Asymptotic distributions of the signal-to-interference ratios of LMMSE detection in multiuser communications

Let ${\mathbf{s}}_k=\frac{1}{\sqrt{N}}(v_{1k},...,v_{Nk})^T,$ $k=1,...,K$, where $\{v_{ik},i,k$ $=1,...\}$ are independent and identically distributed random variables with $Ev_{11}=0$ and $Ev_{11}^2=1$. Let ${\mathbf{S}}_k=({\mathbf{s}}_1,...,{\mathbf{s}}_{k-1},$ ${\mathbf{s}}_{k+1},...,{\mathbf{s}}_K)$, ${\mathbf{P}}_k=\operatorname {diag}(p_1,...,$ $p_{k-1},p_{k+1},...,p_K)$ and \beta_k=p_k{\mathbf{s}}_k^T({\mathb f{S}}_k{\mathbf{P}}_k{\mathbf{S}}_k^T+\sigma^2{\mathbf{I}})^{-1}{\math bf{s}}_k, where $p_k\geq 0$ and the $\beta_k$ is referred to as the signal-to-interference ratio (SIR) of user $k$ with linear minimum mean-square error (LMMSE) detection in wireless communications. The joint distribution of the SIRs for a finite number of users and the empirical distribution of all users' SIRs are both investigated in this paper when $K$ and $N$ tend to infinity with the limit of their ratio being positive constant. Moreover, the sum of the SIRs of all users, after subtracting a proper value, is shown to have a Gaussian limit.Comment: Published at http://dx.doi.org/10.1214/105051606000000718 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Non-classical properties and algebraic characteristics of negative binomial states in quantized radiation fields

We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Peremolov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their nonclassical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail. We also propose two methods of generation of the negative binomial states.Comment: 17 pages, 5 figures, Accepted in EPJ

Entangled SU(2) and SU(1,1) coherent states

Entangled SU(2) and SU(1,1) coherent states are developed as superpositions of multiparticle SU(2) and SU(1,1) coherent states. In certain cases, these are coherent states with respect to generalized su(2) and su(1,1) generators, and multiparticle parity states arise as a special case. As a special example of entangled SU(2) coherent states, entangled binomial states are introduced and these entangled binomial states enable the contraction from entangled SU(2) coherent states to entangled harmonic oscillator coherent states. Entangled SU(2) coherent states are discussed in the context of pairs of qubits. We also introduce the entangled negative binomial states and entangled squeezed states as examples of entangled SU(1,1) coherent states. A method for generating the entangled SU(2) and SU(1,1) coherent states is discussed and degrees of entanglement calculated. Two types of SU(1,1) coherent states are discussed in each case: Perelomov coherent states and Barut-Girardello coherent states.Comment: 31 pages, no figure

Width of the confinement-induced resonance in a quasi-one-dimensional trap with transverse anisotropy

We theoretically study the width of the s-wave confinement-induced resonance (CIR) in quasi-one-dimensional atomic gases under tunable transversely anisotropic confinement. We find that the width of the CIR can be tuned by varying the transverse anisotropy. The change in the width of the CIR can manifest itself in the position of the discontinuity in the interaction energy density, which can be probed experimentally.Comment: 6 pages, 3 figures, update references, published versio