Ruzsa's theorem on Erdős and Turán conjecture

For any set A of nonnegative integers, let σA(n) be the number of solutions to the equation n=a+b,a,b∈A. The set A is called a basis of N if σA(n)≥1 for all n≥1. The well known Erdős-Turán conjecture says that if A is a basis of N, then σA(n) cannot be bounded. In 1990, Ruzsa proved that there exists a basis A of N such that ∑n≤NσA2(n)=O(N). In this paper, we give a new proof of Ruzsa's Theorem.