Approach

This research develops and analyzes the effectiveness of the three-part PDOA spatial identification algorithm. The first part of PDOA is time domain analysisto provide a relative velocity towards the receive antenna. The second part is frequency domain analysis which provides a range to the target signal. The final portion of the PDOA algorithm is the spatial domain analysis, in which two receive antennas provide a bearing to the target signal. The locations provided by all three parts are compared to the same portion of the algorithm from a simulation of the same target signal.

3.1.1 Create Simulation. In order to determine the effectiveness of the spatial identification method, a simulation of the test bed is created to provide a baseline for comparison. These simulations provide verification that, given a good extraction of the phase of a signal, the PDOA metrics can be calculated from captured data. The velocity of the target signal, reflection from the table surface, and the path traveled are modeled in MATLAB. Additive Gaussian White Noise is also added to the simulated signal based on the observed noise floor of the laboratory in use. Multiple simulations are run for each configuration and the results are averaged to establish the baseline performance expected out of the real world system.

3.1.2 Phase of Received Signal. The phase of the captured signal is calcu- lated using a Fast Fourier Transform in MATLAB. Once the I and Q data is imported

X1 freq = fft(x1);

phase x1 fc = angle(X1 freq(kc));

Figure 3.1: Code to Extract Phase of Received Signal

v r(sample) = (3e10/(4*pi*fc))*((phase x1 fc(sample)- phase x1 fc(sample-1))/step); Figure 3.2: Code for TD-PDOA

and the start of the tag response is located in the capture, the FFT is found using the code snippet in Figure 3.1, where kc is the center frequency of the captured signal. Since an EPC Gen 2 tag is used in all tests, the center frequency remains constant at 915 MHz. This step is repeated for every sample captured in each test.

3.1.3 Time Domain PDOA. When the PDOA is analyzed in the time domain it yields the velocity of the target transmitter with respect to the receive sensor. This is done with the code snippet contained in Figure 3.2 in MATLAB based on the phase found in 3.1.2.

This code snippet implements Equation 2.1 described in Chapter 2. The cen- ter frequency, f c, is found for each signal sample piece using FFT. In all cases the distances are in centimeters. The speed of light required in all calculations, c, is also represented in cm/s or 3e10. δφ is calculated by taking the angle of the FFT bin that represents the center frequency of each signal sample. The time delta is simply the time between the two samples stored in the variable named step. If the tag is stationary the phase of sample and sample-1 will be the same resulting in an angular velocity of zero. The function will also report an angular velocity of zero at the center crossing of the tag, when the target is directly in front of the sensor antenna. This

d found(sample) = -(3e10/(4*pi))*((phase x1 fc(sample)-phase x1 fc2(sample))/(fc-fc2)); Figure 3.3: Code for FD-PDOA

point also marks the instant that the function will transition from positive to nega- tive, or negative to positive, velocity as the target transitions from moving towards to away from the sensor antenna.

3.1.4 Frequency Domain PDOA. When the PDOA is analyzed in the fre- quency domain it yields the distance from the target transmitter to the receive sensor. We do this once again based on the phase found in Section 3.1.2 but we also must find the phase of the captured signal at a different frequency. Based on the f c found previously a frequency 1 MHz from the signal center frequency is selected and is rep- resented by the variable f c2. The code snippet in Figure 3.3 implements Equation 2.12 from Chapter 2. The difference, f c − f c2, will remain constant at 1MHz this combined with the fact that the equation relies on the same sample allows this tech- nique to find the range to the target transmitter even if it is stationary. For a target moving in a straight line perpendicular to the antenna array this value will have a minimum value at the center crossing to the sensor antenna.

3.1.5 Spatial Domain PDOA. To analyze the PDOA in the spatial domain, a second antenna is added to the software defined radio. If the phase of the received signal is inspected at each of the receive antennas, a bearing to the target transmitter can be calculated. This bearing to the target transmitter is found using the following the code seen in Figure 3.4. For this calculation, a second capture is taken from

theta found = arcsin(-(3e10/(2*pi*fc))*((phase x1 fc(sample)-phase y1 fc(sample))/a)); Figure 3.4: Code for SD-PDOA

the USRP´s second daughter card. The antenna for this capture is positioned a set distance from the first antenna. In the code, this distance is represented by a and is given in centimeters. The phase for the second capture is calculated using the same function as Section 3.1.2 and the samples are aligned in time. The phase of the second sample is stored in the array phase y1 f c. The SD-PDOA equation assumes that the tag is at a distance greater than one wavelength. The experiment is configured so that the tag is never closer than 86.0 cm – more than double the 37.5 cm wavelength of a 915 MHz signal. The result of this function, theta f ound, is the bearing to the target tag from receive Antenna #1. Negative values distinguish that a target transmitter is on the far side of Antenna #2 relative to Antenna #1. Positive values represent a target transmitter that is on the same side of the Antenna #1 as Antenna #2.