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I was learning Modulation Techniques and was on the topic Phase Shift Keying (PSK). As far as I have understood,

In Binary PSK we encode a single bit on a one signal element and we differentiate between two bits (or two signal elements) by their different phase. And that it's favorable to keep the phase different maximum between the two different signal elements, so we use a phase difference of 180 degrees.

In Quadrature PSK, we want to transmit two bits per signal element. Since there are four different possible combinations of two bit numbers, we want four distinguishable signal element to distinguish between the four combinations. So we use signal elements with four different phases and with a difference between them of 90 degree (which is maximum possible).

Untill here, I seem to understand it. Correct me if anything from above is wrong.

I read from a source that in QPSK, the four different phases are 45°, 135°, 225°, and 315°. The excerpt from the said text is as under

It makes sense to seek maximum separation between the four phase options, so that the receiver has less difficulty distinguishing one state from another. We have 360° of phase to work with and four phase states, and thus the separation should be 360°/4 = 90°. So our four QPSK phase shifts are 45°, 135°, 225°, and 315°

My first question is, aren't phases relative? What are these phase shift of 45°, 135°, 225°, and 315° relative to? My common understanding makes me wonder wouldn't just four sine waves, one not shifted at all, second sifted 90° relative to the first, third shifted 180° relative to the first, fourth shifted 270° relative to the first make more sense and be appropriate to represent different data elements?

The same text states that

The term “quadrature modulation” refers to modulation that is based on the summation of two signals that are in quadrature. In other words, it is I/Q-signal-based modulation. QPSK is an example of I/Q-based modulation.

My second question is, how exactly is four different phases achieved by modulating the amplitude of just two- I & Q signals? At first, it seems to me that I/Q signaling can only be used to shift a signal 90° (i.e., 45° in each direction).

Also, Whether Binary PSK is also done using I/Q-based signals?

There's another question I and Q components and the difference between QPSK and 4QAM which (maybe) addresses my problem, but it's too complicated and mathemaical for a beginner like me.

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    $\begingroup$ Most of your questions are answered in detail in the answer to I and Q components and the difference between QPSK and 4QAM. I vote to close. $\endgroup$ – Dilip Sarwate Sep 25 '19 at 14:02
  • $\begingroup$ Thanks but that answer is a bit too complicated & mathematical for a beginner like me ( the word 'mathematically' specifally mentioned in that question) and also there is no reference of 4-QAM in my question so stop closing every question on basis of one good answer you gave to one question 6 years back. $\endgroup$ – Abhijit Singh Sep 26 '19 at 6:18
  • $\begingroup$ @AbhijitSingh : The answers on the six year old question answer your question. If you don't understand, please try to reformulate this question into a smaller scope, starting from what you do understand and moving towards what you don't understand. For example, start with a question about why use 45°, 135°, 225°, and 315° instead of 0°, 90°, 180°, and 270°. $\endgroup$ – Peter K. Sep 26 '19 at 16:40
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(1) The phases are indeed relative. The numbers 45, 135, 225 and 315 are relative to the transmitter's oscillator. The receiver, of course, has a different oscillator, so it will need to do some procesing to estimate the phases.

Related to this subject, there is also differential modulation, where 1s and 0s are transmitting by changing the phase relative to the previous symbol.

(2) This identity is useful to understand I/Q modulation: $$A_I \cos(2\pi f t) + A_Q \sin(2\pi f_c t) = S_{IQ} \cos(2\pi f_c t - \theta_{IQ}) $$ where $$ S_{IQ} = \sqrt{A_I^2 + A_Q^2}$$ and $$\theta_{IQ} = \tan^{-1}\frac{A_Q}{A_I}.$$ So, as you can see, you can achieve any phase $\theta_{IQ}$ by adding the I and Q signals with appropriate amplitudes.

(3) Binary PSK is just an I signal. Since the two phases in BPSK are zero and 180, the Q portion of the signal is always zero.

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