduces compressed sensing into coprime array to achieve DOA estimation. A search-free DOA estimation method for coprime array is proposed in [12], which avoids spectral peak search and reduces the computational complexity significantly. Compared with the general coprime array, the number of elements required can be greatly reduced under the goal of achieving the same virtual aperture and degree of freedom. Some subspacebased blind estimation methods such as MUSIC and ESPRIT can achieve high-precision CFO estimation They require a virtual carrier and will bring a certain loss of spectral efficiency. Compared with uniform linear array (ULA), coprime array has extended array aperture and reduced mutual coupling effect (3) A low-complexity multiparameter estimation algorithm is proposed to reduce the computational burden, where PM is utilized as the coarse initialization and PARAFAC algorithm as the accuracy estimates. We use lowercase (uppercase) bold character to denote vector (matrix). ð⋅ÞT is transpose of a matrix or vector. ð⋅Þ−1 denotes matrix inverse and ð⋅Þ+ denotes matrix pseudoinverse, respectively. ⊙ represents the Khatri-Rao product. diag ð⋅Þ symbolizes a diagonal matrix that uses the elements of the matrix as its diagonal element. k⋅kF denotes Frobenius norm and trð⋅Þ represents the trace of the matrix, which is the sum of the elements on the main diagonal of the matrix

Preliminaries

Joint Parameter Estimation Algorithm

PARAFAC Algorithm

Simulation Results

Conclusions