Assignment
Consider a one-dimensional cellular network, where each cell has dimension 8 and users can be located symmetrically about the cell centers at coordinates of {-3,-1,1,3}. In each cell, there are 4 channels available each of width 1 Hz. Neglect noise and assume that with the use of channel coding at the Shannon limit we can approach the interference limited channel capacity on each link. Orthogonal CDMA is used within each cell, with interference coming from the neighboring right and left cells. That is, the signals from the immediate neighbors are treated as noise. The power attenuates as the fourth power of distance.
Suppose inner locations are served with power 1. What power P is required for the outer locations to have equal rates? Determine the capacity per channel of the cellular network under the assumption that there is always demand for service at every location (infinite queuing).
Now suppose that instead of CDMA we use an FDMA scheme. For this situation, intuitively, why is it a good idea for users at inner locations to be sharing channels with users in neighboring cells at outer locations?
Determine the power allocation in part (b) that result in equal transmission rates for the inner and outer locations, and determine that rate.
Compare the result in (a) and (c) and comment on what accounts for the difference in rates achieved.
The band at 60 GHz suffers from absorption by oxygen molecules, and so it is not suitable for long-range transmission. However, for short ranges we can neglect this loss as negligible compared to other propagation losses, and so it has been opened for commercial use. Consider radio transmission with P_t=0.01W,h_t=10m,h_r=2m,G_t=G_r=1.5,F=10,T=300K and B=10MHz
For an AWGN channel, and a requirement of P(e)=10^(-6) or smaller, what is the maximum range for uncoded 64-QAM?
The high frequency brings problems with device power efficiency, but allows multiple antennas to be packed tightly. Suppose patch antennas of dimension λxλcan be packed together in a 5cm by 5cm square, whereλis the wavelength. What is the approximate increase in the antenna gain compared to a single antenna? What increase in range results?
In a slow multipath fading situation, comment on the qualitative advantage of using the antenna array for diversity as compared to antenna gain on effect of the range that is reliably achieved. Do you expect a large difference or not, and why?
A problem with high frequency radio is limited propagation through walls and other barriers, since attenuation scales inversely with wavelength. On the other hand, much more spectrum is available at high frequencies than low ones. Suppose we have cognitive radios that can switch bands according to congestion and propagation conditions. In which circumstances should we be using the high or the low frequencies?
OFDM will be used for transmission over a slowly fading channel. Each subchannel has bandwidth 1 Hz, with noise power σ^2=0.01. The power gains of the subchannels are respectively 0.05, 0.25, 0.50 and 0.20.
Given a total transmission power of P=1, what power and bit allocation ( assuminguncoded M-QAM) will maximize the bit rate, for an error rate target of 10^(-6)? (Hint: power allocation to a subchannel only does some good for uncoded modulation if at least one bit per symbol is achievable at the target error rate?
Repeat for P=10
Suppose that instead of OFDM we are using a single carrier scheme with a DFE. What adaptation are required to maintain reliable transmission in this case, under the constraint of fixed transmission power? How would the transmission rate and complexity compare qualitatively to the OFDM approach?
Phones in Motion
The coherence time is defined as the interval after which two signals can be modeled as experiencing nearly uncorrelated fading values for Rayleigh fading. For mobile systems, it is approximately the time to move one-half of a wavelength.
Compute the coherence time for driving at v=50km/hr with cellular transmission at a carrier frequency of 1 GHz.
Suppose BPSK is employed at a bit rate of 1 Mb/s. Diversity of 4 is to be achieved using a combination of reception coding and interleaving. (That is, a permutation matrix scrambles the symbols in the transmitter, and the inverse matrix in the receiver restores their order). What interleaving depth in the symbols is required so that each of the four symbols in the code experiences uncorrelated fading?
Suppose for the situation in part (b) we could just close the link with diversity 4 in Rayleigh fading. The distracted driver of the car by chance pays some attention to the road to notice a clueless pedestrian playing a game on his phone while jaywalking, and slams on the brakes, coming to a stop. Assuming the transmission scheme is adaptive, by what factor must the data rate decrease in order to have reliable transmission now that there is no time diversity provided by the code?
What diversity methods could be used that are independent of vehicle speed? What are some practical limitations on the degree of diversity that can be achieved?