Noise radar range equation

To detect the reflected signal in the presence of thermal white noise, the correlation process (matched filtering) is used according to the fundamentals given above. The received signal will be detected when its power is higher than the thermal noise power P/v multiplied by detectability factor D, e.g. 

The correlation receiver s property described above shows that the detectability factor is equal to 

For medium integration time the time-bandwidth product is limited by the range migration effect [40]  

Assuming that the maximum target velocity is equal to 3M (lOOOm/s), the maximum value of the time-bandwidth product is limited to 150,000. The maximum processing gain is then equal to 51.7 dB. The use of a windowing function will decrease this value by a few dB. The maximum detection range for the noise radar is given by the formula 

To increase the detection range one can increase the transmitted power, antenna gain or integration time. 

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The state-of-the-art in component development for the major system components is discussed here, but first a few words concerning one of the more basic radar performance metrics, signal-to-noise ratio, and the performance of components as related to that metric. Since the radar range equation has a factor of in the denominator, the system SNR must improve by a factor of 16 relative to some baseline value, to... 

The radar range equation was introduced in Sec. 17.1 In practice, estimation of the composite system loss factor and the system noise temperature can be very demanding. 

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