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 Ts = 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 = 9/19̀fd, the coherence bandwidth and delay spread is Bc = 1/̃, and the signal bandwidth is determined by W = 1/Ts.)
1.1 Calculate the Doppler frequency fd, coherence time and coherence bandwidth. (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 = (̀/4̀)^2d^-2, where ̀ is the signal wavelength 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 NF(dB) = 174 + Pr(dBm) – 10log10(W) – SNR(dB) where Pr 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 = 1/4SNR.
1.5 In order to increase the communication range, L-order diversity is exploited (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 ≈ (2L-1/L)(1/4SNR)^L. You can first derive the relationship between the SNR and the distance d, SNR = ̀d^-2, and determine the parameter ̀ in terms of wavelength ̀, noise figure NF, transmit power Pt and bandwidth W etc.