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radar:pulsecompression [2018/06/09 13:55] – romagnoliradar:pulsecompression [2026/04/28 18:24] (current) – mauro
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- For the generic signal >ok! make attention to the titles size!  --- //[[webmaster@localhost|DokuWiki Administrator]] 2018/04/23 12:56// 
  
->  Where do the figures come from? Please cite the document as decribed in [[:start|Welcome!]] --- //[[webmaster@localhost|DokuWiki Administrator]] 2018/05/03 16:16// 
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-> please use caption for tables and figures  ---  //[[webmaster@localhost|DokuWiki Administrator]] 2018/05/03 16:13// 
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-> please tables should be tables not pictures   ---  //[[webmaster@localhost|DokuWiki Administrator]] 2018/05/03 16:13// 
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-> please use numbered equation (if they are not in-line with the text ---  //[[webmaster@localhost|DokuWiki Administrator]] 2018/05/03 16:13// 
  
 ====== Basic concepts concerning Matched filters ====== ====== Basic concepts concerning Matched filters ======
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 The requirements a) and b) are conflicting. However, a method exists for improving the resolution that is The requirements a) and b) are conflicting. However, a method exists for improving the resolution that is
-based on the encoding of the signal transmitted by the radar: // ** The pulse compression** //+based on the encoding of the signal transmitted by the radar: // ** The pulse compression** //.
  
  
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 \begin{equation} h \left ( t \right ) = k cos \left ( 2 \pi f_{0} t - \frac{ \mu t^{2} }{2}  \right ) \: \: \: \:   for   \: \: \: 0<t<T \end{equation} \begin{equation} h \left ( t \right ) = k cos \left ( 2 \pi f_{0} t - \frac{ \mu t^{2} }{2}  \right ) \: \: \: \:   for   \: \: \: 0<t<T \end{equation}
  
-In the figure below there is the impulsive response of the matched filter of the // Chirp signal //+In the figure below there is the impulsive response of the matched filter of the // Chirp signal //.
  
  
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 <figure label> <figure label>
 {{ :media:block_diagram_to_reduce_lateral_lobes.jpg?500 |}} {{ :media:block_diagram_to_reduce_lateral_lobes.jpg?500 |}}
-<caption> block diagram of the system to reduce the lateral lobes [(cite:Teoria)]</caption>+<caption> Block diagram of the system to reduce the lateral lobes [(cite:Teoria)]</caption>
 </figure> </figure>
  
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-Usually, the matched filter to a coded sequence can be made in base band or intermediate frequency. In the modern systems the first solution is adopted, using phase and quadrature **I** and **Q** samples. The transmitted signal is represented by the convolution of a rectangular pulse duration $ \tau $ with the sequence of $N$ components **I** and **Q**  describing the code. After the sampling operation there is a sequence of phase samples of the received waveform :+Usually, the matched filter to a coded sequence can be made in base band or intermediate frequency. In the modern systems the first solution is adopted. The transmitted signal is represented by the convolution of a rectangular pulse duration $ \tau $ with the sequence of $N$ components **I** and **Q**  describing the code. After the sampling operation there is a sequence of phase samples of the received waveform :
  
 \begin{equation} \begin{equation}
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 //Application of Digital/Analog pulse compression and final considerations with advantages and disadvantages of pulse compression.// //Application of Digital/Analog pulse compression and final considerations with advantages and disadvantages of pulse compression.//
  
-As already mentioned in the previous paragraphs; A pulse compression radar, transmits a coded signal with "//low//" peak power and "//long//" time duration. The transmitted signal normally has a rectangular envelope of //T// seconds duration coded in phase or frequency. When received, the signal is "//compressed//" by the matched filter or by filtering with a certain degree of mismatch; The compressed signal lasts $\tau$ seconds, with $ \tau = T / C $ being,  //C// a larger, and sometimes much larger than the unit, called the "**compression ratio**". To obtain the desired duration of $\tau$, the signal must occupy a bandwidth approximately equal to $1 / \tau$. The compressed signal has, in addition to the main peak width $ \tau $, lateral lobes that can be reduced by suitable filters that cause the above-mentioned disadvantage, resulting in an enlargement of the primary lobe and a loss in the peak signal-to-noise ratio.+As already mentioned in the previous paragraphs; A pulse compression radar, transmits a coded signal with "//low//" peak power and "//long//" time duration. The transmitted signal normally has a rectangular envelope of //T// seconds duration coded in phase or frequency. When received, the signal is "//compressed//" by the matched filter or by filtering with a certain degree of mismatch; The compressed signal lasts $\tau$ seconds, with $ \tau = T / C $, being  //C// a larger, and sometimes much larger than the unit, called the "**compression ratio**". To obtain the desired duration of $\tau$, the signal must occupy a bandwidth approximately equal to $1 / \tau$. The compressed signal has, in addition to the main peak width $ \tau $, lateral lobes that can be reduced by suitable filters that cause the above-mentioned disadvantage, resulting in an enlargement of the primary lobe and a loss in the peak signal-to-noise ratio.
  
 ====Limitations of pulse compression==== ====Limitations of pulse compression====
  
-Pulse compression has some disadvantages. It requires a transmitter that can be readily modulated and a receiver with a matched filter more sophisticated than that of a conventional pulse radar. Although it may be more complex than a conventional long-pulse radar. The equipment for high-power pulse compression radar is more practical than that one required by a short-pulse radar with the same pulse energy. When limiting is employed, there can be small-target suppression and possibly spurious false-targets as well [( cite:RadarSystems)] A pulse compression radar has also the following advantages over a radar with the same coverage (same ratio $2E / N_{0} $ with same average power):+Pulse compression has some disadvantages. It requires a transmitter that can be readily modulated and a receiver with a matched filter more sophisticated than that of a conventional pulse radar. Although it may be more complex than a conventional long-pulse radar. The equipment for high-power pulse compression radar is more practical than that one required by a short-pulse radar with the same pulse energy. When limiting is employed, there can be small-target suppression and possibly spurious false-targets as well [( cite:RadarSystems)]. A pulse compression radar has also the following advantages over a radar with the same coverage (same ratio $2E / N_{0} $ with same average power):
  
  
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