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...
Suppose a binary message is transmitted through a noisy channel. The transmitted signal S is equally likely to be 1 or-1, the noise N follows a normal distribution N(0,4), and the received signal is R-S + N. The receiver concludes that the signal is 1 when R > 0 and-1 when R<0. What is the error probability when one signal is transmitted? ·What is the error probability when one signal is transmitted if we triple the amplitude of the transmitted...
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...
5. A binary Z-channel is show in the figure. Assume the input is "0" with probability p and "1" with probability 1-p. (a) What can you say about the input bit if " is received? (b) Find the the probability that the input was "1" given that the output is "0" 0 Input Output 6. A transmitter randomly sends one of the messages in fa1, a2,.. ,an). The receiver either receives the transmitted message with probability p, or mistakenly receives...
(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...
7. The input U of binary communication channel is either -2.5 or +2.5 representing bit values b = 0 and b = 1 respectively, where P(b = 1) = 0.75. The channel output is given by V = U+N where “channel noise” N is a continuous random variable whose pdf is a symmetric triangular function in the range (-3, +3). Assume that U and N are independent. The receiver decodes the channel output to produces a bit value b as...
(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,...
Consider the problem of sending a binary message, 0 or 1, via a signal channel consisting of several stages where transmission through each stage is subject to a fixed probability of error, α ∈ (0,1). Assume X0 = 0 is the original signal that is sent and let Xn, be the signal received at the nth stage. Assume {Xn} is a Markov chain with transition probabilities P00 = P11 = 1−α, P01 = P10 = α Determine the probability that...