We show that for those lattices of Voronois first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that c
onverges to a closest lattice point is found. We show that the series converges after at most $n$ terms. Each vector in the series can be efficiently computed in $O(n^3)$ operations using an algorithm to compute a minimum cut in an undirected flow network.
Estimating the coefficients of a noisy polynomial phase signal is important in fields including radar, biology and radio communications. One approach attempts to perform polynomial regression on the phase of the signal. This is complicated by the fac
t that the phase is wrapped modulo 2pi and must be unwrapped before regression can be performed. In this paper we consider an estimator that performs phase unwrapping in a least squares manner. We describe the asymptotic properties of this estimator, showing that it is strongly consistent and asymptotically normally distributed.
The Coxeter lattices, which we denote $A_{n/m}$, are a family of lattices containing many of the important lattices in low dimensions. This includes $A_n$, $E_7$, $E_8$ and their duals $A_n^*$, $E_7^*$ and $E_8^*$. We consider the problem of finding
a nearest point in a Coxeter lattice. We describe two new algorithms, one with worst case arithmetic complexity $O(nlog{n})$ and the other with worst case complexity O(n) where $n$ is the dimension of the lattice. We show that for the particular lattices $A_n$ and $A_n^*$ the algorithms reduce to simple nearest point algorithms that already exist in the literature.
The lattice $A_n^*$ is an important lattice because of its covering properties in low dimensions. Clarkson cite{Clarkson1999:Anstar} described an algorithm to compute the nearest lattice point in $A_n^*$ that requires $O(nlog{n})$ arithmetic operatio
ns. In this paper, we describe a new algorithm. While the complexity is still $O(nlog{n})$, it is significantly simpler to describe and verify. In practice, we find that the new algorithm also runs faster.
This paper presents new low-complexity lattice-decoding algorithms for noncoherent block detection of QAM and PAM signals over complex-valued fading channels. The algorithms are optimal in terms of the generalized likelihood ratio test (GLRT). The co
mputational complexity is polynomial in the block length; making GLRT-optimal noncoherent detection feasible for implementation. We also provide even lower complexity suboptimal algorithms. Simulations show that the suboptimal algorithms have performance indistinguishable from the optimal algorithms. Finally, we consider block based transmission, and propose to use noncoherent detection as an alternative to pilot assisted transmission (PAT). The new technique is shown to outperform PAT.
