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Unformatted text preview: ECE 154B Homework #6 Due March 7, 2007 1. Making the usual assumptions of equally likely signals in AWGN and an optimal receiver, it can be shown that the probability of symbol error for M/2 orthogonal signals of energy E and their negatives is given as: P[symbol error] = 1 - π 2 1 dx x Q E x M N 2 2 2 )) ( 2 1 ]( ) 2 ( 2 1 exp[- ∞--- ∫ A special case of this for M=4 is the case of QPSK where the 4 signals are: + sin( ϖ t), -sin( ϖ t), + cos( ϖ t), and - sin( ϖ t). For this case, we have derived a formula in class for the probability of symbol error. Show how the above formula reduces to the formula we derived in class. 2. For the case of 4 orthogonal signals and their negatives (i.e., M=8) how should we map 3 binary digits to the 8 waveforms to minimize the probability of binary error at high signal to noise ratio? 3. Do a simulation that simulates the situation described in problem 2. Show how a poor mapping of 3 binary digits to the 8 waveforms results in a larger probability of binary error...
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- Winter '07
- Signal-to-noise ratio, Rayleigh fading, AWGN, binary error, binary error probability