Braess's Paradox in Wireless Networks: The Danger of Improved Technology

When comparing new wireless technologies, it is common to consider the effect that they have on the capacity of the network (defined as the maximum number of simultaneously satisfiable links). For example, it has been shown that giving receivers the ability to do interference cancellation, or allowing transmitters to use power control, never decreases the capacity and can in certain cases increase it by $\Omega(\log (\Delta \cdot P_{\max}))$, where $\Delta$ is the ratio of the longest link length to the smallest transmitter-receiver distance and $P_{\max}$ is the maximum transmission power. But there is no reason to expect the optimal capacity to be realized in practice, particularly since maximizing the capacity is known to be NP-hard. In reality, we would expect links to behave as self-interested agents, and thus when introducing a new technology it makes more sense to compare the values reached at game-theoretic equilibria than the optimum values. In this paper we initiate this line of work by comparing various notions of equilibria (particularly Nash equilibria and no-regret behavior) when using a supposedly "better" technology. We show a version of Braess's Paradox for all of them: in certain networks, upgrading technology can actually make the equilibria \emph{worse}, despite an increase in the capacity. We construct instances where this decrease is a constant factor for power control, interference cancellation, and improvements in the SINR threshold ($\beta$), and is $\Omega(\log \Delta)$ when power control is combined with interference cancellation. However, we show that these examples are basically tight: the decrease is at most O(1) for power control, interference cancellation, and improved $\beta$, and is at most $O(\log \Delta)$ when power control is combined with interference cancellation

Optimal Flying Wings: A Numerical Optimization Study

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97067/1/AIAA2012-1758.pd

Gaussian Interference Channel Capacity to Within One Bit: the General Case

The characterization of the capacity region of the two-user Gaussian interference channel has been an open problem for thirty years. The understanding on this problem has been limited. The best known achievable region is due to Han-Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we extend our results of [1] to general (i.e. possibly asymmetric) channels for the complete capacity region. We show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a simplified Han-Kobayashi type scheme can achieve to within a single bit the capacity for all values of the channel parameters. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios

Validation of helicopter mathematical models

The validation of theoretical flight-mechanics models for helicopters is of considerable practical importance for the design of new rotorcraft. Conventional validation methods have involved comparisons of the responses of simulated and real helicopters to a simple input, such as a step or a pulse. The use of sufficiently small inputs allows the development and validation of linear models which can be used by the control system designer to endow the helicopter with acceptable stability characteristics and handling qualities over a limited operating envelope. For non-linear models, more suited to the investigation of large and rapid manoeuvres, one approach to model validation is to use linearisation about a range of trim conditions and apply system identification and parameter identification techniques. Additionally, it is possible to transform the problem to the frequency domain in order to eliminate subsystems from the validation process. The large amplitudes of typical nap-of-the-earth manoeuvres demand a new approach to validation. Inverse simulation has demonstrated its value in this context