In this two-part paper, we address the problem of finding the optimal
precoding/multiplexing scheme for a set of non-cooperative links sharing the
same physical resources, e.g., time and bandwidth. We consider two alternative
optimization problems: P.1) the maximization of mutual information on each
link, given constraints on the transmit power and spectral mask; and P.2) the
maximization of the transmission rate on each link, using finite order
constellations, under the same constraints as in P.1, plus a constraint on the
maximum average error probability on each link. Aiming at finding decentralized
strategies, we adopted as optimality criterion the achievement of a Nash
equilibrium and thus we formulated both problems P.1 and P.2 as strategic
noncooperative (matrix-valued) games. In Part I of this two-part paper, after
deriving the optimal structure of the linear transceivers for both games, we
provided a unified set of sufficient conditions that guarantee the uniqueness
of the Nash equilibrium. In this Part II, we focus on the achievement of the
equilibrium and propose alternative distributed iterative algorithms that solve
both games. Specifically, the new proposed algorithms are the following: 1) the
sequential and simultaneous iterative waterfilling based algorithms,
incorporating spectral mask constraints; 2) the sequential and simultaneous
gradient projection based algorithms, establishing an interesting link with
variational inequality problems. Our main contribution is to provide sufficient
conditions for the global convergence of all the proposed algorithms which,
although derived under stronger constraints, incorporating for example spectral
mask constraints, have a broader validity than the convergence conditions known
in the current literature for the sequential iterative waterfilling algorithm.Comment: Paper submitted to IEEE Transactions on Signal Processing, February
22, 2006. Revised March 26, 2007. Accepted June 5, 2007. To appear on IEEE
Transactions on Signal Processing, 200