5.2. Loopback Resolution Test
A loopback test was conducted to validate the received signal and experimentally characterize the system’s range resolution. As shown in
Figure 6, the setup consisted of two propagation paths: a 0.1 m reference path and a longer path of either 2.1 m or 4.1 m. The additional 2 m or 4 m propagation length was implemented using air-filled coaxial cables.
The long path was first disconnected to characterize the system response of the 0.1 m reference path, including the effects of the cables and power splitters. A pulse with a digital duration of 5 ns was transmitted through the system. The measured time-domain response (i.e., the received signal) is shown in
Figure 7a. The received pulse is broader than the nominal digital pulse because of the limited RF bandwidth of the system and is further distorted by the frequency response of the power splitters. The peak of the received response occurs at sample 125, corresponding to 625 ns. This delay is attributed to the transmit and receive processing chains, including FPGA processing, and is therefore used as the reference system delay for determining the propagation delay through the longer path [
4,
5]. This is 5 ns later than the reference delay measured in
Figure 4. This misalignment in the reference delay is later discussed in
Section 5.3.
The measured impulse response has its maximum at sample 125. Sample 124 remains slightly above the −3 dB half-power level, whereas samples 123 and 126 are approximately 13 dB below the peak. Thus, the half-power crossing points occur between the available discrete samples rather than exactly at a sample location. With a sampling interval of 5 ns, the left crossing occurs between samples 123 and 124, while the right crossing occurs between samples 125 and 126. Since the right-hand crossing is closer to sample 125 than to sample 126, the measured half-power main-lobe width is slightly greater than 5 ns. This measurement provides an experimental characterization of the temporal width of the received impulse response.
Figure 7b shows the corresponding frequency response obtained from the Fourier transform of the received signal. A pronounced peak is observed at DC in the measured frequency response. This isolated component is attributed to a DC/baseband artifact of the measurement rather than to the RF passband response of the system. Therefore, the DC component was excluded when determining the effective RF bandwidth. The 3-dB bandwidth was calculated relative to the approximately flat passband level away from DC, which more accurately represents the usable RF response of the system. The measured frequency response of the configured system has a half-power bandwidth of 133 MHz, slightly less than the daughterboard’s nominal bandwidth.
For a conventional pulsed radar, the range resolution is approximately related to the pulse duration with , where is the propagation velocity of the wave in the medium. Equivalently, the same relationship can be expressed in terms of the transmitted bandwidth B with . Although with a range-bin spacing (i.e., sampling interval) of 5 ns, a pulse duration of 5 ns can be achieved, the RF front-end in USRP X310 is limited to 160 MHz, resulting in a theoretical range resolution of approximately 0.94 m. This value represents the minimum separation between two ideal point targets that can be distinguished under ideal conditions.
In practical systems, the measured range resolution is generally lower than the theoretical value due to nonideal effects, including phase noise, frequency-step errors, timing instability, antenna bandwidth limitations, multipath propagation, and residual calibration errors. Experimental evaluation using targets at known separations is required to quantify the practical resolution of the implemented radar system.
To evaluate the system’s range resolution, the long path was then connected using either a 2 m or 4 m cable extension. The responses of the two-path configurations were cross-correlated with the single-path reference response, and the delay corresponding to the maximum cross-correlation was used to estimate the range difference between the two targets. The results are shown in
Figure 7c. For the 2 m path difference, only a single peak is observed at 5 ns. Ideally, two peaks should appear: one at 0 ns and a second at approximately 6.7 ns. However, the two responses overlap and cannot be resolved. In contrast, the 4 m path difference produces two distinct peaks at approximately 0 ns and 15 ns, in reasonable agreement with the theoretical delays of 0 ns and 13.3 ns. These results demonstrate that a one-way propagation distance difference of 4 m can be resolved by the proposed system.
It should be noted that this experiment evaluates one-way propagation distance, whereas the resolutions reported in
Table 1 correspond to round-trip radar measurements. Consequently, the 2 m and 4 m one-way path differences are equivalent to round-trip target separations of 1 m and 2 m, respectively. Although
Table 1 predicts a theoretical range resolution of 0.94 m, the experimental results show that two targets separated by an equivalent distance of 1 m cannot be reliably resolved in practice. A practical range resolution of 2 m is achieved in this experiment with the maximum available range-bin spacing of the USRP X310 (i.e., 200 MS/s).
5.3. Radar Measurements
A range measurement radar is implemented in this work to evaluate the X310’s radar capabilities.
Figure 8 shows the measurement setup. The host computer and X310 are loaded on a cart. Two Vivaldi antennas (10 dB gain at 3 GHz) are connected to the TX and RX ports of Channel 0, where the daughterboard is installed. The antennas are parallel and V-polarized, separated by 45 cm, and the cart is placed inside a low-noise environment to isolate ambient effects and confirm proper system operation. A 75 cm × 75 cm aluminum sheet serves as a moving target changing location from close to the antenna to 6 m away and back.
Sampling is done with 200 MS/s for both transmission and reception. The center frequency is set to 2 GHz, and the TX gain is 30 dB. For five repetitions of this measurement, no overrun, underrun, or dropped samples occurred. Each scan takes s including 0.5 s of 100 million recorded samples and 0.6 s of initial wait time. It can provide real-time data acquisition for slow-moving targets. An additional s is incurred by calling MATLAB, which performs post-processing and visualizes the data in parallel with scanning, providing near-real-time visualization of range measurement.
Direct measurement of the peak power of the 5-ns RF pulse using a spectrum analyzer is challenging because of its short duration; a high-bandwidth, high-sampling-rate oscilloscope would provide more accurate temporal characterization. Therefore, the peak output power was estimated from a CW measurement at 2 GHz. According to
Table 3, the measured output power for a TX amplitude of 0.3 was
dBm. Assuming linear amplitude scaling, increasing the TX amplitude to 1 increases the power by
dB, corresponding to an estimated output power of
dBm. With a TX gain setting of 30 dB, the corresponding theoretical level would be approximately 21.3 dBm; however, the X310’s maximum RF output power is approximately 10 dBm. Therefore, the actual peak output power is limited to approximately 10 dBm. No amplifier is used in this radar system (neither low-noise amplifier in receive path nor power amplifier in transmit path).
The radar scans the scene 20 times and updates a two-dimensional image. At each scan position, 100 consecutive impulses are transmitted sequentially over a short time interval and received by the RX channel. Fifty of the 100 received responses are selected and averaged to reduce random fluctuations in the received signal. Although the reflector is moving during these repeated acquisitions, they are collected over a sufficiently short time interval that the target displacement within a set of 50 acquisitions is small compared with the range sampling interval and the effective range resolution. Therefore, the target response remains concentrated within a small range interval during the averaging process, while random measurement fluctuations are reduced.
The resulting averaged signal provides a representative response for each scan position. These responses are then aligned to compensate for scan-to-scan timing variations. A small number of samples of misalignment can occur between consecutive scans because of timing jitter and variations in the data-acquisition and processing sequence. The measured inter-scan misalignment has a mean value of 8.8 ns and a standard deviation of 26.1 ns. The corresponding distribution of the measured timing misalignment is shown as a histogram in
Figure 9.
The first scan, corresponding to a reflector placed at a known reference position, was selected as the temporal reference and calibration position. The magnitude of each subsequent response was cross-correlated with the magnitude of this reference response, and the lag corresponding to the maximum cross-correlation was used to estimate the relative timing offset between scans. The estimated offset was then compensated by applying the corresponding linear phase ramp in the frequency domain. The known reflector position at the first scan was used to establish the reference delay for subsequent range estimation, while the cross-correlation procedure was used to compensate for inter-scan timing variations.
The purpose of this alignment is to compensate for variations in the timing of the stationary system response rather than to remove or compensate for the physical propagation delay of the target echo. Because the transmitter and receiver remain fixed during the scan sequence, the dominant transmitter–receiver crosstalk occurs at approximately the same propagation delay for all scan positions. The cross-correlation therefore identifies the small relative shift of this stationary component caused by inter-scan timing variations. After the estimated shift is applied, the crosstalk is aligned to a common temporal reference across the scans. The physical delay of the reflector is not used as the alignment reference and is not forced to coincide with the reference position. Consequently, as the reflector moves, its echo remains at its corresponding propagation delay, and the change in its delay is preserved for subsequent range estimation.
After temporal alignment, the background response is estimated by averaging the data across multiple scans and subsequently subtracted to suppress stationary system components, particularly the strong transmitter–receiver crosstalk. Because these components occur at approximately the same delay after alignment, their contribution can be effectively reduced through background subtraction. In contrast, the target response changes in delay as the reflector moves through the measurement region. Therefore, the target response is not fully represented by the stationary background and remains visible after subtraction, allowing its range trajectory to be extracted from the resulting range profiles.
The background-removed data are plotted row by row, with each row representing one scan and the corresponding target response at that scan position. As the scan progresses, a new row is added to the range–slow-time plot, allowing the motion of the target to be visualized as a function of scan number.
Figure 10 shows the resulting range–slow-time intensity plot, cropped to the region of interest. The white dashed line represents the ground-truth target trajectory.
Figure 10a shows the amplitude of the background-removed data.
The horizontal axis represents slow time, expressed by the scan number. The left vertical axis represents fast time in nanoseconds and corresponds to the measured round-trip propagation time. The right vertical axis represents the corresponding one-way target range, calculated from the corrected propagation time using the speed of light in free space. The zero-delay reference corresponds to the location of target at first scan. The color bar represents the received-signal amplitude in dB.
For improved visualization and to reduce speckle noise and scan-to-scan fluctuations, the amplitude of the background-removed data was processed using a two-dimensional moving-average filter. The resulting smoothed data are shown in
Figure 10b.
Figure 10c shows a fourfold upsampled version of
Figure 10b, obtained using linear interpolation in both the slow-time and range directions. These smoothing and interpolation operations are used to improve the visualization and facilitate extraction of the target trajectory; they do not increase the fundamental range resolution determined by the system bandwidth.
The target location at each scan was determined from the maximum-amplitude response within the region of interest. As shown in
Figure 10c, the aluminum reflector moves approximately 6 m away from the antennas during scans 1–11 and then moves back toward the antennas during scans 12–20. The estimated target range was compared with the known ground-truth trajectory at each scan position. The ranging error was evaluated for each scan position, and the resulting RMSE, standard deviation, and maximum absolute error are summarized below.
For the background-removed data, the RMSE, standard deviation, and maximum absolute error are 1.99 m, 2.03 m, and 3.95 m, respectively. After applying the two-dimensional moving-average filter, these values decrease to 1.75 m, 1.79 m, and 2.45 m, respectively. For the fourfold-interpolated data, the corresponding values are 1.75 m, 1.76 m, and 2.65 m. The reduction in RMSE and maximum error after smoothing indicates that the moving-average filtering reduces scan-to-scan fluctuations and improves the consistency of the extracted target trajectory. The nearly unchanged RMSE after interpolation indicates that interpolation primarily provides a denser visual representation of the trajectory rather than improving the underlying ranging accuracy or fundamental range resolution. Although this error is larger than the theoretical range resolution and roughly 29% of the total target displacement, the result reflects the practical ranging performance of the complete measurement system under the experimental conditions.
The experiment demonstrates that the implemented software-defined radar can detect and track the motion of the reflector over the investigated range. The quantitative comparison with the known target trajectory provides an experimental measure of the ranging error, while the observed RMSE values characterize the practical ranging performance under the measurement conditions.
The software-defined radar based on the USRP X310 and UBX-160 was successfully implemented using the available sampling rate and RF bandwidth. The measured target delays and resulting range trajectory are consistent with the expected propagation behavior and demonstrate the capability of the system for range measurement and target’s motion visualization.