# Double-Layer Compressive Sensing Based Efficient DOA Estimation in WSAN with Block Data Loss
## 1 Introduction  
As a branch of array signal processing, DOA estimation has been a hot topic in many research fields, such as smart antennas, mobile communication and target tracking [1; 2; 3; 4; 5]. Traditionally, DOA estimation is implemented using sensor arrays, such as in active sonar systems [6; 7], where all sensors have a wired connection to the fusion center (FC). For wireless sensor array networks (WSAN) [8; 9; 10], sensor arrays are deployed in a large sensor field and communicate with the FC via wireless channels. Generally, the data transmission process from sensor arrays to the FC is assumed to be reliable and lossless. Unfortunately, due to the existence of channel noise, multi-path effects and link asymmetry, etc., low-power wireless links often generate a high packet loss rate [11]. Data sent from the sensor array to the FC are often subjected to missing or garbled values, posing a great challenge for information acquisition at the FC. Thanks to the sparsity of monitored signals, the newly-emerged compressive sensing (CS) technique has a broad application prospect in wireless communication because of its ability to recover the raw signal from a small number of random measurements [12; 13; 14; 15]. Additionally, it has been widely used to deal with data loss in wireless sensor networks (WSNs). In [16], the authors presented the low-rank structure, spatial similarity and temporal stability of the environmental data and proposed a novel approach based on CS to reconstruct the lost data. In [17], a CS-based lost datarecovery approach for smart wireless accelerometers used in structural health monitoring (SHM) was proposed, and the raw acceleration signal can be effectively reconstructed, though some data loss may happen. In [18], an oversampled CS source coding was adopted to neutralize the stochastic nature of wireless link disturbances and hence compensate channel erasures, making the data recovery at the sink largely immune to data loss. The work in [19] studied the lossy nature of low-power wireless links and introduced a CS-based channel coding scheme. Utilizing CS reconstruction techniques rather than traditional interpolation methods for lost data recovery, they achieved an enhanced channel utilization and transmission reliability. However, all of these works demonstrated their results in terms of the accuracy of signal recovery, without insight into the level of information acquisition, e.g., the DOA information in WSAN. Besides, there is an issue that has not been investigated yet. Block data loss is common in wireless communication, as data samples are transmitted in the form of packets, and a large packet size is often adopted for high transmission efficiency. However, block data loss often does great harm to various applications. In this paper, we first investigate the adverse effects of block data loss on DOA estimation in WSAN. Subsequently, a double-layer compressive sensing framework is proposed to eliminate its hazards and to realize high accuracy and efficient DOA estimation. Under the double-layer CS framework, DOA estimation is implemented according to the received data samples (the measurement vectors) at the FC. Conventionally, DOA estimation is fulfilled in two stages. We first need to recover the raw sparse vectors and then perform DOA estimation based on them. This process is denoted by DCS-DOA. Furthermore, to avoid the error propagation from signal recovery to DOA estimation in DCS-DOA, we propose a direct DOA estimation technique, called DCS-DDOA, to achieve a better DOA estimation performance. Leveraging a joint frequency and spatial domain sparse representation of the sensor array data, the FC can directly obtain the DOA estimation results according to the same received data samples, skipping the stage of signal recovery. Extensive simulations are carried out to validate that the double-layer CS framework can dispel the detriment of block data loss and yield a superior DOA estimation performance in WSAN.