mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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56 MATCHED FILTERING<br />
2.7 Suppose we have the MIMO scenario in which c = 1, d = 0, e = 2, and<br />
/ = 1. Also, suppose the two received values are r\ — —1.2 and r 2 = —0.8. The<br />
noise power is σ 1 = 100.<br />
a) What is the value of the MF decision variable z\ for si?<br />
b) What is the SINK of zi?<br />
c) What is the value of the MF decision variable z 2 for s 2 ?<br />
d) What is the SINR of ¿ 2 ?<br />
2.8 Suppose we have the dispersive scenario in which c = —2 and d = 1. Suppose<br />
QPSK is sent and r\ = — 3 + j and r 2 = 2 + j'3.<br />
a) What is the value for the MF decision variable for si?<br />
b) What most likely is the I component of «i?<br />
c) What most likely is the Q component of «i?<br />
The math<br />
2.9 Consider a BPSK system with root-Nyquist pulse shaping. Suppose the<br />
medium consists of a single path with delay To = 0 and coefficient po- There is<br />
also AWGN with one-sided PSD 7V () . Assume the receiver uses a matched filter.<br />
a) Express the amplitude of the decision variable in terms of Ef„ N n , and p () .<br />
b) What is the variance of the noise on the decision variable?<br />
c) What is the output SNR?<br />
d) If po = 3 and Et/No = 0.1, what is the probability of a bit error in terms<br />
of the erfc function? If possible, evaluate this to get a numerical result as<br />
well.<br />
2.10 Consider a BPSK system with root-Nyquist pulse shaping. Suppose the<br />
medium consists of a two paths with delays To = 0, τχ = T and coefficients po and<br />
Pi. There is also AWGN with one-sided PSD iVo. Assume the transmitter sends<br />
only one symbol and the receiver uses a matched filter.<br />
a) Express the amplitude of the decision variable in terms of £¡,, No, and po.<br />
b) What is the variance of the noise on the decision variable?<br />
c) What is the output SNR?<br />
d) If po = 3, pi = 2 and Eb/N tt = 0.1, what is the probability of a bit error<br />
in terms of the erfc function? If possible, evaluate this to get a numerical<br />
result as well.<br />
2.11 Consider a BPSK system with root-Nyquist pulse shaping. Suppose the<br />
transmitter sends each symbol twice before sending the next symbol (i.e., s 2 = s\,<br />
Si = S;i, etc.). Suppose the medium consists of one path with delay To = 0 and<br />
coefficient p () . There is also AWGN with one-sided PSD ΛΌ. Assume the receiver<br />
uses a matched filter.<br />
a) Express the matched filter for si in terms of r(t), p(t), T, and pob)<br />
Express the amplitude of the decision variable in terms of Ef,, N», and poc)<br />
What is the variance of the noise on the decision variable?<br />
d) What is the output SNR?
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