Reference constellation for modulating and demodulating the information. In the vector simulation model for the coherent detection, the transmitter and receiver agree on the same Generally the two main categories of detection techniques, commonly applied for detecting the digitally modulated data are coherent detection and non-coherent detection.
#Matlab 64 qam constellation code#
NGray=np.reshape(a,(M)) # reshape to 1xM - Gray code walk on KMap OddRows=np.arange(start = 1, stop = D ,step=2) # identify alternate rows N = np.arange(0,M) # Sequential address from 0 to M-1 (1xM dimension)Ī = np.asarray() #convert linear addresses to Gray codeĭ = np.sqrt(M).astype(int) #Dimension of K-Map - N x N matrixĪ = np.reshape(a,(D,D)) # NxN gray coded matrix Raise ValueError('Only square MQAM supported. S=ref(d) %map information symbols to modulated symbolsįull Matlab code available in the book Digital Modulations using Python class QAMModem(Modem): Ref=constructQAM(M) %construct reference constellation If(((M˜=1) & ˜mod(floor(log2(M)),2))=0), %M not a even power of 2Įrror('Only Square MQAM supported. % output and ref represents reference constellation that can be used in demod % vector d contains symbols whose values range 1:M. % using MQAM modulation, where M specifies order of M-QAM modulation and
%=mqam_modulator(M,d) modulates the symbols defined by the vector d %Function to MQAM modulate the vector of data symbols - d Matlab codeįull Matlab code available in the book Digital Modulations using Matlab – build simulation models from scratch function =mqam_modulator(M,d) The resulting ideal constellations for Gray coded 16-QAM and 64-QAM are shown in Figure 1. Matlab code for dynamically generating M-QAM constellation points based on Karnaugh map Gray code walk is given below. Thus for constructing a M-QAM constellation, the PAM dimension is set as. For example, 16-QAM constellation points can be generated from two 4-PAM signals, similarly the 64-QAM constellation points can be generated from two 8-PAM signals.įor generating 16-QAM, the dimension D of PAM is set to. In one of the earlier articles, I have discussed the method of constructing constellation for rectangular QAM modulation using Karnaugh-map walks, where the inherent property of Karnaugh-maps is exploited to construct Gray coded QAM symbols.Īny rectangular QAM constellation is equivalent to superimposing two Amplitude Shift Keying (ASK)signals (also called Pulse Amplitude Modulation – PAM) on quadrature carriers. Rectangular (symmetric or square) constellations are the preferred choice of implementation due to its simplicity in implementing modulation and demodulation. There exist other constellation shapes (like circular, triangular constellations) that are more efficient (in terms of energy required to achieve same the error probability) than the standard rectangular constellation. The given simulation code is very generic, and it plots both simulated and theoretical symbol error rates for all M-QAM modulation techniques. For more information, see the Use Pulse Shaping on 16-QAM Signal example.Ĭalculate the SNR when the channel has an E b / N 0 of 10 dB.A generic complex baseband simulation technique, to simulate all M-ary QAM modulation techniques is given here. The sps variable is not significant in this example but makes extending the example to use pulse shaping easier.
Convert the ratio of energy per bit to noise power spectral density ( E b / N 0) to an SNR value for use by the awgn function. The modulated signal passes through the channel by using the awgn function with the specified signal-to-noise ratio (SNR). For an example that uses Gray coding with phase-shift keying (PSK) modulation, see Gray-Coded Binary Ordering. Later in this example constellation diagrams show the natural and Gray binary symbol mapping.įor more information on modulation functions, see Digital Modulation. The modulation operation outputs complex column vectors containing values that are elements of the 16-QAM signal constellation. DataMod = qammod(dataSymbolsIn,M, 'bin') % Binary coding with phase offset of zeroĭataModG = qammod(dataSymbolsIn,M) % Gray coding with phase offset of zero
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