The in LFM at the demodulator side the pulse

                     The present OFDM technique with varying envelope characteristics leads to low spectral and power efficiency. An alternative way to improve the efficiency and to provide constant envelope properties is to reduce PAPR, leading to a pre-modulation Gaussian filtering technique. This will act as a front-end for an LFM modulator. The method outlined in 9 as GMSK modulation for digital mobile radio telegraphy will be applied here for pulse compression based radar. Here the last mentioned method is applied to pulse radar by using binary NRZ input data.This is shown in Fig (2), NRZ as data input and after Gaussian filtering, the width of the spectrum reduced from the actual width.

                 This paper also describes the use of pre-modulation LPF (pre-modulation Gaussian filter) which offers the following properties such as constant envelope characteristics, coherent detection capability, better BER performance and better efficiency 9. Gaussian LPF can act as an excellent digital modulation technique for this method. In addition to that, LFM based pulse compression method is included with the above method results reduced the number of side lobes with the main lobe compared with the conventional pulse compression based radar. At the receiver end reducing the side lobe is to be done by using the filtering technique. Pulse compression is based on matched filtering, which basically uses the complex conjugate of the actual radar signal to filter the received signal.

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Here this shows that by the application of the mentioned method with LFM technique the side lobes are reduced drastically.      The auto-correlation function of  LFM with Gaussian envelope is given by 12

 ………………. (2)

 represent the effective pulse duration, is the rate of frequency at time t=0 and is the pulse width.

The effective pulse duration is

………………………………(3)

By considering equation (2) & (3) states that autocorrelation function depends on pulse duration, pulse width and here in LFM at the demodulator side the pulse width is compressed.

    Thus by compressing the pulse width, the autocorrelation function reaches close to unity. Fig (3) shows the autocorrelation for an LFM pulse with a pre-modulation Gaussian filter. And this implies that this technique offers positive correlation at the receiver compared with the conventional based LFM design 7. Here there are no side lobe arrays for three targets. This shows definitely that the above-mentioned method is perfectly suitable to reduce side lobe by the use of a Gaussian filter as a pre-modulation filter. Also, the application of matched filter at the receiver results from the autocorrelated signals obtain less width as compared to reference sinusoidal pulse waveform.

 

                 Autocorrelation function serves radar to detect two closely similar, near and far target signals delayed by itself. In this paper, the autocorrelation function is shown in Fig (3) specifies during each lag the signal exactly matches. For t=0 the signal is correlated, one and two-period lagging intervals, during t=400 and t=800 respectively the signal matches exactly.This will improve the spectral efficiency of LFM based Costas coded radar with a filter design. These signify that the energy spectrum for each N number of subpulses is almost identical. Fig (4) shows the autocorrelation for an LFM pulse without a filter. Here sidelobe arrays are visible with an amplitude of – 65 dB level with main lobe amplitude of -17 dB.

                                   If there is a pre-modulation filter in the transmitter, then the power spectral density of the side lobe can be suppressed considerably 17. Fig (5) shows the autocorrelation of the same LFM  pulse with Costas coding. This shows better correlation but exists side lobes with side and the main lobe of amplitude – 65 and – 17 dB respectively. There is no spectral leakage and thus no discontinuity in waveform compared with Fig (4).

 

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