# Consider a QPSK transmission system where the baseband transmit pulse hTx has bandwidth is the…

Consider a QPSK transmission system where the baseband transmit pulse hTx has bandwidth

is the symbol period) and the carrier frequency is 100 MHz. The modulated signal is amplified and sent through an isotropic antenna (unit gain) to the radio channel. The transmit amplifier has an available power of 2 mW and a resistive output impedance of 10 . The antenna has input impedance given by the series of a resistance R = 10  and an inductance L = 31.8 nH. All the input power is then radiated. At the receiver the isotropic receive antenna has noise temperature 300 K and is matched for the maximum power transfer to the QPSK demodulator. The demodulator noise figure is 4 dB.

a) Represent in a graph the frequency allocation of the waveforms of the digital  and evaluate the channel bandwidth required for the transmission.

b) Represent the electrical scheme of the connection amplifier-antenna at the transmitter. Evaluate the radiated power in dBm, assuming a constant antenna impedance over the useful band.

c) Determine the maximum distance for the receiver to guarantee a symbol error probability lower than 2 · 10−6.

d) Given the same transmit power and symbol period, how could one modify the constellation to achieve a distance greater than the one of point c), keeping the same system performance? What is the price to pay for this change?