# Online Sparse DOA Estimation Based on Sub-Aperture Recursive LASSO for TDM-MIMO Radar
This method consists of a linear least square optimization regularized by an additional penalty term of the \(L_{1}\)-norm as a measure of sparseness. The LASSO method is demonstrated to improve the DOA estimation performance of the array signal, with higher resolution and a lower side lobe [25]. Due to its superiority, many studies have been carried out on LASSO, including computational efficiency and theoretical analysis, etc. [26; 27; 28]. In spite of the performance gain, the current batch LASSO algorithm can only handle the complete aperture data already acquired by the MIMO radar. Since the LASSO algorithm requires operations, such as matrix inversion and matrix multiplication and a large number of iterations; the computational complexity of batch implementation is notably high, especially for massive TDM-MIMO data sets. There are several advances in algorithmic acceleration that might be combined with the LASSO algorithm to mitigate the computational burden. Some fast matrix inversion methods, such as the Newman series [29] and Jacobi method [30; 31], were proposed to handle the problem of high computational complexity. In [32; 33; 34], the Neumann series (NS) is considered to perform matrix inversion approximation (MIA). The main contribution of the Neumann method is to convert the matrix inverse calculation into matrix multiplication, which is more suitable for hardware platforms, but the complexity is equal to or higher than that of the exact calculation method, such as the QR-based method [33]. The Jacobi method reduces the complexity from \(O\big{(}K^{3}\big{)}\) to \(O\big{(}LK^{2}\big{)}\), where \(L\) is the number of iterations. However, the Jacobi method converges slowly and, thus, implies higher latency [35]. Although the above fast matrix inversion methods can reduce the computational complexity of the matrix inversion, the approximation error is introduced, which should be carefully controlled. Furthermore, they only reduce the complexity of the matrix inversion, whereas the burden caused by high-dimensional matrix multiplication and a large number of iterations in the batch LASSO algorithm cannot be well handled. To solve the high-complexity problem of the LASSO method, this paper presents a sub-aperture recursive LASSO method to allow for online DOA estimation. Online processing refers to the way of processing comparing with the traditional batch processing [28; 36; 37]. In the way of batch processing, the processor must wait for collecting the measurement completely, and process the measurement taking additional time cost. In contrast, online processing processes the stream of MIMO sub-aperture measurements accordingly; that is, updating the result when a new sub-aperture measurement is available. The benefit of online processing is that it can save the time cost of measurement collection. Meanwhile, online processing also allows for much less iterations, avoiding high-dimensional matrix inversion and multiplication. From the following analysis, it can be seen that the computational complexity can be reduced from \(O\big{(}K^{3}\big{)}\) to \(O\big{(}K^{2}\big{)}\). This paper is structured as follows. In Section 2, the MIMO radar signal model is reviewed and the TDM-MIMO sub-aperture data reception scheme is derived. Then, the proposed online TDM-MIMO radar DOA estimation method is derived in detail. In Section 3, simulated and real-data results demonstrate the effectiveness of the proposed method. In Section 4, the quantitative comparison and future work are discussed. Section 5 presents the conclusions.