Bit Error Rate Calculation For Qam
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Bit Error Rate Formula
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16 Qam Ber Matlab
best answers are voted up and rise to the top Deriving SER & BER for 4QAM, 16QAM and 32QAM up vote 0 down vote favorite Required to find symbol error rate vs $\dfrac{E_b}{N_0}$ for 4QAM, 16QAM & 32QAM. Thought that SER & BER are the same but did my research to find that BER is $\dfrac{1}{\log_2(M)}$ of SER...(could you please confirm this?) Also found SER for: 4QAM to be: $\text{erfc}\sqrt{\dfrac{E_b}{2N_0}}$ probability of error for 16 qam and that of 16QAM to be: $\dfrac{3}{2} \text{erfc}\sqrt{\dfrac{E_b}{10N_0}}$ Are these values correct? Still have problems to find SER for 32QAM... Hope you can help. derivation share|improve this question edited May 13 '14 at 19:26 jojek♦ 6,70041444 asked May 13 '14 at 19:14 John Smith 112 Take a look at this question and its answers: dsp.stackexchange.com/questions/15996/… –Matt L. May 13 '14 at 19:15 still can't understand the relation (not mentioned anywhere in those questions & answers). Also 16QAM & 32QAM weren't covered in that question.. –John Smith May 13 '14 at 19:23 did my research, cant use that formula when dealing with an odd number of bits per symbol, for which bits per symbol for 32QAM is 5... –John Smith May 13 '14 at 19:41 @JohnSmith: The problem is that there isn't a standard definition of what 32-QAM is. For non-square QAM modulations, there are multiple geometries in which you could implement the constellation, will have an effect on the error rate. You need to specify the exact constellation in order to calculate its theoretical SER. –Jason R May 13 '14 at 19:44 1 Your formulas for BER as a function of SER, the SER for 4QAM and the SER fo
Let us derive the theoretical 16QAM bit error rate (BER) with Gray coded constellation mapping in additive white Gaussian noise conditions. Further, the Matlab/Octave simulation script can be used to confirm that the simulation is
16 Qam Matlab Code
in good agreement with theory. Gray coded bit mapping in 16-QAM modulation As we discussed 16 qam symbol error rate in the previous post on Binary to Gray code for 16QAM, the 4 bits in each constellation point can be considered as two 64 qam matlab code bits each on independent 4-PAM modulation on I-axis and Q-axis respectively. b0b1 I b2b3 Q 00 -3 00 -3 01 -1 01 -1 11 +1 11 +1 10 +3 10 +3 Table: Gray coded constellation mapping for http://dsp.stackexchange.com/questions/16240/deriving-ser-ber-for-4qam-16qam-and-32qam 16-QAM Figure: 16QAM constellation plot with Gray coded mapping Symbol Error and Bit Error probability As can be seen from the above constellation diagram, with Gray coded bit mapping, adjacent constellation symbols differ by only one bit. So, if the noise causes the constellation to cross the decision threshold, only 1 out of bits will be in error. So the relation between bit error and symbol error is, . Note: For very low value of http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/ , it may so happen that the noise causes the constellation to fall near a diagonally located constellation point. In that case, the each symbol error will cause two bit errors. Hence the need for approximate operator in the above equation. However, for reasonably high value of , the chances of such events are negligible. Bit energy and symbol energy As we learned from the post discussing Bit error rate for 16PSK, since each symbol consists of bits, the symbol to noise ratio k times the bit to noise ratio i.e, where, . 16QAM BER From the post detaling the derivation of 16QAM Symbol error rate, we know that the symbol error is, . Combining the above two equations, the bit error rate for Gray coded 16QAM in Additive White Gaussian Noise is . Simulation model The Matlab/Octave script performs the following: (a) Generation of random binary sequence (b) Assigning group of 4 bits to each 16-QAM constellation symbol per the Gray mapping (c) Addition of white Gaussian Noise (d) Demodulation of 16-QAM symbols and (e) De-mapping per decimal to Gray conversion (f) Counting the number of bit errors (g) Running this for each value of Eb/No in steps of 1dB. Click here to download : Script for computing 16QAM BER with Gray mapping Figure: Bit Error Rate plot for 16QAM modulation with G
used in WiMAX and LTE. It allows for transmission of 6 bits symbol which results in higher bit rate and spectral efficiency. The calculation http://www.raymaps.com/index.php/ber-64-qam-awgn/ of bit error rate of 64-QAM is a bit tricky as there are many different formulas available with varying degrees of accuracy. Here, we first calculate the bit error rate (BER) of 64-QAM using a simulation and then compare it to the theoretical curve for 64-QAM. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % FUNCTION TO CALCULATE 64-QAM BER USING SIMULATION % n_bits: Input, number error rate of bits % EbNodB: Input, energy per bit to noise PSD % ber: Output, bit error rate % Copyright RAYmaps (www.raymaps.com) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function[ber]= M_QAM(n_bits,EbNodB); M=64; k=log2(M) EbNo=10^(EbNodB/10); x=transpose(round(rand(1,n_bits))); h1=modem.qammod(M); h1.inputtype='bit'; h1.symbolorder='gray'; y=modulate(h1,x); n=randn(1,n_bits/k)+j*randn(1,n_bits/k); y=y+sqrt(7/(2*EbNo))*n.'; h2=modem.qamdemod(M) h2.outputtype='bit'; h2.symbolorder='gray'; h2.decisiontype='hard decision'; z=demodulate(h2,y); ber=(n_bits-sum(x==z))/n_bits return %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % CALCULATE 64-QAM BER USING FORMULA %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% EbNodB=0:2:16; EbNo=10.^(EbNodB/10); k=6; M=64; x=sqrt(3*k*EbNo/(M-1)); Pb=(4/k)*(1-1/sqrt(M))*(1/2)*erfc(x/sqrt(2)); semilogy(EbNodB,Pb) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Using bit error rate the above functions the BER of 64-QAM is calculated as shown below. Also shown is the constellation diagram of 64-QAM after addition of noise. 64-QAM Constellation 64-QAM BER It is observed that the theoretical curve almost overlaps the simulation results. There is only a very small difference at very low signal to noise ratio. The BER of 64-QAM at 16dB is approximately equal to the BER for QPSK at 8dB. Therefore the 64-QAM can only be used in scenarios where there is a very good signal to noise ratio. In this post we have used built in MATLAB functions for modulation and demodulation. In future posts we try to build up the simulation without using these functions! Post navigation ← OFDM Modulation and Demodulation (AWGN) - II BER of 64-QAM OFDM in AWGN → 3 thoughts on “Bit Error Rate of 64-QAM in AWGN” LINA says: May 20, 2016 at 5:15 am Hi there. May i know why can't i run the codes successfully? John says: December 7, 2011 at 8:20 am The constellation size is controlled b
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