Performance Analysis of Coded Frequency-Hopped Spread-Spectrum Systems with Unknown Interference.

Two classes of problems are considered. In the first class we model the process of communicating in the presence of interference, which is unknown or hostile, as a two-person zero sum game with the communicator and the jammer as the players. The objective functions we consider are mutual information and the channel cutoff rate. The communicator's strategies are distributions on the input alphabet and on a set of quantizers and the jammer's strategies are distributions on the noise power subject to certain constraints. We consider various conditions on the jammer's strategy set and on the communicator's knowledge. For the case with the decoder uninformed of the actual quantizer chosen, we show that, from the communicator's perspective the worst-case jamming strategy is a distribution concentrated at a finite number of points thereby converting a functional optimisation problem into a non-linear programming problem. Moreover, we are able to also characterize the worst-case distributions by means of necessary and sufficient conditions which are easy to verify. For the case with the decoder informed of the actual quantizer chosen we are able to demonstrate the existence of saddle-point strategies. The analysis is also seen to be valid for a number of situations where the jammer is adaptive. The second class of problems we address concerns the performance of orthogonal signalling schemes over channels with unknown partial b and interference. The worst case partial b and interference is very detrimental to orthogonal signalling and does not allow reliable communication even asymptotically at any signal to noise ratio. We investigate the use of diversity as a simple form of coding in such situations. It is shown that two of the three diversity combining schemes analysed, majority logic combining and linear combining, are unable to overcome the worst case partial b and noise, but clipped linear combining is asymptotically able to neutralize the partial b and noise, i.e. allow its effect to be no worse than added white Gaussian noise of equivalent noise spectral density.Ph.D.Systems scienceElectrical engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/161663/1/8801331.pd