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16. (10 points) Bipolar pulse signals, s(t) (i -1,2), of amplitude +1 V are received in...
4.9. A system using matched filter detection of cqually likely BPSK signals, s(t) V2E Tcos o...
4.9. A system using matched filter detection of cqually likely BPSK signals, s(t) V2E Tcos o rand s2(1)-V2 E/T cos (oo t + π), operates in AwGN with a received E,N, of 6.8 dB. Assume that E{z(T) = ± VE (a) Find the minimum probability of bit error, PB, for this signal set and E,/No (b) If the decision threshold is γ= 0.1 VE, find PB. (c) The threshold of γ = 0.1 VE is optimum for a particular set...
A bipolar binary signal, si(t), is a +1- or -1- V pulse during the interval (0, T). AWGN having two-sided power spectra...
A bipolar binary signal, si(t), is a +1- or -1- V pulse during the interval (0, T). AWGN having two-sided power spectral density of 0.005 W/Hz is added to the signal. If the received signal is detected with a matched filter, determine the maximum bit rate that can be sent with a bit error probability ofPB< 10
A bipolar binary signal, si(t), is a +1- or -1- V pulse during the interval (0, T). AWGN having two-sided power spectral density...
Consider a binary modulation scheme in which the transmitted signals are 81-0 and s2=A with prior...
Consider a binary modulation scheme in which the transmitted signals are 81-0 and s2=A with prior probabilities P the received signal is p and P2 1-p. These signals are sent over an AWGN channel and r=si + n for i = 1,2 where n is a Gaussian noise with zero mean and variance No/2. a) Determine the MAP decision regions for this signaling b) Express the error probability in terms of Q-functions.
Consider a binary modulation scheme in which the...
Problem 2 Consider a general QAM scheme with transmitted symbol s(t) R { pulse shape p()71(7,/2)....
Problem 2 Consider a general QAM scheme with transmitted symbol s(t) R { pulse shape p()71(7,/2). a(n) Apr(t - nT) exp (j2 fet)}, where the t-T./2 Let the constellation be a(n)e {2,-2,2j,-2j,0. 1. What is the appropriate matched filter to apply for this signal. Draw the optimum receiver 2. What is the average energy of the constellation, i.., E,? 3. Assume the the received signal is r(t)= s(t) +n(t), where n(t) is AWGN with variance 1. Find the error probability...
1) Handout problem 7.7. (Hint: Write down the expression for the average probability of error P,,...
1) Handout problem 7.7. (Hint: Write down the expression for the average probability of error P,, which will involve Po,P1,fo 1),。。), and the threshold λ, and then minimize P, by setting dP/άλ-O. Use the Fundamental Theorem of Calculus to compute dP/d.) Problem 7.7 In a binary PCM system, symbols 0 and 1 have a priori probabilities Po and p1, respectively. The conditional probability density function of the ran- dom variable Y (with sample value y) obtained by sampling the matched...
A digital communication system uses the signals si(t) and s2(t) shown in Fig. 1 to t equally like...
A digital communication system uses the signals si(t) and s2(t) shown in Fig. 1 to t equally likely bits '0' and '1', respectively. The signaling duration is 4 seconds. The receiver uses a filter h(t) shown in Fig. 2 s1 (t) s2(t) 0 Figure 1: Set of signals in Problem 1 h(t) 0 Figure 2: h(t) in Problem 1 (a) Determine the parameter ri for this system. HINT: Remember that ri is equal to this convolution 81(t) * h(t) evaluated...
3. (30 points) A binary communication system transmits signals s(t) (i 1,2). The receiver samples the received signal r(t) s(t) + n(t) at T and obtain the decision statistic r(T) S (T) n(T) a + n...
3. (30 points) A binary communication system transmits signals s(t) (i 1,2). The receiver samples the received signal r(t) s(t) + n(t) at T and obtain the decision statistic r(T) S (T) n(T) a + n, where the signal component is either an +A or a2-A with A >0 and n is the noise component. Assume that s1 (t) and s2(t) are equally likely to be transmitted and the decision threshold is chosen as zero. If A 1 and the...
4.9. A system using matched filter detection of cqually likely BPSK signals, s(t) V2E Tcos o rand s2(1)-V2 E/T cos (oo t + π), operates in AwGN with a received E,N, of 6.8 dB. Assume that E{z(T) = ± VE (a) Find the minimum probability of bit error, PB, for this signal set and E,/No (b) If the decision threshold is γ= 0.1 VE, find PB. (c) The threshold of γ = 0.1 VE is optimum for a particular set...
A bipolar binary signal, si(t), is a +1- or -1- V pulse during the interval (0, T). AWGN having two-sided power spectral density of 0.005 W/Hz is added to the signal. If the received signal is detected with a matched filter, determine the maximum bit rate that can be sent with a bit error probability ofPB< 10
A bipolar binary signal, si(t), is a +1- or -1- V pulse during the interval (0, T). AWGN having two-sided power spectral density...
Consider a binary modulation scheme in which the transmitted signals are 81-0 and s2=A with prior probabilities P the received signal is p and P2 1-p. These signals are sent over an AWGN channel and r=si + n for i = 1,2 where n is a Gaussian noise with zero mean and variance No/2. a) Determine the MAP decision regions for this signaling b) Express the error probability in terms of Q-functions.
Consider a binary modulation scheme in which the...
Problem 2 Consider a general QAM scheme with transmitted symbol s(t) R { pulse shape p()71(7,/2). a(n) Apr(t - nT) exp (j2 fet)}, where the t-T./2 Let the constellation be a(n)e {2,-2,2j,-2j,0. 1. What is the appropriate matched filter to apply for this signal. Draw the optimum receiver 2. What is the average energy of the constellation, i.., E,? 3. Assume the the received signal is r(t)= s(t) +n(t), where n(t) is AWGN with variance 1. Find the error probability...
1) Handout problem 7.7. (Hint: Write down the expression for the average probability of error P,, which will involve Po,P1,fo 1),。。), and the threshold λ, and then minimize P, by setting dP/άλ-O. Use the Fundamental Theorem of Calculus to compute dP/d.) Problem 7.7 In a binary PCM system, symbols 0 and 1 have a priori probabilities Po and p1, respectively. The conditional probability density function of the ran- dom variable Y (with sample value y) obtained by sampling the matched...
A digital communication system uses the signals si(t) and s2(t) shown in Fig. 1 to t equally likely bits '0' and '1', respectively. The signaling duration is 4 seconds. The receiver uses a filter h(t) shown in Fig. 2 s1 (t) s2(t) 0 Figure 1: Set of signals in Problem 1 h(t) 0 Figure 2: h(t) in Problem 1 (a) Determine the parameter ri for this system. HINT: Remember that ri is equal to this convolution 81(t) * h(t) evaluated...
3. (30 points) A binary communication system transmits signals s(t) (i 1,2). The receiver samples the received signal r(t) s(t) + n(t) at T and obtain the decision statistic r(T) S (T) n(T) a + n, where the signal component is either an +A or a2-A with A >0 and n is the noise component. Assume that s1 (t) and s2(t) are equally likely to be transmitted and the decision threshold is chosen as zero. If A 1 and the...
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