Qam Probability Of Error
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2012 In May 2008, we derived the theoretical symbol error rate for a general M-QAM modulation (in Embedded.com, DSPDesignLine.com and dsplog.com) under Additive White Gaussian Noise. While re-reading that
16 Qam Bit Error Rate
post, felt that the article is nice and warrants a re-run, using OFDM bit error probability of m-ary quadrature amplitude modulation as the underlying physical layer. This post discuss the derivation of symbol error rate for a general M-QAM modulation. The
16 Qam Symbol Error Rate
companion Matlab script compares the theoretical and the simulated symbol error rate for 16QAM, 64QAM and 256QAM over OFDM in AWGN channel. Enjoy and HAPPY NEW YEAR 2012 !!! Quadrature Amplitude Modulation (QAM) 64 qam matlab code schemes like 16-QAM, 64-QAM are used in typical wireless digital communications specifications like IEEE802.11a, IEEE802.16d. In this post let us derive the equation for probability of symbol being in error for a general M-QAM constellation, given that the signal (symbol) to noise ratio is . The general M-QAM constellation The number of points in the constellation is defined as, where is the number of bits in each constellation symbol. In this symbol error rate and bit error rate analysis, it is desirable to restrict to be an even number for the following reasons (Refer Sec 5.2.2 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]): 1. Half the bits are represented on the real axis and half the bits are represented on imaginary axis. The in-phase and quadrature signals are independent level Pulse Amplitude Modulation (PAM) signals. This simplifies the design of mapper. 2. For decoding, symbol decisions may be applied independently on the real and imaginary axis, simplifying the receiver implementation. Note that the above square constellation is not the most optimal scheme for a given signal to noise ratio. Average energy of an M-QAM constellation In a general M-QAM constellation where and the number of bits in each constellation is even, the alphabets used are: , where . For example, considering a 64-QAM () constellation, and the alphabets are . For computing the average energy of the M-QAM constellation, let us proceed as follows: (a) Find the sum of energy of the individual alphabets (b) Each alphabet is used times in the M-QAM constellation. (c) So, to find the average energy from constellation symbols, divide the product of (a) and (b) by.The average energy is, . Plugging in the number for 64-QAM, . Plugging in the numb
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Symbol Error Rate Definition
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Ofdm Dsplog
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theoretical QAM Bit Error Rate or Symbol Error Rate reference curve. Parameters Name Type Range Block Diagram https://awrcorp.com/download/faq/english/docs/VSS_Measurements/qam_berref.htm 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 QAM 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 use log scaling. error rate 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 BER/SER Meter parameter is set to "Auto", the measurement will compute the bit error probabilities Pb for symbol error rate 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. When M is an even power of 2 (M=2k, k is even) the following equations are used [1]: where Q(x) is the Gaussian integral or Q-function: and is approximated numerically, Es is the average symbol energy, N0 is the noise power spectral density and M is the number of signal levels. For other values of M an approximate upper bound is calculated from [1]: The measurement computes bit error probabilities from the symbol error probabilities using the following approximation [1]: This approximation assumes Gray coded square QAM constellations, which is not realizable for all values of M. References [1] Xiong, F., Digital Modulation Techniques, pp. 438-439 Prev Up Next Home Please send email to awr.support@ni.com if you would like to provide feedback on this article. Please make sure to include the article link in the email. Legal and Trademark Notice