In this paper, we propose to re-engineer the wireless backhaul two-tier heterogeneous networks architecture by developing a novel cooperative transmission scheme based on non-orthogonal multiple access (NOMA). To effectively manage severe interference from the newly introduced backhaul communications, we employ the cochannel time division duplexing combined with spectrum partitioning between two considered tiers. This paper's novelty lies in the formulation to solve for the NOMA decoding order, which affects the rule of the cooperation between small cell transmissions. We propose two optimization problems of jointly designing the NOMA decoding order together with the transmit beamforming at the macro base station and power allocation at the small cells which maximize the total achievable rate and the number of satisfied users, respectively. The first and second formulated problems are both mixed integer non-convex and are generally NP-hard. To solve them, we first employ the difference of convex functions to present the formulated binary variables and then equivalently transform the optimization problems into more tractable forms. Finally, we develop an iterative low-complexity algorithm based on successive convex approximation technique and majorization minimization method, which is provable to eventually converge at a sub-optimal solution. Numerical results are extensively studied to corroborate that our proposed strategy outperforms the conventional designs in terms of total achievable rate and number of satisfied users.