14 Xaver™ Through-Wall UWB Radar Design Study

The Xaver™800 and Xaver™400 through-wall radar (TWR) systems for police and military applications were developed by the engineers of Camero, Inc. These radar systems are easily usable and show the occupants and objects hidden from view behind all types of walls, and they are especially beneficial to military, police, fire, and emergency responders. The Xaver™ TWR systems incorporate sophisticated design and signal processing techniques to build a real-time 3D display of the occupants of a room or building behind reinforced concrete walls. These systems can show living objects and trace their movements to predict future locations. Immobile objects appear in a different color to show the general plan of the area.

This chapter discusses the through-wall (TW) operational problem, examines the constraints on TWR design, shows earlier state-of-the-art systems, explains the unique antenna array theory, and summarizes the time delay calibration and signal processing systems. The examples of Xaver™800 TWR high-resolution imaging show the results of the advanced design concepts. Amir Beeri, Ron Daisy, and Jacob Oaknin provided the papers explaining the antenna theory and channel alignment techniques. Chapter 15 explains the signal acquisition system. Chapter 16 presents the time delay calibration system.

14.2 Xaver™ Radar Design Objectives

14.2.1 Functional Objective: Provide High-Quality Real-Time 3D Imagery inside Buildings

UWB TWR offers the best solution for looking through a solid medium to see what lies behind a wall or inside a building. The user can see the locations and movements of people and the positions of stationary objects, for example, furniture, interior walls, and other obstacles. Imagine a combat situation as shown in Figure 14.1 where the enemy hides behind a concrete wall. Although several companies have built and marketed TWR systems, the engineers of Camero, Inc., have developed the Xaver^™400 and Xaver^™800 TWRs to provide maximum situational awareness and ease of use. The objectives of TWR system design included the following aspects:

Images

FIGURE 14.1
Soldiers and police need a way to determine who and what lies behind solid walls of building and rooms. They must distinguish between living occupants and furniture or walls. Xaver™ TWR can provide this information in real time. (With permission from Camero, Inc., Israel, © 2010.)

Provide a lightweight and easily usable system
Provide a system with an imaging capability through all forms of building construction including reinforced concrete walls
Present a real-time 3D display showing the location and movement of all living objects behind a wall
Show the location of furniture, doors, interior walls, barricades, partitions, and so on
Provide a record of the images for analysis, historical, training, and legal purposes
Permit remote viewing of the display by command centers

14.2.2 Frequency Selection

Xaver™ frequency selection considered the requirements for material penetration and bandwidth for high spatial resolution. Radio signals penetrate walls with more or less attenuation depending on the construction, as shown in Figure 14.2a. Although higher frequencies can provide finer spatial resolution, the signal attenuation increases with the signal frequency. Figure 14.2b shows typical attenuation properties of common building materials. In the extreme case of imaging inside a concrete block building, the least attenuation was found at frequencies below 4 GHz. Considering penetration and fine resolution, an optimum frequency range of 3-10 GHz was selected for the Xaver™ series of TWRs [1,2].

14.2.3 TW Imaging Technologies

Radar technology offers several approaches to TW target personnel detection including micro-Doppler, synthetic aperture radar (SAR), and UWB signals [1]. Table 14.1 summarizes the merits of these three methods:

Micro-Doppler has high sensitivity to movement and can detect signs of life and identify targets by their distinctive motion-induced frequency shifts. It may use continuous wave signals or variants including linear frequency modulation and compressed chirp signals. Micro-Doppler has a problem with near-far (dynamic) range, which means all target returns arrive together. This intertarget interference prevents the normal usage of the device. In the case of a highly attenuative wall, the operator may be the strongest interference source [3].
SAR can provide good spatial resolution and imaging with a narrowband signal, but requires an antenna moving over a known long base line. Further, SAR processing will displace moving objects from their actual location, which poses a disadvantage to the tactical TWR user. It has a problem showing real-time movement that may smear the image [4].
UWB signals can use the frequencies needed to penetrate walls and provide the fine spatial resolution required for imaging. A UWB TWR system can locate targets in three dimensions and accurately track moving persons in real time to provide an accurate image to the user [4].

Images

FIGURE 14.2
TWR designs must compromise between signal penetration and resolution. (a) The optimum band for TW radar systems falls between 300 MHz and 3 GHz. (From Jon, E., Sens., Rev., 23, 205-211, 2008.) (b) Typical attenuation of radio signals by building materials. Lower frequencies have less attenuation. (Used with permission from Frazier, L.M., “Radar surveillance through solid materials,” Paper 2938-20, Figure 3, SPIE Photonics East Conference, November 1996, Figure 3, 139-146, © 1996 SPIE.)

TABLE 14.1
TWR Imaging Techniques

	UWB	Micro-Doppler	SAR
Strength	3D location possible from static sensor	Detect signs of life	Best sensor resolution
Strength	Track multiple targets	Highly sensitive	Mature bistatic operation
Weakness	Low imaging resolution	Poor location information	Requires mobile sensor or known moving target characteristics
Weakness	Low angle resolution	Target discrimination complex	High processing load
Weakness		Dynamic range and intertarget interference prevent normal use	Problems showing real-time movement

Source: Jon, E., Sens. Rev., 23, 205-211, 2008.

14.3 State-of-the-Art TWRs

UWB and SAR can provide tactical imaging but have different uses. The SRC Inc., formerly Syracuse Research Corporation, O-PEN™ SAR system shown in Figure 14.3a has a truck-mounted antenna using a narrowband signal. Because it requires a moving antenna and known base line, the operators must drive through an area to collect an SAR picture of the buildings and the objects or people in them. The O-PEN™ narrowband signal permits micro-Doppler processing to look for breathing persons and distinguish between people and stationary objects. This provides a solution to quickly scouting an area and finding potential threats. Command centers can use the information to direct squad level searches with handheld TWR systems [5].

Endoacustica srl and Cambridge Consultants produce handheld TWR systems for use by soldiers, police, and emergency responders. The Endoacustica Prisma™ and Cambridge Consultants Prism 200™ systems must be held near the wall or mounted on a tripod during tactical surveillance operations. Figure 14.3 shows pictures of these systems. Table 14.2 compares the characteristics of the Prisma^™ and Prism 200^™ systems. Both systems use approximately the same frequency spectrum. Figure 14.4 compares the displays from the O-PEN™ and Prism 200™ TWR [6,7].

Images

FIGURE 14.3
Examples of two TWR systems concepts. (a) The SRC, Inc., O-PEN™ radar uses SAR technology and can drive through an area to search buildings for occupants and send imagery to a command center. (Courtesy of SRC, Inc., © 2010. , http://www.srcinc.com/uploadedFiles/src/what-we-do/O-PEN.pdf [accessed on March 30, 2011].) (b) The Cambridge Consultants Prism 200™ Covert Surveillance radar gives the user a real-time image of activities behind a wall. (Courtesy of Cambridge Consultants, © 2010. http://www.cambridgeconsultants.com/prism_200.html [accessed on April 5, 2011].)

TABLE 14.2
State-of-the-Art TWR System Characteristics

Images

FIGURE 14.4
Examples of TW imaging. (a) The SRC, Inc., O-PEN™ synthetic aperture generated display. Micro-Doppler processing helps to identify people in the image. (Courtesy of SRC, Inc., © 2011, http://www.srcinc.com/uploaded-Files/src/what-we-do/O-PEN.pdf (accessed on March 30, 2011).) (b) SRC, Inc., O-PEN™ display showing breathing persons inside a building. (Courtesy of SRC, Inc., © 2011, http://www.cambridgeconsultants.com/prism_200.html (accessed on April 5, 2011).) (c) Cambridge Consultants Ltd. Prism™ 200 3D display. (Courtesy of Cambridge Consultants Ltd., © 2010, http://www.cambridgeconsultants.com/prism_200.html (accessed on April 5, 2011).)

14.4 Designing the Camero Xaver™400 and 800 Series TWR Systems

Given the state of the art in TWRs, the engineers of Camero, Inc., set out to improve the performance of TWR systems by providing a better user display and a movement record of persons. This required finding a way to improve the imaging to give an easily understandable 3D picture that would make stationary and living targets immediately distinguishable to the operator. These efforts led to the development of the Camero Xaver™800 and Xaver™400 systems shown in Figures 14.5 and 14.6. The antenna optimization, signal processing, and time delay calibration systems described in Chapters 15 and 16 produced the displays shown in Figure 14.7.

Images

FIGURE 14.5
The Camero Xaver^TM800 system gives the operator a high-resolution display of the moving occupants and fixed objects behind a solid wall for intelligence and surveillance operations. The large displacement between the multiple antennas aids in angular resolution. (Courtesy of Camero, Inc., Israel, © 2010.)

Images

FIGURE 14.6
The Camero Xaver™400 lightweight (2.95 kg) handheld TWR gives military and security force operators a realtime picture of the people and objects behind nonmetallic building walls of all construction including reinforced concrete. (Courtesy of Camero, Inc., Israel, © 2010.)

14.4.1 The Camero Xaver™800 TWR

The Xaver™800 design has the user features needed for intelligence and surveillance purposes. Superior imaging and angular resolution come from an array of 24 unsymmetrically spaced antennas. Four of these arrays fold down for transportation. As shown in Figure 14.5, the operator must move to a covered position and set up the system on a tripod. A cable carries imagery information to the remote display shown in Figure 14.5c. Figure 14.7a shows a sample of the display showing moving and stationary targets. Table 14.3 shows the important specifications of the Xaver™800 and 400 systems [2].

14.4.2 The Camero Xaver™400 Handheld TWR

Figure 14.6 shows the lightweight (2.95 kg) handheld Xaver™400 radar system for paramilitary operators in tactical search and rescue operations. The display shown in Figure 14.7b gives an immediate picture of what lies behind a wall. The ability to penetrate reinforced concrete makes it valuable for use in urban environments and against military fortifications [1].

14.5 Camero Xaver™ Radar Advanced Design Features

The Camero engineers Jacob Oaknin, Ron Daisy, and Amir Beeri took a new approach to maximizing TWR performance by finding a smart geometrical configuration of antenna elements for antenna arrays. They optimized the Xaver™800 and Xaver™400 systems’ geometrical configuration of antenna elements, emitters, and receivers to fully utilize the available dimensions and provide high-quality imaging.

Images

FIGURE 14.7
The Camero Xaver™ antenna array, time delay calibration, and signal processing systems can provide an operator display showing fixed objects and people. It also makes a record of people’s movements for predicting actions, planning tactics, and documentation. (a) Xaver^™800 3D display showing the location of people and objects inside a closed room or building. (b) The Xaver^™400 2D display distinguishes between people (light circles and time display two people labeled) and fixed objects (grey circles indicated for fixed objects). (Courtesy of Camero, Inc., Israel, © 2010.)

To get the most performance, the communication concept of information capacity was applied to an antenna array. Then the information capacity was developed as a figure of merit for antenna geometry designs. A linear Gaussian model helped to find an explicit expression for this measure to evaluate antenna array configurations. Section 14.5.1 presents the antenna system model, and Section 14.5.2 shows how the antenna configuration information capacity was derived. Finally, Section 14.5.3 shows some examples of antenna array element placements and discusses their relative calculated performance [8].

14.5.1 The Antenna System Model

To model the antenna system performance, the engineers started with an array of transmitters and receivers arranged in a given aperture. As shown in Figure 14.8, each transmitter emits a burst of wideband energy toward a scene obscured by the visually opaque obstacle. The obstacle reflects part of this energy back to the antenna array. The receivers collect scattered waves from the target and those returning through the obstacle. Under the Born approximation this takes the incident field in place of the total field as the driving field at each point in the scatterer. The received signal was modeled at the receiver rcvr_i, located at distance r_i results from a transmission from transmitter xmtr_j, located at distance r_j, as

TABLE 14.3
Camero Xaver™400 and Xaver™800 TWR Characteristics

Images

y_{i j} (t) = \int d^{3} r \frac{p (t - Δ T_{i j} (r))}{| r_{i} - r | | r_{j} - r |} I (r), (14.1)

$y_{i j} (t) = \int d^{3} r \frac{p (t - Δ T_{i j} (r))}{| r_{i} - r | | r_{j} - r |} I (r), (14.1)$

where I(r) indicates the object reflectivity at position r and ΔT_ij, (r) = (| r_j − r | + |r_j - r |)/c gives the round trip delay from transmitter xmtr_j to scattering location r back to the receiver rcvr_i. The term p(t) indicates the pulse transmit/receive pulse shape (consisting of both the receiver and transmit antenna response) and c indicates the velocity of light. All positions use a reference frame where the origin coincides with the center of the antenna array as shown in Figure 14.8. By setting p(t) band-limited, we can discretize both the time domain (t→kδt, for integer k) and the spatial domain (r→ξδx + ηδy + ζz for integers ξ, η, ζ). We can approximate Equation 14.1 by the following matrix relation

{\underline{y}}_{i j} = {\underline{\underline{A}}}_{i j} \underline{x}, (14.2)

${\underline{y}}_{i j} = {\underline{\underline{A}}}_{i j} \underline{x}, (14.2)$

Images

FIGURE 14.8
Antenna system model TW imaging using the Born approximation.

where y_ij defines a column vector of length L corresponding to the samples of the continuous signal y_ij(t), $\underline{x}$ $\underline{x}$ is a column matrix of vector length N whose components are unknown values of the discretized reflectivity in each voxel (volume element). Then the L × N matrix ${\underline{\underline{A}}}_{i j}$ ${\underline{\underline{A}}}_{i j}$ shows the contribution of the different voxels to the time domain signal. Column K of ${\underline{\underline{A}}}_{i j}$ ${\underline{\underline{A}}}_{i j}$ consists of samples of a signal contributed by the unit voxel k. Extending Equation 14.2 to the case of K transmitter/receiver pairs, where each pair contributes a similar matrix relation as in Equation 14.2 and concatenating them, gives

\underline{y} = \underline{\underline{A}} (\underline{θ}) \underline{x}, (14.3)

$\underline{y} = \underline{\underline{A}} (\underline{θ}) \underline{x}, (14.3)$

where $\underline{y} = ({\underline{y}}_{0}^{T}, {\underline{y}}_{1}^{T}, ..., {\underline{y}}_{K - 1}^{T})^{T}$ $\underline{y} = ({\underline{y}}_{0}^{T}, {\underline{y}}_{1}^{T}, ..., {\underline{y}}_{K - 1}^{T})^{T}$ , and $\underline{\underline{A}} (\underline{θ}) = ({\underline{\underline{A}}}_{0}^{T}, {\underline{\underline{A}}}_{1}^{T}, ..., {\underline{\underline{A}}}_{K - 1}^{T})^{T}$ $\underline{\underline{A}} (\underline{θ}) = ({\underline{\underline{A}}}_{0}^{T}, {\underline{\underline{A}}}_{1}^{T}, ..., {\underline{\underline{A}}}_{K - 1}^{T})^{T}$ . The indices give an alternative labeling of the different transmit/receive antenna pairs used above (the i, J labeling). $\underline{θ}$ $\underline{θ}$ indicates the sensor’s parameter as the locations of the transmitters and receivers. The column vector y (of length M = KL) holds K concatenated (joined in a string) signals each having L samples. The matrix $\underline{\underline{A}}$ $\underline{\underline{A}}$ has dimensions M × N.

The imaging system uses this model to find $\underline{x}$ $\underline{x}$ (the 3D image behind the obstacle), given the measurement $\underline{y}$ $\underline{y}$ . Note that in most practical designs, Equation 14.3 is highly undetermined, that is, M ≪ N so that the system has fewer equations than unknowns. The literature has numerous works dealing with the problem of solving ill-posed undetermined lines equations [9]. Each solution method uses some sort or regularization and/or constraints by posing the original problem as an optimization problem generally written as

\begin{matrix} \min_{\underline{x}} {‖ y - \underline{\underline{A}} \underline{x} ‖ + φ (\underline{x})}, \\ s . t . c (\underline{x}), \end{matrix} (14.4)

$\begin{matrix} \min_{\underline{x}} {‖ y - \underline{\underline{A}} \underline{x} ‖ + φ (\underline{x})}, \\ s . t . c (\underline{x}), \end{matrix} (14.4)$

where $φ (\underline{x})$ $φ (\underline{x})$ is an appropriate regularization term (or additional information) that introduces a penalty for unwanted solutions. The term $c (\underline{x})$ $c (\underline{x})$ indicates an appropriate constraint to be fulfilled by the solution. Reliable solutions to problems of a type represented by Equation 14.4 have a high dependence on the conditioning of the matrix $\underline{\underline{A}} (\underline{θ})$ $\underline{\underline{A}} (\underline{θ})$ in terms of the level of dependence of its rows. Higher conditioning gives better imaging performance in the presence of measurement and/or numerical noise. The design of the antenna geometrical configuration directly affects the conditioning matrix encapsulated in the parameters vector $\underline{θ}$ $\underline{θ}$ . For example, in the case of a highly symmetric antenna geometrical configuration, different pairs of transmitter/receiver pairs may receive the same information from a scene, which introduces redundancy in the received information. Finding a good antenna configuration should eliminate this problem.

14.5.2 Measuring Antenna Quality Based on Information Theory

Information theory can be used to measure and evaluate antenna configurations. This measurement has the same meaning as a channel capacity in communications theory. The antenna array configuration has an analogy to code design that increases the immunity to noise in a given channel. This measurement quantifies the expected performance of an imaging system based on given geometrical design.

To determine the information capacity of an antenna configuration, we consider the voxels information $\underline{x}$ $\underline{x}$ as a stochastic (random) variable with given (a priori) probability density function (PDF), p_x ( $\underline{x}$ $\underline{x}$ ). This defines the information capacity of the antenna configuration $\underline{θ}$ $\underline{θ}$ as

C (\underline{θ}) = I (\underline{y}, \underline{x}) = I (A (θ) \underline{x}, \underline{x}), (14.5)

$C (\underline{θ}) = I (\underline{y}, \underline{x}) = I (A (θ) \underline{x}, \underline{x}), (14.5)$

where $I (\underline{y}, \underline{x})$ $I (\underline{y}, \underline{x})$ indicates the mutual information between $\underline{x}$ $\underline{x}$ and $\underline{y}$ $\underline{y}$ . This quantity directly measures the amount of information about $\underline{x}$ $\underline{x}$ captured into $\underline{y}$ $\underline{y}$ using an antenna aperture with a configuration $\underline{θ}$ $\underline{θ}$ . We define the mutual information as

I (\underline{y}, \underline{x}) = H (\underline{y}) - H (\underline{y} | \underline{x}), (14.6)

$I (\underline{y}, \underline{x}) = H (\underline{y}) - H (\underline{y} | \underline{x}), (14.6)$

where the entropies (the amount of information that is missing before reception) in the last equation are given by

\begin{matrix} H (\underline{y}) = \int d \underline{y} p_{Y} (y) \log (p_{Y} (\underline{y})) \\ H ((\underline{y} | \underline{x}) - \int d x \int d y p_{x y} (x, y) \log (p_{Y | X} (\underline{y} | \underline{x})) . \end{matrix} (14.7)

$\begin{matrix} H (\underline{y}) = \int d \underline{y} p_{Y} (y) \log (p_{Y} (\underline{y})) \\ H ((\underline{y} | \underline{x}) - \int d x \int d y p_{x y} (x, y) \log (p_{Y | X} (\underline{y} | \underline{x})) . \end{matrix} (14.7)$

Now we must provide specific details about the different distributions and assume

Normal distributions for all cases to ease the mathematics.
Voxels in space have identically independent distributions (IIDs) and take their distributions as zero-mean Gaussian

$p_{x} (\underline{x}) - (\frac{γ^{2}}{2 π})^{N / 2} e^{- γ^{2} ‖_{X} ‖_{2}^{2} / 2}, (14.8)$ $p_{x} (\underline{x}) - (\frac{γ^{2}}{2 π})^{N / 2} e^{- γ^{2} ‖_{X} ‖_{2}^{2} / 2}, (14.8)$

which indicates our prior knowledge about the scatterers in space.
The measurement noise can be modeled as an additional Gaussian

$\underline{y} = ℓ \underline{\underline{A}} (\underline{θ}) \underline{x} + \underline{n}, (14.9)$ $\underline{y} = ℓ \underline{\underline{A}} (\underline{θ}) \underline{x} + \underline{n}, (14.9)$

where $\underline{n}$ $\underline{n}$ , a column vector of length M shows the additive zero-mean white Gaussian noise that has variance σ², and ℓ indicates the obstacle loss assumed to be dispersive. This gives a PDF of

$P_{Y | X} (\underline{y} | \underline{x}) = (\frac{1}{2 π σ^{2}})^{M / 2} e^{- ‖ \underline{y} - \underline{A} \underline{x} ‖_{2}^{2} / (2 σ^{2})} . (14.10)$ $P_{Y | X} (\underline{y} | \underline{x}) = (\frac{1}{2 π σ^{2}})^{M / 2} e^{- ‖ \underline{y} - \underline{A} \underline{x} ‖_{2}^{2} / (2 σ^{2})} . (14.10)$
To calculate the entropies above, we need the joint distribution of $\underline{x}$ $\underline{x}$ and $\underline{y}$ $\underline{y}$ given by

$p_{X Y} (\underline{x}, \underline{y}) = p_{Y | X} (\underline{y} | \underline{x}) \cdot p_{x} (\underline{x}) . (14.11)$ $p_{X Y} (\underline{x}, \underline{y}) = p_{Y | X} (\underline{y} | \underline{x}) \cdot p_{x} (\underline{x}) . (14.11)$
Because the joint distribution is Gaussian as well, we also need the distribution of y calculated by marginalizing (limiting) $p_{X Y} (\underline{x}, \underline{y})$ $p_{X Y} (\underline{x}, \underline{y})$ to get

p_{Y} (\underline{y}) = \int d \underline{x} p_{X Y} (\underline{x}, \underline{y}) . (14.12)

$p_{Y} (\underline{y}) = \int d \underline{x} p_{X Y} (\underline{x}, \underline{y}) . (14.12)$

Because we have a Gaussian PDF, this makes $p_{Y} (\underline{y})$ $p_{Y} (\underline{y})$ Gaussian as well.

This gives us the information capacity of Equation 14.5 as

C (\underline{θ}) = \frac{1}{2} \log [\det (\underline{\underline{I}} = + \frac{ℓ^{2}}{γ^{2} σ^{2}} \underline{\underline{A}} (\underline{θ}) \underline{\underline{A}} (\underline{θ})^{T})] . (14.13)

$C (\underline{θ}) = \frac{1}{2} \log [\det (\underline{\underline{I}} = + \frac{ℓ^{2}}{γ^{2} σ^{2}} \underline{\underline{A}} (\underline{θ}) \underline{\underline{A}} (\underline{θ})^{T})] . (14.13)$

Taking the singular devaluation decomposition (SVD) [10] to the matrix $\underline{\underline{A}}$ $\underline{\underline{A}}$ provides a simpler expression for the information capacity so that

C (\underline{θ}) = \frac{1}{2} Σ_{i - 1}^{r} \log [\frac{ℓ^{2} λ_{i}^{2}}{γ^{2} σ^{2}} + 1], (14.14)

$C (\underline{θ}) = \frac{1}{2} Σ_{i - 1}^{r} \log [\frac{ℓ^{2} λ_{i}^{2}}{γ^{2} σ^{2}} + 1], (14.14)$

where ${λ_{i}}_{l - 1}^{r}$ ${λ_{i}}_{l - 1}^{r}$ indicates the singular (matrix determinant = 0) values of $\underline{\underline{A}}$ $\underline{\underline{A}}$ , given by the nonzero diagonal components of the diagonal (M × M) matrix $\underline{\underline{Λ}}$ $\underline{\underline{Λ}}$ in the SVD decomposition $\underline{\underline{A}} = \underline{\underline{u}} \underline{\underline{Λ}} {\underline{\underline{V}}}^{T}$ $\underline{\underline{A}} = \underline{\underline{u}} \underline{\underline{Λ}} {\underline{\underline{V}}}^{T}$ (which always exists for any matrix).

Results: In practical radar terms we can translate Equation 14.14 as follows:

Term ℓ²/γ²σ² describes the received signal-to-noise ratio (SNR).

Term 1/γ² shows the power of the voxels in space translated via the matrix $\underline{\underline{A}}$ $\underline{\underline{A}}$ to the power of the time domain signals.

The term $ℓ^{2} λ_{i}^{2} / γ^{2} σ^{2}$ $ℓ^{2} λ_{i}^{2} / γ^{2} σ^{2}$ shows the SNR of the “eigen-channel” coming from the projection of the information in space of the eigenvector defined by the ithcolumn of the matrix $\underline{\underline{V}}$ $\underline{\underline{V}}$ . In this case, $\underline{\underline{V}}$ $\underline{\underline{V}}$ gives an N × N unitary matrix whose columns form a basis for the voxel’s space. The first r columns span the space in the voxel’s space within which the system can interact, whereas the remaining columns span the null space of the voxel space; this subspace consists of information for which the systems have no channel to “communicate” with and thus cannot be reconstructed based on the received signals.

Significance: Small values for γ_i means that the ith channel suffers from higher loss due to the actual aperture configuration. We set the ${SNR}_{i} = λ_{i}^{2} ℓ^{2} / (γ^{2} σ^{2})$ ${SNR}_{i} = λ_{i}^{2} ℓ^{2} / (γ^{2} σ^{2})$ and rewrite Equation 14.14 as

C (\underline{θ}) = \frac{1}{2} Σ_{i = 1}^{r} 10 \log_{10} [S N R_{i} (\underline{θ}) + 1] (14.15)

$C (\underline{θ}) = \frac{1}{2} Σ_{i = 1}^{r} 10 \log_{10} [S N R_{i} (\underline{θ}) + 1] (14.15)$

Information theory states that communication channel of bandwidth B has a capacity of $C (\underline{θ}) = B \log [S N R + 1]$ $C (\underline{θ}) = B \log [S N R + 1]$ . Using this concept, we can see how the information capacity of an antenna array configuration equals the sum of the capacities of all its eigen-channels of unit bandwidth. Using this analogy, the measure for the expected performance of antenna configurations was used exactly as the channel capacity works as a measure for designing codes for communication channels.

From this communications theory concept, we can rewrite Equations 14.11 through 14.15 differently to give the results in the standard dB SNR units:

S N R_{e f f} = Σ_{i = 1}^{r} 10 \log_{10} [S N R_{i} (θ) + 1], (14.16)

$S N R_{e f f} = Σ_{i = 1}^{r} 10 \log_{10} [S N R_{i} (θ) + 1], (14.16)$

which indicates that eigen-channels with SNR close to zero do not contribute to the effective SNR; only channels with SNR considerably greater than 1 contribute to SNR_eff.

Now, we apply Equation 14.13 to an antenna configuration $\underline{θ}$ $\underline{θ}$ , build the matrix $\underline{\underline{A}}$ $\underline{\underline{A}}$ , and calculate the determinant of $\underline{\underline{P}} = \underline{\underline{I}} + ℓ^{2} / (γ^{2} σ^{2}) \underline{\underline{A}} {\underline{\underline{A}}}^{T}$ $\underline{\underline{P}} = \underline{\underline{I}} + ℓ^{2} / (γ^{2} σ^{2}) \underline{\underline{A}} {\underline{\underline{A}}}^{T}$ . This matrix has a size of M × M, which could approach M ~ 100,000 for practical designs and results in a highly complex calculation task. Using the symmetry of $\underline{\underline{P}}$ $\underline{\underline{P}}$ positive definite quality, we can calculate this determinant using the Cholesky decomposition [10] that provides a complexity of O(M³).

To reach conclusions while using the above model, real measured time domain SNRs need to be related to the value of ℓ²/(γ²σ²). Under the assumption of Gaussian IID voxels in Equation 14.8, the received signal power defined by E[y^Ty]/M becomes

s = \frac{ℓ^{2}}{γ^{2}} \frac{1}{M} \underset{i}{Σ} λ_{i}^{2} \equiv \frac{ℓ^{2} \bar{γ^{2}}}{γ^{2}}, (14.17)

$s = \frac{ℓ^{2}}{γ^{2}} \frac{1}{M} \underset{i}{Σ} λ_{i}^{2} \equiv \frac{ℓ^{2} \bar{γ^{2}}}{γ^{2}}, (14.17)$

which gives the SNR as

SNR = \frac{ℓ^{2} \bar{λ^{2}}}{γ^{2} σ^{2}} . (14.18)

$SNR = \frac{ℓ^{2} \bar{λ^{2}}}{γ^{2} σ^{2}} . (14.18)$

For a single transceiver element antenna case, calculating the singular values (designated{γ_0i}) gives an appropriate scaling factor for calculating ℓ²/( γ²σ²) for a given SNR as

\frac{ℓ^{2}}{γ^{2} σ^{2}} = \frac{S N R}{\bar{λ_{0}^{2}}}, (14.19)

$\frac{ℓ^{2}}{γ^{2} σ^{2}} = \frac{S N R}{\bar{λ_{0}^{2}}}, (14.19)$

where $\bar{λ_{0}^{2}} = (1 / M) \underset{i}{Σ} λ_{0 i}^{2}$ $\bar{λ_{0}^{2}} = (1 / M) \underset{i}{Σ} λ_{0 i}^{2}$ is calculated from the above-defined reference aperture.

14.5.3 Examples of Antenna Information Capacity

The information capacity of six different antenna configurations was calculated to evaluate the possibilities. Each configuration consisted of four transceivers and four receivers, respectively, indicated by x marks and circles in Figure 14.9. The model assumed that the receivers corresponding to the transceivers will not receive when their transmitter transmits. The proposed configurations started with a symmetric array (no. 1) arranged in a Cartesian grid. We gradually deformed the arrangement to break the symmetry in configuration nos. 2-6. In the second configuration, the lower row elements were moved to reduce their interdistance. In the third configuration, the two receivers in the lower row were moved toward the aperture center. The fourth configuration resulted from rotating the receivers in the first configuration. In the fifth configuration, the two transceivers in the lower row of the fourth configuration were moved toward the receiver in this row. In the sixth configuration, the arrangement of the receivers in the fifth configuration were slightly deformed. The antenna information capacities required for each case were then calculated by building the matrix $\underline{\underline{A}}$ $\underline{\underline{A}}$ , which resulted from the discretization process described earlier. The space configuration required choosing a domain of interest, which used a 1-m-wide strip centered at a range of 7 m from the aperture center. The comparison of Figure 14.9 shows the SNR_eff of all configurations relative to the first configuration, for different SNR conditions for the received signals (where we extracted the constant ℓ²/γ²σ² using Equation 14.19 and the corresponding reference antenna configuration).

14.5.4 Antenna Array Configuration Conclusions

The work of the Camero engineers showed that symmetrical antenna array configurations do not produce the best results in terms of SNR and information capacity. Instead, it was found that less symmetry of the antenna elements produced a higher expected antenna performance. In each case, the array performance was measured in terms of the effective SNR. A higher effective SNR gives the system better immunity from additive noise. For a bad signal (low SNR) case, the differences between the configurations became less significant. This resulted from the fact that when the SNR decreases, more eigen-channels become masked by the noise and are unusable. At the same time, the dominant eigenchannels, which contribute most of the effective SNR, seem more immune to additive noise in all configurations. In the case of a relatively adequate 20-dB SNR in all configurations, it was found that the array configuration no. 6 (Figure 14.9) showed a superiority of 3.4 dB compared with the simple symmetrical Cartesian arrangement of the elements in configuration no. 1. Thus, breaking the antenna configuration symmetry can improve the aperture performance.

Xaver™ radars use antenna configurations determined by these methods to improve their information capacity and overall imaging performance.

14.6 Camero Xaver™ Radar High-Resolution TW Imaging

14.6.1 Background and Objectives

Camero engineers Eyal Hochdorf, Amir Beeri, and Ron Daisy developed an innovative approach for 3D high-resolution imaging of objects or people hidden behind obstacles for the Camero Xaver™800 micropower UWB radar. This helps the Xaver™800 radar to provide 3D images with good resolution for objects hidden behind walls. The 2D radar displays of Figure 14.4 show typical low-resolution images (“blobs”) and “motion detection” capabilities of less advanced UWB TWR systems. The Xaver™800 image shown in Figure 14.7a illustrates the technology improvements in terms of 3D imagery and discrimination between moving and stationary objects.

Images

FIGURE 14.9
Comparison between six different antenna array configurations. The second column shows the elements arrangement. The last three columns show the differences between the effective SNR of each configuration and the base line configuration no. 1. Adjustment of the transceivers (xs) and receivers (circles) resulted in improved SNR and better performance. (Jacob, O. et al., “Antenna array design for ‘through wall imaging’ systems by means of information maximization,” Camero Tech., Ltd., Israel, 2008; Courtesy of Camero, Inc., Israel, © 2010.)

14.6.2 Technical Problems in High-Resolution Real-Time Radar Imaging

High-resolution real-time UWB radar imaging requires solving two major problems: (1) improving the SNR of radar returns and (2) synchronizing the time returns from multiple transmitters and receivers. This section summarizes the topics covered in Chapter 15, “The Camero, Inc., Radar Signal Acquisition System for Signal-to-Noise Improvement,” and Chapter 16 “The Camero, Inc., Time Delay Calibration System for Range Cell.” Chapters 15 and 16 contain complete explanations based on the patent documents.

14.6.2.1 SNR Ratio Improvement with the Camero Signal Acquisition System (SAS)

Many things can diminish the strength of a transmitted radar signal to degrade and limit the system’s ability to detect objects and form images. The target range and radar crosssection will determine how much of the incident signal returns to the receivers. Material-penetrating and TWR systems have additional problems because obstacles or dense media will reduce the signal strength in addition to the natural range attenuation.

Under the best conditions, the free space path loss over a range r naturally reduces the received signal strength by a factor of 1/r⁴, which attenuates the signal by 12 dB for each doubling of a target range. Solid media may introduce losses approaching 30 dB or more when imaging through obstacles in TW or underground environments. Target scattering magnitude (radar cross section) can vary and a typical imaging system can expect variations ranging 20 dB or more. This means that UWB radar systems will require a high dynamic range for the SAS, which places special demands on the analog-to-digital converters (ADC) used in signal processing. For example, the dynamic range in an SAS designed to work with a target range from 1 to 8 m requires about 86 dB, and increasing the target range to 32 m will require a dynamic range of about 110 dB.

All of these factors decrease the SNR and limit the system detection and imaging performance. One approach to increasing the SNR for better information recovery integrates multiple signal returns to compensate for the signal losses and improve the received SNR.

Camero engineers developed and patented the “Signal Acquisition System and Method for Ultra-Wideband (UWB) Radar” to improve the SNR of TWR signals. The SAS breaks the radar return into range cells and then performs a series of analog and digital integrations on the signal from each range cell for multiple returns. SAS processing can perform more integrations on more distant range cells to improve the system SNR for imaging. In Chapter 15 a detailed description of the patented process of the Camero SAS is given [12].

14.6.2.2 Time Return Synchronization with the Camero Time Delay Computation System (TDCS)

UWB imaging radar systems with multichannel arrays require an accurate knowledge of time delays in each transmitter and receiver subsystem. The nature of the UWB imposes a high requirement of ~10-15 picoseconds alignment accuracy between all channels. To combine range information from reflectors, we need to exactly align (synchronize) all the time domain peak signal returns in time. Excessive variation in the actual time delay of each channel will produce blurred images. Exact alignment of all system channels helps focus images and removes image spatial distortions. The Camero Xaver^™800 TWR system has a bandwidth that translates into a sensitivity of relative time delays on the order of a few picoseconds, so we need a very precise channel assignment mechanism.

Time delays between channels result from constant and variable time delay inaccuracies. The constant delays result from variations in the front-end hardware of each channel, the antenna element, the RF component, the sampler components, timing design, and circuit board materials. Manufacturing variations and temperature changes of the electronic components cause the variable delays. Compensating for the variable time delays requires accurate measurement of constant and variable time delays in each channel.

To synchronize the channels, the Camero engineers developed a system for continuously calculating the time delays of each transmitter and receiver channel for correctly estimating the range to each reflecting object, and focusing the array returns for highresolution imaging. Chapter 16 presents a full discussion of the company patent “Timing Varying Calculations of Internal Delays in Transmitters and Receivers” [13].

14.7 Experimental Results in High-Resolution Imaging

14.7.1 The Camero Xaver™800 TWR System

The Xaver^™800 shown in Figure 14.10 was designed with a bandwidth of several GHz and an autocorrelation time in the order of tens of picoseconds. This tripod-mounted TWR has an optimized 24-element antenna array based on the principles described in Section 14.5. Figure 14.13 shows the system from the back (antenna) side with the antennas in the operating position, in the front side the antennas are folded to their nonoperational or traveling position. The multiple transmitter-receiver channels’ range cells require time delay alignment of a few picoseconds provided by the time delay calibration system (TDCS) described in Chapter 16.

14.7.2 Time Delay Compensation Effects

To illustrate the effects of coherent alignment, the image of a small simple spherical object was taken. Figure 14.11a shows the initial state of the image with zero delay estimator vector; Figure 14.11b shows the image during the coherent registration process, before the delay estimator vector reached its final value; Figure 14.11c shows the image when the coherent registration has almost converged to stable time off sets, so the image appears nearly focused.

Figure 14.11 demonstrates the importance of coherent registration with a simple object. The results of imaging on a more complex object have even more marked effects. Generally, wide system bandwidths have higher sensitivity to coherent registration. Coherent registration becomes a necessary and important part of high-resolution imaging systems with very wide bandwidths.

Images

FIGURE 14.10
The Camero Xaver™800 TW surveillance radar used in the experiments. (a) Antenna side showing the deployed antennas and dielectric radomes covering the 24-element array designed to give the maximum efficiency by the skewed placement described earlier. (b) The front side showing the operators console and display, which can detach for remote operation. (Courtesy of Amir, B. and Ron, D., High-Resolution Through-Wall Imaging, Camero, Inc., Israel, © 2010.)

Images

FIGURE 14.11
Imaging results during coherent alignment on a single spherical target. (a) The alignment starts with a zero error vector, which produces the unfocused image. (b) The improved image as the error vector adjusts. (c) Final image produced in the convergence state when the system has determined the time delay errors and corrected for them. (Courtesy of Amir, B. and Ron, D., High-Resolution Through-Wall Imaging, Camero, Inc., Israel, © 2010.)

Figure 14.12 presents two Xaver™800 imaging examples showing how coherent registration helps image the specular (mirror-like) areas of the bending person and the person with the dog. Registration makes the images appear relatively clear and sharp. We have enough resolution to distinguish between the body parts of the man and identify specific objects. Figure 14.12a shows the person’s body parts including hands, legs, head, and torso. Strict coherent registration helps achieve high-resolution images of the specular points. These objects would appear as low-resolution blobs without channel alignment. Figure 14.12b shows the person and the dog in sufficient detail—we can make out two separate objects, one appears tall and looks like the person, the other short object looks like the dog. Coherent registration helps the observer intuitively understand the position of the dog and the meaning of the scene.

Images

FIGURE 14.12
Camero Xaver™800 radar images showing the effects of coherent registration. (a) The many specular areas of the bending person help distinguish hands, arms, head, and torso. (b) The image clearly distinguishes between the person and the dog by their spatial separation and different configurations. (Courtesy of Amir, B. and Ron, D., High-Resolution Through-Wall Imaging, Camero, Inc., Israel, © 2010.)

14.8 High-Resolution TWR Imaging Conclusions

Successful high-resolution UWB radar imaging as demonstrated in the Xaver™800 TWR system resulted from

A greater than 3-GHz signal bandwidth that results in autocorrelation times of tens of picoseconds to give fine spatial resolution.
The unsymmetrical antenna array design based on an advanced communication systems theory approach to antenna information efficiency. We demonstrated how skewing the array geometry can maximize the antenna information capacity and improve system performance. These results run counterintuitive to the obvious and logical notion of arranging elements in a regular symmetric pattern.
The time delay calibration system for measuring internal delays of each range information channel in real time. It applies the delays to coherently register the radar returns from each transmitter-receiver channel to focus the images. The coherent registration system corrects the time delay errors introduced into the system by the electrical characteristics of channel components. This helps reconstruct the objects from the multiple channels of received signals by building images with aligned digital volume elements (voxels).
The SAS processing that improves the SNR of the radar returns through analog and digital integration. Using variable integration to build the signal strength of more distant returns helps to provide good quality imaging at all ranges. The active operator interface lets the user adjust the signal processing to get the best image possible.

Acknowledgments

I (James D. Taylor) wish to extend special thanks Eyal Hochdorf of Camero USA for his cooperation in providing the background materials and his participation in preparing the chapter. Eyal approved my proposal for writing a chapter presenting the Xaver^™ radars as a case study in the problems and solutions to through-wall vision.

References

1. Camero USA Corp. Xaver 400™ compact, tactical through-wall visions system. Camero USA Corp., Vienna, VA. Online: http://www.camero-tech.com/files/files/Xaver400.pdf (accessed January 23, 2012).

2. Camero USA Corp. Xaver 800™ through-wall vision system. Camero USA Corp., Vienna, VA. Online: http://www.camero-tech.com/files/files/Xaver800.pdf (accessed January 23, 2012)

3. Frazier, L.M. Radar surveillance through solid materials, Paper 2938-20, SPIE Photonics East Conference, Boston, MA, November 1996, pp. 139-1146.

4. Jon, E. Latest advances in through-wall radar sensing for security applications. Sensor Review, Vol 23, No 3, 2008, pp. 205-2211.

5. SRC, Inc., O-Pen™. Online: http://www.srcinc.com/uploadedFiles/src/what-we-do/O-PEN.pdf, 2011.

6. Endoacustica Security and Surveillance Technology. PRISMA through-wall radar—Law enforcement only, Endoacustica Security and Surveillance Technology, Italy, © 2001-2010. Online: http://www.endoacustica.com/details_prisma_en.htm

7. Cambridge Consultants. Covert intelligence through wall radar. Online: http://www.cam-bridgeconsultants.com/prism_200.html, 2011.

8. Jacob, O., Ron, D., and Amir, B. Antenna array design for “through wall imaging” systems by means of information maximization. Camero Tech., LTD, Israel, 2008.

9. Cichocki, N.A. and Amari, S.I. Adaptive Blind Signal and Image Processing. John Wiley & Sons, Singapore, 2002.

10. Meyer, C.D. Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia, PA, 2001.

11. Amir, B. and Ron, D. High-Resolution Through-Wall Imaging. Camero, Inc., Israel, 2010.

12. Gazelle, D., Beeri, A., and Daisy, D. Signal Acquisition System and Method for Ultra-Wideband (UWB) Radar. U.S. Patent No. 7,773,031 B2, August 10, 2010.

13. Hochdorf, E., Timar, R., Beeri, A., and Gazelle, D. Timing Varying Calculations of Internal Delays in Transmitters and Receivers. U.S. Patent No. 2008/0261536 A1, October, 23, 2008.

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14 Xaver™ Through-Wall UWB Radar Design Study