# Why is the symbol duration in QPSK twice the bit duration?

I saw many answers for such questions by writing down equations such that the symbol is formed of n bits so the duration of the symbol in QPSK must be n multiple of the bit duration.

I am not convinced as from my understanding, QPSK is making use of the phase to represent two bits together using same bit symbol we used to transmit a bit. Let's assume that the symbol used to transimit a bit will take x seconds, then the phase-shifted version (QPSK symbol) will take the same x seconds.

Can anyone please make the situation clearer for me?

• If you transmit two bits per symbol - which is what QPSK does -, the symbol rate is half the bit rate. It's hard for me to understand what exactly it is that you don't understand. Apr 4, 2023 at 14:04
• @MattL. I just found this. "The mathematical analysis shows that QPSK can be used either to double the data rate compared with a BPSK system while maintaining the same bandwidth of the signal, or to maintain the data-rate of BPSK but halving the bandwidth needed. In this latter case, the BER of QPSK is exactly the same as the BER of BPSK – and believing differently is a common confusion when considering or describing QPSK. The transmitted carrier can undergo numbers of phase changes" en.wikipedia.org/wiki/… Apr 4, 2023 at 14:08
• @AhmedWaleed so, did that clear it up? Apr 4, 2023 at 14:10
• I think so. Should i post the answer myself or close the question as i am new to the platform? @MarcusMüller Apr 4, 2023 at 14:12
• If it's OQPSK, i think it's more like 1 bit per symbol. Or maybe it's 1 bit per half symbol. Apr 4, 2023 at 23:35

In QPSK, we send 2 bits in one symbol in x secs.

So symbol duration is x secs.

Bit duration is x/2 secs.

In BPSK, one bit per symbol is sent.

So symbol duration is x secs and bit duration is also x secs.

It's is a matter of definition. If you look to the bit as an information so without any doubt, if the QPSK symbol takes T then this equivalent to say that the single bit takes T/2 on average. But if you are comparing BPSK (1 bit per symbol) and QPSK regarding the symbol duration then we cannot say that because QPSK is representing two bit per symbol then QPSK symbol duration must be twice the BSPK one who represents only one bit per symbol. and the reason is that QPSK symbol duration is a design decision.

These two figures show two different QPSK schemes with different symbol duration:

• I am not sure what you mean by with QPSK we cannot say that and that the symbol duration with QPSK is a design decision. What you are say you can say for both BPSK and QPSK. The symbol duration for both is a design decision, and the bit rate (number of bits per second) is the symbol rate x the number of bits/symbol. The bit duration is the reciprocal of the bit rate (number of seconds per bit). What you apply to BPSK applies to QPSK. QPSK is 2 bits/symbol and BPSK is 1 bit/symbol. It's as simple as that. Apr 9, 2023 at 12:28
• You can make a similar plot as you show with BPSK with different symbol durations. Apr 9, 2023 at 12:29