Abstract-To achieve the full multiplexing gain of MIMO interference networks at high SNRs, the interference from different transmitters must be aligned in lower-dimensional subspaces at the receivers. Recently a distributed "max-SINR" algorithm for precoder optimization has been proposed that achieves interference alignment for sufficiently high SNRs. We show that this algorithm can be interpreted as a variation of an algorithm that minimizes the sum Mean Squared Error (MSE). To maximize sum utility, where the utility depends on rate or SINR, a weighted sum MSE objective is used to compute the beams, where the weights are updated according to the sum utility objective. We specify a class of utility functions for which convergence of the sum utility to a local optimum is guaranteed with asynchronous updates of beams, receiver filters, and utility weights. Numerical results are presented, which show that this method achieves interference alignment at high SNRs, and can achieve different points on the boundary of the achievable rate region by adjusting the MSE weights.

SUMMARYWe derive the minimum mean square error (MMSE) solution to vector precoding for frequency flat multiuser scenarios with a centralised multi-antenna transmitter. The receivers employ a modulo operation, giving the transmitter the additional degree of freedom to choose a perturbation vector. Similar to existing vector precoding techniques, the optimum perturbation vector is found with a closest point search in a lattice. The proposed MMSE vector precoder does not, however, search for the perturbation vector resulting in the lowest unscaled transmit power, as proposed in all previous contributions on vector precoding, but finds an optimum compromise between noise enhancement and residual interference. We present simulation results showing that the proposed technique outperforms existing vector precoders, as well as the MMSE TomlinsonHarashima precoder, and compare the turbo-coded performance to the capacity of the broadcast channel.

We present Kripke modal transition systems (Kripke MTSs), a generalization of modal transition systems [27,26], as a foundation for three-valued program analysis. The semantics of Kripke MTSs are presented by means of a mixed power domain of states; soundness and consistency are proved. Two major applications, model checking partial state spaces and three-valued program shape analysis, are presented as evidence of the suitability of Kripke MTSs as a foundation for threevalued analyses.

Abstract-We study distributed algorithms for updating transmit precoding matrices for a two-user Multi-Input/Multi-Output (MIMO) interference channel. Our objective is to maximize the sum rate with linear Minimum Mean Squared Error (MMSE) receivers, treating the interference as additive Gaussian noise. An iterative approach is considered in which given a set of precoding matrices and powers, each receiver announces an interference price (marginal decrease in rate due to an increase in interference) for each received beam, corresponding to a column of the precoding matrix. Given the interference prices from the neighboring receiver, and also knowledge of the appropriate cross-channel matrices, the transmitter can then update the beams and powers to maximize the rate minus the interference cost. Variations on this approach are presented in which beams are added sequentially (and then fixed), and in which all beams and associated powers are adjusted at each iteration. Numerical results are presented, which compare these algorithms with iterative water-filling (which requires no information exchange), and a centralized optimization algorithm, which finds locally optimal solutions. Our results show that the distributed algorithms perform close to the centralized algorithm, and by adapting the rank of the precoder matrices, achieve the optimal high-SNR slope.

This expository paper simplifies and clarifies Steifen's depiction of data flow analysis (d.Ja. ) as model checking: By employing abstract interpretation (a-i. ) to generate program traces and by utilizing Kozen's modal mu-calculus to express trace properties, we express in simplest possible terms that a d&a. is a model check of a program's a.i. trace. In particular, the classic %ow equations for bit-vector-based d-Jo. s reformat trivially into modal mu-Cal&us formulas., A surprising consequence is that two of the classical d&a. s are exposed as unsound; this problem is analyzed and simply repaired. In the process of making the above discoveries, we cIarify the relationship between a. i. and d-&a. in terms of the often-misunderstood notion of collecting semantics and we highlight how the research areas of %ow analysis, abstract interpretation, and mode1 checking have grown together. AcknowledgementsBernhard Steffen, Carolyn Talcott, and Mitchell Wand studied drafts of this and a related paper and made many useful suggestions. Also, Stephen Brookes, Edmund Clarke, OIivier Danvy, Peter Mosses, and Cotin Stirling are thanked for hosting, me during my sabbatjcal year journeys. Refereices[l] S. Abramsky and C. Hankin, editors. Abstract interpmtationof declarative languages. Ellis Horwood, chichester, 1987.