Solution for Homework 3

1. Solution for Problem 1.
2. Solution for Problems 3.1 through 3.3
3. 1. The function SimulateCOSTChannel.m is explained in detail in Transparencies on the Wireless Channel starting on the slide with page number 337.
   2. See slide numbered 349 in Transparencies on the Wireless Channel for a plot for v=10km/h. Also see MATLAB script plot_MultiPathSinusoid.m for how this plot is generated.
   3. See slides number 294-297 in Transparencies on the Wireless Channel for comparable plots and MATLAB script plot_BuildingsISI_30}.m for how those plots were generated; note that this script does not use SimulateCOSTChannel.m.

4. Delay spread

   is the temporal extent of dispersion introduced by the channel. When delay spread is large relative to the symbol period significant intersymbol interference is introduced.

   Doppler spread

   is the range of frequency shifts a signal transmitted over a fading channel may experience. The Doppler shifts are induced by time-varying channels. In essence they describe the rate of change of the channel.

   Fading

   refers the time-variability of the channel. The variations are induced by user mobility. A communication system using a fading channel should include provisions to combat fading. Different measures are required depending on the rate of change:

   slow fading:

   the channel remains constant over several symbol periods. The receiver has to track, i.e., continuously re-identify, the channel. Also since deep fades can persist for an extended number of symbol periods, time-diversity in the form of coding/interleaving should be employed.

   fast fading:

   the channel changes appreciably over a single symbol period which is too fast for tracking. Hence, non-coherent modulation techniques should be employed. Orthogonal frequency shift keying is a well suited modulation format.

5. FDMA (100 Kbit/s, infinitely long frames)

   The symbol period is approximately 10 microseconds which is larger than the usual delay spread of a few microseconds in cellular environments. Hence no significan ISI will be introduced and a simple, linear equalizer should suffice. On the other hand, the channel frequency response will change significantly over approximately 300 bit periods (at 100km/h) and hence continuous tracking of the channel (possibly just the carrier phase) is required. The narrow bandwidth does not provide frequency diversity (flat fading) and other forms of diversity should be considered, e.g., time diversity via coding/interleaving and/or spatial diversity via multiple antennas.

   TDMA (1000 Kbit/s, frame length: 500 bits)

   The symbol period of 1 microsecond may result in severe ISI that requires a non-linear equalizer to overcome. The equalizer requires an embedded training sequence to identify the channel. On the other hand the channel will be approximately constant over the entire frame and no tracking is required. The large bandwidth leads to built-in frequency diversity.

   I included a paper on access methods (PDF) that I wrote a while ago for your reference.