15.2.1 Signal, Noise, and Receiver Dynamic Ranges

15.2.2 Receiver SNR Improvement

The combined signal strength losses mean that UWB radar receivers must have a wide dynamic range to amplify signals without distortion from saturation at the highest return signal strengths. For example, a UWB through-wall radar system for a target range of 1-8 m requires about 86-dB dynamic range. Increasing the target range to 32 m will require a dynamic range of about 110 dB, and so on. This means that analog-to-digital convertors (ADCs) must have a large input range [1].

Integration of multiple signal returns to compensate for the signal losses can improve the received SNR for better information recovery. The signal processing literature discusses many examples of coherent integration schemes for improving signal detection capabilities. Generally, this process holds the received signals from different transmit-receive cycles and sums them repeatedly. Adding successive returns will increase the strength of the deterministic (repetitive and known) part of the signal. Dissimilar random noise signal components will not sum as quickly as the deterministic signal returns. Adding more returns to produce longer integration times will produce greater improvements in the SNR [2,3]. However, simple integration of all returns does not solve the dynamic range issue because close-range return signals will have a higher SNR than those from more distant returns.

15.3.1 The Camero, Inc., SAS Components and Signal Processing

The SAS can integrate at least one received signal by using the following physical components:

• At least one sampler configured to sample the received signal and to provide samples of different range cells

• At least one analog integrator coupled to the sampler and configured to integrate the said samples whereby compensating at least part of the signal loss and giving rise to analog samples

• At least one analog/digital converter coupled to the analog integrator and configured to convert said analog samples into digital samples

• At least one digital integrator coupled to the analog/digital converter and configured to integrate said digital samples

The signal acquisition method uses the following steps:

• Sampling the received signal and saving samples of different range cells

• Performing analog integration of the range cell samples to partly compensate for the signal loss and to produce analog samples

• Sending each integrated range cell sample through an ADC and creating digital range cell samples

• Integrating the digital range cell samples with standard computational techniques

15.3.2 Camero, Inc., Signal Processing

The SAS takes multiple samples of at least one range cell and processes them through an analog integrator for N_a integration cycles. The digital integrator performs N_d digital integration cycles. This gives an overall number of integration cycles N = N_a × N_d. To achieve a desired SNR profile, radar image frame rate, and/or desired dynamic range, the SAS method can vary the number of integration cycles and/or number of analog and/or digital integrations for samples of different range cells.

Figure 15.1 shows the overall block diagram of a UWB radar imaging system with N > 1 transmitters (TX) and M > 1 receivers (RX) arranged in, or coupled to, an antenna array (13). At least one transmitter sends a pulse signal (or other UWB waveform such as an M-sequence coded signal) into the imaged space and at least one receiver captures the scattered/reflected signal. Several receivers capture the reflected signal to achieve a high-quality image. The process can repeat for each transmitter either simultaneously or separately with different coding for each transmitter (e.g., M-sequence UWB coding). The received signals travel to the SAS (14) coupled to the antenna array. The image reconstruction and display system uses the sampled and integrated signals for the range cells in each transmitter-receiver channel to construct an image of the reflectors in range.

15.3.3 SAS SNR Improvement

Under normal radar conditions, the received SNR decreases with target range because of the increased 1/r ⁴ attenuation. Integrating a signal for N cycles amplifies the signal by a factor N and the noise root-mean-square (RMS) amplitude by a factor of N. Thus we may improve the SNR by integrating the signal over multiple cycles to compensate for all the system losses. When properly configured with multiple channels, the SAS can take signals from many receivers, integrate them, and control the signal acquisition process.

Signals from all receivers for each transmitter integrated in the SAS (15) pass to an image reconstruction and display system (16). Image reconstruction methods can use many different appropriate techniques such as ellipsoidal back-projection. Although many radar systems provide integration by way of digital sampling, the Camero, Inc., SAS samples the received signal on a uniform grid over the time domain at a given Nyquist criterion sampling rate and converts it to discrete digital samples. To achieve the required SNR, the SAS repeats sampling of the return signal at a given instant and performs an analog integration followed by digital integration using well-known digital signal techniques.

The frame rate of real-time radar imaging or other critical radar systems determines the signal acquisition period. This means the imaging frame duration sets the completion time for signal acquisition. During the frame period, the number of transmission/reception cycles (maximum integration number) required for integration must not exceed the total number of transmitted pulses within the frame duration defined by the pulse repetition frequency (PRF) and the number of transmitters N. In many cases, we cannot achieve a required SNR with this maximal integration number.

To get around the maximal integration number constraint, parallel sampling can be performed that samples the received signal on different L > 1 instants. This approach will shorten the additional signal acquisition time by a factor L. This parallelism requires each receive channel to have a very fast ADC sampler with enough bits to fit the required dynamic range and fast electronics to transfer the samples from the many ADCs. This can involve high hardware expenses and power consumption.

15.3.4 Designing the Camero, Inc., SAS

Considering the problems and objectives described above, the engineers needed to find a way to decrease the requirement for dynamic range and the speeds of the ADCs and other digital electronics. The Camero, Inc., SAS has broad applications outside the UWB radar shown in Figure 15.1 and may find applications in other UWB radars. Note how a synthetic aperture radar would provide the equivalent of the multiple transmitters and receivers shown here.

After reviewing the problems and literature of conventional radar signal acquisition methods, the sampling and digitizing configuration was devised (20) (Figure 15.2). The SAS includes a UWB sampler block (21) coupled to an analog integration block (22) coupled through an ADC (23) to a digital integration block (24) Typically, each separate acquisition channel (20) contains the same components and connects to a particular receiver.

To explain the Camero, Inc., SAS operation as shown in Figure 15.2 (20), consider the case of static targets moving slowly compared with the shortest transmitted wavelength during a frame interval. In this case, the periodic received signal is r(t) with a period T = 1/PRF, where PRF indicates the transmission pulse repetition frequency. The sampler block (21) repeatedly samples the received signal r(t) by tuning the sampling instants to the range cells at time t = T₀ + nΔT. The nth sampling phase corresponds to the target range nΔTc/2 (where c is the speed of light in vacuum; ΔT is the sampling interval; T₀ corresponds to the time of transmission of short UWB pulse by a selected transmitter in the current transmit/receive cycle and the factor 2 accounts for the round trip of the scattered wave).

The sampled signal goes to the analog integration block (22), which requires a reset at the beginning of each range cell. The sampling and analog integration process repeats for the desired number cycles as described later.

The analog integrator (22) output goes to the ADC (23) for conversion into a digital sample. The stream of digital samples S_n corresponds to the integrated received signal at the nth range cell, which then goes to the digital integration block (24) for further integration by means of discrete time signal processing. The Camero, Inc. SAS has a unique feature because of the following:

• The analog integration block configuration compensates for at least part of the signal losses

• The digital integration block configuration can substantially compensate for the nominal free space propagation losses

There are several ways to approach the problems of compensation for known/expected losses. For example, in different implementations

• The configuration of the analog integration block can substantially compensate for the nominal free space propagation and the digital integration block can compensate for factors such as obstacle-oriented losses, RCS variations

• The analog integration block may compensate for obstacle-oriented losses and/or expected RCS variations

• The analog integration may partially compensate for propagation losses, and the digital integration block may complete the desired compensation for signal losses

• The Camero, Inc., SAS has provisions for a variable number of integration cycles in accordance with the following:

  • Range (based on reception time)

  • Desired SNR profile providing better values of SNR for different range cells for a given RCS

  • Signal loss compensation

For example, to achieve a range-independent SNR for a predefined target RCS, the near range cells will receive a smaller number of integration cycles compared with far ones. In another case, the SAS can maximize the SNR for a subrange of special interest within the constraints of overall integration time, by setting the number of integration cycles for corresponding range cells on account of the integration of other range cells.

The SAS has great flexibility and can use different integration plans to cover any kind of predefined relationship between a number of integration cycles and range/reception time (range cell index). For example, the SAS can be programmed to a desired SNR profile and/or desired compensation for signal losses.

The total SAS may include a database (25) and processor (26) coupled with a digital integration block (24) and/or the analog integration block (22), which is coupled to each receiver channel Rx_m. This feature lets the user integrate the database and processor with one or more blocks of the SAS (e.g., with the digital integration block). For example, the database may have precalculated integration plans(s) for a range independent SNR profile or a maximized SNR for selectable subranges, and so on.

15.3.5 Camero, Inc., SAS Calculation of Integration Cycles

By applying some previous information, the number of integration cycles can be calculated based on a known dependence between the nominal propagation path loss and target range/reception time. Some variations on this idea include the following:

• Programming precalculated numbers of integrated cycles required for compensation of other types of signal losses such as those caused by a predefined obstacle or expected loss. This would let the operator adjust the processing for looking through different types of construction in through-wall radars based on expected losses.

• Programming the SAS to calculate the required numbers of integration cycles with the help of adaptive and/or learning algorithms. This requires having some external interface (27) to obtain data from an image reconstruction system, user, and so on. The adaptive/learning algorithms may complement the precalculated integration plan(s) by enabling path loss compensation in real conditions (e.g., airborne radars) or replacing (partly or fully) the precalculated integration plan(s) by providing on-demand and/or online calculations of the required integration.

The number of integration cycles N required to increase the SNR from some initial value SNR₀ to a target value SNR_t can be determined by the following equation with SNR values

in dB:

A well-known radar equation found in A. Ishimaru’s Electromagnetic Wave Propagation, Radiation and Scattering [4] states that for a given fixed RCS target, the received SNR depends on the reception time t as follows:

where SNR(t) indicates the SNR at the starting receive time t₀.

Equations 15.1 and 15.2 were used to devise an integration plan with the required SNR as a function of the receiving range (SNR profile). For example, an integration plan for a range independent SNR profile for a fixed RCS target is defined as

In this case, N(t) indicates the required number of integration cycles for different range cells as a function of reception time. N₀ gives the number of integration cycles for t = t₀ given by N₀ = 10^{[SNR t} ~^SNR(t°^)]/1°.

This plan compensates for free space propagation losses and gives a range-independent SNR profile. The Camero, Inc., SAS was designed such that it can predefine and store this integration plan in the system database. Depending on the particular radar antenna array geometry, the SAS may require an individual integration plan for each transmitter/receiver pair. For special cases where the antenna aperture has larger dimensions than the range, all receivers can use the same integration plan. A nonlimiting general example can show the case of an integration plan with a range-independent SNR profile. From Equation 15.3, the signal and noise can be described as the following functions of reception time (or range):

In this situation, the received signal amplitude ν for a given RCS without noise is proportional to v(t) ∝ v₀(t₀/t)². This means that the received power varies inversely as range (ct/2)⁴ or t⁴, so the amplitude [square root of power] becomes inversely proportional to t². Therefore, the signal amplitude v_is and RMS noise amplitude v_iN at the integrator output working according to the integration plan of Equation 15.3 would give

where ν_Νrms describes the additive white noise RMS amplitude.

Thus Equation 15.5 shows how to achieve a constant SNR and an integrated signal (and noise) level that increases with range. Implementing the plan with only an analog integrator requires large number of bits to cope with the extended signal dynamic range at the ADC input. As shown in Figure 15.1, there is a similar problem when building an integration plan with only a digital integrator. To solve these problems, the Camero, Inc., SAS splits the integration process into two parts: analog integration followed by digital integration. This approach gives us an additional degree of freedom because we can design it for two separate integrators according to different criteria. For example, we can minimize the signal dynamic range of the ADC to reduce costs and get an adequate SNR at the output of the digital integrator.

The Camero, Inc., SAS can split the overall number of integration cycles N(t) into N_a(t) analog integration cycles and N_d(t) digital integration cycles so N_a(t) × N_d (t) = N(t). Given this, if Na(t)=Nd(t)=N(t), then we get the received signal amplitude at the output of the analog integration block as vis(t)=v0N0. According to this proposed integration plan, the received signal from a given RCS target becomes range independent after the analog integration. This compensates for the free space path loss and minimizes the expected signal dynamic range at the input of the ADC port. For example, this can reduce the ADC dynamic range requirements from 86 to 110 dB, as described in Figure 15.1, to less than 50 dB for some environments, where the obstacle caused variations contribute to 30 dB losses and target RCS diversity contributes to 20 dB losses.

Some versions of the Camero, Inc., SAS may perform the analog-to-digital conversion of the analog integrator output once, for each period of analog integration as shown in Figure 15.3. This will considerably reduce the required ADC conversion rate for integration plans with the number of analog integrations strictly greater than 1. This helps the SAS to use relatively low-cost slow ADCs. The SAS can reduce the signal acquisition power consumption that depends on the ADC conversion rate. Those familiar with signal processing would know that many variations exist for the equivalent and/or modified functionality of the SAS.

15.3.6 Alternate Signal Integration Methods

The Camero, Inc., SAS can have many implementations, but the following examples show some basic approaches: (1) off-line a priori information plan; (2) interactive user integration and noise plan; (3) automatic adaptive plan; and (4) online automatic predefined adaptive integration plan. The patent covers all variations of these.

1. Off-line a priori information plan: This off-line plan assumes a priori known system operation information about fixed losses and/or noise sources and takes this into account during the system design phase or in preparation for a specific use. We can summarize the a priori information by the following:

   SNR(t)=F1(t),P(t)=F2(t),FR,⁢(15.6)

   where SNR(t) describes the expected SNR versus reception time (or range) given by the a priori known function F₁(t); P(t) is the expected received power at reception time t (corresponding to a target of given RCS located at range ct/2); and FR is the required imaging frame rate. We can supply F₁(t) and F₂(t) with a table or a mathematical representation such as the one shown in Equation 15.2 (i.e., SNR(t) = SNR(t₀) - 40 × log₁₀(t/t₀), [dB]). Generally F₁(t) depends on F₂(t) because the received SNR depends on the received power and the receiver frontend additive noise profile F₁(t) = F₂(t)/P_noise(t), where P_noise(t) is the additive noise power profile (which typically comes from thermal sources at the frontend and has a profile P_noise(t) = const). The plan may require additional information for calculating the integration plan as shown in Table 15.1.

   We can then calculate the required analog, N_a(t), and digital, N_d(t), integrations from

   Na(t)≤Vmax(ADC)AFEZ0P(t),⁢(15.7)
   Nd(t)=N(t)Na(t),⁢(15.8)

   where N(t) is the total integration plan (according to the required integrated SNR profile) given by

   N(t)=10[SNRf(t)-F1(t)],⁢(15.9)

   TABLE 15.1
   Camero, Inc., SAS Off-Line A Priori Information

   Required Information	Symbol	Function/Description	Source
   SNR profile goal	SNRt(t)	Required integrated SNR vs. reception time (or range)	Given
   ADC limit	Vmax(ADC)	Maximum admissible ADC input voltage (ADC saturation power)	ADC specifications
   Frontend gain	AFE	Gain between antenna and ADC with no integration	Measured
   Characteristic impedance	Z0	Frontend characteristic impedance	Measured
   Pulse repetition rate	PRR	System transmission PRR	Design specifications

   which is subject to the constraint

   ΣtN(t)≤PRF/FR.⁢(15.10)

   This constraint ensures that the total number of cycles used to acquire the signal does not exceed the number of transmitted pulses in the frame duration. We can increase the system PRF or decrease the imaging frame rate FR to satisfy the constraint.

   This Camero, Inc., SAS off-line a priori integration plan may provide a better utilization of ADC bits and give an integrated signal with the desired SNR profile SNR_t(t). Note that because the equations for N_a(t) and N_d(t) have integer values, we must round results of calculations to the closest integer, subject to N_a(t), N_d(t) > 1. The calculation should include at least one cycle of integration for each range cell, otherwise it makes the radar equivalent to one with no processing.

2. Interactive user integration and noise plan: This plan will have a user interface that permits adjusting the number of analog integrations N_a(t) and digital integrations N_d(t). The operator can interactively recognize a subrange with poor imaging or detection performance and change the integration plan by using more transmission cycles to integrate the signal at this subrange.

3. Automatic adaptive plan: This plan uses special purpose algorithms capable of analyzing the quality of integrated received signals and/or reconstructed images to adjust the system to achieve predefined goals. This might work by including a processor/database to collect statistics about the integrated signal power versus range. By analyzing these statistics we might recognize an abrupt decrease in signal power at some range (corresponding to a reception time denoted by t’) in the mean received power and related to an obstacle at the corresponding range. The processor can then increase N_a(t) for t > t’ to remove the discontinuity. In this case, Equation 15.8 (for N_d(t)) will determine N_a(t) and N_d(t) within the constraint of Equation 15.10 (i.e., Σ N(t) < PRF/FR).

4. Online automatic predefined adaptive integration plan: This plan uses special purpose algorithms, which use feedback from integrated received signals and/or reconstructed image to modify the integration plan to achieve a predefined goal. For example, as the system operates, the processor/database may collect statistics about the integrated received power versus range. These statistics could indicate an abrupt decrease or discontinuity in the mean received signal power at some range corresponding to reception time t’, indicating the presence of an obstacle at that range. The processor may use these algorithms to increase N_a(t) for t > t and cause the discontinuity to vanish. Again N_a(t) and N_d(t) are related through Equation 15.8, N_d(t) = N(t)/N_a(t), and fulfill the constraint of Equation 15.10.

15.3.7 The Camero, Inc., SAS General Operating Principles

Figure 15.3 shows a generalized operating diagram of how the Camero, Inc., SAS works in accordance with some of the embodiments described earlier. During operation the SAS captures a signal from each of the n transmitters (TX1,TX2, . . . , TXN) sequentially during a frame (31). This means each transmitter acquires the received signals (32) for the entire range. The SAS takes the different simultaneous sampled range cells (t₀, t₁, etc.) for all m receivers (RX1,RX2, . . . , RXM) and performs N_a analog and N_d digital integrations on each analog integrated sample. As mentioned earlier, the number of analog and digital integrations for each range cell can vary according to a priori assumptions about the range, or as required, based on image analysis or operator adjustment. The system resets the analog integrators (typically one per receiver) prior to each integration section. In Figure 15.3, r_1/M (t₃) and r_1M (t_i) stand for the integrated sample corresponding to the received signal at receiver M at times t₃ and t, respectively, received from the reflected signal from transmitter TX1. As shown in the figure of the integration plan example, the number of integration cycles (N_d, N_a, etc.) differs for different range cells.

We can imagine other signal acquisition schemes capturing the frame sequentially, range cell after range cell (in an increasing order), so that each range cell runs sequentially over all transmitters.

The Camero, Inc., SAS may take the form of a suitably programmed computer, or a computer program, or a machine-readable memory embodying a program of instruction to perform the functions described here.