Novel continuous phase DDS model for linear Chirp Signal Simulation in Pulse Compression Radar

Abstract

One of the most common signals used in radar applications is chirp signal, as well as Linear chirp signal is used for radar transmitters and communication. “Direct Digital Frequency Synthesis (DDFS or simply DDS), also known as Numerically Controlled Oscillator (NCO), is a technique using digital-data and mixed/analog-signal processing blocks as a means to generate real-life waveforms that are repetitive in nature” [1]. Common method of chirp signal generation is DDS and the legacy systems are SAW devices or Direct Analog Synthesizer (DAS). In This work we present a novel time-sample based model to simulate DDS signal in a manner proper for DDS computer simulation (MATLAB). The main purpose of this model is to describe DDS signal behavior and some other aspects in different applications which could be used in the future works. The presented model helps us to select the main parameters to achieve reliable replacement of analytical chirp signal in the way that this closed form expression (simulation model) can be presented to evaluate and compare the DDS-CG signal with its mathematical counterpart. The presented model uses continuous phase frequency-shift keying concept (CPFSK). Accuracy verification of the model is investigated by comparison with mathematical representation of signal named using RMSE term in time domain. Furthermore, the pulse compression method as the most important usage of DDS-CG also is used to investigate the behavior of presented model in the way that the result of pulse compression in equivalent receiver (Matched filter) is evaluated. The minimum required number of steps (M_min) to model the analytic chirp signal by the CPMSFK guarantees the minimum defined similarity (50%, 90%) with the measure of normalized RMSE. SNR loss due to non-ideal properties of w.r.t ideal chirp output calculated and the efficiency of model is verified. In This work we present a novel time-sample based model to simulate DDS signal in a manner proper for DDS computer simulation (MATLAB). The main purpose of this model is to describe DDS signal behavior and some other aspects in different applications which could be used in the future works. The presented model helps us to select the main parameters to achieve reliable replacement of analytical chirp signal in the way that this closed form expression (simulation model) can be presented to evaluate and compare the DDS-CG signal with its mathematical counterpart. The presented model uses continuous phase frequency-shift keying concept (CPFSK). Accuracy verification of the model <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tilde{x}_{M}[n]$</tex> is investigated by comparison with mathematical representation of signal named <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x(n)$</tex> using RMSE term in time domain. Furthermore, the pulse compression method as the most important usage of DDS-CG also is used to investigate the behavior of presented model in the way that the result of pulse compression in equivalent receiver (Matched filter) is evaluated. The minimum required number of steps (M_min) to model the analytic chirp signal by the CPMSFK guarantees the minimum defined similarity (50%, 90%) with the measure of normalized RMSE. SNR loss due to non-ideal properties of w.r.t ideal chirp output calculated and the efficiency of model is verified. The minimum required number of steps (M_min) to model the analytic chirp signal by the CPMSFK <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tilde{x}_{M}[n\vert$</tex> guarantees the minimum defined similarity (50%, 90 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">%</sup> ) with the measure of normalized RMSE. SNR loss due to non-ideal properties of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tilde{y}_{M}[n]$</tex> w.r.t ideal chirp output <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$y[n]$</tex> calculated and the efficiency of model is verified.