Vanishing integrals for Hall-Littlewood polynomials

It is well known that if one integrates a Schur function indexed by a partition $\lambda$ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of $\lambda$ have even multiplicity (resp. all parts of $\lambda$ are even). In a recent paper of Rains and Vazirani, Macdonald polynomial generalizations of these identities and several others were developed and proved using Hecke algebra techniques. However at $q=0$ (the Hall-Littlewood level), these approaches do not work, although one can obtain the results by taking the appropriate limit. In this paper, we develop a direct approach for dealing with this special case. This technique allows us to prove some identities that were not amenable to the Hecke algebra approach, as well as to explicitly control the nonzero values. Moreover, we are able to generalize some of the identities by introducing extra parameters. This leads us to a finite-dimensional analog of a recent result of Warnaar, which uses the Rogers-Szeg\"o polynomials to unify some existing summation type formulas for Hall-Littlewood functions.Comment: 31 page

Hybrid Analog and Digital Precoding: From Practical RF System Models to Information Theoretic Bounds

Hybrid analog-digital precoding is a key millimeter wave access technology, where an antenna array with reduced number of radio frequency (RF) chains is used with an RF precoding matrix to increase antenna gain at a reasonable cost. However, digital and RF precoder algorithms must be accompa- nied by a detailed system model of the RF precoder. In this work, we provide fundamental RF system models for these precoders, and show their impact on achievable rates. We show that hybrid precoding systems suffer from significant degradation, once the limitations of RF precoding network are accounted. We subsequently quantify this performance degradation, and use it as a reference for comparing the performance of different precoding methods. These results indicate that hybrid precoders must be redesigned (and their rates recomputed) to account for practical factors.Comment: Accepted in Globecom 16 W