The following algorithms are available:
Car speed analysis
Ski/snowboard speed analysis
FMCW radar
Stepped frequency radar
Signal-to-Noise ratio calculation
Super-resolution peak detection
Angle-of-arrival
Generation of antenna-arrays
Additionally a simulator for FMCW systems has been developed, see below. Also, the variation in distance caused by a corner reflector in high resolution radar applications has been calculated, see below.
Car speed analysis
Radar can be used to measure the speed of a car. The speed measurement can be performed in a contact-less manner, so contact to a rotating wheel is not required and the diameter of tires is no longer relevant. GPS is no alternative due to potential masking by high-rise buildings and multi-path effects. The figure below shows a comparison between radar (the trace in blue) and GPS (the trace in red). The car is driven over different types of roads with different speeds. The figure shows that from 0 to 3 minutes and around 8-9 minutes GPS calculates a certain car-speed while the car is waiting for a traffic light! At 29 minutes GPS fails to capture the acceleration and deceleration of the car. The simple algorithm that has been developed to transform the radar data to to car velocity shows more accurate results than the GPS-reference! A detailed schematic for the analog/RF electronics is available.
Ski/snowboard speed analysis
Similar to the car speed analysis, the velocity of ski’s and snow-boards can be measured. Also here the measurement can be performed in a contact-less manner. The car speed algorithm has been modified to transform the radar data to display the velocity of the ski/snowboard, as displayed in the figure below. The figure shows a comparison between radar (the trace in blue) and GPS (the trace in red). The ski/snowboard is taken out on a real-life ski-route in the snow. The figure shows that from 0 to 5 minutes, the skier is waiting for the ski-tow, with sometimes some progress. GPS gives random results. From 4 to 7 minutes, the ski-tow goes uphill with an average of 6 km/h as displayed by the radar measurement. GPS again gives random results. Around 12 minutes, GPS misses the fast increase in speed. Around 14 minutes, GPS is blocked by trees and completely misses correct speed readings. Around 24 to 25 minutes, the skier is still as shown by the radar speed. GPS again gives erroneous results. The velocity calculated by the radar is much more accurate than the GPS results. A detailed schematic for the analog and RF electronics is available.
FMCW radar
Algorithm for Frequency Modulated Continuous Wave (FMCW) radar require special attention to obtain the optimum performance in resolution, accuracy. Algorithms for data capturing, signal optimization and calculation of radar cross-section or radar-cross-section equalization on range profiles are available.
Stepped frequency radar
Instead of a chirp radar, the RF frequency can also be stepped, as shown in the figure below. In this case the frequency is stepped in 200 MHz steps in a 1 GHz bandwidth in 1 millisecond. The received data requires a special algorithm for processing the data and resulting in a range plot. This algorithm processes the data in an optimised manner. Additionally the analysis also shows the limits and consequences of stepped frequency radar compared to an FMCW radar.
Signal-to-Noise ratio calculation
In radar it is important to estimate and calculate the signal-to-noise ratio of signals. Three traces are shown: the cyan trace acts as reference, while algorithm 1 is shown in the dark blue trace and algorithm 2 is shown in the red trace. The new algorithms in red and blue calculate the signal-to-noise ratio from a minimum of 10 dB (algorithm1 in blue) or even down to 0 dB (algorithm 2 in red).
Super-resolution peak detection
Due to the discrete nature of digital signal processing and fourier transforms, the accurate detection of peaks in the received signal is limited to discrete values. In-between discrete values can be interpolated, but still resolution is limited. A new algorithm has been devised to obtain super-resolution accuracy, see the figure below. It shows the relative error versus distance for various algorithms. The default peak detection algorithm (the trace in cyan) shows a increase in error versus distance. The interpolated trace (in magenta) shows approximately two times better results. The new algorithm (the traces in dark blue, red and black) shows even lower errors, especially algorithm2 (the red trace). An improvement close to 40x is obtained compared to the default algorithm.
Angle-of-arrival
In the case that multiple transmitters or receivers are available, the angle-of-arrival of the various objects can be calculated. This algorithm calculates the angle-of-arrival including error on the angle.
Generation of antenna arrays
The drawing of antenna arrays can be quite cumbersome. Therefore a program has been written that uses the PCB-layer definition, the antenna-array factor or power distribution over the various antennas and then generates the antenna array(s) in a format that can easily be read in a 3D-EM simulation program, and by PCB-drawing tools. Two examples show the versatility of the program. Generation time is in the order of seconds.
FMCW simulator
A screen-shot of the radar simulator is shown below. Sliders of values boxes can be used to specify the distance to the target, the sweep bandwidth, the chirp time and the radar cross section of the target. The number of data points and the window for the Fourier Transform can also be set as pre-programmed choices. The program instantaneously calculates the distance resolution, the minimum sample frequency, and the resulting frequency from the object-reflection. Additionally the program displays whether aliases occur in the sampling. Two graphs show the resulting time-domain and frequency-domain response of the radar. Using the sliders directly show the consequences and the time and frequency-domain responses.
Corner Reflector Analysis
Corner reflectors are often used for radar measurements, but in high resolution measurement scenarios they deviate from the (expected) ideal behavior. A full analysis of the deviations from the ideal behavior has been performed and is available, please contact us at
info@single-chip-radar.com.