radar system unit 5 part 1 design and importance

Radar

1. DETECTION OF RADAR SIGNALS IN NOISE The two basic operations performed by radar. Detection of presence of reflecting objects. Extraction of information from the received wave form to obtain such target data as position. Detection of desired signal along with rejection of undesired noise clutter and interference In radar is called SIGNAL PROCESSING>

2. MATCHED FILTER RECEIVER A network whose frequency-response function maximizes the output peak-signal-to-mean noise (power) ratio is called a matched filter If the bandwidth of the receiver pass band is wide compared with that occupied by the signal energy, extraneous noise is introduced by the excess bandwidth which lowers the output signal-to-noise ratio. If the receiver bandwidth is narrower than the bandwidth occupied by the signal, the noise energy is reduced along with a considerable part of the signal energy.

3. Maximizes the output peak-signal-to-mean-noise (power) ratio for a fixed input signal-to-noise (energy) ratio is H(f) = GaS*(f) exp ( -j2pift1)

4. The filter whose frequency-response function is given by equation has been called the North filter, the conjugate filter, or more usually the matched filter. It has also been called the Fourier transform criterion . The matched filter frequency-response function may similarly be written in terms of its amplitude and phase spectra / H( f ) ) and exp [-j ].

5. Derivation for frequency response of Match filter The output peak signal to mean noise ratio Rf is maximized by the frequency response function of the linear time invariant filter The ratio Rf is twice the average signal to noise power ratio when the input signal S(t) is rectangular sine wave pulse

6. The mean output noise power is

7. Schwartz's inequality states that if P and Q are two complex functions, then The equality sign applies when P = kQ , where k is a constant

8. applying the Schwartz inequality to the numerator of Eq .

9. Correlation function and Cross correlation receiver The cross correlation function R (t) of two signals y(λ) and s(λ), each of finite duration The input is yin (t) = s(t) + n(t)

10. The output of the filter with impulse response h(t) is Substitute equation

11. Cross Correlation Receiver

12. The input signal y (t) is multiplied by a delayed replica of the transmitted signal s(t - Tr ), and the product is passed through a low-pass filter. The cross-correlation receiver of Fig. tests for the presence of a target at only a single time delay Tr. Targets at other time delays, or ranges, might be found by varying Tr. However, this requires a longer search time.

13. Efficiency of Non matched filter The maximum efficiency of the single-tuned filter occurs for Bτ ≈ 0.4. The corresponding loss in signal-to-noise ratio is 0.88 dB as compared with a matched filter

14. Efficiency of Non matched filter compared with Matched filter

15. Efficiency, relative to a matched filter, of a single-tuned resonant filter and a rectangular shaped filter, when the input signal is a rectangular pulse of width τ. B filter bandwidth.

16. Matched filter with Non-White noise The frequency-response function of the filter which maximizes the output signal-to-noise ratio is

17. For white noise [Ni(f)]2 = constant and the NWN matched-filler frequency-response function reduces to The second is the matched filter when the input is white noise and a signal whose spectrum is S(f )/Ni(f ).