BER Vs Eb/No for QPSK and BER were discussed in the previous articles.Click below to see the posts if you have missed them earlier. (BER Vs Eb/N0 for QPSK modulation over AWGN), (BER Vs Eb/N0 for BPSK modulation over AWGN) BER Vs Eb/No for 8-PSK is discussed here. A baseband simulation model for 8-PSK modulation is given below. Simulation Model: (click to enlarge the figure) Transmitter: A complex baseband M-PSK signal is represented by $$ s_{n}(t)=\sqrt{\frac{2E_{s}}{T}}cos(\omega t+\theta_{n} ) \mid n=1,2,..M $$ where \(E_s\) is the symbol energy of each M-PSK Symbol, \(T\) is the bit period, θn is the phase shift for each of the symbol. For 8-PSK, \(M=8\). In 8PSK modulator, every 3 input data bits are mapped to one complex-valued 8PSK symbol (where as in QPSK 2 input bits are mapped to one complex-valued QPSK symbol). Each symbol is gray coded prior to mapping them to the 8-PSK constellation (this is to allow only one bit change in the constellation, there by avoiding abrupt phase changes in the constellation which may lead to addition errors in the receiver) . In 8PSK there are eight possible symbols that can be transmitted. We will use eight different phases ( 22.5°, 67.5°, 112.5°, 157.5°, 202.5°, 247.5°, 292.5°, 337.5° ) to represent each 8-PSK symbol. Each symbol is 45° away from adjacent symbols (see the constellation diagram below). The 8PSK symbols are transmitted over an AWGN channel that adds Gaussian Noise to the transmitted symbol. Receiver: The demodulation process is performed by finding one of the eight […]
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