Probability Of Error In Qpsk
Contents |
6, 2007 Given that we have discussed symbol error rate probability for a 4-PAM modulation, let us know focus on finding the symbol error probability for a QPSK (4-QAM) modulation bpsk vs qpsk scheme. Background Consider that the alphabets used for a QPSK (4-QAM) is (Refer qpsk constellation diagram example 5-35 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]). Download free e-Book discussing theoretical and simulated error rates for the digital modulation schemes like BPSK, ber for qpsk matlab code QPSK, 4-PAM, 16PSK and 16QAM. Further, Bit Error Rate with Gray coded mapping, bit error rate for BPSK over OFDM are also discussed. Interested in MIMO (Multiple Input Multiple Output) communications? Click here to dpsk see the post describing six equalizers with 2×2 V-BLAST. Read about using multiple antennas at the transmitter and receiver to improve the diversity of a communication link. Articles include Selection diversity, Equal Gain Combining, Maximal Ratio Combining, Alamouti STBC, Transmit Beaforming. Figure: Constellation plot for QPSK (4-QAM) constellation The scaling factor of is for normalizing the average energy of the transmitted symbols to 1, assuming that all the
16qam
constellation points are equally likely. Noise model Assuming that the additive noise follows the Gaussian probability distribution function, with and . Computing the probability of error Consider the symbol The conditional probability distribution function (PDF) of given was transmitted is: . Figure: Probability density function for QPSK (4QAM) modulation As can be seen from the above figure, the symbol is decoded correctly only if falls in the area in the hashed region i.e. . Probability of real component of greater than 0, given was transmitted is (i.e. area outside the red region) , where the complementary error function, . Similarly, probability of imaginary component of greater than 0, given was transmitted is (i.e. area outside the blue region). . The probability of being decoded correctly is, . Total symbol error probability The symbol will be in error, it atleast one of the symbol is decoded incorrectly. The probability of symbol error is, . For higher values of , the second term in the equation becomes negligible and the probability of error can be approximated as, . Simulation Model Simple Matlab/Octave script for generating QPSK transmission, adding white Gaussian noise and decoding the received symbol for various values. Click here to down
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of
Oqpsk
this site About Us Learn more about Stack Overflow the company Business Learn 8psk more about hiring developers or posting ads with us Signal Processing Questions Tags Users Badges Unanswered Ask Question _ dqpsk Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. Join them; it only takes a minute: Sign http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/ up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Compute probability of error to each QPSK symbol up vote 0 down vote favorite I'm trying to compute the probability error function of a QPSK modulation. I have a single user, who send a determined symbol $x = \frac{1}{\sqrt 2} http://dsp.stackexchange.com/questions/31544/compute-probability-of-error-to-each-qpsk-symbol \left(1+1j\right)$. Then I estimate at the receiver that symbol with different equalizers. I'm wondering how I could get the error probability of estimate a different symbol of the sent by the user, and compare the got error probabilities between equalizers. That means compute for each equalizer: $P\left(x_{\rm est} = \frac{1}{\sqrt 2}\left(1+1j\right) \big\vert x = \frac{1}{\sqrt 2}\left(1+1j\right)\right)$ $P\left(x_{\rm est} = \frac{1}{\sqrt 2}\left(1-1j\right) \big\vert x = \frac{1}{\sqrt 2}\left(1+1j\right)\right)$ $P\left(x_{\rm est} = \frac{1}{\sqrt 2}\left(-1-1j\right) \big\vert x = \frac{1}{\sqrt 2}\left(1+1j\right)\right)$ $P\left(x_{\rm est} = \frac{1}{\sqrt 2}\left(-1+1j\right) \big\vert x = \frac{1}{\sqrt 2}\left(1+1j\right)\right)$ Up to now, I have: P1_Eq1 = 0.5*erfc(-real(x_est_Eq1)/sqrt(n_power)) * 0.5*erfc(-imag(2)/sqrt(n_power)); P2_Eq1 = 0.5*erfc(-real(x_est_Eq1)/sqrt(n_power)) * (1-0.5*erfc(-imag(2)/sqrt(n_power))); P3_Eq1 = (1-0.5*erfc(-real(x_est_Eq1)/sqrt(n_power))) * (1-0.5*erfc(-imag(2)/sqrt(n_power))); P4_Eq1 = (1-0.5*erfc(-real(x_est_Eq1)/sqrt(n_power))) * (0.5*erfc(-imag(2)/sqrt(n_power))); But I think that use x_est_Eq1, which is the estimated symbol using the equalizer 1, in that place is incorrect. I'd appreciate your help. digital-communications qpsk share|improve this question edited Jun 16 at 0:04 Gilles 1,3433924 asked Jun 15 at 14:17 Pep 12 1 This answer should have all the information (and more) that you need. Please note that it is appreciated if you show us your efforts. "I'm having problems" does not exactly pinpoint wher
theoretical QPSK Bit Error Rate or Symbol Error Rate reference curve. Parameters Name Type Range https://awrcorp.com/download/faq/english/docs/VSS_Measurements/qpsk_berref.htm Block Diagram System Diagram N/A BER/SER Meter System BER/SER Meter N/A Modulation Type List of options N/A Statistic Type List of options N/A Result The measurement plots a theoretical QPSK bit or symbol error probability along the y-axis and the swept variable (typically Eb/N0 or Es/N0) along the x-axis. The y-axis should normally be set to probability of use log scaling. Graph Type This measurement can be displayed on a rectangular graph or tabular grid. Computational Details The measurement generates a reference curve based on the type and settings of the meter block selected in the BER/SER Meter setting. If the Statistic Type parameter is set to Auto, the measurement will compute the probability of error bit error probabilities Pb for BER meters and symbol error probabilities Ps for SER meters. Values for Pb or Ps are calculated for each power value specified in the meter's SWPTV parameter. For QPSK, the symbol error probability is related to the bit error probability by [1]: Ps=2Pb-Pb2 The following QPSK modulation types are supported: COHERENT QPSK: [1] where Q(x) is the Gaussian integral or Q-function: and is approximated numerically. Eb is the average bit energy, Es is the average symbol energy and N0 is the noise power spectral density. OPTIMUM DIFFERENTIAL QPSK: [2] The measurement approximates optimum differential QPSK as: SUBOPTIMUM DIFFERENTIAL QPSK: [3] The measurement approximates suboptimum differential QPSK as: COHERENT DIFFERENTIAL QPSK: [4] The measurement approximates coherent differential QPSK as: which is applicable at high SNR. References [1] Xiong, F., Digital Modulation Techniques, pg. 159 [2] Xiong, F., Digital Modulation Techniques, pg. 164 [3] Xiong, F., Digital Modulation Techniques, pg. 165 [4] Xiong, F., Digital Modulation Techniques, pg. 167 Prev Up Nex