DOA Estimation Based on Approximate l0 Norm of Natural Logarithm Composite Function

doi:10.12382/bgxb.2022.0025

Abstract

Abstract:

A DOA estimation algorithm based on a natural logarithm compound function approximating l₀ norm is proposed to address the issues of slow convergence and low accuracy of existing compressed-sensing-based DOA estimation algorithms. We transform the problem of solving the l₀ norm into an optimization problem of approximating the l₀ norm by using a natural logarithm compound function. The Newton iteration method is employed to obtain the iteration expression of the natural logarithm compound function (for approximating l₀ norm).The optimal solution of Newton iteration is obtained through inside and outside double-loop iteration, where the outside loop controls the magnitude of function approximation factor σ, and the inside loop solves the Newton iteration expression using the steepest descent method. The optimal solution of the approximate l₀ norm is obtained after finite iterations, and the estimated value of DOA can be obtained. Simulation results show that the proposed algorithm achieves effective DOA estimation under the condition of a single snapshot, and outperforms the existing smoothened l₀ norm algorithm and its improved algorithms in terms of speed and accuracy.

Key words: DOA estimation, compressed sensing, approximate l₀ norm, natural logarithm composite function

SHAN Zebiao, CHANG Limin, LIU Xiaosong, WANG Yuxiang. DOA Estimation Based on Approximate l₀ Norm of Natural Logarithm Composite Function[J]. Acta Armamentarii, 2023, 44(5): 1521-1528.

Figures/Tables 11

Fig.1 DOA estimation of three sources based on NLSL0 algorithm

Fig.2 DOA estimation of four sources based on NLSL0 algorithm

Fig.3 DOA estimation of five sources based on NLSL0 algorithm

Table 1 RMSEs and success probabilities of DOA estimation with amplitude-phase inconsistency

幅度误差	相位误差	均方根误差/(°)	成功率/%
N(0,0.1)	N(0,10)	1.5845	91.17
N(0,0.2)	N(0,10)	2.1935	90.57
N(0,0.1)	N(0,20)	1.5743	91.10

Table 2 RMSEs of DOA estimation for off-grid signals

DOA	30.0°	30.2°	30.5°	30.7°	30.9°
0°	0.8488°	0.8763°	0.9042°	0.8609°	0.8395°
0.2°	0.8521°	0.8795°	0.9523°	0.8830°	0.8621°
0.5°	1.0237°	1.0392°	1.0416°	1.0211°	1.0199°

Fig.4 RMSEs of DOA estimation using different algorithms versus SNR

Fig.5 Success probability of DOA estimation using different algorithms versus SNR

Fig.6 RMSEs of DOA estimation of different algorithms versus array elements

Fig.7 Success probability of DOA estimation of different algorithms versus array elements

Table 3 Number of iterations and RMSEs required by different algorithms

算法	迭代次数/次	均方根误差/(°)
NLSL0	6	0.3134
SL0	8	0.3873
ISL0	16	0.3742
WSL0	19	0.3317

Table 4 Calculation time and RMSEs of different algorithms

参数	算法
参数	NLSL0	SL0	ISL0	WSL0	OMP
时间/s	0.0157	0.0189	0.0185	0.0233	0.0132
误差/(°)	0.7483	1.9039	1.0392	0.8573	4.5706

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DOA Estimation Based on Approximate l₀ Norm of Natural Logarithm Composite Function

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