Timeline for Exact formula for 8-PSK BER
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4, 2021 at 10:11 | comment | added | Okan Erturk | Hello, it is assumed that the error occurs only when the consecutive symbol is decoded. Since the constellation is Gray coded, the number of bit error is proportional to $1/(\log_2(M)$ symbol error. This is a quite tight approximation and practically acceptable. | |
| Dec 2, 2021 at 16:54 | comment | added | Dilip Sarwate | -1 This answer gives a formula for the symbol error probability, and not the bit error probability (neither the specific values of BER for the three bits (not all the same), nor the average BER). | |
| Nov 25, 2021 at 21:12 | comment | added | Okan Erturk | Hello, $\theta$ is the dummy variable that the integral is taken over. There was a typo, $\bar{\gamma}$ is the SNR which is defined as $E_s/N_o$ where $E_s$ is the average symbol energy, and $N_o$ is the power spectral density of the additive noise. | |
| Nov 25, 2021 at 21:09 | history | edited | Okan Erturk | CC BY-SA 4.0 |
added 2 characters in body
|
| Nov 24, 2021 at 16:38 | comment | added | Dilip Sarwate | What is $\theta$ in the formula? What is $\bar{\gamma}$? What is $\gamma_3$? None of these symbols seem to be defined in this answer. Also, $P_M$ sounds more like a symbol error probability, not a bit error probability, which is what the OP is looking for. | |
| Nov 20, 2021 at 16:57 | comment | added | TimWescott | I would not consider $Q$ to be exact, whether it's in a math package or not. To find a numerical value of it a package evaluates a similar (but simpler) version of the integral that @okanerturk gives you. While there's probably some highly optimized arithmetic behind calculating it in a math package, it's still a numerical solution to a messy nonlinear integration, and will never, ever, be "exact". | |
| Nov 20, 2021 at 12:00 | comment | added | Marcus Müller | @Loran sorry, see my comment on your question: the decision regions of 8-PSK are not rectangular like in BPSK and QPSK, so the formula is more complicated then that. Did you want an easy formula? Your question said exact! I haven't gone through the paper Okan cites, but I trust it – so, this is the right answer, and I would have expected the formula to be much much longer. | |
| Nov 19, 2021 at 23:59 | comment | added | Loran | Gray mapping or not. | |
| Nov 19, 2021 at 23:51 | comment | added | Loran | For BPSK and QPSK, \begin{equation} p_{BER}=Q\left(\sqrt{\frac{2E_b}{N_o}}\right) \end{equation} I want to know if a formula such as this exist in the literature for 8-PSK. Again, I am not looking for bounds, pairwise probability of error, SER, approximation, infinite sums, integrals, etc., but a formula involving the $Q$ function or the $erfc$ function. | |
| Nov 19, 2021 at 22:50 | comment | added | Loran | Thanks Okan. I want to know if the exact formula using the Q function or complementary error function exists in the literature --functions that have existed for some time in mathematical packages, just like exp, sin, tan, ln, etc. | |
| Nov 19, 2021 at 22:38 | comment | added | Okan Erturk | I think you are looking for an expression including some well-defined functions like $sin$, $tan$ $log$, etc. Actually, these functions can not be expressed exactly without using infinite sum as well. For example for binary case (BPSK), the BEP exists in terms of the $Q$ function, which is nothing but a special representation of an integral! In M-PSK it is assumed that the symbols are gray mapped, therefore, a symbol error results in a bit error. | |
| Nov 19, 2021 at 22:32 | comment | added | Loran | I am not asking for pairwise probability of error approximations, BER approximations from SER, the use of bounds, infinite sums, ets. Is there an exact formula for the BER of 8-PSK in the literature that you are aware of? I have never encountered it. | |
| Nov 19, 2021 at 22:19 | history | answered | Okan Erturk | CC BY-SA 4.0 |