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Modeling Technology Critical for Radar System Designs

With lowering Size, Weight and Power (SWaP) an increasing priority, vendors of small box products are answering the call for high performance computing in tightly integrated systems.

HONGLEI CHEN, SOFTWARE ENGINEER
RICK GENTILE, PRODUCT MANAGER
MATHWORKS

Radar system design is a complex, multi-domain challenge. As phased array antennas are used in new designs, an extended set of capabilities including electronic beam steering and spatial signal processing techniques are possible. These added capabilities come with a corresponding increase in system level complexity. In addition, growing levels of interference sources due to a crowded RF spectrum, as well as smaller cross-section targets contribute to the increased challenge of achieving desired radar performance levels.

A system simulation framework can be a critical part of today’s system design workflow to help reduce the risks brought on by the increases in system level and environmental complexity. Modeling multi-domain radar systems can help drive design decisions and detect design issues early on in the project. For example, evaluating a radar’s ability to detect low cross section targets or adding the right level of signal processing to remove unwanted noise sources. These same types of models can be used to help justify upgrades to mature, fielded systems before any hardware is procured or developed. In addition, aspects of life cycle planning for radar systems can be assessed by understanding how systems perform as failures occur.

From Waveform to Detections

It’s useful to review some ways a model can be used to assess a range of design challenges, including all of the areas described above. Figure 1 shows a multi-domain, system-level model created in Simulink. The model covers radar blocks from waveform generation, to the transmit and receive chain, to the spatial signal processing components. Environmental and target modeling are also included to complete the system scenario.

Figure 1. Multi-domain radar system model.

The model shown in Fig 1 represents a low power X-band radar which can detect targets with small RCS values (< 0.5 m2). The required radar coverage for the system in this example is 35 km with a range resolution of 5 meters. This type of radar is typical of a system considered to help fill gaps within a network of larger surveillance systems. Each of the building blocks shown in Figure 1 can also be easily implemented in MATLAB as well. The building blocks can each can be set to match the desired system configuration. For example, parameters such as the waveform description, the required transmit power, and the antenna gain are parameterized and can be directly configured in each of the blocks. Sample MATLAB code for radar pulse level processing is included here (Code 1).

Code 1. MATLAB code for radar pulse processing.

Designing the Waveforms

Once we have the requirements set for the range and Doppler resolution and the minimum and maximum range of the desired coverage, we can interactively design the appropriate baseband waveform parameters needed to achieve these requirements in our system. Figure 2a and Figure 2b show a combination of waveform parameters that can be used to achieve the requirements described earlier. The resulting “waveform characteristics” from these baseband parameters are highlighted in the figure to show the requirements have been met. Fig 2a and Fig 2b also include the corresponding matched filter response which aligns with our performance goals for this system.

Figure 2a and …

… Figure 2b. Baseband waveform design and corresponding matched filter.

For this type of radar system, we are trying to design a system that requires a low transmit peak power with the intent to translate directly into a lower cost solution. With a lower cost and lower system complexity, it should be easier to deploy more systems. We also have to balance the low power requirement with the need to detect low cross section targets. This requires designing an array for the X-band system with a large gain.

Building an Array

We can interactively design and analyze the array parameters including the geometry, element spacing, lattice structure, and element tapering. An example is shown in Figure 3a and Figure 3b. The array is a 36×36 element array with uniform spacing between each element and the resulting array geometry is shown in Fig 3 (a). The radar beam that can be generated with this type of array can be steered in azimuth and elevation. Fig 3 (b) shows the beam at the radar boresight angle. An antenna array of this size for X-band is small enough that it can be easily mounted on a variety of support structures, which makes deploying this type of system much easier.

Figure 3a. 36×36 Uniform Rectangular Array (URA).

Figure 3b. Corresponding beam pattern at radar boresight in 2D and 3D.

We can use this array design directly in the system model. Due to the large number of elements in the array, the resulting antenna directivity allows the peak power to be less than 20 watts. This is based on the array directivity of 34.73 dBi. Taylor weighting has been applied to reduce the sidelobe levels. If a higher level of fidelity in our model is needed, we can design a specific antenna element using a full-wave solver in Antenna Toolbox. We also have the ability to model the effects of mutual coupling between antenna elements, which typically impacts the beam pattern as it is steered off boresight in both azimuth and elevation. This allows us to easily see how the array design affects the performance and provides us with an earlier opportunity to either change the design or adjust the requirements for downstream processing.

“What If” Analysis

Before we move on to some of the other radar blocks, it is interesting to note that the model can also be used to support a variety of specific “what-if” analysis exercises that relate to more detailed design trade-offs and life cycle planning. For example, we have a framework in place which we can reference for the best implementation for array thinning techniques. Alternately, Figure 4a and Figure 4b show an example where we can evaluate the impact of failed elements in the array. This can be important for determining maintenance cycles. For a radar site that is not staffed 24/7, multiple failures can be tolerated before a site is visited and the failures are repaired. The beam pattern (also shown in Fig 4) shows the degradations in the beam pattern with 15 percent of the elements failed.

Figure 4a and …

….Figure 4b. 36×36 array with failed elements and corresponding beam pattern analysis.

Similar analysis can be performed at the subarray level too. Figure 5 shows an example where the array is built up from 6×6 subarrays. The resulting beam pattern is also shown with 10 of the 36 subarrays in a failed state. Again, this type of data can be used to determine how many subarrays should be implemented. It can also be used in a way similar to the maintenance concept described earlier.

Figure 5. 36×36 element array built up with subarrays and the pattern with 10 of the subarrays failed.

Modeling a Complete Scenario

There are tools available for each component to help you quickly complete a system model. In our example, we create targets of varying complexity (including RCS fluctuations and angle and frequency dependent RCS behavior). We can also set these targets in motion in the model. This can provide insights into whether the design meets all performance goals. Environmental factors such as line-of-sight propagation effects due to rain, fog and gas, as well as channel fading can be included to improve the fidelity of the model.

To emulate the complex RF environment, signal source models can also be integrated to test interference mitigation techniques and to assess complexity levels prior to implementation. In our model, we add targets with an RCS value of 0.05 m2. This type of scenario has taken on new importance with the increased use of drones and UAVs.

Fidelity in the RF domain can also be extended by building up subarrays with models of RF components such as phase shifters, amplifiers, etc. Simulink can serve as a great platform to perform multi-domain simulation because it provides customizable block libraries, and solvers for modeling and simulating dynamic systems. Since it is integrated with MATLAB, algorithms can be incorporated into models and simulation results can be exported to MATLAB for further analysis.

Forming Multiple Beams

In our signal processing subsystem, we form multiple beams that cover various azimuth and elevation angles in front of the array. These same channels are also used to estimate the directions that the returned signals are arriving from. The matched filter shown in Fig 2b provides the system with a processing gain which improves the detection threshold. A time varying gain is added to the model so that a constant threshold can be used for detection across the entire detectable range. The resulting pulses are non-coherently integrated. The combination of these techniques allow processed returns for a single integration interval to support target detections at a desired signal-to-noise ratio (SNR). Results can be visualized in a variety of ways, including the ones shown in Figure 6ab, (with Figure 6c) (Power vs. Time, Intensity vs. Time, and a view of the scenario playing out).

Figure 6a, Figure 6b and …

…Figure 6c. Detection for three small RCS targets with in an X-band radar model

All three target returns are above the threshold, and therefore can be detected. In this example, the simulated targets have a non-fluctuating RCS of 0.5 m2 and are located throughout the area of radar coverage. It should be noted that the blocks used in the simulation are scalable. Each input and output is clearly defined such that custom blocks can be swapped into the model or extended to an existing block. One of the resulting data sets from the model is I/Q data generation for each processing interval.

Assessing Radar Network Coverage

Using this model as a starting point, we can also investigate ways to perform analysis on potential networks of radars. For example, Figure 7 shows a simple configuration where three systems are placed with overlapping coverage to ensure there are no gaps. Each of the first three views represents the SNR in the area of coverage. Relating back to our example, the fourth view represents the locations in coverage within which the SNR is at least 5 dB, which is our goal given the combination of signal processing and integration that we implemented.

Figures 7. SNR view for three radar systems with overlapping coverage.

Time and Cost Savings

Modeling a radar system early in the design process can save countless hours and reduce program costs by exposing design issues in the early stages of the project. In addition to finding design issues, a range of what-if analysis efforts can be accomplished without having to build any hardware. This analysis can be performed on the full range of system components, from the antenna to detections.

This type of radar model can also be used to either simulate a radar system for signal processing development or generate the radar echo(s), which can then be fed into “downstream” data post-processing systems. The resulting IQ data can then be used to tune algorithms. Once the algorithm is tuned, developers can easily replace the synthesized data with measured data at any location in the model.

Off-the-shelf radar model components provide all of the basic building blocks for a full system model, but the simulation framework has the flexibility to be extended with custom additions for each portion of the radar design. As demonstrated in the examples above, the radar system design workflow, from requirements analysis, to design trade-offs, to system development, can benefit from this work.

Mathworks
Natick, MA
(508) 647-7000
www.mathworks.com