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This paper proposes a linear frequency modulation (LFM signal) and biphase coding (BC signal) mixed modulation signal called LFM-BC signal. LFM-BC signal has both LFM signal and BC signal two kinds of traditional signal advantages but makes up for their shortcomings. In this paper, LFM-BC signal, LFM and BC signals are studied and compared from the time characteristic and frequency characteristic of the signal, fuzzy function, pulse compression and Doppler characteristics and low probability of interception (LPI) characteristics.

LFM signal and BC signal are often used in pulsed radar. LFM signal has the lower side of the sidelobe after pulse compression, and its Doppler frequency is not sensitive, but the signal form is relatively simple, vulnerable to interference. As the BC signal can use code agile technology, BC signal anti-jamming performance is better, but the BC signal is more sensitive to Doppler frequency [

In order to integrate the advantages of LFM and BC signals, make up for the shortcomings of the two, this paper proposes a mixed modulation signal with intra-linear chirp and inter-pulse phase coding. This hybrid modulation signal has both LFM and BC signal advantages, but also makes up for their own shortcomings. LFM-BC signal obtains large signal to noise ratio to improve by small time and narrow bandwidth, to avoid the large time and wide bandwidth problems [

In this paper, we study and compare the mixed-modulation signal and the LFM and BC signal from the aspects of the time characteristic and frequency characteristic, fuzzy functions, pulse compression and Doppler characteristics, low intercepting characteristics, in order to verify the application of mixed- modulation signals.

The time-domain expression of the LFM signal is as follows:

where

The time-domain expression of the BC signal is as follows:

where T is the sub-pulse width,

At the same time

where

mixed modulation signal with intra-linear chirp and inter-pulse phase coding can be expressed as:

The signal frequency domain expression can be obtained from the time domain expression of the signal and the Fourier transform property.

The frequency domain expression of the LFM signal is:

The frequency domain expression of the BC signal:

where

Since the mixed modulation signal corresponds to the convolution of the LFM signal and the BC signal in the time domain, the frequency domain is the product of the two spectra [

It can be seen from the formula that the spectrum of the mixed modulation signal depends mainly on the shape of

ditional factor

only in the original LFM signal on the spectrum to bring some glitches, not too much to change its spectral shape.

The

According to the definition of fuzzy function, the fuzzy function of LFM signal is:

The fuzzy function of the BC signal is expressed as:

where,

Substituting

The fuzzy function

The following figure shows the fuzzy functions of the three signals.

It can be seen from

function graph center is similar to the pin-type. The LFM-BC has good measurement properties.

When the LFM signal has the Doppler frequency of

The above equation shows that when f_d = 0, the output pulse has a sinc function type envelope. When f_d ≠ 0, the sinc function envelope will produce a displacement, causing the ranging error, while the output pulse amplitude slightly decreased [

Generally radar LFM pulse waveform has a coupling between the Doppler frequency and the measured distance. That is, when the measured target exists Doppler frequency, the radar measurement target distance and the target where the real distance there is a certain difference.

The following figure illustrates the effect of Doppler frequency on pulse output. The following figure shows the pulse output when the Doppler frequency

It can be seen from

The output of the BC signal through the matched filter is its autocorrelation function

In this paper, 13-bit Barker code as an example to analyze the two-phase pulse pressure output. Barker code is a binary pseudo-random sequence code

The following figure shows the pulse output when the Doppler frequency

It can be seen from

The impulse response of the LFM-BC signal is,

Let

It can be seen from the formula, the LFM-BC signal matching filter is exactly the LFM signal matched filter and the BC signal matched filter impulse response convolution.

The frequency domain is expressed as,

We can divide the compression process into two steps: The first step through

the LFM filter, get the BC signal. The second step is then through the BC matched filter to obtain the final pulse compression signal. The two-step pulse compression process can also be done in one step.

The following figure shows the pulse output when the Doppler frequency

It can be seen from

The intercept factor

wide product of the transmitted waveform. That is

the signal width, B is the adjusted signal bandwidth, K is the combined effect of other factors [

Let the chirp width of the chirp signal be

the intercepting factor is:

Set the number of BC signal bit P, sub-pulse width is still

LFM-BC signal first pulse within the pulse frequency, and then pulse phase coding. So the time width of the LFM-BC signal is

That is, the interception factor of the LFM-BC signal is

code length, the wider the bandwidth of the LFM signal, the more obvious the improvement of the intercept factor of the LFM-BC signal [

The LFM-BC signal has the smallest intercept factor, so the signal has better low intercept performance. It can prevent the signal from being intercepted by the receiver to detect and intercept, thereby enhancing the radar in the battlefield combat capability and viability.

The mixed modulation signal (LFM-BC signal) of LFM signal and BC signal proposed in this paper inherits the advantages of two kinds of single modulation methods, and has some improvement. The implementation of this combination is relatively simple, is a practical combination of signal. At the same time, Doppler shift has little effect on LFM-BC signal. The LFM-BC signal requires a smaller code length than the pure phase code, and the required time-bandwidth product is smaller than the LFM. So the LFM-BC signal obtains a large signal to noise ratio improved by small time and narrow bandwidth. In addition, the LFM-BC signal has a more complex form of signal, making it difficult to extract the radar by the radar intercept receiver. This is the signal characteristic required by the LPI radar.

This work is supported partly by National Natural Science Foundation of China under Grant No. 61301205 and No. 61571146, National Defense Based Science Research Pro-gram under Grant No. JCKY2013604B001. This paper is funded by the International Exchange Program of Harbin Engineering University for Innovation-oriented Talents Cultivation.

Dou, Z., Song, W.D. and Zhang, W.X. (2017) Study on the Characteristics of LFM Signals, BC Signals and Their Mixed Modulation Signals. Int. J. Communications, Network and System Sciences, 10, 196-205. https://doi.org/10.4236/ijcns.2017.108B021