The paper is at http://web.stanford.edu/~boyd/papers/pdf/rob_downlink_bf.pdf .Lookiing at equation (1), it is evident that there is a typo, specifically, a missing square on the abs(h’w) term in equation (5). With that missing square, it is indeed a SOCP. Without it, as you presented the problem, it is non-convex.
The key step you need is to model a term such as
norm([x sigma]). With that hint, I’ll let you work it out for this problem. Please read the CVX Users’ Guide first, as this forum is no substitute for doing so. If you use CVX 3.0beta, you can use abs(x) inside the norm.