Consider a system in which the average normalized power at t

Consider a system in which the average normalized power at the transmitter must 6 volts^2 or less. The system must be designed to transmit over a bandpass channel that passes frequencies in the range: 200 kHz lessthanorequalto f lessthanorequalto 600 kHz The attention is such that only 80% of the transmitted signal\'s power is present at the input of the receiver. The system operates in thermal noise that has a power spectral density of: N_0/2 = 0.9 times 10^-5 volts^2/Hz. The system requirements are a transmission speed of: 50,000 bits/sec, and a probability of error: P_b = 10^-4 or less. What is the binary modulation technique you recommend? Justify your answer Can the transmission speed be increases without exceeding the bandwidth of the channel (assume at least 95% in band power)

Solution

1 C o h e r e n t B i n a r y P S K • In a coherent binary PSK system, the pair of signals, s1(t) and s2(t), used to represent binary symbols 1 and 0, respectively, are defined by where 0 t < Tb and Eb is the transmitted signal energy per hit. • In order to ensure that each transmitted bit contains an integral number of cycles of the carrier wave, the carrier frequency fc = nc /Tb for some fixed integer nc . • A pair of sinusoidal waves that differ only in a relative phaseshift of 180 degrees, as defined above, are referred to as antipodal signals.

• A coherent binary PSK system is therefore characterized by having a signal space that is one-dimensional (i.e., N = 1) and with two message points (i.e., M = 2). The coordinates of the message points equal