64 Qam Error Rate
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used in WiMAX and LTE. It allows for transmission of 6 bits symbol which results in higher bit rate and spectral efficiency. The calculation bpsk bit error rate of bit error rate of 64-QAM is a bit tricky as there bit error rate for qpsk matlab code are many different formulas available with varying degrees of accuracy. Here, we first calculate the bit error rate 64 qam matlab code (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 of 16 qam bit error rate 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 the
Probability Of Error For 16 Qam
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 by the para
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64 Qam Modulation
Topic Teardown: Fed's Robo-Car Policy SLIDESHOW: EE Times Silicon 60: 2016's Emerging 16 qam symbol error rate Companies to Watch NEWS & ANALYSIS: GE Plugs into Industrial Internet NEWS & ANALYSIS: pMTJ Is Where the 16 qam ber matlab MRAM Action Is BLOG: Qualcomm Mobilizes in Embedded Processors Design How-To Symbol error rate for M-QAM modulation Krishna Pillai, www.dsplog.com5/21/2008 03:00 PM EDT 2 comments NO RATINGSLogin to Rate http://www.raymaps.com/index.php/ber-64-qam-awgn/ Tweet Quadrature Amplitude Modulation (QAM) schemes like 4-QAM (QPSK), 16-QAM and 64-QAM are used in typical wireless digital communications specifications like IEEE802.11a, IEEE802.16d. In this post we'll derive the probability of a symbol being in error for a general M-QAM constellation, given that the signal (symbol) to noise ratio is . Defining the general M-QAM constellation The number http://www.eetimes.com/document.asp?doc_id=1275567 of points in the constellation is defined as, where is the number of bits in each constellation symbol. In this analysis, it is desirable to restrict to an even number for the following reasons (Refer Sec 5.2.2 in [1]): Half the bits are represented on the real axis and half the bits are represented on the imaginary axis. The in-phase and quadrature signals are independent level Pulse Amplitude Modulation (PAM) signals. This simplifies the design of the mapper. 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. However, considering that typical implementations prefer the reduced complexity, let us keep this assumption. Average energy of an M-QAM constellation In a general M-QAM constellation where and are even, the alphabets used are: , where . For example, considering a 64-QAM () constellation, and the alphabets are . To compute the average energy of the M-QAM constellation: Find th
the transmission medium per time unit using a digitally modulated signal or a line code. The symbol rate is measured in baud (Bd) or symbols per second. In https://en.wikipedia.org/wiki/Symbol_rate the case of a line code, the symbol rate is the pulse rate in pulses per second. Each symbol can represent or convey one or several bits of data. The symbol rate is related to the gross bitrate expressed in bits per second. Contents 1 Symbols 1.1 Relationship to gross bitrate 1.2 Modems for passband transmission 1.3 Line codes for baseband transmission 1.4 Digital error rate television and OFDM example 1.5 Relationship to chip rate 1.6 Relationship to bit error rate 2 Modulation 2.1 Binary modulation 2.2 N-ary modulation, N greater than 2 2.3 Data rate versus error rate 3 Significant condition 4 See also 5 References 6 External links Symbols[edit] A symbol may be described as either a pulse in digital baseband transmission or a tone in passband bit error rate transmission using modems, representing an integer number of bits. A theoretical definition of a symbol is a waveform, a state or a significant condition of the communication channel that persists for a fixed period of time. A sending device places symbols on the channel at a fixed and known symbol rate, and the receiving device has the job of detecting the sequence of symbols in order to reconstruct the transmitted data. There may be a direct correspondence between a symbol and a small unit of data. For example, each symbol may encode one or several binary digits or 'bits'. The data may also be represented by the transitions between symbols, or even by a sequence of many symbols. The symbol duration time, also known as unit interval, can be directly measured as the time between transitions by looking into an eye diagram of an oscilloscope. The symbol duration time Ts can be calculated as: T s = 1 f s {\displaystyle T_{s}={1 \over f_{s}}} where fs is the symbol rate. A simple example: A baud rate of 1 kBd = 1,000 Bd is synonymous to a symbol rate