Direction of Arrival Estimation Using Compresive Sensing - Usman, Koredianto
Direction of Arrival (DoA) of an object is a terminology on radar and sonar associated with the object arrival angle relative to position of an observer. DoA estimation techniques evolved from the classical era spurred by military needs especially in World War I and World War II, to the era of domestic applications such as navigation systems up till the era of distributed radar network (RDN) and wireless sensor network (WSN) at this time. In the era of RDN that has properties of low power as well as many sensors but limited transmission bandwidth, conventional DoA estimation technique such as Minimum Variance Distortionless Response (MVDR) and Multiple Signal Classi_cation (MUSIC) along with their derivative algorithms that rely on high resolution with large data samples cannot meet the needs of these distributed systems. One of the most promising techniques to reduce data and improve e_ciency is compressive sensing (CS). The use of CS for data reduction has been widely practiced by researchers on various applications including the DoA estimation. There are three main CS schemes for DoA estimation, which are: time sparsity, space sparsity, and angle sparsity schemes. The angle sparsity scheme provides the highest level of compression compared to the other two, so this scheme is widely popular among researchers. Although the advantage on small data size, the DoA estimate using angle sparsity CS requires a heavy reconstruction process. Several techniques had been proposed by researchers to speed up the computation time CS reconstruction, for example, using unitary transformation to change complex-valued signal to real-valued one for faster reconstruction. In this research, a different approach is proposed to speed up computation time using non-exhaustive scanning techniques. Non-exhaustive scanning is performed by scanning on limited directions where an object is located a priori. This non-exhaustive scanning technique can reduce the scanning direction about one third to one fifth as compared to the complete scan. With fewer scanning directions, the reconstruction process becomes faster. In addition, sensitivity of this non-exhaustive scanning in noisy environment is reduced by adding side scans. Three side scans are proposed in addition to non-exhaustive scanning which are the uniform, random, and progressive side scans. Computer simulation results show that the performance of non-exhaustive search with side scan is almost the same as the performance of complete scan with the number of scans one third less. Nevertheless, computation time in simulated cases did not increase three times correspondingly but only increased by about 70 percent. The nonlinearity of this relationship occurs because non-exhaustive technique needs more iteration compared to the complete scanning method. In addition to the non-exhaustive with side scan technique; this research also proposes two CS reconstruction algorithms in effort to speed up computation time. The first algorithm is weight point algorithm (WP Algorithm) and the second one is _rst order norm minimization via second order norm minimization (L1-L2 Algorithm). The WP Algorithm is based on the geometric interpretation of the solution problem of CS reconstruction by minimizing first order norm, while L1-L2 Algorithm is based on the second order norm solution and the searching for the direction to the _rst order norm solution from the already obtained second order norm. The direction search is performed by looking the highest projection of the second order norm solution to each coordinate axes. The L1-L2 Algorithm exploits the advantages of a second order norm solution which can be obtained analytically therefore no iteration is required in this process. The WP Algorithm has an advantage on the construction stability in high coherence environment, but computation complexity grows exponentially to the signal length, so that WP Algorithm is not practical for large dimension signals. The L1-L2 Algorithm, on the other hand, has faster computation time compared to convex programming and better stability than the greedy technique such as orthogonal matching pursuit (OMP). Simulation of L1-L2 algorithm for DoA estimation gives faster reconstruction speed as compared to reconstruction time using convex programming. The schemes and algorithms proposed in this research are thus expected to contribute as a stepping stone for the implementation of CS technique for DoA estimation on RDN in particular and for WSN applications in general.