Optimized antenna arrays and integrated RF front ends significantly enhance radar systems, boosting detection accuracy, resolution, and adaptability. These advancements are critical for ensuring reliable performance in complex environments, enabling precise targeting and robust operation under demanding conditions. By integrating various analytical techniques to accurately simulate and optimize complex RF systems like radar, this comprehensive digital twin approach enables radar designers to consistently compare real-time operational data with theoretical expectations, ensuring a robust, system-level design and verification process. This type of approach, known as Model-Based Design, enables teams to collaborate seamlessly, minimizing redesign delays and accelerating algorithm development for existing radar systems. It also reduces risks associated with developing new, complex radar systems before hardware is built.

The Model-Based Design approach is applicable across diverse radar architectures, as it integrates top-down design with bottom-up verification using measured data. Additionally, using models as executable and verifiable specifications allows designers to balance component requirements with digital signal processing complexity, reducing development time, and minimizing costly iterations by streamlining the design process and enhancing the reliability and efficiency of the overall system performance. 

Model-Based Design of a radar system starts by linking the required performance to the component specifications, and follows these steps:

1. The radar equation to assess the link budget for a given distance, resolution, and probability of detection and determines the required signal-to-noise ratio (SNR) for the TR module. The SNR is used to identify the total transmit power, the receiver noise figure, and the antenna array gain. 
2. From the above high-level specifications, a placeholder system-level model of the radar including the TR module and antenna arrays is built, ensuring that the placeholder system model meets our top-level performance specification. 
3. The TR module is then designed: The RF budget is analyzed using Friis and harmonic balance. The fidelity of the radar model is increased by including impairments such as impedance mismatches, antenna coupling, and non-linearity. 
4. A dual-polarized antenna is designed and integrated into an 8x8 array.
5. In the end, digital beamforming algorithms for electronic scanning are added to the system.

What makes this approach “model-based” is that after each component design stage (C – E above), the component is substituted back into the maturing placeholder model. With each component added, simulations are conducted to verify that the system-level model still meets the top-level performance specifications. This cycle of design - simulate - verify repeats until each component is integrated in the top-level design.  What makes this approach especially appealing is that it promotes early discovery of system-level specification failures caused by high-level interactions of component-level design choices. Problems can then be addressed before the physical prototyping begins.  Figure 1 shows the top-level architectural model.

Figure 1: Top-Level Radar System Architecture: Radar, environment, and targets. ©2025 The MathWorks, Inc.

Radar System-Level Design

Consider a S-band monostatic surveillance radar operating at 2.4GHz (F_c). It is required to identify a stationary or slow-moving target with 10 sqm of radar cross section (s) and located at 40 km distance with 90% probability of detection (P_d) and 1e-6 probability of false alarm (P_fa). First, the static link analysis of the radar system is performed at the power-level. As a second step, a system-level model of the radar system is built. 

A. Radar Link-Level Analysis

First, design the linear FM waveform to achieve the desired unambiguous maximum range (Rmax) of 40 km and range resolution (R_s) of 150 m.  To meet the given specifications, use TR modules with peak transmit power (P_t) of 200 W, a noise figure of 4 dB (equivalent to the system noise temperature T_s of 728 K), and an antenna with 7 dBi directivity. To further increase the transmit power and achieve the desired maximum range, use an array of 8x8 antenna elements, leading to a transmit antenna gain G_t equal to 43 dBi Equation (2). The antenna array is also used in the receiver, however, as signals are combined in the digital domain, the receiver antenna gain G_r is equal to the directivity of the single antenna Equation (3) plus the sensor array gain (~18 dB). Notice that any signal processing gain applied after the RF receiver does not change the SNR. The radar equation is used in its common form to compute the available SNR at the receiver. 

Where k is Boltzmann’s constant and l is the wavelength (0.125 m). On the right-hand side of Equation (1) all parameters except the target range and radar cross section (RCS) are under control of the radar designer. Is the computed SNR sufficient to make a detection? 

It depends on the desired probability of detection, and the maximum acceptable probability of false alarm. These probabilities define the minimum required SNR to make a detection, also known as detectability factor. The detectability factor additionally depends on the RCS fluctuation and type of detector. 

The Radar Toolbox is used to verify that for a non-fluctuating target the minimum required SNR is 8.3 dB when using a non-coherent receiver integrating 4 pulses. As this threshold is higher than Equation (1), it should be improved by either increasing the available SNR or by decreasing the detectability factor. The latter approach might be more attractive in practice through the application of signal processing techniques that do not require hardware changes. For example, integrating 10 pulses reduces the detectability factor to 5.3 dB as shown in Figure 2. 

Figure 2: Radar budget analysis. Requirements are met with the sub-system specifications given. ©2025 The MathWorks, Inc.

B. Radar Signal-Level Model

The static link analysis of the radar system performed at the power-level provides the basis for an I-Q signal-level model that can be used for further design elaboration and verification. By comparing the outcome of the static radar analysis against sample-by-sample simulation results, the SNR is found to be sufficient for detecting the target. 

Figure 3: Radar system-level model with placeholders for the TR module, antennas, and array gain. Target detections are shown in the bottom-left scope. ©2025 The MathWorks, Inc.

The radar model includes linear FM waveform generation, target modeling, and a digital signal processing algorithm including a matched filter, time varying gain adjustment, and coherent pulse integration. The simulation includes 4, non-fluctuating targets at different distances. The model is built in Simulink and introduces placeholders for the TR module and transmit and receive antennas. This model will be referred to henceforth as the “placeholder” radar model. 

The antenna gain is given in terms of directivity for the single element (7 dBi), while the array factor is approximated with the number of elements:

The output power of each transmitter is 53dBm (200W) achieving an EIRP of 96dBm. The receiver array factor is modeled at the output of the receiver, where the 64 signals are combined, consistently with the noise budget analysis: 

The simulation results confirm that all four targets are detected, with the target farther away just above the noise floor (shown in Figure 3) as predicted by the radar budget analysis.

C. Transmit/Receive Module Design

The radar link analysis provides two specifications to meet the detectability threshold: transmitter output power equal to 53 dBm, and receiver noise figure equal to 4 dB. Starting from these two specifications, a case-study TR module is designed, with a common path controlled by switches. 

Following the same approach described in the previous section, the static budget analysis at the power-level is first performed before building a signal-level model. The model is further elaborated to include data-sheet specifications and measured data of commercial-off-the-shelf RF components and used as a digital twin for the TR module.

 RF Budget Analysis

The static RF budget analysis is first performed using Friis equations. Using RF Toolbox and following a top-down approach, a gain and noise figure is provided for each component in the chain. 

Figure 4: Initial RF budget analysis for the receive path specifications. ©2025 The MathWorks, Inc.

The three switches that control transmit / receive mode and select the common path introduce a negligible insertion loss. The common path chain is made of an amplifier for which the gain and noise figure are specified, a programmable phase shifter, and a tunable attenuator. The transmitter is made of the common path chain, a driver amplifier, a power amplifier (PA), followed by an isotropic antenna. The transmit gain is approximately 50 dB, resulting in 53 dBm of output power for an input signal of 3 dBm. The receiver is made of an isotropic antenna, a low-noise amplifier (LNA), a stage amplifier, followed by the common path chain. The receive gain is 39 dB and the noise figure is 2.3 dB as shown in Figure 4.

TR Module Signal-Level Model

The static RF budget analysis of the TR module performed at the power-level provides the basis for a model that operates at the signal-level. In addition to the controllable switches, common path, amplifiers, and the antenna, the model also includes two circulators to separate transmit and receive paths. 

The model shown in Figure 5 is built using the circuit envelope library of RF Blockset. Circuit envelope simulation is based on harmonic balance, and it allows accounting for higher order non-linear effects while using a simulation time step that is commensurate to the signal bandwidth (MHz) rather than the center frequency (2.4 GHz). 

This technology provides a tradeoff between speed and fidelity that allows combining hardware representative RF models together with digital signal processing algorithms.

Figure 5: RF signal-level model of the TR module. This testbench can be used to verify power and noise levels for TX and RX configurations. ©2025 The MathWorks, Inc.

The model provides a framework for exploring the impact of RF effects such as leakage, non-linearity, and impedance mismatches. Power and noise levels can be measured in between stages and at the output of the antenna, providing insights before lab prototyping. For example, part of the transmitted signal leaks to the receiver port due to reflections and finite isolation in the switches and circulators. The TR module in the placeholder radar system-level model shown in Figure 3 is replaced by the circuit envelope model of Figure 5. The switches are controlled in such a way that when the linear FM waveform is generated the transmit path is active, while when no waveform is generated, the receiver is listening for target echoes.

TR Module Bottom-Up Model

The signal-level model of the TR module is extended to include measurement data and data-sheet specifications of commercial off-the-shelf RF components. For this case study, the focus is on the receiver LNA, transmitter PA, common path amplifier, and input/output circulators. 

Figure 6: AM-AM/AM-PM characterization data used for the transmitter PA (left). S-parameter transmission data for the circulator (right): continuous lines for measured data; dashed lines for rational fitting results. ©2025 The MathWorks, Inc.

The LNA is characterized with an S-parameters Touchstone file including input/output impedance, gain (approximately 15 dB at 2.4 GHz), reverse isolation, and noise figure (2 dB). Additionally, the output referred to IP3 (40 dBm) is also specified. The specifications of the common path amplifier include the available power gain (14 dB), noise figure (5 dB), input referred IP3 (24 dBm), 1 dB compression point (23 dBm), and saturation output power (26 dBm). The PA is characterized by AM-AM/AM-PM data shown in Figure 6, left. The circulators are modeled with a 3-port S-parameters Touchstone file. The data is fitted with a rational algorithm [4] to enable model-order reduction and time-domain in simulation (Figure 6, right). The noise added by the circulators is estimated based on the insertion loss and included in the simulation.

Despite having higher gains for the LNA and common path amplifier compared to the initial budget, the overall SNR is reduced. The peak transmitted power is limited by the PA saturation and further attenuated by the circulator losses: harmonic balance analysis shows that the gain is reduced from 50 to 46.5 dB (Figure 7). The receiver noise figure is increased from 2.3 to 4 dB due to losses of the circulator positioned in front of the LNA.

The simulation results of the updated radar model confirm that it is harder to detect the more distant target. The designer has the option to either use a PA with higher saturation power, circulators with lower losses, or further enhance the digital signal processing algorithm. Each of these choices has consequences in terms of power and cost. For this case study, it was decided to increase the number of integration pulses.

Figure 7: Non-linear RF budget analysis for the transmit path, including RF component specifications for the common path amplifier, PA, and circulators. ©2025 The MathWorks, Inc.

D. Antenna Design 

For this case study, a dual polarized patch antenna is designed using Antenna Toolbox.  The design is based on the example and retargeted to be resonant at 2.4 GHz. The method of moments is used to analyze the design and compute S-parameters and the far-field radiation pattern (Figure 8).  

Figure 8: S-parameters of the dual polarized patch antenna (left). Far-field radiation pattern for a single element (right) with directivity of 8.7dBi. ©2025 The MathWorks, Inc.

The electromagnetic analysis of the antenna confirms that the directivity exceeds 8 dBi, and it highlights the need for an impedance matching network to minimize losses that might reduce the SNR. For this case study, a 2-element L-topology matching network is built for each of the antenna feed ports.

The antenna, impedance matching components, and Wilkinson power divider feed network are added to the signal-level model of the TR module (Figure 9). The antenna is modeled with S-parameters and the embedded element radiation pattern. Rational fitting is used to model near-field and far-field characteristics over frequency and enable time-domain simulation of phi-theta polarization components. 

Figure 9: Signal-level model of the TR module. In yellow: blocks using measured data. In blue: antenna with matching and feed network. ©2025 The MathWorks, Inc.

The antenna is integrated within an 8x8 rectangular array. The array analysis shows that the receiver array gain has been overestimated for example when steering the beam at an arbitrary angle such as 30 deg Azimuth, and 75 deg Elevation, as the maximum directivity is 23 dBi rather than 25 dBi. The EIRP and SNR are consequently reduced. The analysis also allows to verify the width of the main beam and potential presence of grating lobes shown in (Figure 10). 

Figure 10: Far-field radiation pattern of the 8X8. ©2025 The MathWorks, Inc.

To finalize the virtual prototype of the radar, the antenna arrays must be integrated together with the beamforming algorithm. Assuming each antenna is connected to a single TR module leads to a system of 64 elements. The Simulink placeholder model is extended using a “for-each” construction suitable for parallelization (Figure 11). Input signals are expanded from scalar to vectors, and one TR module is simulated for each sample. Pattern superposition of the isolated antenna element is used to compute the array gain in the direction of departure and arrival. The infinite array approach can be used for large arrays to improve the fidelity and estimate coupling effects.

A narrowband beamforming algorithm is used to instantaneously compute phase shifts applied in transmit and receive mode, assuming reciprocity of the monostatic array configuration. The instantaneous excitation applied to the array can be used to verify the pointing direction of the main beam while also accounting for non-linear, dispersive, leakage, and phase shift quantization effects.

Moving targets and Swerling models can be included to study tracking algorithms. Interfering signals can be added to assess the robustness of the digital signal processing chain in hostile conditions or to anticipate receiver desensitization. Additionally, dual and quad polarized configurations can be studied using a complex scattering matrix to model the target RCS. 

Figure 11: Radar system-level model including 64 TR modules and 8x8 transmit and receive antenna arrays. ©2025 The MathWorks, Inc.

In this blog, a comprehensive Model-Based Design approach for transmit/receive (TR) modules and antenna arrays integrated into radar systems, using an S-band surveillance radar as a case study was described. By employing and combining multiple commercially available techniques this methodology is applicable and extendable to a wide range of radar designs.

At each step, results were compared with theoretical calculations using the radar equation, array factor analysis, and Friis RF budget analysis as starting points. The characterization data for RF components were integrated into the model through a bottom-up approach. Techniques like harmonic balance and electromagnetic analysis help to model non-linearity, dispersion, and impedance mismatches.

The methodology allows for the building of a virtual prototype for testing different RF components and verifying radar performance. By using a digital twin, insights are gained into design and system-level performance before moving on to costly and labour-intensive lab testing.

To learn more about the topics covered in this blog and explore your own designs, see the examples below or email me at abhishet@mathworks.com.

• Radar Link Budget Analysis: Use the Radar Designer app to perform radar link budget analysis and design a FMCW radar system based on a set of performance requirements.
• Radar Signal and Data Processing: Learn how to perform signal and data processing operations on recorded and simulated radar data.
• MATLAB and Simulink for RF Systems: Learn how to design and evaluate multifunction RF systems like radar, wireless communications, and electronic warfare systems.
• PCB components catalogue: Learn how to create, visualize, and analyze characteristics of components like transmission lines, filters, splitters, couplers, stubs etc., used on a printed circuit board.
• Simulation of RF systems with antenna blocks: Use antenna blocks to incorporate the effect of an antenna in a RF simulation.
• Antenna and array analysis: Perform port, surface and field analysis of antenna and arrays.