Abstract:

Consider a competitive “spectrum economy” in a communication system
where multiple users share a common frequency band and each of them, equipped
with an endowed “monetary” budget, will “purchase” its own transmit power spectrum
(taking others as given) in maximizing its Shannon utility or pay-off function
that includes the effects of interference and subjects to its budget constraint. A market
equilibrium is a price spectrum and a frequency power allocation that independently
and simultaneously maximizes each user’s utility. Furthermore, under an equilibrium
the market clears, meaning that the total power demand equals the power supply for
every user and every frequency. We prove that such an equilibrium always exists for
a discretized version of the problem, and, under a weak-interference condition or the
Frequency Division Multiple Access (FMDA) policy, the equilibrium can be computed
in polynomial time. This model may lead to an efficient decentralized method
for spectrum allocation management and optimization in achieving both higher social
utilization and better individual satisfaction. Furthermore, we consider a trading
market among individual users to exchange their endowed power spectrum under a
price mechanism, and we show that the market price equilibrium also exists and it
may lead to a more socially desired spectrum allocation.

Key words: Spectrum management , Competitive economy equilibrium , Convex
optimization , Complementarity