IEEE Project Abstract

The lattice L(A) of a full-column rank matrixA 2 Rmn is defined as the set of all the integer linear combinations of the column vectors of A. The successive minimai(A); 1  i  n; of lattice L(A) are important quantities since they have close relationships with the following problems:1) shortest vector problem, 2) shortest independent vector problem, 3) successive minima problem. These problems arise from many practical applications, such as communications and cryptography. This paper first investigates some properties ofi(A). Specifically, we develop lower and upper bounds oni(A), where A are respectively the Cholesky factor of G1+G2and (G1 + G2)􀀀1 for two given symmetric positive definitive matrices G1 and G2. The bounds are respectively expressed asthe successive minima of L(A1) and L(A2), and L(^A1) andL(^A2), where A1;A2; ^A1 and ^A2 are respectively the Choleskyfactors of G1;G2;G􀀀11 and G􀀀12 . Then we show how some properties of i(A) are used to design a sub optimal integer forcing strategy for cloud radio access network (C-RAN). Our approach provides much higher time efficiency, while keeping the same achievable rate as the algorithm reported by Bakouryetal.. Simulation tests are performed to illustrate our main results