# What is the phase coded modulation?

I'm trying to understand what is the "phase coded modulation" and how does it work.

As far as I know, Although the linear frequency modulated (LFM) waveform continues to be the workhorse of modern radars, there is growing interest in the use of phase-coded (PC) waveforms. Phase coding can be used to reduce radio frequency interference (RFI) between adjacent radars and make the waveform less vulnerable to exploitation, and more robust to interference.

and I'm not a familiar with like these radio frequency engineering. So.

Is the Phase modulation same "phase coded modulation"? I'm confused that because there are several types modulation way in https://kr.mathworks.com/help/comm/ug/digital-modulation.html#fp45657

• Kind of Modulation
• Amplitude modulation
• Phase modulation
• Frequency modulation
• Continuous phase modulation
• Trellis-coded modulation

But I can't find anywhere about Phase coded modulation.

Would you help me to understand what is the "phase coded modulation" and how does it work with very very simple example for referencing?

Phase-coded modulation is another name for direct-sequence spread-spectrum (DS/SS) modulation. In a typical DS/SS communication scheme using binary phase modulation, a single bit is transmitted not as a sinusoidal pulse of duration $T$ and phase either $0$ or $\pi$ depending on whether the bit being transmitted is $0$ or $1$, but rather as a sequence of successive $N$ shorter sinusoidal pulses of duration $T/N$ with phases $0$ or $\pi$ as defined by a specific binary sequence (called a spreading sequence) $\mathbf b$ of length $N$ or its complement $\mathbf{\bar{b}}$ according as the data bit $d$ is $0$ or $1$. For example, with $N=7$, we would have a phase-coded transmission describable as $$\begin{array}{ccccc} d=0 &\leftrightarrow &\mathbf b = (1,1,1,0,1,0,0) &\leftrightarrow &(\pi,\pi,\pi,0,\pi,0,0)\\ d=1 &\leftrightarrow &\mathbf{\bar{b}} = (0,0,0,1,0,1,1) &\leftrightarrow &(0,0,0,\pi,0,\pi,\pi) \end{array}$$ In the communication context, the interference between two different phase-coded transmissions using two different spreading sequences is determined by the cross-correlation between the spreading sequences. In the radar context, $\mathbf{\bar{b}}$ is not needed, but interference between two radar signals with different spreading sequences is still determined by the cross-correlation between the spreading sequences. The term spreading refers to the fact that the phase-coded signal has a bandwidth $N$ times larger than the non-phase-coded signal. Because the energy is spread over a larger bandwidth, the signal doesn't interfere as much with narrowband signals, and is not easy to detect even by broadband scanners. Thus, covert communication or covert scanning is easier, and signals are not that easy to jam, either by narrowband jamming or by broadband jamming, because the correlation receivers reject both kinds of jamming more easily.