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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.
Suppose that binary PSK is used for transmitting information over an AWGN with a power spectral density of ½ N0 = 10-10 W/Hz.
Determine the SNR required to achieve an error probability of 10-5.
Compare the power efficiency of this system with a 16-level PAM system.
Determine the three conditional probabilities of error: Pe given that s(t) was sent, Pe given that -s(t) was sent, and Pe given that 0 was sent.
Determine the autocorrelation and power density spectrum of the three-level sequence {Bn}.
Determine the average transmitter powers for the two signal constellations, and compare the two powers.
Determine a set of orthonormal functions for the four signals shown in Figure .
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