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BPSK using carriers other than sinusoidal wave

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I am currently a student in communications & electronics engineering undergrad working on a small project employing Direct sequence spread spectrum. For simplicity and since I am using TTL level gates I have used XOR gates as mixers. After spreading the data with the PN CODE, using a second XOR gate with square wave (2MHz toggling between logic high 5V and logic low 0v) carrier which in principle should give BPSK signal.

The thing is my professors who are evaluating the project refuses this concept claiming that the carrier must be sinusoidal in order to generate BPSK signal. They even claim square wave doesn’t have a phase and therefore cannot be switched 0 and 180 degrees!

Now are they correct in their saying?, and if not how to convince them otherwise since all text books seem to explain BPSK using sinusoids as it’s easier for calculation.

If someone has seen a book that explains this in detail please mention it!

Attached below is the circuit and description taken from ARRL spread spectrum source book.

enter image description here


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