## 4 Experiment of Direction Finding  
The entire schematic of the direction-finding system with the single-patch multi-beam antenna is shown in Figure 12. The eight radiation patterns from the single antenna receive the powers (p1,..., pN) from the target in the azimuth plane, and the received powers are input into the training data of the DNN algorithm. Figure 11: Radiation pattern of the single-patch multi-beam antenna: (**a**) single port excitation and (**b**) dual port excitation. Figure 10: Return loss of the single-patch multi-beam antenna. Figure 9: Fabricated antenna and measurement: (**a**) fabricated antenna, (**b**) coaxial feeding, (**c**) return loss measurement, and (**d**) radiation pattern measurement. In the DNN architecture, let \(\mathbf{p}=[\text{P}_{1},\cdots,\text{P}_{\text{N}}]^{\text{T}}\) denote the measured power according to various patterns as training input data and \(\mathbf{a}=[\text{a}_{1},\cdots,\text{a}_{\text{L}}]^{\text{T}}\) denote the classified direction sector as training output data in the training phase, where N is the number of patterns and L is the number of direction sectors. \(\mathbf{p}\) and \(\mathbf{a}\) are datasets for supervised training according to each angle in the direction sector. For direction finding through supervised training, the neural network architecture comprises a sparse auto-encoder (SAE) and softmax classifier layer [28] for output classification. The SAE helps to reduce the influence of noise and perturbations in the input [29]. Therefore, in many propagation environments, the training input data can reduce the effect of distortion. In the training phase, the values of the hidden layer units are expressed as  
\[\mathbf{h}=f(\mathbf{W}\mathbf{p}+\mathbf{b}) \tag{1}\]  
where \(f(\cdot)\) is a non-linear activation function, \(\mathbf{W}\in\mathbb{R}^{\text{M}\times\text{N}}\) denotes the weight matrix, and \(\mathbf{b}=[\text{b}_{1},\cdots,\text{b}_{\text{M}}]^{\text{T}}\) denotes the bias vectors where M is the number of nodes in the hidden layer greater than or equal to the number of inputs. The weight and bias values are updated and determined by the repetitive backpropagation using the measured power values in the multiple hidden layers. After the training phase, the test data are used as the input to verify that the proposed system can find the correct direction. The direction-finding experiment is conducted in the following order. First, the azimuth plane to be detected is divided into eight sectors with an equal angle of 45\({}^{\circ}\). For training the DNN algorithm, signal sources are placed in order for all sectors. In addition, signals generated from signal sources for each sector are received with eight patterns of the single-patch multi-beam antenna, as shown in Figure 13a. Finally, the eight signal values  
Figure 12: Schematic of the proposed direction-finding system. for all sectors are used as training data for the DNN algorithm. After training is completed, the direction-finding performance is presented by suggesting the actual number of sectors where arbitrarily placed signal sources are located, as shown in Figure 13b. The direction-finding experiment is performed in a sufficiently large space where the LOS (line-of-sight) environment is almost satisfied. The test antenna of the Tx (transmission) used a microstrip patch antenna operating at 2.4 GHz. The test antenna is connected to the signal generator and transmits continuous wave signals at 2.4 GHz. The test antenna and single-patch multi-beam antenna are 1.5 m away from the ground to reduce reflection on the ground. The SP4T (single pole four-throw) switch is controlled by an FPGA (field programmable gate array) to perform the generation of eight beams. The received power values are accumulated in the laptop through the SDR (software-defined radio) equipment USRP-2922. Training data required for DNN inputs are constructed based on the received power values according to the location of each sector of the test antenna.