Efficient heterogeneous parallel programming for compressed sensing based direction of arrival estimation

Abstract

In the direction of arrival (DoA) estimation, typically sensor arrays are used where the number of required sensors can be large depending on the application. With the help of compressed sensing (CS), hardware complexity of the sensor array system can be reduced since reliable estimations are possible by using the compressed measurements where the compression is done by measurement matrices. After the compression, DoAs are reconstructed by using sparsity promoting algorithms such as alternating direction method of multipliers (ADMM). For the given procedure, both the measurement matrix design and the reconstruction algorithm may include computationally intensive operations, which are addressed in this study. The presented simulation results imply the feasibility of the system in real-time processing with energy efficient implementations. We propose employing parallel programming to satisfy the real-time processing requirements. While the measurement matrix design has been accelerated 16× with CPU based parallel version with respect to the fastest serial implementation, ADMM based DoA estimation has been improved 1.1× with GPU based parallel version compared to the fastest CPU parallel implementation. In addition, we achieved, to the best of our knowledge, the first energy-efficient real-time DoA estimation on embedded Jetson GPGPUs in 15 W power consumption without affecting the DoA accuracy performance. K E Y W O R D S compressed sensing, direction of arrival estimation, embedded GPGPU, parallel programming, real time computing INTRODUCTIONIn many engineering applications, the main concern is to solve a linear system with many unknowns and fewer equations. In such systems, infinitely many solutions might satisfy the system and the goal is to find the best one among them. Traditionally, the solution having the minimum energy (i.e., the minimum 𝓁 2 -norm) is selected. Compressed sensing (CS) 1,2 is a signal processing technique that recovers sparse signals from fewer number of measurements. It can be applied to many fields since most natural signals are sparse in some transformation domain. 3 However, the problem of finding the most sparse solution is NP-hard. 4 Instead, CS proposes using 𝓁 1 -norm minimization, which is a well-known sparsifying algorithm leading to convex optimization problems that can be efficiently solved using algorithms based on alternating direction method of multipliers (ADMM). 5 In addition to this novel reconstruction approach, CS theory also enables accurate estimations by using compressed measurements provided that the measurement matrix satisfies some energy-preserving conditions. 1,2 Direction of arrival (DoA) estimation is a well-known research area in which the CS based techniques are commonly used. Typically, sensor arrays are used as the signal impinges on each sensor in different times causing a phase