Such a channel is also referred to as a Flat Fading Channel. A single tap channel means that it does not introduce any Inter Symbol Interference (ISI). It has an amplitude which is Rayleigh distributed and a phase which is Uniformly distributed. The term Rayleigh Fading as used above means a single tap channel that varies from one symbol to the next. Rayleigh Fading is a commonly used term in simulation of Digital Communication Systems but it tends to differ in meaning in different contexts. Lastly we explain some of the terms used above. As with the AWGN case each additional bit per symbol requires about 1.5-2 dB in signal to ratio to achieve the same BER.Īlthough not shown here similar behavior is observed for higher order modulation schemes such as 1024-QAM and 4096-QAM (the gap in the signal to noise ratio for the same BER is increased to about 5dB). All modulation schemes use Gray coding which gives a few dB of margin in the BER performance. The bit error rates of four modulation schemes 4-QAM, 16-QAM, 64-QAM and 256-QAM are shown in the figure above. % EbNodB: Input, energy per bit to noise power spectral density % FUNCTION THAT CALCULATES THE BER OF M-QAM IN RAYLEIGH FADING The inputs are the number of bits to be passed through the channel, the alphabet size and the Energy per Bit to Noise Power Spectral Density in dB respectively whereas the output is the bit error rate (BER). The function “QAM_fading” has three inputs, ‘n_bits’, ‘M’, ‘EbNodB’ and one output ‘ber’. The complex random channel coefficient so generated has an amplitude which is Rayleigh distributed and a phase which is uniformly distributed. As usual the fading channel introduces a multiplicative effect whereas the AWGN is additive. The one-tap Rayleigh fading channel is generated from two orthogonal Gaussian random variables with variance of 0.5 each. We now discuss the BER performance of M-QAM in Rayleigh fading. Selected BibliographyĮTSI Standard EN 300 744: Digital Video Broadcasting (DVB) Framing structure, channel coding and modulation for digital terrestrial television, European Telecommunications Standards Institute, Valbonne, France, 1997.We have previously discussed the bit error rate (BER) performance of M-QAM in AWGN. This approach makes derivation of soft decisions easy for any signal constellation through the use of the built-in block. Noise variance needs to be provided and it is computed using the received signal and the signal generated by the DVB-T 64-QAM Mapper. In-phase and quadrature phase signal components are extracted after appropriately scaling the received signal, and then they are shifted to obtain soft decisions for various bits.Īlternative: In the alternative form, the built-in Rectangular QAM Demodulator block is configured to compute exact bitwise log-likelihood ratios (LLRs). Original: In the original form, soft decisions are computed using a subsystem-based implementation.
![matlab 64 qam matlab 64 qam](http://www.dsplog.com/db-install/wp-content/uploads/2008/04/64qam_constellation_plot.png)
To see how the alternative version implements the 64-QAM Demapper, compare the alternative DVB-T 64-QAM Demapper subsystem in commdvbt_alt example with the original DVB-T 64-QAM Demapper subsystem in the commdvbt example. To examine the performance of the example, use the sink blocks that are included in it, listed in the table below. Due to this the receive delay for the 'outer' error rate calculation block is a total of 6 + 11 = 17 frames. Thus the total delay for the model excluding Convolutional Interleaving/Deinterleaving is 9003+136+653 = 9792 which is equal to 6 frames as the frame size at the 'inner' Error rate calculation block is 1632.Ĭonvolutional Interleaving/Deinterleaving with 12 rows of shift registers adds a delay of 11 frames. Rate 3/4 coding also causes the 12004 delay to manifest as 12004*3/4 = 9003. In order to align the actual codewords before feeding into the Convolutional Deinterleaver an extra delay of 1632-979 = 653 samples is added. With a traceback depth of 136, the Viterbi decoder also adds a further delay of 136, bringing the total delay to 843+136 = 979.
![matlab 64 qam matlab 64 qam](https://it.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/40714/versions/1/screenshot.png)
Since 2176 is the input frame size to the Viterbi Decoder mod(12004,2176) results in a delay of 1124 which corresponds to 1124*3/4 = 843 samples due to rate 3/4 coding. This results in a delay of 12004 samples. 2176 to 756 resulting in 756 sample delayħ56 to 9072 resulting in 9072 sample delayħ56 to 2176 resulting in 2176 sample delay