| Points: 1)30 | 2)25 | 3)15 | 4)30 |
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- Consider
the downlink of a GSM system, where the operating frequency is 950 MHz. The
receiver sensitivity is given as−102 dBm for this standard. The output power of
the transmit amplifier is 31.62 W.
The transmit antenna gain is 5 dB, while the receive antenna gain is unity. The
fading margin (the safety margin to the sensitivity to compensate the degradation
in signal quality due to fading) is determined as 12 dB. The path loss exponent
is defined as 3.5 and 4.5 for line-of-sight (LOS) and
non-line-of-sight (NLOS) environments, respectively.
- Calculate the transmit power in dBm. Calculate the effective isotropic radiated power in dBm?
- Calculate the path loss (in dB) for a reference distance of d0 = 100 m using Friis free space equation (consider unity antenna gains in this reference calculation).
- Using the simplified (log-distance) path-loss model for a reference distance of d0 = 100 m, calculate the maximum distance d = dmax that can be covered in LOS and NLOS enviroments.
- Due to random blockage from objects, it is observed that the measured signal level at the maximum distance (for theLOS or NLOS scenario) have a Gaussian (normal) distribution with mean −90 dBm and variance σ2 = 25 dB2. Predict the probability that the received signal level is greater than the sensitivity value.
- Repeat part d) without a fading margin, i.e., with a mean signal strength of −102 dBm. Please comment on your results.
- In this question, using MATLAB, each student will generate its own and unique 4-tap power delay profile following theprocedures given below. Generate three uniformly distributed random variables between 0 and 5 and sort them in ascending order by including the reference time delay of 0 us. Adjust tap powers using exponential function as exp(-[time samples]). An example is given below.
rng(’shuffle’); time=[0,sort(rand(1,3)*5)];power=exp(-time); stem(time,power)
- Compute the mean excess delay (¯τ) and RMS delay spread (στ) for your power delay profile. Verify your answers using MATLAB by writing two scripts for (¯τ) and (στ).
- Calculate the coherence bandwidth and determine the conditions for flat fading?
- Obtain the maximum bit rate (without using an equalizer) that can be achieved using i) BPSK, ii) QPSK, and ii)16-QAM. Which modulation format (with minimum order) should be selected to support HD streaming with 1 Mbps.
- If the modulation carrier frequency is 1.8 GHz, is the channel slow or fast fading for a speed of 100 km/h and bit rate of 0.5 Mbps for QPSK?
- A cellular system is operating in an environment with Nco number of interfering co-channels and a path loss exponent of n. If the required signal-to-interference ratio is SIR dB for satisfactory forward channel performance, write a MATLAB script that calculates the cluster size N for maximum capacity. Use your script to calculate N for the following cases with
SIR = 19 dB.
- n = 4.5, without sectoring.
- n = 3, without sectoring.
- n = 4, with 60o sectoring.
- n =
3, with 120o sectoring.
- In a wireless communication system operating
under Rayleigh fading conditions, 64-QAM is used to support
high-ratetransmission with a bandwidth of 1 MHz. The transmit power is given as
0 dBm and the total path loss between the transmitter and receiver is given as
80 dB. The noise power spectral density is N0 = 10−19 W/Hz. a) What is the spectral efficiency? What is the supported data rate?
- Calculate the average received signal-to-noise ratio (SNR) for raised cosine pulses with β = 1.
- Calculate the SNR per symbol (¯γs) and SNR per bit (¯γb) at the receiver.
- Using nearest neighbor approximation, first, express the symbol error probability of the selected modulation format inAWGN channel. Then, express and calculate the approximate probability of symbol error in Rayleigh fading. Compare this result with the exact result obtained in MATLAB with integral command. e) Find the bit error probability with Gray encoding.
