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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?
By how many decibels does this system underperform a binary antipodal signaling system with the same eb/N0 ?
Plot the constellation, and using the constellation, find the energy in each signal. What is the average signal energy and what is Ebavg?
From this result, determine the additional transmitted energy required in the 8-PSK signal to achieve the same error probability as the four-phase signal.
Digital information is to be transmitted by carrier modulation through an additive Gaussian noise channel with a bandwidth of 100 kHz and N0 = 10-10 W/Hz.
Determine the power spectral density of the transmitted signal s(t), assuming that the carrier frequency is f0 (assuming f0 >> 1/T ).
Determine the autocorrelation functions for the MSK and offset QPSK modulated signals .
The two noises n1 and n2 are arbitrary- not necessarily Gaussian, and not necessarily independent.
Determine the optimum detector for an AWGN channel and the optimum threshold, assuming that the signals are equally probable.
If the signals are equiprobable, express the error probability of the optimal detector in terms of the average SNR per bit.