16.4.1 Objectives of the Time Delay Measurement Process

Figure 16.5 gives the general steps in the time delay measurement process. The TDCS determines the time of arrival of the initial direct signal in the receiver RF channels by directing each transmitter n to send a direct (transmitter to receiver without any reflection) signal and recording the arrival time in the designated receiver unit m. It then calculates the channel nm internal delay by subtracting the arrival time from the transmit time. Because we know the distance between each direct link nm and constant time delays, we will also know when to expect the received signal and to discriminate it from any other signal. The TDCS signal-processing algorithms use the calculated time delays to bring all channels into synchronization as shown in Figure 16.5.

16.4.2 Time Delay Measurements

This section explains the patented time delay measurement process. Figure 16.6 shows the relation of the time delay of the direct link between a transmitter and a receiver and the delay of a reflecting object (target). For example, assume that we need to determine in real time the location of an object (20). The transmitter (21) sends a signal toward the object (20), which reflects it back toward the receiver (22). We designate the reflected signal as the indirect signal. The travel time D_measured depends on the actual signal travel time in space (D_sp) plus the time delays in the transmitter (D_tx) and the receiver (D_rx). We can express the signal travel time in space as

The nominal channel time delays provided by the manufacturer’s measurements or calculated by the initial array position measurements will probably vary during the operation of the radar system; therefore, we need a way to determine the real-time receiver and transmitter internal delays D_tx and D_rx. Because the transmitter and receiver delays vary over time, we must continuously recalculate the real-time delays Dtx′ and Drx′ to accurately determine the actual range from the antenna to the target from Dsp′, the signal travel time in space:

We can provide the calculated delays for either the particular system unit, for example, D_tx for transmitter (21) and D_rx for receiver (22), or as the cumulative internal delay for each link nm (23) so that the link delay equals D_L = D_tx + D_rx [1].

If the antenna array has some relatively large distance (24) between the transmitter (21) and the receiver (22), we may need to consider this link for calculating the real-time internal delays Dtx′ and Drx′. For delay measurements, the transmitter side lobe can serve as the direct signal (24). In the initial stage of processing, we can measure the delay of a direct signal from the transmitter (21) through the direct link (24) to the receiver (22) and store it for use in further computations.

Any change in the time of arrival between the initial and real-time terms indicates a change in the internal delays of the transmitter and receiver (e.g., D_tx, D_rx). Based on the initial internal delays and the specific calculated change in the time delay, we can determine the internal delays Dtx′ and Drx′ from Equation 16.2 and use them to determine Dsp′ and the true location of the object.

Now, we can apply this to an array of transmitters and receivers as shown in Figure 16.7 to show the operating concept, which applies to any number of antenna elements and any geometry. The array (300) couples to a processor unit (301) and then to a storage unit (302). The antenna geometry remains constant during the initial and later real-time stages. The array may use any geometry as long as the relative position of the elements remains the same. In this array, a transmitter has a position at the top of the array (31), and a receiver is at the bottom inner part (33) of the lower-right wing (34). Both the transmitter and the receiver antennas face toward the front of the array, with their axes parallel to the Z coordinate (25). Each transmitter signal will have a substantial main lobe and some smaller side lobes in the X-Y plane of the array [1].

Figure 16.7 shows a direct link (39) between the transmitter (31) and the receiver (33). This array (300) includes four transmitters (31, 35, 36, and 37) in the respective four wings. Each wing has three receivers in addition to the eight receivers in the centre part (38). This gives a total of 4 transmitters and 20 receivers for a total of 80 transmit-receive links. A single transmitter and receiver link can only determine the range of the reflecting object. To perform three-dimensional (3D) object location and imaging, we require more transmitters and receivers. As a general rule, the higher is the number of the transmitter-receiver pairs, the higher is the object-locating precision.

Figure 16.8 shows the method for calculating initial delays from a direct transmit link between the transmitter (43) and the receiver (44). The TDCS (11) of Figure 16.5 will calculate 24 initial internal delays for the antenna array (400) with 4 transmitters and 20 receivers, using the processor (401) and storage (402). The system starts by selecting a reference object, such as the flat metal plate (41) or any reflecting reference object of opportunity. The signal path from the transmitter (43) to the object (41) to the receiver (44) becomes the indirect link. This antenna array will have 80 indirect links covering all transmitter-receiver combinations. The TDCS calculates the initial internal delays for each transmitter and receiver at fixed and prevailing conditions, for example, 25°C and batteries in a fully charged state.

The time delay calculation procedure in the processor (401) comprises the following steps:

1. The TDCS calculates the distance to the reference object (41) relative to the array, or it can know the distance that is physically measured to the desired level of accuracy.

2. The computer system directs each transmitter to transmit a main lobe signal at the reference object (41) and then configures the receivers to receive the reflected signal.

3. Each signal from a specific transmitter reflected from the reference object to a specific receiver produces a specific indirect link (42). As shown, the process will establish 80 different indirect links. Each reflected signal follows a different path and will have a different timing. This provides enough information to determine the distance and orientation of the plate as well as the initial internal delay of each transmitter and receiver.

4. The TDCS algorithm will choose a single transmitter as a standard with “zero” delay and calculate the timing delays of all other transmitters and receivers with respect to the standard unit. Assuming a “zero delay” helps to check system performance and to average the results; however, there is no requirement for the zero delay.

5. The TDCS as shown now has 80 equations for the range to the reference object. Because it assumed a zero delay for one transmitter, it has 23 unknown internal delay variables for the 3 transmitters (Tx₂-Tx₄) and 20 receivers (Rx₁-Rx₂₀). The reference object (41) adds three more variables for distance D and orientation (0,1 angles). Now the system has 26 unknown variables to determine.

6. The TDCS processor (401) can use many possible procedures to calculate the 26 variables from the variables obtained from the 80 channel equations.

7. One TDCS algorithm can use an iterative procedure performed as follows:

   • The system estimates the plate (or reference object, terms used interchangeably) position and orientation. This sets three unknown variables to arbitrary values.

   • Using arbitrary plate-orientation values, the TDCS algorithm can calculate the spatial distance of an indirect link (i.e., T_x → plate → R_x) for each of the 80 channels. This can use per se geometrical equations. The plate and two points (T_x and R_x) form a triangle. Because of the known locations of T_x and R_x, the TDCS searches for a triangle such that the angles between the reflecting point, T_x, and R_x are equal. The TDCS does this by iteration and gets the resulting sum of both triangle sides for the spatial distance.

   • The TDCS algorithm then uses linear equation back substitution and averaging relative to the measured delay, and it can obtain 80 equations of the type

     Dtx+Drx+Dsp=Dmeasured,⁢(16.3)

     where D_rx is the sought receiver’s initial internal delay, D_tx is the transmitter’s initial internal delay, and D_sp is the 3D spatial delay of the T_x-R_x indirect link (the summation of the distance from transmitter to object to receiver). We can demonstrate that the orientation of the plate has a single optimum position with respect to minimum measurement error—hence iterative repositioning of the plate at an orientation and a distance where the measurement error tends to decrease and reaches a minimum. This eventually allows extraction of the delays as well as determining the distance and orientation of the plate.

8. Assuming the TDCS has calculated and stored (402) the initial internal delays under predefined condition, the calibration stage proceeds when it determines the indirect signal’s time of arrival (14) shown in Figure 16.5. This requires determining all direct line (T_xn-R_xm) delay times for all m × n signals (80 in this example) by using signal peak or envelope detection or other techniques.

   Figure 16.9 shows the signal waveforms at the time of arrival (a), after detection (b), and the time-delay process determination (c). When a signal such as the one shown in (a) enters an absolute module (51) followed by a low-pass filter (LPF) module (52), it emerges with the detected envelope form shown in (b). The detected signal goes to a threshold detector (53), which detects a rising and falling edge where the signal samples crossed the threshold value. The differential module (54) detects these edges and performs an exclusive-or (XOR) operation on any two consecutive samples. One version of the TDCS algorithm sets the threshold high enough to overcome noise and small signals and also low enough to allow for any signal decrease caused by temperature and/or low voltages, for example, 2-3 dB below the peak value. The differential keeps the rising-edge sample as the “early” indicator and the falling-edge sample as the “late” indicator. Any circuitry or waveforms will work and the TDCS may take other forms different from the one shown in Figure 16.9a.

   

   FIGURE 16.9
   Camero TDCS time delay determination procedure: (a) The received signal passes through the LPF (522) and emerges with the detected envelope shown in (b). Time delay calculation takes place in the modules of (c). (Adapted from Hochdorf, E. et al., Automatic Delay Calibration and Tracking for Ultra-Wideband Antenna Array, U.S. Patent No. 2008/0261536 A1, October 23, 2008; Composite of U.S. Patent 2008/0261536 A1 Figs. 5 and 6.)

9. For real-time determination of the object’s location, the TDCS must do the following:

   • First, determine the times of arrivals of direct signals (between transmitters and receivers) shown in Figure 16.6 (15).

   • Second, determine the changes in direct signal arrival times compared to those determined during the calibration stage as shown in Figure 16.6 (16).

   • Third, determine the sought real-time internal delay based on these, as shown in Figure 16.6 (12). Because internal delays can change over time; determining the real-time location of an object with high precision requires the continuous recalculation of current (real-time) internal delays.

To illustrate how the time delay computation works, we can use the case of the 4-transmitter and 20-receiver array shown in Figure 16.8. Now, suppose that the array has a stored list of 80 (initial) time-of-arrival values for each of the 80 T_x-R_x direct links. The Camero TDCS calculates the current time-of-arrival values for the 80 direction links using the method described in Figure 16.9. One version of the Camero TDCS will compare the current time-of-arrival values to determine changes in the direct signal’s time-of-arrival values. As shown in Figure 16.9, the system compares the direct link “early” and “late” values with the stored values from the initial phase (56). This determines an estimate “early drift” (early change) and “late drift” (late change). Calculating the average of both drifts establishes a single change value for each direct link. This calibration phase determines a specific delay for each direct link. The algorithm then subtracts this delay from each indirect (transmitter-object-link) link to cause all the links to line up in time (synchronize) as demonstrated in Equation 16.1. This will neutralize the corresponding D_tx and D_rx for each link.

Taking the case of a single link, the Camero TDCS determines the change Δ in the arrival time for a given direct link to the corresponding (real-time) link; it can determine the corresponding (real-time) internal delay of this direct link as D_tx + D_rx + Δ. We can rewrite this equation as Dtx′+Drx′=Dtx+Drx+Δ where Dtx′ and Drx′ indicate the real-time internal delays of the transmitter and receiver for that particular link. The system could provide the real-time internal delays separately (i.e., two distinct values Dtx′, Drx′) or in the combined form of Dtx′+Drx′ for both the transmitter and the receiver. The Camero TDCS subtracts this delay for each indirect link to line up all the links in time. Equation 16.2 demonstrates this for each indirect link and uses the corresponding Dtx′ and Drx′ (real-time internal delay) to neutralize the real-time link delays.

The Camero TDCS can calculate the changes for all links for the case shown in Figure 16.8. Blockages may occur between some elements in the special case of a densely packed planar array system with many transmitters and receivers. The TDCS system can calculate the delay changes for specific blocked links without observing the change in arrival time in that link. The calculation uses the change estimated in other links as long as they share transmitters and receivers. For example, if the TDCS system has calculated the real-time delays for T_x1-R_x1 (link #1), T_x2-R_x1 (link #21), and T_x2-R_x17 (link #37), then, the real-time delay calculation for T_x2-R_x17 works like this:

Using a system such as this, the TDCS could determine the entire 24 real-time delays for the 20 receivers and 4 transmitters with only 24 links instead of the 80. Considering the estimation errors, the TDCS could use the full number of channels for redundancy and improved range-estimation accuracy. Note that the Camero TDCS could work using a wide range of methods for measuring and estimating the delays of any transmitter and receiver array elements based on indirect methods like the one shown above.

16.5.1 Design Objectives and Requirements

Several design issues occurred during early work with prototype Xaver™ series through-wall radars. We found that the through-wall return signals from human targets tend to be ~20 dB less compared with signals from large static objects such as the back wall. When we observed the overall reflection, we found it difficult to detect the human targets. We decided to employ the infinite impulse response (IIR) filter, which differentiates between static and dynamic targets. The IIR mechanism can separate the signal by removing the static returns and leaving the dynamic (moving target) part, which we want to display.

Now we found that the delay calibration could harm this static-dynamic target-differentiation process. If we relaxed the IIR after 30 s and wanted to change the delay due to the offset in a specific channel, then this would harm the IIR convergence.

At first, we decided to correct the delay after the IIR stage to avoid harming its convergence. Later, we decided to introduce a more accurate correction mechanism and evaluated its influence on the IIR. As it turns out, the standard IIR static reduction was damaged by less than 1 dB due to the extremely small-scale correction of the delay channel, and we could correct the delay prior to the IIR filter.

We found that improved through-wall imaging required the following:

1. Modifying the moving delay compensator before the IIR filter. This resulted in the following design requirement of adding a moving delay compensator to the front end before the IIR filter by

   1. Adding a compensation delay before the IIR, which required IIR suppression of less than 1/100 (-40dB).

   2. Modifying the delay calibration loop using an interpolation of 1:128 (total) and detecting the fine (track) delay using a cross-correlation filter.

   3. Adding a feature to reset the IIR once the delay loop is locked.

2. Adding a wall-proximity compensation feature to detect the presence of walls and to determine the additional time delay caused by the wall for ranging and image formation. Solutions included the following:

   1. Detecting the signal time delay estimation when the system is close to a wall.

   2. Recording the signal after the IIR locks again and then detecting the signal time delay.

3. Eliminating the receiver long-period antenna ringing from direct signals (from transmitter n to receiver m in the array). This effect produced false targets at close ranges. We determined that adding a larger low-pass filter (LPF) for the acquisition phase by moving from a 12-tap LPF to a 44-tap filter would solve the problem [6].

4. Increasing the delay loop accuracy, which had an estimated error of 2-mm standard deviation and 7-mm peak-to-peak. Using a correlator loop solved the problem.

16.5.2 Design of Time Delay Estimation Block

The delay estimation system takes the output of the delay compensator. The delay estimation block shown in Figure 16.10 follows the module that removes delay compensator components from the signal before analog-to-digital sampling. This time delay estimation block has the following stages:

1. Acquisition: This mode estimates the location of the channel relative to a reference with coarse accuracy.

2. Track mode : After acquiring the coarse estimation for all channels, the system goes into a fine tracking mode to estimate the direct channel location. This uses correlation detection of the signal against a known signal. The calibration phase stores the direct signal and then correlates it against the return signal.

   

   FIGURE 16.10
   Camero Xaver^TM through-wall radar system TDCS: (a) General block diagram. (b) The detailed diagram shows how the TDCS estimates the signal delays and corrects the timing using a 1:128 interpolator. (Used with permission from Camero, Inc., Kfar Netter, Israel, © 2007.)

3. Wall mode: This mode assures that the system has no motion with respect to the wall. It works by detecting the wall and waiting for the IIR to lock, indicating that the system is mechanically stable with respect to the wall. After IIR lock, the system stores the actual direct signal combining direct channels and wall reflections as a reference signal for future work. The wall estimator operates all the time. When the system leaves the wall, the normal acquisition/tracking mode returns. To improve the estimation, we interpolate the signal by 128 as shown in Figure 16.9 [6].

16.5.3 Performance of TDCS

Figure 16.11 shows the results of the TDCS-driven closed-loop registration process described earlier. This example starts with a zero-delay estimator vector. After only a few iterations, each channel starts to converge with a different time offset. This example shows the convergence process of five different channels. Note that the system had significant initial time offsets and could not produce good imaging results without the corrections. The system can firmly establish the time delays after about 20 frames [2].