Suppose a wireless transmission is carried out in a fading channel, where the delay spread is = 10 us. The time duration of a symbol is Tg = 100us, carrier frequency is 800MHz, and the receiver is moving at a speed at 40 km/h. (Hint: The relationship between coherence time and Doppler spread is Tct = 199 fa, the coherence bandwidth and delay spread is Be = 1, and the signal bandwidth is determined by W = 1/T..) Calculate the Doppler frequency fd, coherence time and coherence band- width. (6 points) 1.2 Specify whether the system is in flat fading or frequency fading? Is it in slow fading or fast fading? (6 points) 1.3 Briefly explain the physical causes of delay spread and Doppler frequency spread. (6 points) 1.4 Suppose BPSK modulation is used and the path loss model between the transmitter and the receiver is PL = (h)?d-?, where is the signal wave- length and d is the distance between the transmitter and the receiver. The transmit power is limited to 30dBm. The applications require a BER of 0.01 percent. The receiver frontend has a noise figure of 5dB. What is the maximum range between the transmitter and the receiver? (8 points) Hint: Noise figure is defined as NFdB) = 174 + Pr(dBm) 10 log10(W) SN R(dB) where P.is the power of the received signal, W is the signal bandwidth, and SNR is the signal- to-noise ratio output from the receiver. The BER performance of BPSK under flat fading channel is Pe = asi 4SNR 1.5 In order to increase the communication range, L-order diversity is ex- ploited (using repetition transmission at different time). Write down the expression between transmit range d and Pe. (8 points) Hint: The BER under L-th order diversity in terms average SNR can be expressed as: Pe ~ (2471) (45NR)". You can first derive the relationship between the SNR and the distance d, SNR=ad-2, and determine the parameter a in terms of wavelength , noise figure NF, transmit power P and bandwidth W etc