Simulation and Implementation of Signal Processing for LFM Radar Using DSK 6713

Abstract

This research aims to propose a comprehensive simulation and implementation methodology for LFM (Linear Frequency Modulated) Radar Signal Processing and its application, using digital signal processing techniques on the DSP Starter Kit (DSK) 6713 board. The motivation behind this study is to develop control software based on MATLAB R14 and SIMULINK to model various system software tasks, including detection, A/D conversion, Fast Fourier Transform (FFT), modulation, accumulation, decision-making, and target detection. The simulations are categorized into two groups: ideal beat frequency and parameterized beat frequency. We introduce several important terminologies for consideration, including pulse compression, SNR, matched filter, Doppler effect, and more. The use of real-time data exchange (RTDX) will facilitate the generation of input data and enable real-time calculations for outputs, leading to the creation of machine code for the DSP chip. This process aims to ensure data verification calculations and enhance the credibility and performance of the proposed methodology. By conducting thorough simulations, verification, and practical testing, the study demonstrates the satisfactory credibility and performance of the developed method. Using this research, we aim to contribute to the advancement of LFM Radar Signal Processing and enable its efficient implementation using digital signal processing techniques on the DSP Starter Kit (DSK) 6713 board.

1. Introduction

Radar is a wireless technology used for detecting, measuring, and tracking targets. Radar systems acquire information about the target’s position, velocity, direction, and other characteristics by emitting electromagnetic waves and receiving the signals reflected back from the target. The main components of a radar system include: 1. Transmitter: generates and emits electromagnetic waves, typically in the radio frequency range; 2. Antenna: used for transmitting and receiving electromagnetic waves, converting them into electromagnetic fields in space or converting received electromagnetic waves into electrical signals; 3. Receiver: receives and amplifies the target’s echo signals received by the antenna, converting them into electrical signals; 4. Signal processor: processes, filters, demodulates, and analyzes the received signals to extract information about the target, such as distance, velocity, angle, etc.; 5. Display: presents the processed target information to the operator in a visualized manner. The operation of radar is based on the principle of electromagnetic wave propagation and interaction with targets. When a radar transmitter emits electromagnetic waves, a portion of the energy is reflected back from the target surface, which is called an echo signal. By measuring the characteristics of the echo signal, such as signal time delay, frequency changes, and power, radar systems can infer the target’s position, velocity, and other features [1,2,3].

Among them, the LFM (Linear Frequency Modulated) radar is also named the linear frequency-modulated continuous wave (LFMCW) radar. The LFMCW radar utilizes a continuous wave signal with linearly varying frequencies over a certain time duration. Therefore, the name LFMCW radar primarily describes its characteristics of using continuous wave signals and frequency modulation to measure the distance, velocity, and direction of target objects. The transmitted signal is typically a frequency-modulated signal called a “chirp signal”. When this chirp signal is emitted towards a target and reflected back, the receiver receives an echo signal relative to the transmitted signal. As the target object and the environment scatter and reflect the signal, the received echo signal contains information about the target’s distance and velocity. By analyzing the frequency changes and delays of the received signal, the distance and velocity of the target object can be calculated [4,5]. It is mainly applied in 1. Autonomous vehicles: LFMCW radar is used in vehicle sensing systems to achieve functions such as obstacle detection, distance measurement, and vehicle position tracking [6,7,8,9,10]; 2. Drones and unmanned aerial vehicles: LFMCW radar can be used for obstacle detection, collision avoidance, and terrain mapping in unmanned aerial vehicles to enhance flight safety and navigation capabilities [11,12,13,14,15]; 3. Defense systems: LFMCW radar is used for target detection and tracking in military and defense applications, such as target identification, missile defense, and surveillance systems [16,17,18,19,20]; 4. Industrial applications: LFMCW radar can be used for distance measurement, displacement detection, object identification, and motion tracking in industrial settings for automation control and robotics applications [21,22,23,24].

MATLAB and Simulink are powerful numerical computing and programming environments that provide a rich set of tools and libraries for radar signal processing, data analysis, and simulation. MATLAB/Simulink allows customization of the frequency variation pattern of the transmitted signal and simulation of the signal’s emission, reception, and processing processes. It enables the design of target object models, including distance, velocity, and scattering characteristics, and the generation of simulated echo signals. Signal processing and analysis are then performed to extract information about the target object’s distance, velocity, direction, and other parameters. Various toolboxes for radar simulation and signal processing, such as the Phased Array System Toolbox and Signal Processing Toolbox, provide functions and algorithms that facilitate the simulation and analysis of LFMCW radar [25,26,27].

This paper proposes the use of Fast Fourier Transform (FFT) [28,29,30] to transform frequency-domain data into the desired distance and velocity data for display on the radar screen. In summary, the characteristics of LFMCW radar include lower power requirements for the transmitter, higher sensitivity for the receiver, larger bandwidth for higher range resolution, and simpler structure. However, it also has some drawbacks, such as shorter detection ranges and coupling between distance and velocity [1,25,31]. For the development of a search radar within a range of 50 km, designing an LFMCW radar using DSP technology has more advantages than disadvantages. Therefore, this paper uses TI’s TMS3206x chip to design target recognition algorithms. The process generally involves detection, A/D conversion, FFT, magnitude calculation, accumulation, decision making, target detection, and angle/distance pairing steps. First, we construct a model using MATLAB software [28] to generate signals, then use FFT to analyze the spectrum signals. The target signals are obtained by applying a threshold value, and via calculations, the distance and target signals are acquired, which are then displayed on the screen using a program. The simulations are categorized into two groups: ideal beat frequency and parameterized beat frequency. We introduce several important terminologies for consideration, including pulse compression, SNR, matched filter, Doppler effect, and more. Real-time control processing of data is achieved using MATLAB’s RTDX (Real-Time Data eXchange). Subsequently, the main program is converted into machine code via TI CCS (Code Composer Studio) [32,33] and downloaded to the SDRAM memory of DSP Starter Kit (DSK) 6713 for physical operation execution.

The contributions of this paper are described as follows:

(1)

Novel Approach in Linear Frequency Modulated Radar Signal Processing. This paper presents a distinct and novel approach to Linear Frequency Modulated Radar Signal Processing, utilizing the DSK 6713. By leveraging MATLAB R14 and SIMULINK, the proposed method enables the application of digital signal processing techniques on the DSK 6713 board, offering a more versatile and efficient platform for radar signal processing. Unlike the existing literature, which mostly discusses filters, images, audio, and impulse response using the DSK 6713, this paper focuses on radar applications.

(2)

Development of Control Software for Essential System Tasks. The key contribution lies in the development of control software that models essential system tasks, including detection, A/D conversion, FFT, modulation, accumulation, decision-making, and target detection. This comprehensive software implementation allows for real-time data processing and target identification, significantly enhancing the capabilities of the LFMCW radar system.

(3)

Efficient MATLAB/SIMULINK Compilation Parameters. The paper elaborates on the efficient setting of MATLAB/SIMULINK compilation parameters and memory map, which is crucial for readers to save valuable time and avoid unnecessary trial-and-error during their own research or implementations. This information serves as a practical guide for researchers and practitioners working with LFMCW radar signal processing and the DSK 6713 board.

(4)

Relevance to ADAS (Advanced Driver Assistance Systems) and Long-Range Target Detection. The research’s potential contribution to ADAS for self-driving cars is highlighted, as the current emphasis primarily lies on millimeter-wave radar. By combining simulation and practical implementation, the LFMCW radar system developed in this study demonstrates its ability to accurately detect multiple targets and achieve an impressive effective range of up to 45 km. Such capabilities make it particularly useful for coastal surveillance to prevent smuggling activities.

(5)

ADAS and Short-Range Detection. The LFMCW radar’s modulation time duration $T$ can be shortened, enabling precise target detection within a short range of 0 to 100 m. This advancement holds immense potential for ADAS development, especially in self-driving cars. Unlike traditional millimeter-wave radar used for short-range detection, the LFMCW radar proves to be a novel and effective alternative, accurately detecting multiple targets in close proximity.

(6)

Coastal Alarming and Defense. The LFMCW radar’s capabilities extend beyond short-range detection. With an effective range of up to 45 km, it becomes a valuable tool for coastal surveillance and defense. Its long-range reach makes it particularly suitable for combating smuggling activities and enhancing security measures along coastal regions. The radar’s adaptability and broad coverage provide crucial situational awareness for timely responses to potential threats.

In summary, the research demonstrates the LFMCW radar’s dual strengths, short-range capabilities for ADAS, and long-range suitability for coastal alarming and defense. Its versatility makes it an invaluable technology with broad implications for enhancing safety and security in various applications. Our study aims to provide clarity on this matter. The primary contribution of our proposed model lies in its innovative approach to tackling the challenges of cost-effectiveness, particularly by utilizing the DSK 6713 board for the development and verification of LFMCW radar algorithms. We emphasize the utilization of MATLAB’s Real-Time Workshop (RTW), which offers a rapid and efficient platform for generating results. This is a departure from the conventional complex C language approach, which can be time-consuming and potentially yield erroneous outcomes. By leveraging RTW, we significantly enhance the accuracy and efficiency of signal processing within LFM radar systems.

Moreover, we extend the existing knowledge by incorporating real data sourced from a signal generator. This integration not only mitigates CPU time delays but also ensures a more precise verification process. Our approach not only optimizes LFM radar signal processing but also maximizes the utility of the DSK 6713 board for radar applications. This innovative fusion of RTW, DSK 6713, real data, Fast Fourier Transform (FFT), beat frequency analysis, and target distance estimation positions our proposed model as a valuable advancement in the field.

2. LFMCW Radar Introduction

This radar system utilizes the variation of the transmitted signal’s frequency over time while measuring the difference between the received frequency and the transmitted frequency to determine the distance. The LFMCW radar signal can be modulated in both positive and negative directions, as shown in Figure 1.

In Figure 1a, we illustrate the time duration of modulation in both the positive and negative directions. Figure 1b shows the transmitted frequencies represented by solid lines, while the thicker solid lines indicate the received echo frequencies. The received echo frequencies with the Doppler effect are depicted as dashed lines. However, it is important to note that this paper assumes the neglect of the Doppler effect in its analysis. The difference between the transmitted and echo frequencies, known as the beat frequency $F_b$, is illustrated in Figure 1c, where the solid line represents the frequency difference for stationary targets and the dashed line represents the frequency difference for moving targets. Figure 1d shows the frequency sweeping time duration of the signal, with the computation time of the FFT being shorter than the sweeping time duration [33,34,35]. The variables in Figure 1 are explained as follows:

• $T$: modulation time duration,
• $B$: modulation bandwidth,
• $f_0$: transmitted base frequency,
• $R_0$: target distance,
• $c$: speed of light,
• $f_d$: Doppler effect frequency,
• $F_b$: beat frequency which difference between transmitted and received signals,
• $F_{b+}$: beat frequency which difference between transmitted and received signals in positive modulation = $F_b+f_d$,
• $F_{b-}$: beat frequency which difference between transmitted and received signals in negative modulation = $F_b-f_d$.

From the physical interpretation, the time interval between the transmission and echo can be deduced as

$$t=\frac{2R_0}{C}$$

(1)

Also, since the Doppler effect, $F_b$ can be eliminated by adding $F_{b+}$ and $F_{b-}$ and dividing by 2, the target distance can be obtained using the following equation:

$$R_0=\frac{F_{b}C}{2\mu }$$

(2)

where $\mu =\raisebox{1ex}{$B$}\!\left/ \!\raisebox{-1ex}{$T$}\right.$ is the modulation coefficient. Defining the range resolution as the error between the actual distance and the measured distance $\Delta R=R-R_0$, and the spectral resolution as $\Delta F_b=\raisebox{1ex}{$f_s$}\!\left/ \!\raisebox{-1ex}{$N$}\right.$, where N is the number of points in the FFT operation and $f_s$ is the signal sampling frequency, the expression for the range resolution is given by

$$\Delta R=\frac{f_{s}C}{2\mu N}$$

(3)

Considering the capabilities of DSP processing and system requirements, the choice of N should strike a balance. A larger N or lower sampling rate improves range resolution, but it is essential to avoid confusion between the frequency band and the sampling rate. For instance, if N is too large, the spectral resolution becomes stronger, resulting in a higher SNR (signal/noise ratio) and potential detection of unwanted signals. Therefore, to maintain clarity, the range of consideration for N is between 30 kHz and 512 kHz.

Regarding the sampling rate, it only needs to satisfy the Nyquist theorem, which requires a signal frequency to be at least double that of the sampling frequency to avoid spectral overlap. In this case, the receiver bandwidth is approximately 1.5 MHz, so a sampling rate of 3 MHz is sufficient to ensure an accurate representation of the signal and meet the Nyquist criterion. This sampling rate provides an adequate margin to capture the necessary information for the radar system.

3. System Design and Simulation

In this section, the design and simulations are divided into two parts: one for the ideal beat frequency and another for the parameterized beat frequency.

3.1. Simulation of Ideal Beat Frequency

To validate the reasoning from the previous section, we conducted simulations using Matlab/Simulink [28], The conceptual diagram is shown in Figure 2. The input signal from the radar is processed via an FFT operation, followed by selecting the maximum value and applying a threshold to determine the output result.

The scanning speed of the radar is 24 rpm. In addition to calculating the distance for scanning, the azimuth angle (direction) and signal strength of the targets need to be determined for display. For example, when the modulation bandwidth $B=1.8286 \mathrm{MHz}$ is set to a specific value $T=1 \mathrm{ms}$ and the modulation coefficient $\mu =1.8286\times {10}^9$ is adjusted accordingly, the beat frequency $F_b=512 \mathrm{kHz}$ between the transmitted and received signals can be calculated using Equation (2), resulting in a desired measurable distance of 41.999 km.

FFT stands for ‘Fast Fourier Transform,’ an efficient algorithm used to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, FFT is utilized to identify the different ranges of targets. It finds extensive use in signal processing, image processing, audio processing, communication systems, and various scientific and engineering domains. Figure 3a depicts the spectrum diagram obtained using the ‘fft’ command in MATLAB for a 512 kHz signal with 1024 points of FFT. The plot displays a single peak at 512 kHz, representing the frequency of the sine wave, without any additional alias peaks. For our specific application, we used an LFM radar to calculate distances. After performing simulations with a sampling frequency of 2048 kHz for a 512 kHz signal, we utilized FFT with point sizes of 1024, 2048, and 4096. The FFT point number of 1024 was chosen for implementation to minimize hardware and computational consumption while still achieving accurate results. The distances calculated using FFT point size 1024 showed no errors, as shown in Figure 3b, demonstrating the effectiveness of the chosen configuration for our radar system.

To assess the distance measurement error, we calculated the different beat frequency $F_b$ between the transmitted and received signals for different targets with fixed modulation bandwidth $B=1.8286 \mathrm{MHz}$. The results of beat frequency differences of 30 kHz, 40 kHz, and 100 kHz using Equation (2) are shown in Figure 4.

Remark 1.

In this subsection, we intentionally avoided delving into the intricacies of the radar front-end transmitter and receiver electrical devices. Our primary focus was on the execution of the algorithm and its interaction with the DSK 6713 hardware platform. We assume that the raw beat frequencies are obtained from the front filter and the radar electronic system. Consequently, this paper demonstrates the utilization of beat frequencies in the development of algorithms, such as target distance measurement. Other analyses, including data verification, the Doppler effect of moving targets, antenna analysis, noise analysis, and more, are presumed to be conducted under ideal conditions. For more detailed applications, please refer to Mahafza, B. R. [25].

3.2. Simulation of Parametric Beat Frequency Effects

In this subsection, our focus will center on key topics derived from the received echo signal of the radar receiver’s front-end. These topics encompass closed-loop simulations for both transmit and receive models, pulse compression, matched filters, SNR analysis, and range resolution.

The primary objective and contribution of this paper lies in establishing a technology that utilizes a simple board to demonstrate the fundamental concepts of the LFM radar operation. Furthermore, our aim is to bridge the gap between two seminal books: Mahafza’s work [25], which provides theoretical knowledge of radar but lacks hardware implementation, and Rulph’s work [33], which provides detail method and knowledge of signal processing but lacks discussion of radar. Fromthis endeavor, we aspire to create a comprehensive resource that seamlessly blends theoretical insights with practical implementation, facilitating a deeper understanding of the LFM radar technology.

3.2.1. Terminologies of LFM Radar

The well-known and widely-used radar waveform model can be represented by the following simplified equations for the transmitted and received signals.

Transmitted Signal model:

$$S_t(t)=\cos [2\pi f_0(t)+{\phi }_t(t)]$$

(4)

Received Signal model:

$$S_r(t)=\cos [2\pi f_0(t-\tau )+{\phi }_r(t)]$$

(5)

where $f_0$ is the radar operating frequency (carrier frequency), $t$ is time, $\tau$ is the time delay introduced by the target’s range, and ${\phi }_t(t)$ and ${\phi }_r(t)$ are phase functions that describe the phase modulation of the transmitted and received signals, respectively. The key concept here is that the transmitted signal has a phase that changes with time due to modulation ${\phi }_t(t)$, and the received signal’s phase is affected by the target’s range, which introduces a time delay $\tau$. These phase functions and time delay $\tau$ all depend on the specific modulation and target interaction characteristics within a given radar system.

To facilitate the simulation of models (4) and (5), we consider the following terminologies:

• SNR;

SNR is a measure of the signal’s strength relative to the noise level in the received signal. It is influenced by various factors, including the transmitted power, target characteristics, system losses, and noise level.

The simplified formula for SNR in radar systems involves several parameters:

$$SNR=\frac{P{G}^2\sigma }{{(4\pi )}^3{R}^{4}k{T}_{e}FL}$$

(6)

where $P$ is the peak power of the transmitted signal, $G$ is the antenna gain, $\sigma$ is the radar cross-section of the target, $R$ is the range to the target, $k$ is Boltzmann’s constant, $T_e$ is the effective noise temperature, $F$ is the noise figure of the radar system, and $L$ is the total radar losses.

This equation provides a quantitative measure of the SNR in a radar system. It indicates how much stronger the desired signal (represented by $P{G}^2\sigma$) is compared to the noise and interference (represented by ${(4\pi )}^3{R}^{4}k{T}_{e}FL$). A higher SNR indicates a more favorable signal/noise ratio, which is essential for reliable radar operation and target detection. In practical radar system analysis and design, we use this equation to estimate the SNR under various operating conditions and to determine the system’s performance in detecting and tracking targets in the presence of noise and interference.

• Range resolution;

Range resolution refers to the ability of the radar to distinguish between two targets that are located at nearly the same range but at slightly different distances from the radar transmitter. This is particularly important in applications where precise target localization is required, such as in tracking and identifying multiple targets in close proximity. Therefore, for most radar applications, a smaller range resolution is preferred as it allows for better target discrimination and localization.

According to Equation (3), the range resolution is inversely proportional to the bandwidth $B$ and directly proportional to the time duration $T$. This formula demonstrates that increasing $B$ will improve range resolution but results in shorter $T$. However, care must be taken to avoid range ambiguities in the radar system. The maximum unambiguous range $R_{\max }$ is related to $T$ as follows:

$$R_{\max }=c\ast T/2$$

(7)

To prevent range ambiguities, the radar system must ensure that $R_{\max }$ is greater than the expected target range. In practice, selecting appropriate values for $B$ and $T$ involves trade-offs between range resolution, SNR, range ambiguity, and hardware limitations.

• Pulse Compression;

Pulse compression is a radar signal processing technique used to improve the range resolution of a radar system without the need for extremely short, transmitted pulses. It involves transmitting a long pulse that is modulated in frequency (chirped) and then processing the received signal to compress it in time. This compression effectively increases the range resolution while still using a longer transmitted pulse for better target detection.

The basic equation of a linear frequency-modulated (LFM) chirp signal is as follows:

$$S_c(t)=A\cos (2\pi f_{0}t+\beta \pi t^2)$$

(8)

where $A$ is the amplitude of the signal, $f_0$ is the starting frequency, and $\beta$ is the chirp rate. The chirped signal is transmitted, and when it reflects off a target and is received by the radar receiver, it can be processed using a matched filter to compress the signal in time. The matched filter effectively reverses the frequency modulation, resulting in a compressed pulse that allows for improved range resolution.

The key advantage of pulse compression is that it enables radar systems to maintain good target detection capabilities (due to the longer transmitted pulse) while achieving fine range resolution (similar to that of a much shorter pulse).

• Doppler effect;

The Doppler effect is a change in the frequency or wavelength of a wave in relation to an observer, which moves relative to the source of the wave. In radar applications, the Doppler effect can be used to measure the relative velocity between a radar system and a target. When a radar signal reflects off a moving target, the frequency of the returned signal is shifted from the transmitted frequency. The amount of frequency shift is directly proportional to the target’s radial velocity (velocity along the line of sight) relative to the radar system. The formula to calculate the Doppler effect $f_d$ is as follows:

$$f_d=\frac{2\nu }{\lambda }$$

(9)

where $\nu$ is the radial velocity of the target relative to the radar system in meters per second (m/s) and $\lambda$ is the wavelength of the radar signal in meters (m). The Doppler effect is positive when the target approaches the radar (positive radial velocity) and negative when the target moves away from the radar (negative radial velocity).

• Matched filter;

The matched filter model is used to maximize the SNR and improve target detection. It is designed to detect a specific known signal waveform in the presence of noise and interference. The matched filter works by correlating the received signal with a replica of the transmitted signal. The output of the matched filter is represented as follows:

$$y(t)=S(t)\ast h(t)$$

(10)

where $S(t)$ is the received signal, which may contain noise and interference and $h(t)$ is the matched filter impulse response, which is a replica of the transmitted signal. When the received signal matches the transmitted signal, the output will have a peak, indicating the presence of a target at a specific range.

3.2.2. Simulation Results and Comparisons

The simulations were conducted to verify five cases with different target ranges: 42 km, 31 km, 21.3 km, 13.1 km, and 2.6 km, as listed in

Table 1. Simulation parameters.

Parameters	Case 1	Case 2	Case 3	Case 4	Case 5
$R$	42 km	31 km	21.3 km	13.1 km	2.6 km
$f_0$	1 MHz	1 MHz	1 MHz	1 MHz	1 MHz
${\phi }_t(t)$	10°	10°	10°	10°	10°
$T$	1 ms	1 ms	1 ms	1 ms	1 ms
$B$	$1.8286 \mathrm{MHz}$	$1.8286 \mathrm{MHz}$	$1.8286 \mathrm{MHz}$	$1.8286 \mathrm{MHz}$	$1.8286 \mathrm{MHz}$
$\beta$	$B/T$	$B/T$	$B/T$	$B/T$	$B/T$
SNR	0.9	0.89	0.87	0.86	0.85
$f_d$	1 kHz	900 Hz	800 Hz	700 Hz	600 Hz
$f_s$	4 MHz	4 MHz	4 MHz	4 MHz	4 MHz

. The simulation procedure flowchart is illustrated in Figure 5, and the results are presented in Figure 6. From the simulation results, it is evident that the peak of pulse compression becomes very pronounced, allowing us to distinguish the added noise and moving target within a range of approximately 10 m. The simulation results also demonstrate consistent range resolutions. The miss distance and the ability to distinguish targets around the target are summarized in

Table 2. Simulation performance comparison.

Performances	Case 1	Case 2	Case 3	Case 4	Case 5
Miss distance	105 m	100 m	90 m	50 m	40 m
Distinguish ability	−14.1 dB	−13.5 dB	−14.2 dB	−14.2 dB	−18.4 dB

. Notably, the range miss distance is worst in case 1 and best in case 5. Additionally, for distinguishing ability, cases 2 to 5 all exhibit around −14 dB, while case 1 performs best at −18 dB under the same conditions. In conclusion, pulse compression is more suitable for near targets. For longer-range targets, adjusting the time duration can improve target detection and range resolution.

4. DSK 6713 Design and Verification

It is important to emphasize that we will not delve into the details of transmitter and receiver equipment in this section. This decision is driven by the complexity and cost associated with reconfiguring the interfaces of connections with the transmitter and receiver, particularly when utilizing a simple starter kit like DSK 6713.

In order to make digital signal processing more closely resemble reality by integrating TI’s CCS with MATLAB for data transmission, a method called RTDX is provided on the MATLAB platform. RTDX allows for real-time data capture and display on a computer. Its functionality involves setting up, opening, enabling, and transmitting data via a software link to the target board. Once the transmission is complete, the memory data is cleared for the processing of the next set of data. In Simulink, the two most important blocks for RTDX applications are “From RTDX” and “To RTDX”. For example, we can write a simple program to control the amplitude of a sine waveform using channel ichan1 and send the data out viaochan1.

The CPU of TMS320C6713 is indeed a fixed-point DSP that uses a RISC (Reduced Instruction Set Computer) architecture and operates at a speed of 225MHz. Its core includes 64 32-bit general-purpose registers, 2 32-bit multipliers, and 6 ALUs (Arithmetic Logic Units), capable of executing multiple instructions simultaneously, typically up to eight instructions per cycle. Each instruction cycle can perform two reads and one write operation. There are EMIF (External memory interface) blocks, in which each EMIF is divided into four chip enable spaces called CE (Chip enable) space, with CPLD occupying CE1 of EMIF CE1, and the addressing space ranges from 0x90080000 to 0xA0000000. The EMIF has four separate addressable regions called chip enable spaces (CE0-CE3). The SDRAM occupies CE0 while the Flash and CPLD share CE1.CE2 and CE3 are generally reserved for daughter cards. The CPU operates at a speed of 225MHz, with 64 Mbytes of synchronous DRAM and 512 Kbytes of non-volatile Flash memory (256 Kbytes usable in default configuration). The SDRAM is mapped at the beginning of CE0 (address 0x80000000). The total available memory is 8 megabytes. The integrated SDRAM controller is part of the EMIF and must be configured in software for proper operation. The memory addressing space can reach 32 bits, and the purpose of each block is shown in Figure 7.

The CPLD can be used to verify the correctness of preliminary functionality, reducing the burden of designing and manufacturing some peripheral devices. The four CPLD memory-mapped registers allow users to control CPLD functions in software.On the 6713 DSK, the registers are primarily used to access the LEDs and DIP switches and control the daughter card interface. The registers are mapped into EMIF CE1 data space at address 0x90080000.

Table 3. CPLD Register Definitions of DSK 6713 (referenced from DSK 6713 Technical Reference) [32].

Name	Bit 3	Bit 2	Bit1	Bit 0
USER_REG	USER_LED 3	USER_LED 2	USER_LED 1	USER_LED 0
	R/W	R/W	R/W	R/W
	0 (off)	0 (off)	0 (off)	0 (off)

providesa high-level overview of the CPLD registers and their bit fields.

The experiments were performed using MATLAB/Simulink, DSK 6713 development board, and the TI CCS 3.1 integrated development environment software. Five experiments were conducted to measure the results at different distances, with beat frequencies of 512 kHz, 378 kHz, 260 kHz, 160 kHz, and 32 kHz, corresponding to measured distances of 42 km, 31 km, 21.3 km, 13.1 km, and 2.6 km. The detailed operations for Simulink [28] and CCS [32] can be found in Appendix A.

In the DSK, according to Table 3, four registers are used to control the functions of the CPLD. The first register, USER_REG, is used to read/write control signals for LED lights and read DIP switches. We use bits 0 to 3 of USER_REG with an offset of 0 to drive the LEDs and verify the correctness of the algorithm. Since there are only four bits, there can be at most 16 degrees shown by the four LEDs. In this implementation, the distance values are verified with a gap of 10 km between each division. When LED 0 represents the LSB (Least Significant Bit) and LED 3 represents the MSB (Most Significant Bit), the LED states are as follows: 0 stands for LED off and 1 stands for LED on (light). In this configuration, when the distance is between 0 and 10 km, the binary value displayed on the LEDs will be 0000.

When the distance is between 10 and 20 km, the value is 0001. When the distance is between 20 and 30 km, the value is 0010. When the distance is between 30 and 40 km, the value is 0011. When the distance is above 40 km, the value is 0100. The precise distance values are obtained by reading the values from memory and interpreting them on a computer. This is achieved using MATLAB’s real-time data exchange (RTDX) via built-in blocks to transmit the results of hardware execution back to the host computer via USB. The RTDX blocks do not have an effect during the simulation stage and only become active after downloading the machine code to the target board using CCS. The steps involve adding the “To RTDX” block to the Simulink model, compiling and downloading the code, activating the RTDX channel, and establishing communication between the computer and the target board. The experimental results are shown in Figure 8. These five subfigures all contain LEDs and were zoomed in from the photo of the DSK 6713 board. This demonstrates that the LEDs are lit up, and the numbers displayed on the screen correspond to measured distances of 42 km, 31 km, 21.3 km, 13.1 km, and 2.6 km. These results indicate that the developed algorithm was successfully downloaded to the board’s SDRAM and then executed viathe CPLD to drive the LEDs, performing the correct actions.

The DSK 6713 is equipped with multiple integrated McBSPs (Multichannel Buffered Serial Ports), denoted as McBSP0 and McBSP1. Each McBSP is equipped with its own set of control registers and data buffers, enabling autonomous configuration and operation. McBSPs serve as versatile serial communication interfaces, commonly utilized to establish connections between DSPs and various external devices, including analog-to-digital converters (ADCs), digital-to-analog converters (DACs), codecs, and memory devices. This flexibility facilitates the transmission and reception of serial data in diverse formats, such as I2S (Inter-IC Sound) and TDM (Time Division Multiplexing). It is essential to consider the memory map, ensuring proper alignment of each port with the corresponding memory address. This configuration is crucial for accurate setup within Matlab/Simulink’s C6000 Blocks parameters, as discussed in the previous part.

In this part, we present an empirical implementation that utilizes McBSP1 to establish a connection with a signal generator, effectively capturing a real sine signal. The use of A/D blocks in Simulink for DSK 6713 streamlines the experimental setup, yielding outcomes consistent with the previously described methodology. These results are conveyed via the illumination of LEDs, as demonstrated in Figure 9. This depiction showcases the process of a sine signal generated by a signal generator, passed through McBSP1 (the line-in port) of the DSK 6713, and subsequently validated within a designated distance range, confirmed by the activation of LED indicators. The LED results obtained from the physical implementation match those observed in the simulation.

Remark 2.

The deployment of the TMS320C6713 DSP offers a notably cost-effective solution for radar signal processing, showcasing its substantial potential across various domains, particularly within radar-based systems. This DSP not only demonstrates prowess in algorithm verification and validation but also enhances the efficiency of these processes. By providing researchers and engineers with the capability to rigorously test and fine-tune algorithms, we ensure the precision, accuracy, and efficacy of these algorithms before seamlessly integrating them into intricate radar systems. This proactive approach significantly mitigates the risk of errors and substantially bolsters the overall reliability of radar-based applications.

5. Conclusions

This paper is dedicated to the construction of a linear radar model using MATLAB software to generate frequency signals. These frequency signals were subsequently subjected to Fast Fourier Transform (FFT) analysis, enabling the extraction of target signals via a defined threshold value. By executing relevant calculations, both the distance to the target and the target signal itself were determined. The simulations were categorized into two groups: ideal beat frequency and parameterized beat frequency. We introduced several important terminologies for consideration, including pulse compression, SNR, matched filter, Doppler effect, and more. The obtained results were then presented on the screen using a dedicated program.

The experimental process unfolded in two distinct stages. Initially, numerical simulations were conducted to rigorously validate the accuracy and correctness of the algorithm. Subsequently, real-time data exchange (RTDX) techniques were harnessed for the real-time control and processing of data. The core program underwent conversion into machine code using TI CCS (Code Composer Studio), which was subsequently downloaded into the SDRAM memory of the DSK 6713 for actual physical operation.

The experimental phase encompassed the generation of distance calculations via the utilization of five distinct frequencies. These calculations were subject to verification via RTDX data retrieval and manifested using the illumination of physical LEDs, effectively affirming the precision and efficacy of the proposed method.

In addition, the feasibility of the proposed approach was validated using a real data experiment, yielding results in alignment with simulation outcomes. Furthermore, we acknowledge the potential for extending the application of this method to other domains, a subject warranting further exploration in future research.