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Determine the value of the output of the matched filter at the sampling instant t = nTc.
A Hadamard matrix is defined as a matrix whose elements are ±1 and whose row vectors are pairwise orthogonal.
What is the optimum maximum-likelihood detector for the two possible transmitted signals?
Sketch a block diagram of the receiver (demodulator and detector) that employs noncoherent (envelope) detection.
If the data sequence is uncorrelated, determine and sketch the power density spectrum of the signal transmitted by DPSK.
Assuming that it is desired to transmit information at the rate of R bits/s, determine the required transmission bandwidth .
Three equiprobable messages m1, m2, and m3 are to be transmitted over an AWGN channel with noise power spectral density ½ N0.
Design an optimal matched filter receiver for this system. Carefully label the diagram and determine all the required parameters.
What is the expression for the threshold value rth such that forr > rth the optimal detector makes a decision in favor of s1(t)?
Assuming an antipodal signaling scheme (X = ±A) and a constant ? = 1, what is the optimal decision rule and the resulting error probability?
In a binary communication system two equiprobable messages s1 = (1, 1) and s2 = (-1, -1) are used.
Two equiprobable messages are transmitted via an additive white Gaussian noise channel with noise power spectral density of N0/2 = 1.
In a block diagram, give the precise specifications of the optimal receiver using matched filters. Label the block diagram carefully.
What is the best power allocation strategy by the transmitter,what is the optimal decision rule at the receiver, and what is the resulting error probability?
In the second path the signal is subject to a random amplification A and additive noise n2(t). The random variable A takes values ±1 with equal probability.
Suppose the signal s(t) is passed through a correlator that correlates the input s(t) with s(t).
Express this error probability in terms of a single integral, and thus show that the symbol error probability for a biorthogonal signal set.
Suppose that this signal is corrupted by AWGN, which is represented by its equivalent lowpass form z(t).
Let Pe1 denote the error probability in part 2 when an optimal receiver is designed for the new noise power spectral density N1.
Each set may be used to transmit one of four equally probable messages over an additive white Gaussian noise channel.
Determine the optimum decision boundaries for the detector, assuming that the SNR is sufficiently high that errors occur only between adjacent points.
Determine the relative amplitudes of the signals for the two carriers so that eb/N0 for the two channels is identical.
When the additive noise at the input to the demodulator is colored, the filter matched to the signal no longer maximizes the output SNR.
Consider a digital communication system that transmits information via QAM over a voice-band telephone channel at a rate of 2400 symbols/s.
If Gray coding is used, what is the bit error probability in terms of the same parameters used in part 1?