![1. Consider the signal set in Figure 1 for binary data transmission over a channel disturbed by AWGN. The noise is zero-mean and has two-sided PSD No/2. As usual, si(t) is used for the transmission of bit 0 and s2(t) is for the transmission of bit 1. Furthermore, the two bits are equiprobable. Si CC) s2(t) .A 0 Figure 1: A binary signal set, considered in Problem 1 Find and draw an orthonormal basis {фі (t),F2(t)) for the signal set. (b) Draw the signal space diagram and the optimum decision regions. Write the expression for (c) Draw the block diagram of the receiver that implements the optimum decision rule in (b). (o) Draw the block diagram of the receiver that implements the optimum decision rule in (b) the optimum decision rule. 1 volt and assume that No 10-3 watts/hertz. What is the maximum bit rate that 10-6 can be sent with a probability of error P(error] (e) Draw the block diagram of an optimum receiver that uses only one correlator or one matched filter. average energy is maintained at AT/2 but the probability of error is as small as possible. Explain (f) Assume that signal s1(t) is fixed. However, you can change s2(t). Modify it so that the](http://img.homeworklib.com/questions/60e906c0-b2b7-11ec-b59a-ed3feb59401c.png?x-oss-process=image/resize,w_560)
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1. Consider the signal set in Figure 1 for binary data...
1. A 4-ary signal set is given as So(t)-0,0StsT SI(t)-A cos(oot), OStsT Si(t)A sin(oot) + A...
1. A 4-ary signal set is given as So(t)-0,0StsT SI(t)-A cos(oot), OStsT Si(t)A sin(oot) + A cos(oot), 0StsT Assume (oT = 2m for some integer n. The signals are transmitted over an AWGN with noise power spectral density = N-2. The receiver uses the ML decision rule (ie, he assumes all signals are equiprobable) Choose a suitable set of Orthonormal basis functions and find (and sketch) the geometric representation of this signal set (called signal constellation). Clearly identify the decisions...
Problem 4 A base-band digital communication system using binary signals shown in the Figure for transmission...
Problem 4 A base-band digital communication system using binary signals shown in the Figure for transmission of two equiprob able messages. The transmitted signal is s(t), i e {1,2} and the recieved signal is r(t) s(t)+n(t), where nit) is the AWGN with power-spectral density No/2. 1. In a block diagram, give the precise specifications of the optimal receiver. What are the characteristics of the matched filter and the sampler and decision device? 2. Find the error probability of the optimal...
1. Let us consider a digital binary communication system, in which the fol- lowing signal s1(t)...
1. Let us consider a digital binary communication system, in which the fol- lowing signal s1(t) is transmitted for '0' and signal s2(t) is transmitted for '1' and these two signals are equal probability P('O' is transmitted) P(1' is transmitted). For these two signals and their correspond- ing basis functions, answer the following questions [40 points -2 0t<0.5; 0<t<0.5 -1 0.5 <t< 1 2 s2(t) -1 0.5<t1. s1(t) otherwise 0 otherwise 0 0<t<0.5; -1 0.5 <t1. otherwise 1 10t<1 0...
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...
3. (40 points) A binary communication system transmits signals s (0) (i = 1, 2). The...
3. (40 points) A binary communication system transmits signals s (0) (i = 1, 2). The receiver samples the received signal r(t) = s(t)+ n(t) at T and obtain the decision statistic r =r(T) = S(T) + n(T) = a, un, where the signal component is either a = + A or a, = -A with A >0 and n is the noise component. Assume that s (6) and s(l) are equally likely to be transmitted and the decision threshold...
9.1-1 In a baseband binary transmission, binary digits are transmitted by using A p(t) 0t<T -A...
9.1-1 In a baseband binary transmission, binary digits are transmitted by using A p(t) 0t<T -A p(t) 0t< Th sending 1 sending 0 The bit duration is Th second, and the pulse shape is 2t p(t) = 1 - Ть 0 tT Here data bits 0 and 1 are equally likely. The channel noise is AWGN with power spectrum N/2. (a) Find the optimum receiver filter h(t) for sampling instant tm = Th and sketch h(t) in the time domain....
Problem 1: A baseband digital communication system employs the signals shown below (Figure 1) for transmission....
Problem 1: A baseband digital communication system employs the signals shown below (Figure 1) for transmission. The channel has no attenuation and the noise is AWGN with power-spectral density NO/2. The probability of transmitting sı(t) is twice that of sz(t). S1() T12 O TV2 T Figure 1 2 a) Find an appropriate orthonormal basis for the representation of the signals. 7 b) Plot the constellation diagram in term of average symbol power. c) Draw the decision regions assuming equally likely...
Please help me these questions of "Principles of Communications" subject. Thanks in advance! Problem 2: PCM syst...
Please help me these questions of "Principles of Communications"
subject. Thanks in advance!
Problem 2: PCM system (40 points)coo h Consider a polar binary PCM system with number of bits per sample v 8 and the 4 KHz. Assumed that the channel is AWGN. voice bandwidth a) Assumed that one voice signal is transmitted using above PCM system, find the bit rate at the output of PCM transmitter and the minimum channel bandwidth. b) Assumed that 24 voice signals are...
Please With recognizable hand writing. Thank you. Question 2. (40 Points) Consider a BPSK modulation with...
Please With recognizable hand writing. Thank you.
Question 2. (40 Points) Consider a BPSK modulation with 2 signals: 2 where ??(t) and ?1 (t) for t E 10, T,l form a set of orthonormal basis functions. Signals so(t) and si(t) are equiprobable. We suppose that the transmission channel introduces an additive white Gaussian noise n(t). Thus, the received signal is given by r(t) s(t)+n(t), where the additive white Gaussian noise has power spectral density No/2. toT Y-X+N rit) a(t)+n(t) Figure...
Problem 6.15 The received signal in an on-off keyed digital communication system is given by (t)n(t)...
Problem 6.15 The received signal in an on-off keyed digital communication system is given by (t)n(t) 1 sent n(t) 0 sent where n is AWGN with PSD σ2-N0/2, and s(t)-A(1-14)1(-1,11 (t), where A > 0, The received signal is passed through a filter with impulse response h(t).) to obtain z(t)(yh)(t) Remark: It would be helpful to draw a picture of the system before you start doing the calculations (a) Consider the decision statistic Z z(0) 1). Specify the conditional distribution...
1. A 4-ary signal set is given as So(t)-0,0StsT SI(t)-A cos(oot), OStsT Si(t)A sin(oot) + A cos(oot), 0StsT Assume (oT = 2m for some integer n. The signals are transmitted over an AWGN with noise power spectral density = N-2. The receiver uses the ML decision rule (ie, he assumes all signals are equiprobable) Choose a suitable set of Orthonormal basis functions and find (and sketch) the geometric representation of this signal set (called signal constellation). Clearly identify the decisions...
Problem 4 A base-band digital communication system using binary signals shown in the Figure for transmission of two equiprob able messages. The transmitted signal is s(t), i e {1,2} and the recieved signal is r(t) s(t)+n(t), where nit) is the AWGN with power-spectral density No/2. 1. In a block diagram, give the precise specifications of the optimal receiver. What are the characteristics of the matched filter and the sampler and decision device? 2. Find the error probability of the optimal...
1. Let us consider a digital binary communication system, in which the fol- lowing signal s1(t) is transmitted for '0' and signal s2(t) is transmitted for '1' and these two signals are equal probability P('O' is transmitted) P(1' is transmitted). For these two signals and their correspond- ing basis functions, answer the following questions [40 points -2 0t<0.5; 0<t<0.5 -1 0.5 <t< 1 2 s2(t) -1 0.5<t1. s1(t) otherwise 0 otherwise 0 0<t<0.5; -1 0.5 <t1. otherwise 1 10t<1 0...
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...
3. (40 points) A binary communication system transmits signals s (0) (i = 1, 2). The receiver samples the received signal r(t) = s(t)+ n(t) at T and obtain the decision statistic r =r(T) = S(T) + n(T) = a, un, where the signal component is either a = + A or a, = -A with A >0 and n is the noise component. Assume that s (6) and s(l) are equally likely to be transmitted and the decision threshold...
9.1-1 In a baseband binary transmission, binary digits are transmitted by using A p(t) 0t<T -A p(t) 0t< Th sending 1 sending 0 The bit duration is Th second, and the pulse shape is 2t p(t) = 1 - Ть 0 tT Here data bits 0 and 1 are equally likely. The channel noise is AWGN with power spectrum N/2. (a) Find the optimum receiver filter h(t) for sampling instant tm = Th and sketch h(t) in the time domain....
Problem 1: A baseband digital communication system employs the signals shown below (Figure 1) for transmission. The channel has no attenuation and the noise is AWGN with power-spectral density NO/2. The probability of transmitting sı(t) is twice that of sz(t). S1() T12 O TV2 T Figure 1 2 a) Find an appropriate orthonormal basis for the representation of the signals. 7 b) Plot the constellation diagram in term of average symbol power. c) Draw the decision regions assuming equally likely...
Please help me these questions of "Principles of Communications"
subject. Thanks in advance!
Problem 2: PCM system (40 points)coo h Consider a polar binary PCM system with number of bits per sample v 8 and the 4 KHz. Assumed that the channel is AWGN. voice bandwidth a) Assumed that one voice signal is transmitted using above PCM system, find the bit rate at the output of PCM transmitter and the minimum channel bandwidth. b) Assumed that 24 voice signals are...
Please With recognizable hand writing. Thank you.
Question 2. (40 Points) Consider a BPSK modulation with 2 signals: 2 where ??(t) and ?1 (t) for t E 10, T,l form a set of orthonormal basis functions. Signals so(t) and si(t) are equiprobable. We suppose that the transmission channel introduces an additive white Gaussian noise n(t). Thus, the received signal is given by r(t) s(t)+n(t), where the additive white Gaussian noise has power spectral density No/2. toT Y-X+N rit) a(t)+n(t) Figure...
Problem 6.15 The received signal in an on-off keyed digital communication system is given by (t)n(t) 1 sent n(t) 0 sent where n is AWGN with PSD σ2-N0/2, and s(t)-A(1-14)1(-1,11 (t), where A > 0, The received signal is passed through a filter with impulse response h(t).) to obtain z(t)(yh)(t) Remark: It would be helpful to draw a picture of the system before you start doing the calculations (a) Consider the decision statistic Z z(0) 1). Specify the conditional distribution...
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