Probability density function of equiprobable signals
Please answer the folllowing question, consider the binary communication channel in which 0 and 1 are equally likely to be sent. The signal is given below. The receiver calculates the decision varibale R and applies the following decision rule. Find the expression for the porbability density function of R given that a 0 was transmitted.
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(25 points) A binary communication system transmits signals s,() (i1,2). The receiver samples the received signal r() s,()+n(t) at T and obtain the decision statistic r r(T)- a, -+A or a,-A with...
(25 points) A binary communication system transmits signals s,() (i1,2). The receiver samples the received signal r() s,()+n(t) at T and obtain the decision statistic r r(T)- a, -+A or a,-A with A>0 and n is the noise component. Assume that s,(1) and s,() are equally likely to be transmitted and the decision threshold is chosen as zero. If the noise component n is uniformly distributed over [-2, +2] and A-0.8, derive the expression of BER of this system. s,...
(25 points) A binary communication system transmits signals s,(0) (i1,2). The receiver samples the received signal r(t) s,()+n(t) at T and obtain the decision statistic r-r(T) s,(T)+ n(T)-a, +n,...
(25 points) A binary communication system transmits signals s,(0) (i1,2). The receiver samples the received signal r(t) s,()+n(t) at T and obtain the decision statistic r-r(T) s,(T)+ n(T)-a, +n, where the signal component is either a, = +A or a,--A with A >0 and n is the noise component. Assume that s (t) and s,() are equally likely to be transmitted and the decision threshold is chosen as zero. If the noise component n is uniformly distributed over [-2, +2]...
(25 points) A binary communication system transmits signals s,(0) (i1,2). The receiver samples the received signal r(t) s,()+n(t) at T and obtain the decision statistic r-r(T) s,(T)+ n(T)-a, +n,...
(25 points) A binary communication system transmits signals s,(0) (i1,2). The receiver samples the received signal r(t) s,()+n(t) at T and obtain the decision statistic r-r(T) s,(T)+ n(T)-a, +n, where the signal component is either a, = +A or a,--A with A >0 and n is the noise component. Assume that s (t) and s,() are equally likely to be transmitted and the decision threshold is chosen as zero. If the noise component n is uniformly distributed over [-2, +2]...
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...
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...
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...
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 3. A binary message either 0 or 1 is transmitted by wire. However, data sent...
Problem 3. A binary message either 0 or 1 is transmitted by wire. However, data sent over the wire is subject to channel noise disturbance. If x is the value sent (either 0 or 1), then the value received at the other end is R-x+x, where Ņ represents the noise. Assume that Ņ is a normal random variable with mean μ 0 and variance σ2-0.04. Assume that a message sent is equally likely to be 0 or 1. When the...
Problem 3. A binary message either 0 or 1 is transmitted by wire. However, data sent...
Problem 3. A binary message either 0 or 1 is transmitted by wire. However, data sent over the wire is subject to channel noise disturbance. If x is the value sent (either 0 or 1), then the value received at the other end is R-x+x, where Ņ represents the noise. Assume that Ņ is a normal random variable with mean μ 0 and variance σ2-0.04. Assume that a message sent is equally likely to be 0 or 1. When the...
Help me please! Thank you!! 1. Consider the signal set in Figure 1 for binary data...
Help me please! Thank you!!
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...
(25 points) A binary communication system transmits signals s,() (i1,2). The receiver samples the received signal r() s,()+n(t) at T and obtain the decision statistic r r(T)- a, -+A or a,-A with A>0 and n is the noise component. Assume that s,(1) and s,() are equally likely to be transmitted and the decision threshold is chosen as zero. If the noise component n is uniformly distributed over [-2, +2] and A-0.8, derive the expression of BER of this system. s,...
(25 points) A binary communication system transmits signals s,(0) (i1,2). The receiver samples the received signal r(t) s,()+n(t) at T and obtain the decision statistic r-r(T) s,(T)+ n(T)-a, +n, where the signal component is either a, = +A or a,--A with A >0 and n is the noise component. Assume that s (t) and s,() are equally likely to be transmitted and the decision threshold is chosen as zero. If the noise component n is uniformly distributed over [-2, +2]...
(25 points) A binary communication system transmits signals s,(0) (i1,2). The receiver samples the received signal r(t) s,()+n(t) at T and obtain the decision statistic r-r(T) s,(T)+ n(T)-a, +n, where the signal component is either a, = +A or a,--A with A >0 and n is the noise component. Assume that s (t) and s,() are equally likely to be transmitted and the decision threshold is chosen as zero. If the noise component n is uniformly distributed over [-2, +2]...
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...
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...
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...
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 3. A binary message either 0 or 1 is transmitted by wire. However, data sent over the wire is subject to channel noise disturbance. If x is the value sent (either 0 or 1), then the value received at the other end is R-x+x, where Ņ represents the noise. Assume that Ņ is a normal random variable with mean μ 0 and variance σ2-0.04. Assume that a message sent is equally likely to be 0 or 1. When the...
Problem 3. A binary message either 0 or 1 is transmitted by wire. However, data sent over the wire is subject to channel noise disturbance. If x is the value sent (either 0 or 1), then the value received at the other end is R-x+x, where Ņ represents the noise. Assume that Ņ is a normal random variable with mean μ 0 and variance σ2-0.04. Assume that a message sent is equally likely to be 0 or 1. When the...
Help me please! Thank you!!
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...
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