Digital Signal Processing (DSP) Algorithms for CW/FMCW Portable Radar Muhammad Zeeshan Mumtaz, Ali Hanif, Ali Javed Hashmi National University of Sciences and Technology (NUST), Islamabad, Pakistan Abstract Continuous Wave (CW) and Frequency Modulated Continuous Wave (FMCW) radars are used for target detection by the use of Radio Frequency (RF) waves. CW radars are used for Doppler velocity estimation whereas FMCW radars are used for range estimation. This paper is focused on real-time DSP algorithm for target differentiation from noise in Simulink implemented as block model and two additional post-processing DSP algorithms for Doppler velocity and range estimation implemented as MATLAB script codes for CW and FMCW radars respectively [1]. First, Static clutter rejection technique has been implemented on range estimation algorithm for spotting only moving targets, which formulates the basis of Moving Target Indicator (MTI) mode of the FMCW radar. Second, Accelerating Target Indicator (ATI) mode has also been developed for Doppler velocity algorithm for CW radar. The above mentioned DSP algorithms have been successfully developed and tested on a small portable CW/FMCW radar. This radar is an improved version of the portable radar developed in MIT IAP [1] [2] Radar Course with some hardware modifications and major software up-gradations. Only software up-gradations have been addressed in this paper. This portable radar comprises of an RF Front End (both for Transmission and Reception portions) and analog circuitry. The final output of the portable radar has been provided to the Data Acquisition device for further processing in computer. I. INTRODUCTION FMCW/CW radars are preferred on pulsed radars due to the fact that their maximum range is relatively independent of the maximum power but it depends upon number of FFT samples and bandwidth of the portable radar, which will be discussed in detail in the subsequent paragraphs. These factors permit low transmission power which results in low probability of interception (LPI). CW radars are used for velocity estimation using the concept of Doppler frequency shift. Doppler frequency shift is the change in the frequency observed by the radar receiver as compared to the transmission frequency, when an object is moving relative to the radar. The transmission frequency is always constant while received frequency is continuously compared with it as shown in Figure 1. Frequency Figure 1 : Frequency versus Time graph for CW Radar Doppler frequency shift (f d ) is obtained after comparison of transmission and reception waves and object velocity is estimated by the following equation [3] : In symbolic form: Time f t + f d Velocity resolution is the minimum velocity that can be observed by the radar. It depends upon two factors: minimum detectable Doppler shift which further subject to the minimum sampling frequency and radar wavelength. Minimum sampling frequency is usually constrained by the Data Acquisition device used for capturing real-time data for signal processing. Maximum velocity can easily be determined by multiplying velocity resolution with f t f t - f d
number of Nyquist samples. By Nyquist information theorem [4], for complete collection of information, FFT sampling rate must be twice the analog signal frequency. Therefore, targets is equal to frequency chirp rate because if beat frequency is less than frequency chirp rate, the difference between transmission and reception frequencies cannot be noticed. So range resolution is obtained after substituting. ( ) ( ) FMCW radars are used for range estimation using the concept of Beat Frequency. The most common type of frequency modulation is linear frequency modulation (LFM). In LFMCW operation, the transmission frequency is linearly increasing and decreasing with time. The received frequency is also increasing and decreasing in similar fashion. But there is a time delay between both signals which would induce a frequency difference called Beat frequency. The concept of beat frequency is illustrated in Figure 2. Frequency Frequency Sweep Time (1/f) Bandwidth (BW) Beat Frequency (f b ) Transmission Wave Reception Wave Maximum range can be easily calculated by multiplying range resolution with number of Nyquist samples. II. ( ) PORTABLE RADAR OPERATION CW/FMCW portable radar was developed and tested thoroughly as shown in Figure 3. This radar constitutes of five main parts: i. RF Front End ii. RF Antennae iii. Analog Circuitry iv. Data Acquisition device v. Radar Data Processor CW/FMCW Radar Circuitry Time Figure 2 : Frequency versus Time graph for LFMCW Radar Beat frequency (f b ) is acquired after comparison of transmission and reception waves and range is calculated by the following equation [5] : Transmission Antenna Reception Antenna Figure 3 : Developed Portable Radar In symbolic form: Range resolution is the minimum distance or space between two targets so that they can be differentiated as two separate targets. For range resolution, the minimum beat frequency for differentiating two RF Front End is further sub-divided into two portions: Transmission Front End and Reception Front End. Transmission Front End constitutes of RF Voltage Controlled Oscillator (VCO), RF Amplifier and RF Splitter, while Reception Front End contains RF Low Noise Amplifier (LNA) and RF Mixer. RF signals are transmitted and received by two parabolic antennae. In Transmission Front End, RF VCO generates a voltage dependent frequency signal which is tuned by
function dependent analog signal. For long range transmission in the air, the signal is strengthened by RF Amplifier. RF Splitter divides the signal into two parts: a. Transmission signal to the transmission antenna b. Reference signal to the RF Mixer in the Reception Front End The transmission signal after striking the target scatters in all directions. Some portion of the scattering radiations reaches back to the receiving antenna as target echo. This echo contains Doppler frequency shift or beat frequency along with the base transmission frequency. In Reception RF Front End, target echo received at reception antenna is amplified by RF LNA and sent to the RF Mixer for separating Doppler shift or beat frequency. Analog circuit is infact waveform generator used for ramp wave output as tunning voltage for RF VCO for effective LFM operation while determining the target range. Data Acquisition device is a device that converts analog signals into digital samples for further processing in computing machines. Data Acquisition device used for this radar is Integrated audio soundcard used with computers. Analog signal from RF Mixer is fed to the sound card which after sampling provides the data to the Radar Data Processor. Radar Data Processor is categorized in two types of algorithms: a. Real-time DSP Algorithm b. Post-processing DSP Algorithms Both types of DSP algorithms will be discussed in detail in the subsequent sections. III. REAL-TIME DSP ALGORITHM Before discussing Real-time DSP algorithm, the input of the algorithm, which is the output of RF Mixer, will be overviewed in mathematical domain. The output of the RF Mixer is an analog signal that contains sum and difference frequency signals of the transmitted and received frequencies. As the Local Oscillator (LO) (reference signal from transmitter) and RF port (signal from reception antenna) input signals of the RF mixer are ( ) and ( ( ) ), the RF mixer output (Φ) is: [ ( ( ) ) ( )] i. Digital Sampling of the output of RF Mixer (Φ) with 44100 FFT points. ii. Low Pass filtering at cut-off frequency of 22.05 KHz (Analog frequency = No. of FFT points/2). The operational frequency of testing CW/FMCW radar is 2.26-2.59 GHz. The sum frequency signal is in range of 4.52-5.18 GHz which is rejected by the audio soundcard while the difference frequency signal which has frequency equal to Doppler shift or beat frequency is sampled at a rate of 44.1 KHz. The sampled data is to be processed and displayed in such a way that velocity and range of the target can be visually interpreted. For this purpose, the Real-time DSP algorithm is formulated in form of block model in Simulink as shown in Figure 4. Figure 4: Real-time DSP block model in Simulink Real-time DSP algorithm shown in above figure performs four basic tasks: 1. Data reception from Data Acquisition device 2. Real-time Target Display 3. Real-time Frequency Shift Display 4. Data transfer to Post-Processing DSP algorithms For Data reception from audio soundcard, a Simulink block From Audio Device has been utilized. This block collects the data from audio soundcard and defines the sampling rate, sampling channels, output data type and frame size as Figure 5 shows its block parameters. The Data Acquisition device (Integrated audio soundcard) performs two tasks:
Targets Figure 7: Real-time Frequency Shift Display Figure 5: Block Parameters of "From Audio Device" After Real-time Target Display and Real-time Frequency Shift Display, data is transferred to the MATLAB workspace for post-processing DSP algorithms. Signal To Workspace block has been used for this purpose with block parameters shown in Figure 8. There is a magnitude difference between target echo and idle reflections (i-e no target) while continuously plotting the output of RF Mixer (Φ) with respect to time. Therefore, for Real-time Target display, Time Scope block has been used as shown in Figure 6. There is a noise level in the scope (due to idle reflections) but targets are easily differentiable from it in form of peaks. The magnitude of peaks depends upon radar cross section area (RCS) and velocity/range of the targets. Targets Figure 8: Block Parameters of "Signal To Workspace" Figure 6: Real-time Target Display As Doppler frequency shift or beat frequency is involved in the target echo, so for better understanding of radar concepts and as secondary scope for target identification, Spectrum Analyzer block with magnitude-frequency plot has been used as illustrated in Figure 7. The magnitude of peak depends upon RCS of the target. IV. POST-PROCESSING ALGORITHMS After Real-time DSP, the signal is sent to MATLAB Workspace as mentioned in the previous section. Two Post-processing DSP algorithms are applied on the signal in workspace: a. Doppler velocity estimation b. Range estimation These algorithms are modified version of the MATLAB codes applied on portable radar developed in MIT IAP Radar Course [1] [2]. The modifications are: 1. Three- Dimensional (3-D) Doppler velocity plotting 2. Accelerating Target Indicator (ATI) (Doppler velocity estimation)
3. Static Clutter Rejection (SCR) technique (Range estimation) Three Dimensional (3-D) Doppler velocity plotting Doppler velocity is the radial vector component (with respect to radar position) of the true velocity of the target. The concept of Doppler velocity is illustrated in the following diagram: display. The following two plots highlight the difference in Doppler velocity estimation without engaging ATI mode and after engaging the ATI mode. True velocity of target (v) Ɵ Doppler velocity of target (v cos(ɵ)) Radar Figure 9: Pictorial explanation of Doppler velocity concept Figure 11: Doppler velocity estimation without ATI mode In 3-D Doppler velocity plotting, velocities of the targets indicated in Real-time Target Display are calculated and displayed in Doppler velocity versus time plot with relative signal amplitude as third dimension, as depicted in the following plot: Targets Figure 12: Doppler velocity estimation with ATI mode Static Clutter Rejection (SCR) technique In Range estimation, ranges of targets detected in Real-time Target Display are calculated and displayed. Range versus time plot with color, the third dimension assigned to the relative signal amplitude is shown below: Figure 10: 3-D Doppler velocity plot The target moving in front of the radar was aluminum plate of a physical area of 0.1m 2, moved at specific time instants. The relative signal amplitude is again taken as fourth dimension shown as color of the plot for ease in target visualization in the display. Accelerating Target Indicator (ATI) mode In ATI mode, all the targets that are either at rest or moving with constant velocity are rejected. Only the velocities of the accelerating targets are visible on the Ranging of a humanbeing (Without clutter rejection) Figure 13: Range estimation without clutter rejection
The moving target in front of radar is a humanbeing, whose movement is depicted by the help of arrows. But its movements cannot be comprehended well because of the presence of static targets around the radar. To counter this problem, SCR technique is applied by the help of single delay line canceller or 2-pulse clutter rejection. The concept of single delay line canceller can be conceived by following diagram: Received Signal x(t) Time Delay x (t)= x(t)-x(t-1) x(t) + x(t-1) The relative signal amplitudes of the static targets remain constant over time. So, x (t) for static targets is zero. While moving targets have continuously varying relative signal amplitudes, so they are still detected even after delay line canceller. After applying SCR technique, the range plot more clearly display the moving targets as shown below: Σ Output Signal - x (t) Figure 14: Block diagram of single delay line canceller have also been conversed in detail for their application in better target comprehension. REFERENCES [1] Skolnik, M.I., Introduction to Radar Systems, 3 rd Edition. [2] Ian Moir and Allan Seabridge, Military Avionics Systems, Aerospace Series, Wiley Publications, 2006. [3] A. Jalil, H. Yousaf, F. Fahim and Z. Rasool, "FMCW Radar Signal Processing Scheme, Proceedings of International Bhurban Conference on Applied Sciences & Technology, Islamabad, Pakistan, 10 13 January, 2011. [4] Eugin Hyun, and Jong-Hun Lee, Method to Improve Range and Velocity Error Using De-interleaving and Frequency Interpolation for Automative FMCW Radars, International Journal of Signal Processing, Image Processing and Pattern Recognition, Volume. 2, No. 2, June 2009. [5] Stove, A.G., Linear FMCW radar techniques, Radar and Signal Processing, IEEE Proceedings, Part F. Vol. 139, Issue 5, October 1992. [6] Xu Xiaoping. Liu Jianxin, Han Yu, and Ding Qingsheng, Simulation of Digital Signal Processor on FMCW Radar, Vol. 2, No. 2, June 2004. [7] Cukrov, Moving Target Indication, Elecronics in Marine, Proceedings Elmar 2004, 46 th International Symposium. [8] Mahafza, Radar Systems, Analysis and Design using MATLAB, Chapman & Hall/CRC. Figure 15: Range estimation with clutter rejection V. CONCLUSION Real-time and post-processing algorithms for FMCW/CW radars in MATLAB and Simulink have been precisely focused in this paper. Real-time data has been first collected from radar hardware and processed for real-time target display in Simulink and then sent to the post-processing algorithms for Doppler velocity and range estimations. The concepts of 3-D Doppler velocity plotting, Accelerating Target Indicator (ATI) and Static Clutter Rejection (SCR) with delay line canceller